The Authority and Transmission of the New Testament

Introduction

I write as an amateur with an interest in the relationship between classical philosophy, science (particularly physics), and classical theism. I'm interested in the subject, try to remain well-read (though obviously not as well-read as the professionals), and occasionally write some words on the topic which I hope are not completely unreasonable. Being an amateur has its disadvantages. I have a full time job unrelated to this work. I have numerous other commitments and interests. What writing I do on the topics has to fit into the free time I have left. And this blog is only a small part of that writing. As witnessed by the infrequency of these posts. And the length of time it has taken me to write this one. I always seem to be running out of time.

Which isn't entirely off-topic for this post.

Back in 2019, I wrote a post about the A and B theories of Time. This is an important and much disputed topic in the philosophy of science. It's well worth discussing. I framed the post as a response to Edward Feser's presentation in Aristotle's revenge, chapter 4. I have a great deal of respect for Professor Feser. I encountered and came to accept a generally Thomist philosophy before I encountered his work. By then I had the general ideas in place that would become What is Physics. But the ideas were unpolished and needed refining. Professor Feser's work, both on his blog and just as importantly his books, really helped me convert the book from a very rough draft to the less rough version that I published. His work turned my disorganised thoughts and ignorance concerning classical philosophy from a major embarrassment for someone with my ambitions into (I hope) merely a mild embarrassment. There are differences between our world-views (he is a Roman Catholic, I am a classical evangelical Anglican; he is from the US, I am British, with all the cultural differences that involves). But on the specific topics of the philosophy of God, philosophy of man, natural philosophy, and ethics, there's very little we disagree on. Except that he is far more knowledgeable than I am, and my lesser knowledge no doubt leads me into mistakes which he would avoid.

But very little disagreement isn't no disagreement. The philosophy of time is one of the few places where I read Professor Feser's philosophical work and have a significant disagreement. Professor Feser was kind enough to respond to my post shortly after I wrote mine. I wanted to respond when I saw it. Various people asked if I could respond. But I had various other projects to complete first. Those projects aren't yet complete, but, after about seven years, I decided it was long enough, and it was time to reply. But better late than never. (That's my apology for not writing this post sooner.)

The second reason it has taken me so long to write this is that, even by my standards, this is a very long post. My apologies for that.

The terms of the debate

Firstly, I should give a brief recap.

There are numerous different philosophies of time. These are usually divided into two camps, the A-theories of time and the B-theories. The difference between these camps (as I define it) is that in the A-theories there is an objective notion of the present, while in the B-theories the notion of the present is only subjective.

So in the A-theory, there is an objective sense in which some moment being now. This is experienced by all of reality simultaneously. The traditional form of the A-theory is presentism, where only the present is ontologically actual. The past exists only as memory, the future is just unactualised potency. There are other forms of the A-theory. The growing block theory sees both the past and present as real, while the future is unactualised potency. The shrinking block theory sees the present and future as real, but not the past (I am not sure anyone holds to this theory, but I include it for completeness). The moving spotlight theory is part way between the A- and B- theories. It sees the universe across all of time as having an actual existence, but one particular moment is objectively highlighted as being the present. This gradually moves across the temporal axis, highlighting first one moment and then the next.

The alternative camp is the B-theory. Here the notion of the present is only subjective. All notions of time are relative. There is no absolute scale for the time. You can say "this event is six years after that reference event," once you have agreed that one particular direction is "after" and the other "before", but not "this event is at this number of years absolutely." For example, our AD/BC scale takes a miscalculation of the date of the birth of Christ as the zero point, and we measure time relative to that. (Although technically there isn't a year zero, as the concept of zero was unknown when the dating scheme was invented, but to make the mathematics easier I prefer to forget about that.) The concept of the present in the B-theory then just reduces to "the present is the time simultaneous with this thought" or "this word." Like all temporal indicators, it is measured relative to something else.

There are two main variations of the B-theory. I call these the static block and dynamic block. The static block theory treats the dimension of time as basically just the same as the dimensions of space. We are all familiar with three dimensional space. For the moment, I'll restrict the discussion to Euclidean space, to make things simpler. Here every point is parametrised by three numbers, one for each dimension, indicating a distance in some agreed units from some arbitrarily chosen origin. We can easily extend this to a four dimensional space by adding another number. That fourth dimension is time. So we think of moments in time as simply a slice of this four dimensional space keeping one coordinate constant, and varying the others. There is no preferred direction in space, so in the static block theory likewise there is no preferred direction in time. There is no absolute origin in space, only relative distances, so likewise no absolute origin in time. Just as a being can have extension in space, we can think of it as having extension in time. In our normal language, we think of that as it extending from past to future. So a rock was created at one time and over a certain volume of space when it was eroded and became detached from a cliff. It then endures until it is eventually eroded into sand at a later time. There is thus a four-dimensional volume indicating when the rock existed, with boundaries to the left and right, up and down, forward and back, and past and future. Where the rock exists in space (relative to, say, the center of the sun) changes over time. Likewise when the rock exists in time varies over its position in space. In each of these, whether something is left or right is just a convention depending on how we order the scale along that axis. If the spatial origin is in the middle of the screen, then we can say that the points on one side of it have negative coordinates, and those on the other positive coordinates. We traditionally place the negative numbers on the left of the screen, but this is just an arbitrary convention. If we reflect in a mirror, the negative numbers switch to the other side of the screen. It is just as valid a way of doing it. But we can define "left" to just mean that side parametrised by negative numbers, and which way we have the numbers increase is just arbitrary convention, then the notions of left and right are just arbitrary convention. Similarly, the distinction between past and future is equally just a matter of whether we choose to have the numbers parametrising temporal coordinates as ascending or descending. It's not an objective fact of the universe, but merely a subjective convention just as whether something is left or right is a subjective convention.

I imagine that if Professor Feser reads that last paragraph he would be screaming at me. Probably for several reasons, but for one in particular. Didn't I read his post? Or books? I will get to his objections in due time. For now, I will just say that I am not proposing that this description is how things really are, but how some static block B-theorists might think how things really are.

I'm still leaving that main objection to one side (and digging myself deeper into the hole), but there is an obvious secondary objection, which is to say "But time isn't the same as space." Which is true. But the picture I presented above isn't completely useless. There is a mathematical transformation known as a Wick rotation, which replaces the time coordinate with the square root of minus one multiplied by the time coordinate. This makes various calculations in theoretical physics easier. For example, it removes an inconvenient pole when calculating propagators for Feynman diagrams. It also converts the Hamiltonian into an imaginary number, meaning that the weight for paths in the path integral formulation becomes real, making it much easier for numerical simulations. I'm not saying that this trick is how things really are in the universe, but that there is this mathematical trick to make space and time equivalent in the mathematical formulation illustrates how a static block B-theory advocate might believe space and time to be basically the same thing, only with minor and philosophically unimportant differences.

That main difference for a static block B-theory advocate is related to how distances are measured. In Euclidean space, the distance between two points is given by Pythagoras' theorem. The square of the distance is the sum of the squares of the relative distances along the three orthogonal coordinate axes. The equivalent to distance in Minkowski space-time is the proper time. The square of the proper time is the square of the relative duration in time minus the square of the relative distances along the three spatial distances. That minus sign is, for the static block B-theorist, the only difference between space and time.

This leads to an obvious problem. Why do we experience time as having a flow and direction? There is no objective temporal direction in this philosophy. The laws of physics are mostly time-reversible. I write mostly because there are a few exceptions. CP-violating interactions in the weak nuclear sector also violate a strict time reversibility (although one can maintain time reversibility by combining time reversal with various other transformations). The second law of thermodynamics suggests a tendency over time towards an equilibrium state. As the universe is not in equilibrium, that creates an asymmetry between past and future. So many static block B-theorists believe that the apparent arrow of time must emerge from some physical theory, even if the details of that have yet to be fully worked out. Thermodynamics is the leading candidate for that theory.

I often see papers where a local decrease in entropy is interpreted as time running backwards. To my mind that's reading far too much into the experimental results, but it's what happens when you combine a static block model with the notion that the direction of time is determined by the direction of increasing entropy. Here is one example. We should be cautious about these claims. What is reversed is not time itself, but some proxy standing in for time. In the work I cited it references the polarisation of photons. Others might say that entropy might temporarily decrease at the microscopic level. None of these actually involve a reversal of time as I (or Professor Feser) would understand it. They assume that the arrow of time emerges from some physical theory which contains a quality which most of the time correlates with the direction of time, and then flip that quality in a specific circumstance, and claim that indicates a reversal of the flow of time. No it doesn't. It is also consistent with the proposal that the quality used as a proxy for time's direction doesn't always correlate with the actual flow of time.

The static block B-theory is also widely regarded as undermining the concept of causality. After all, if there is no real distinction between past and future (but only an apparent one due to the direction of entropy increase, for example), then there is no real distinction between cause and effect. The Aristotelian notion of act and potency is also said to be threatened. How can we say something is in potency if it is also in act (albeit at a different moment in time)? I think this last problem is avoidable by insisting that saying "this state is actual" is incomplete. Instead we should just complete the statement by saying "this state is actual at this given time" (where the time is measured through difference in duration from some reference point). This is, in effect, what A theorists do in any case: they use "this state is actual" as shorthand for "this state is actual at the time corresponding to the objective present." There is still an implicit reference to a time. B-theorists just make this explicit, and generalise it so the same language can be used to discuss substances as they were in the past or will be in the future.

Another issue is how we can say that something comes to be, when (in some sense) in a static block universe everything always is. The obvious way to avoid this is to parametrise something's existence by the time when it exists. Instead of saying, A exists, we say that A exists from time t1 to time t2, while B exists from time t2 to time t3. The presentist's statement B exists is combined with his statement the current time is this, which lies between t2 and t3, and the two descriptions agree about what exists (or existed or will exist) in the universe at a given time. But there is a more subtle difference. The presentist, at time t2, will happily say that B comes into existence at that time, meaning that it exists now but it didn't exist a moment in the past. The static block cannot say the same thing. He cannot even say that B starts existing at time t2. The phrases comes into existence and starts existing imply a priority or ordering in time. The static block theorist cannot say that t2 represents the start of B's existence and t3 the end, because fundamentally the directionality in time is either just an illusion or emerges from something like the laws of thermodynamics, which themselves are dependent on the various processes which are said to be explained by causation. If causation requires an ordering in time, and the macroscopic theories of thermodynamics are dependent on the microscopic theory (with its causation), and the ordering in time arises only from thermodynamics, then everything is just a big circle and meaningless.

As such, the static block B-theory seems to be inconsistent with Aristotelian efficient causation. I'm not going to dispute this conclusion. The problems I have highlighted (alongside others, such as Professor Feser's remaining objections to the B- theory) are enough for me to regard the static block B-theory with suspicion.

However, there is an alternative B-theory of time, which I call the dynamic block theory. This agrees with the static block theory in that there is no objective sense of the present, and that one can only discuss relative durations in time (so we can't say that an event occurred at time t2, but only a difference in time t2 from some other event). It differs from the static block theory in that it states that there is an objective direction and flow to time. In other words, there isn't an apparent arrow of time that emerges from some physical theory, but a real and fundamental arrow of time that has to be put into our physical theories if they are to reflect the fundamental aspects of reality. Just as we put in that there are three space and one time dimension. We can create physical models with different numbers of dimensions. They just don't correspond to reality. We can create physical models which lack an objective arrow of time. They just don't correspond to reality.

The difference between time and space isn't just that minus sign in the metric, but more fundamental and more basic than any physical representation. Constructing a physical representation of the universe requires creating a mapping between points and moments in real space time and an abstract geometrical representation of space time. If we are to have any hope of success, that representation has to resemble reality. So, for example, (unless you happen to be a string theorist, which I'm not), you give the representation three temporal and one spatial direction because that's what's observed in reality. It is not something derived from the theory, but something more fundamental assumed by the theory and specifically put into the theory so it captures this important feature of reality.

There is nothing fundamental about the concept of geometrical spaces which states that within those spaces there is a direction in time. But neither is there anything fundamental which states that there have to be three spatial dimensions, rather than two or four. We add the information about the number of dimensions into the representation, which in turn becomes one of the premises of the theory. Likewise, if we consider that time in reality objectively has a direction, we incorporate this as an additional axiom into the theory. It isn't naturally part of a geometrical description, but there is nothing to stop us from adding it as an additional constraint on the theory if that is what's required to make the theory sufficiently well match reality to make useful predictions.

Indeed, I would say that quantum physics, particularly the path integral formulation (which, in its space-time basis, relies on time ordering), and the Born postulate describing an unpredictable change in the wavefunction on wavefunction collapse, both presuppose a direction in time.

From the perspective of the dynamic block B-theorist, it is a mistake to try to derive the direction of time from the laws of physics. It is an axiom upon which the laws of physics (particularly when thought of as a tool used to make predictions) are based.

Equally, the dynamic block B-theorist has no problem with the concepts "earlier than" or "later than." Time t2 might only be expressible as a difference from some subjectively chosen origin, rather than objective value, but it is still objectively later than time t1. Different observers might disagree about what number to assign to parametrise t2 relative to their subjective notions of now, but everyone would agree that t2 is later than t1.

Because the dynamic block B-theorist maintains a direction and ordering in time, he is not subject to the difficulties experienced by the static block B-theorist with regards to causality. He can identify the earlier event as the cause and the later event as the effect. He can say that things come into existence. He cannot say this state is now actual, but only this state is actual at a time t2 after this chosen zero point in time, but there is no disadvantage here. We can map between one person's subjectively chosen zero point and another, which means the two people describe the same content in their statements even if using different languages.

The dynamic block B-theory differs from the moving spotlight theory because the moving spotlight theory still believes that there is an absolute time scale (the zero point of the time scale can be objectively chosen based on when the spotlight is currently pointing at). The dynamic block B-theory only regards statements regarding relative temporal differences between events as objective, and denies there is any absolute scale or objective singling out of any moment as now. The dynamic block theory differs from all of the moving spotlight, presentism and the growing and shrinking block models in this respect. It also disagrees with them that only the present (or present and past, or present and future) are real.

I don't believe that the dynamic block B-theory is new to me. Pruss' adorned B-theory discussed in this paper (for example) is a similar model. This paper by Robert Koons Robert Koons advocates a different variation of the B- from mine, but earlier in the paper he mentions three options, a strict A theory, a strict B theory, and an intermediate theory. My proposal is his intermediate theory. Professor Feser has engaged with Koons here. And there are almost certainly other examples I am unaware of.

So, to my mind, the problems with the static block theory all reduce to the proposition that the direction of time is subjective. Remove that proposition gives the dynamic block theory, and the problems disappear. That doesn't mean that we should accept the dynamic block theory (ahead of presentism, for example), but would, if true, mean its an option for someone sympathetic to Aristotle's overall philosophy.

My main concern with Professor Feser's reply to me is this. I accept that his objections are powerful arguments against the static block theory. But I don't advocate the static block theory. I advocate the dynamic block theory. I am yet to be convinced that his objections are so strong against that.

My position and Professor Feser's

In my earlier post, I was responding to Professor Feser's comments in Aristotle's revenge. Professor Feser advocates for Presentism. He characterised the B-theory as what I call the static block theory.

All events - whether past, present, or future - are all equally real, as different parts of a single unchanging Parmedian "block". Temporal passage and the now are, on this view, illusionary. An event is now or present only relative to our consciousness of it, and not as a matter of objective fact.

The dynamic block B-theory doesn't fit this description. It agrees with the description in that it accepts that all events are equally real (at least from a God's eye view). It partially agrees that concept of now is not the same as in the A- theories, although I prefer to use the word "subjective" rather than illusionary. By subjective I mean that the concept is real and relevant, but varies from one observer to another. (Sorry, that's the physicist in me using the word "observer". In this context it can be generalised to any existent substance in space and time.) By objective I mean that the concept is real and relevant and the same for all observers. "Julius Caesar was assassinated today" is a concept that was perfectly real and relevant at one point in history, but not in other points, so its subjective. "Julius Caesar's assassination occurred between 39 and 41 years before the death of Herod the Great" is an objective statement, since all observers who know of both events should accept it (or reject it, if I have my chronology wrong) no matter when it was stated. I would understand illusionary as meaning that it is neither subjectively or objectively correct, but merely has the false appearance that leads people into thinking it is correct in one of those two senses.

But the dynamic block theory disagrees with this description in every other way. Temporal passage is neither illusionary nor subjective, being an objective fact of the world. I dislike the word "unchanging" in this definition because if change means "change in time" then that's a feature of the dynamic block. At time 1 the system is in state A. At time 2, the system is in state B. If A is not equal to B, then that's a change in time. Nor do I regard the dynamic block theory as Parmedian, denying the actualisation of potentia. Again, at time 1 the being actually in state A is potentially in state B. At time 2 that potentia is actualised. This is exactly the same process as in presentism, only in presentism actualisation is only possible at the privileged time known as the present. In the dynamic block theory, we can look back (or forward) and observe that at each moment of time there was/is/will be actualisation of potentia, and there is no objective difference between those events beyond their ordering in time.

Professor Feser offers the following arguments against the static block theory:

1. Different regions of space exist all at once, while different moments of time exist successively.
2. The spatial dimensions differ profoundly from time. a) You can rotate in space to convert width to height, but not convert a spatial dimension to a temporal one. b) You use a ruler to measure length and a clock to measure time, but not vice versa.
3. Time has a direction and flow that space lacks.
4. A region of space can be occupied by one thing, then vacated by it, and occupied by another thing. Time is not like that.
5. The geometrical treatment of space time cannot be the whole story. Physical objects occupy space time, while lines, planes and points don't.
6. The treatment of space and time is abstract in physics. We start with a mapping to geometry, i.e. mapping space to lines and planes. Secondly, physicists deal with the abstraction, rather than space and time themselves.
7. The four dimensional view of space time collapses the distinction between time and eternity.

In my post, I respond to all of these, and argue that they are either irrelevant or only apply to the static block theory and not the dynamic block theory. I'll come back to some of them again below.

In favour of Presentism, Professor Feser offers the following arguments.

1. Socrates died is a true statement, and the past tense in that phrase is a key aspect of that truth. Tense is thus a real part of the world. This implies that the present is a real fact of the world, requiring an A-theory of time.
2. Conscious experience taken at face value also points to there being something special about the present and the passing of time.

In my post, I argued that these are only reasons to accept the objective passage of time, and thus don't contradict the dynamic block theory.

He also offered various objections to the growing/shrinking block and moving spotlight models, which aren't relevant here (although I discuss his objections to the moving spotlight model towards the end of this post).

I advocate for a dynamic block theory of time.

In physics, we start with the real world. This is accessible to experiment, but not to theory. Theory (like all rational inquiry) requires an abstract representation of reality. When I think about a cat, what I have in my mind isn't the cat in itself, but only a representation of the cat. In Aristotelian philosophy of mind, if I understand the cat correctly, my representation of it mirrors its form. This is part of the cat, but it still isn't the cat, because it lacks the cat's matter. Thus what I think of is merely an abstract representation, albeit one that accurately corresponds to the cat's form in reality, corresponding to the extent that the cat' form as it exists in my intellect is the cat's form as present in the actual cat merely expressed in a different mode. Even discussing concepts such as potentiality in Aristotelian metaphysics requires a representation of those concepts, which accurately and precisely reflects the correspondent in reality but is still distinct from it.

To obtain the representation in physics, we take physical reality, and perform a one-to-one mapping between important aspects of reality and corresponding points in a geometrical representation. It is then also convinient to perform a one-to-one mapping between the geometrical representation and a numerical representation. (This second step is equivalent to the jump from Euclid's geometry, to Descartes' representation of geometry by using coordinate axes to identify each point in Euclid's space with a set of numbers. Only we are using a Minkowski/Riemann geometry instead of a Euclidean geometry). We are then ready to perform calculations.

Two key observations need to be emphasised at this point. The first is that the mapping in physics is one-to-one. You can map from an unique configuration in reality to an unique representation in the theory, and from an unique representation in the theory to a unique representation in reality. If the theory is modelled with the correct dynamics, this correspondence is maintained across time. This allows the theory to make accurate predictions for future events. In fact, we find the correct dynamics by testing those predictions against what happens in reality. This distinguishes the scientific method from (my understanding of) Hume and Kant's philosophies, where the mapping is only one way. In their philosophies, the world of ideas was initially informed by reality (mapping from reality to the abstract), but then it lost the connection and became its own thing, disconnected from reality. This disconnect from the scientific method is one of many reasons to reject the philosophies of Hume, Kant and their successors.

The second observation is that, despite this correspondence, we should not confuse the representation with reality. There are aspects of reality which aren't mapped to the representation. There are intermediate steps in the representation which don't correspond to anything in reality. And our representation might well be incomplete or inaccurate. We don't yet fully understand the dynamics of the model (although neither do we understand nothing; our current understanding is really, really good, at least it makes incredibly precise predictions, and the rival general approaches don't and can't); there might also be things we don't yet know about the statics (i.e. additional particle species we haven't yet observed). There are many people who make the mistake of confusing representation and reality (e.g., see my comments above concerning the arrow of time). Professor Feser accuses me of being one of them.

But equally, we shouldn't say that the representation is entirely disconnected from reality. Clearly it's not. If it were, it wouldn't be able to make successful predictions. In particular, what I'm concerned with is the structure of the dynamical model. Why do we need to use that particular structure, rather than some other? What is it about reality that constrains us in that way? We can make the mistake of confusing the model with reality, but its equally a mistake to think that we can't make inductions about the nature of reality from the model. The difficulty is in finding the right balance between those two mistakes. One method to resolve that difficulty is falsification, which might not allow us to say "this is true," but at least allows us to say "these rivals of this position are false."

There are several questions we might want to address. I'll focus on one of them: "Given an initial state A at time t1, what is the probability that the physical state will finish in a final state B at time t2?" Probability is to be interpreted as an extension of logic used to predict frequency distributions. It relates each possible output with a number. That set of numbers obeys Kolmogorov's axioms, and is calculated from various premises. Those premises include the initial state of the system (I will suppose for this basic introduction that this is known without imprecision), and various mathematical rules which I will call the laws of physics. This set of numbers obeys the same rules as a frequency distribution. Because the mappings between reality and the representation are one-to-one, we can take this calculated probability distribution, and map it back to give a prediction for a frequency distribution. We then switch our focus back to reality, and perform the experiment a sufficiently large number of times. Each time, we start from the same initial state. We observe the outcome, and gradually tabulate the frequency at which each outcome occurs. We then compare this observed frequency distribution against the predicted frequency distribution. They won't line up exactly, since we can only run the experiment a finite number of times, among other reasons. If they diverge drastically enough, there is something wrong with the theory (in particular the expression of the laws of physics used in the calculation doesn't accurately represent what happens in reality), and it needs to be refined. If the prediction agrees with the observation, then we try to reduce the imprecision in the observation and prediction, and try again until we either find a contradiction or (hopefully one day) give up and conclude the theory can't be refined any further.

What is mapped from reality to the numerical representation? Firstly, we need to be able to represent material substances. My particular interest is in particle physics, so I will concern myself with what we believe to be fundamental particles -- electrons, photons, quarks and so on. That avoids any complications arising from considering compound particles. In particular, we consider possible states of these particles. These are analogous to Aristotelian potentia. There are some complications in quantum physics, arising from non-unique representations of the particles (e.g. the space-time representation or the momentum-energy representation, not to mention complications around renormalisation) and the notion of superposition. But the general principle from Aristotelian metaphysics holds. At any given moment of time (including what is to us the present) one state in one particular basis is actual (i.e. a representation of what the actual particle in reality), while the other states in that basis are in potency (i.e. a representation of what the actual particle could become after its state is changed).

Note, as an aside, that I prefer psi-epistemic interpretations of the wavefunction, i.e. a superposition in our wavefunction means that we don't know which state we would observe after performing a measurement that causes the particle to decohere into that particular basis, rather than saying the particle is ontologically split between different states. In particular I prefer a theistic variation of Griffith's and Gell-Mann's consistent history interpretation (the main difference is my model emphasises God's role in actualising potency, which, in my view at least, resolves the problems in the standard consistent histories approach in explaining non-local correlations of events for entangled particles). Psi-epistemic interpretations avoid completely the measurement problem (which I often phrase as how you can jump from an ontological measure of the amplitude/probability of a quantum particle to an epistemic use of that probability as a predictor for a frequency distribution for particle from many different repeats of the experiment). Of course, some would say that psi-epistemic interpretations have other problems instead, though to my mind these are usually based on assumptions derived from other interpretations or which break the rules of quantum physics. That's not so important to this post, but should be the lens through which this section is interpreted.

We also need a means to represent change. This is done through creation and annihilation operators. An annihilation operator represents the destruction of a particle in a physical state at a particular moment in time. A creation operator represents the creation of a particle in a physical state at the same moment in time. By pairing together an annihilation operator for a particle in one state with a creation operator for a particle in a different state we represent the change of the particle from one state to another. By paring annihilation operators for one type of particle with creation operators for another type of particle, we can represent spontaneous generation and corruption (using Aristotelian vocabulary for the process in reality, and physicist vocabulary for the equivalent process in the representation).

Finally, and perhaps most pertinently for this post, we need to represent space and time. These are mapped to a geometrical space. Euclidean space in the early mathematical representations of Aristotle's physics. Euclidean space coupled with an Euclidean time in Newtonian physics. Then a Minkowski space-time in Einstein's special relativity and the standard model of particle physics. Or a Riemann space time with a Minkowski signature in general relativity.

Why do we need to map from physical space and time to a geometrical space-time? Because we need to think about physics, and thinking requires working in an abstract representation. We can only think about abstract (or immaterial) concepts. Why a geometrical space-time, and not some other representation? Firstly, and perhaps most importantly, because it leads to correct predictions. Secondly, because the geometrical space time is constructed from various axioms. A two or more dimensional Euclidean space is built on five axioms (expressed here in my words):

1. A definition of a straight line (expanded by later commentators as the line which minimises the distance between any two points on the line).
2. That straight lines can be extended indefinitely
3. That all right angles are equivalent.
4. The definition of a circle as the line where all points on the line are equidistant from another point.
5. Draw two straight lines and another line intersecting them. The intersecting line intersects line A nearer the top of the page, and B nearer the bottom of the page. Let a be the angle in the lower right segment between A and the intersecting line. Let b be the angle in the upper right segment between b and the intersecting line. If a + b is less than the sum of two right angles, the lines will meet to the right if extended far enough. If it is more than the sum of two right angles, the lines will meet to the left. If it equals the sum of two right angles the lines are parallel and will never meet.

Everything else in Euclidean geometry is built from these five axioms.

We can also identify lines, circles, right angles and distances in physical space. They appear to follow the same rules. (This is where if I were being rigorous I would have a long quibble concerning general relativity, but I will put that to one side.) A Euclidean geometrical space is not the same as physical space. The geometrical space is an abstract concept; physical space is a feature of the real world. But they obey the same rules. And this gives us good reason to think that we can create a one-to-one mapping between points in physical space and a geometrical representation of that space.

A second, and to the contempoary physicist, even more important, link between the physical world and the abstract representation of it is symmetry. There are many transformations which can be defined both in our own world and the abstract representation. I'll use rotation as an example. We can rotate a square object around its midpoint. We can also map all the points on that square to the geometrical representation, and construct a mathematical operation that changes the points in the same way that the physical rotation changes the points in physical space. This is our representation of the rotation. A symmetry is defined as when we perform a transformation that leaves the object looking exactly the same as when we started. We notice that the square object has a symmetry. If we rotate it through an integer multiple of right angles around its centre, then it looks exactly the same. Likewise the geometrical representation of the square has the same symmetry. Symmetries have a one to one mapping between representation and reality.

We also need the same points that are next to each other in the physical space to be next to each other in the geometrical representation (topological structure), consistent definitions of continuity in reality and the representation, and consistent definitions of how we measure distance (metrical structure).

Not every possible geometrical representation will map to reality. One can, for example, try to map our three dimensional physical space to a two dimensional geometrical space. We can still identify each point in physical space with a point in its representation; each contains an infinite number of points. But we lose any useful description of which points are next to each other. This representation isn't going to be useful.

To be useful, the abstract representation needs to reflect the symmetries, topology and metric of the real physical space. These are all concepts which can be defined in both the physical space and its abstraction.

As stated, one of the goals in physics is to take an initial state and make predictions about the probability that it will evolve into each given final state. For this we need four things. Firstly, a representation of physical space and the things in it. Secondly, a mapping between physical space and the things in it and their representation. Thirdly, a prescription to simulate how things evolve in time in the representation. I will call this prescription the laws of physics. Fourthly, a mapping back from the representation to physical space.

Obviously we can write down many different prescriptions for how things evolve in time. Each prescription will contain imprecision, for example key constants only known to +/- a certain amount, and there is imprecision in our measurements of the initial and final states, meaning there will also be imprecision in our conclusions. But there is a true form of the laws of physics, and only those which include it within their range of precision will draw the right conclusion within its range of precision.

But why is this particular prescription correct? The answer of contempoary physics is because it represents the symmetries of the real world. One of the great insights of the last fifty years or so is that these symmetries greatly constrain the possible laws of physics. If different symmetries apply, or they aren't present, then you get very different laws. Indeed, contempoary quantum physics has reached the point that you can define any theory through its symmetries, a list of particles, and various dimensionless constants describing the interaction strengths between the particles. We also require mathematical consistency. General relativity is also built around respecting an additional symmetry. Symmetry is thus very likely to be key to any theory of quantum gravity; as such I would be shocked if my argument for the dynamic block theory of time would be inapplicable once we have quantum gravity.

Symmetries are based on transformations which both correspond to actual changes in the real world and can be represented in the abstraction. Rotation and translation (whether local or global) are obvious examples. The key symmetries behind the standard model of particle physics include global rotation and translations in space, local gauge transformation, scale invariance, and Lorentz symmetry and time-translation. General relativity is based on symmetries concerning local rotations and translations. (A global transform applies to every thing in the universe; a local transformation differs from place to place). The most important symmetries for this discussion are those which state that the action is symmetric under Lorentz transformations and time translations.

Both of these correspond to things in the real world. We are very familiar with time translations; it is what happens when we move from past to future. Lorentz transformations correspond to changes in velocity. The Lorentz symmetry is what ensures that when someone on the ground and someone in the train each measure precisely the same speed of light relative to their own motion. Lorentz transformations are in effect just a rotation between the space and time dimensions. They have a slightly different mathematical form because of the minus sign in the metric, but they are to a hyperbolic geometry what a rotation is in Euclidean geometry. I'm discussing the abstract representation here, but we know that there are actions in physical space equivalent to the abstract transformations (rotation or changing velocity), and we know there is a one-to-one mapping between the abstraction and reality. It's not unreasonable to say the same conclusion applies to physical space and say there is an underlying analogue between the rotation and velocity change transformations in physical space.

Note that this is just the introduction to my argument for the dynamic block theory of time. I haven't got to the actual argument yet. I'm not arguing special relativity directly proves the B-theory. Professor William Lane Craig (among others) has responded to those naive arguments. I'm just introducing the concepts in preparation for something a bit more sophisticated.

So why do the laws of physics need to be defined in terms of these particular symmetries? The only reason could be that their real-world equivalents are important in the real world.

In the abstraction, these symmetries define the Hamiltonian operator. (Technically, they constrain the action, which is computed from the Lagrangian, which is in a 1-to-1 correspondence with the Hamiltonian.) I simplify a little, but this allows us to calculate the probability that, given you have a particular initial state at a particular moment in time, there will be a specified output state at the next moment of time. I'm not alone in saying, and I think Professor Feser would agree with me, that these quantum states in the abstraction map to potentia in the real world. So the real world analogue to the situation described by the Hamiltonian is that we have a substance in act at a particular moment in time. This substance has numerous powers, which define how it can change in the next moment of time. There are several different potentia which it might change into. There is nothing in the substance which determines which of these potentia will be actualised, but in practice one of them is going to be actualised. Therefore something outside the substance "decides" how the substance is going to change.

What is that something? The answer depends on your natural philosophy. In my own philosophy, God plays an essential role in actualising these potentia. God has free will, meaning that He is not compelled to actualise any given potentia. But He is also rational, meaning that we can repeat many times, and draw up a frequency table of each outcome, and that frequency table will be consistent between different runs of the experiment. The Hamiltonian allows us to calculate a probability distribution which predicts this frequency distribution. So the Hamiltonian describes (in as much as it can be described) God's actions as He selects which potentia He is going to actualise.

And this explains why the Hamiltonian has these symmetries. Consider God's omnipresence. This means that God is causality connected to everything at any point in the universe. If two distant points contain the same configuration of matter, and God has no special purpose (which would lead to a miracle), then there is no reason why, given enough samples, God would act differently in either place. So God treats things in one point in the universe in the same way as any other point in the universe. In the Hamiltonian, that corresponds to a translation symmetry. Likewise, God wouldn't act differently because the substance is facing in one direction rather than another. That implies the Hamiltonian ought to have a rotational symmetry. Likewise I have argued that all the symmetries constraining the Hamiltonian reflect the divine attributes. In other words, given God, we expect these laws of physics to satisfy these symmetries. Add in the requirements of fine tuning and mathematical consistency, and there is only a small number of laws of physics consistent with the assumption that God exists. On the other hand, if atheism is true, unless you have a multiverse sampling all possible laws of physics, there is no good reason why the universe should obey these symmetries or have these parameters. Theism explains the structure of the laws of physics; atheism doesn't (unless you suppose a multiverse, which has its own problems).

For the same reason, we need to take Lorentz symmetry and time translation symmetry seriously. These I relate to God's timeless eternity. Just as God is causally connected to any substance at any point in space, and regards them all the same (leaving aside the miraculous), so He is causally connected to any substance at any point in time and regards them all the same (leaving aside of the miraculous). God doesn't single out any point in space as special. Neither does God single out any moment in time as special. Analogously to rotations in space, God doesn't regard any velocity as special. There is no absolute velocity which has any measurable effects on physics; it just depends on the relative velocities between different substances. This explains why the action has time-translation and Lorentz symmetry.

If no point in space is regarded by God as anything special, how can there be an objective moment singled out as being now? More significantly, the Lorentz transformation is intrinsically four-dimensional. It mixes space and time coordinates. I'm going to have to express this in four-dimensional picture, because I can't express it in a three plus one dimensional picture (which I think says much in itself).

Suppose that I am travelling through the universe at a constant velocity (if I were accelerating I would notice a gravitational force) in my rocket-powered swivel chair. I will obviously regard myself as being simultaneous with myself. But I will also regard myself as being simultaneous with many other points in the space-time. For me, the set of all those points defines the slice in space-time that I regard as now. I will call this set of points the C-now.

How do I know when the various points are in the C-now? One means is to have numerous clocks moving through the universe at a velocity identical to my own. When those clocks record the same time as my own clock, they are simultaneous with me. Of course, I will need to wait until the light signals catch up to me. But if there are various events happening next to those clocks when the time on those clocks are identical, I can say those events are simultaneous. Again, I am being a physicist here and using clocks and physical measurement devices as part of the definition of simultaneous, but I doubt that a robust definition of simultaneous can be constructed with a finite speed of light could be constructed which doesn't reduce to a definition similar to this.

Suppose also that Professor Feser is also travelling through the universe in his rocket-powered armchair. Since he is a better philosopher than I am, he has a more powerful rocket and will be travelling faster than me. At one particular moment, he will overtake me and will be alongside me. At that moment, we both agree that we are simultaneous with each other. At the location in space we both occupy (near enough anyway), his now corresponds to my now. But Professor Feser will also have numerous other points in space-time which he regards as being simultaneous with himself, or in his now. This defines the F-now set of points.

The C-now and F-now sets don't contain the same points. They both contain the location which we both occupy at that moment. But otherwise they will be different. I will regard the other location/moments in the F-now set as being in my future. Professor Feser will regard the other points in the C-now set as being in his past. (We can't use this to share information about the future because Professor Feser won't know what happens at those points until light signals reach him, by which time they will also be in my past.)

This is counter-intuitive, because we don't usually travel at fast enough relative speeds to notice the difference. But it is implied by the theory of special relativity (recall that the space-time points in the theory are in a one-to-one mapping with reality), and confirmed by experiment. I regard an event happening at a particular point in space as being simultaneous with me. Professor Feser thinks a different moment of time at that point in space will be simultaneous himself. And we both regard ourselves as simultaneous with each other. This doesn't make sense unless we have subjective notions of the present.

As stated, this is not my argument that the present is in fact merely subjective. It might still be there is an objective notion of the present, which agrees with either Professor Feser, myself or maybe neither of us. Why should we decide what's simultaneous with ourselves in this way? Maybe there's an objective reference frame, and we should use the equations of special relativity to adjust our own measurements of our personal passage of time to recast them back into that objective frame.

So which of us is correct? Which of our now's corresponds to the objective now of the A-theory of time? We can only both be correct if the concept of now is only subjective (i.e we can only define what it means to be now relative to a given inertial frame), consistent with the B theory but not the A-theory. Or are neither of us correct, and the objective now is in a different inertial frame. Let's call the O-now as the set of points/moments corresponding to the objective now of the A-theory.

But as soon as we single out one set of points, or one inertial frame, in this way, we have to ask "Why isn't that reflected in physical law?" The concept of the O-now violates Lorentz symmetry. What I mean by that is we say that one frame in reality in special. But suppose our laboratory is travelling at a fixed velocity relative to that special frame. The laboratory is thus in a different reference frame; the people in that laboratory might have a C-now or F-now view of reality. They each perform their experiments, deduce the laws of physics, and come up with an action. They are smarter than us, and their actions describe quantum gravity. It describes everything about how the universe evolves in time (baring miracles) and the possible states of matter. Suppose there is a means of measuring which reference frame corresponds to the O-now. Whatever that thing is, it will be visible in the action. Thus the two observers will come up with slightly different actions based on their relative velocities compared to the O-frame. That's not an inconsistency; they will be able to use the formulae of special relativity to map between them, and say "given this action in this reference frame, a scientist will compute this other action in this different reference frame," and possibly in the i>O-frame the action would be in its simplest possible form (or some other means indicates that it corresponds to the objective present). But, of course, in reality, they don't measure any difference. The action is the same in all reference frames. There is no means to measure the O-frame.

That there is no means to measure the O-frame doesn't prove there is no O-frame, as Professor Feser noted in his reply to me. But we have to ask "Why, assuming that there is an O-frame, isn't that reflected in the laws of physics?" There are many self-consistent and possible expressions of quantum field theory which do violate Lorentz symmetry; which do have a measurable O-frame. Why isn't one of these true, rather than one of the much smaller number of theories which do reflect Lorentz symmetry? On the other hand, if you deny the existence of the O-frame, and say there is no ontological priority between reference frames (metaphysically none of them are more significantly than any other), then the action pretty much has to reflect Lorentz symmetry. A philosophy that accepts the existence of the O-frame has considerably less explanatory power than one which denies it.

The argument then becomes similar to those used in fine tuning arguments for God. We can say that if God exists, and desired to create a universe capable of supporting life, the parameters constraining the theory have to be within this small range. The probability of the parameters being suitable for life is relatively high. If God does not exist, or doesn't desire to create a universe capable of supporting life, then the parameters can take any value that leads to a self-consistent theory. The probability of the parameters being suitable for life is exceptionally low. We then use Bayes theorem, assuming the prior probabilities are similar, to reverse the conditions, and say that given the parameters are such that the universe is capable of supporting life, the probability of such a God existing is much greater than the alternative. The argument in my case is that if the dynamic block theory corresponds to God's view as the universe as He decides which potentia to actualise is true, then its pretty much certain that the laws of physics will satisfy Lorentz symmetry. If presentism or another A-theory is true, the probability that it will satisfy Lorentz symmetry is exceptionally low, since there are numerous other possibilities consistent with that philosophy. Then we use Bayes' theory, assuming roughly equal prior probabilities, to say that the probability of the dynamic block theory being correct is exceptionally larger than presentism. And this time, since we are discussing a metaphysical principle that ought to be true in all realities, I don't think you can avoid the conclusion by postulating a multiverse.

A fundamental principle is that the symmetries that constrain the physical theory should also be symmetries arising from the relevant aspect of reality that "decides" which potentia should be actualised. Without that principle, we can't explain why the model needs those symmetries to make accurate predictions. In my own philosophy, that aspect concerns God's decision about which potentia to actualise in each particular individual event. In a non-multiverse atheistic philosophy, it would concern whatever plays the same role in that philosophy as God does in mine. In a multiverse atheistic philosophy, it would concern the relationships between the universes. No matter your philosophy of physics, some mechanism in reality is needed to determine that this potentia should be actualised rather than that one, and that mechanism would explain why Lorentz symmetry is needed in the representation. It would in some way reflect the equivalent symmetry in reality. If God, or whatever mechanism plays the role of God in an alternative philosophy, can distinguish an O-now, then there isn't an equivalent symmetry in reality. Thus such a symmetry ought not to be important in the physics describing God's actions.

The B theory has no such problem, as it denies that there is an O-now. In fact, the B-theory pretty much demands that the laws of physics respect Lorentz symmetry (or its analogues in Riemann geometry once we add in general relativity). That's not surprising, since the B-theory was proposed to make sense of special relativity.

There are two ways of looking at this. We can ask "If reality in some fundamental way violates Lorentz symmetry, then why does the expression of physical law which makes correct predictions require Lorentz symmetry?" The issue is more acute because the notion of the objective now is perfectly rational. We can map it to a geometry, work out the symmetries corresponding to that geometry, and construct a physical theory based on those symmetries. This would be the 3+1 Euclidean geometry of Galilean relativity. This has different symmetries, which don't constrain physical law in the same way (the Yang-Mills part of the action would be particularly troublesome). At best you have the same problem as atheism: you will lack the predictive power of the B theory. At worst you will be forced to accept laws of physics that makes incorrect predictions concerning reality.

Alternatively, one can ask "Given the laws of physics respect Lorentz symmetry, there is no objective way of measuring which points/moments are in the O-now set. It has no physical influence. The concept is redundant. Why then maintain there is such a set?" Obviously, this would fail if there was an alternative reason to accept the that the points in O-now are in some way distinct from the points in the C-now or F-now sets. But what reason could there be? It can't come from observation, because we know from physics the concept of the O-now doesn't affect any observation. It can't come from philosophy, because there are (I maintain) no good philosophical objections to the dynamic B-theory. The only good solution is to deny that the O-now set plays any role in either physics or philosophy, and adopt a dynamic B-theory. This approach doesn't formally prove there is no O-now ontologically (that would require the additional step of verificationism, or perhaps Occam's razor which also falls short of proof). But there is also the epistemological side of things: our justification for believing that such a view is true. If there is no evidence for something, at best it's an open question, or at worst (if there is evidence for its rivals, or the rival theories better explain the evidence) it suggests we ought to reject that thing.

Professor Feser's response

I first of all must thank Professor Feser for his well balanced and respectful response to my original post. He makes a number of points in response to my case. I'll state each of them in a separate sub-section, and then respond to them in turn in the next section.

Verificationism

I began my post by emphasising that the "world" studied by physicists is an abstract representation of the real world. There are two bijective (two way) mappings: from real space to geometric space, and from geometric space to a coordinate systems. Both the geometric space and coordinate systems are abstract space.

Professor Feser accepts this, but argued that I had rushed over its implications. Why is the relativity of coordinate systems "so deeply enshrined in physics that I don't think that anybody can rationally challenge it?" Professor Feser responds that the reason is related to the verificationism that was popular in the early twentieth century. This is the belief that a statement is only meaningful if it is either empirically verifiable or a tautology.

Verificationism can be either a philosophical position (i.e. a statement about the objective world) or a methodological constraint. Special relativity plus philosophical verificationism would hold that because an absolute reference frame is not observable, positing it is meaningless. Philosophical verificationism is distinctly problematic. For example (and there are more sophisticated arguments than this) its definition (alluded to in the previous paragraph) is itself neither empirically verifiable or a tautology, so if it is true its own definition is meaningless, in which case it can't be true.

Methodological verificationism suggests that Physics is unconcerned with statements that aren't empirically verifiable or tautologies. There might be such things; they are just beyond the scope of physics. The problem with methodological verificationism is that it doesn't tell us anything about the real world. It has no metaphysical implications. Consequently, any conclusions which assume methodological verificationism equally don't have any metaphysical implications.

So the absence of an absolute reference frame in special relativity only implies an absence of an absolute reference frame in reality if we add in the hidden assumption of philosophical verificationism. It would only give reason to suppose there is no absolute frame in reality if there are independent grounds for thinking that physics would reveal an absolute frame if it were there. If so, it would be those independent grounds doing the philosophical work rather than the physics.

Structural realism

The next part of my post described the importance of symmetry in physics. I tied this to the philosophy of structural realism, which Professor Feser adopts. I stated "The reason that the abstract representation used by physics is successful is that it maintains the same relationships between the representations of the objects as exists in reality."

Professor Feser defines structural realism as a middle ground between instrumentalism (where physics is merely a useful tool for making predictions) and a hard realism that states the mathematical structure is identical to what's really there. Structural realism states that physics reveals mathematical relations, but doesn't tell us about the intrinsic nature of the entities related by those relations.

To put it in terms of my own practical example (hopefully not misrepresenting Professor Feser), physics describes certain relations between mathematical objects which represent electrons and other mathematical objects which represent photons. I will call this the abstract-electron and abstract-photon. But what we are interested in are not the mathematical abstractions, but electrons and photons in the real world (real-electrons and real-photons).

The instrumentalist states that we cannot deduce from physical theory anything about real-electrons and real-photons, except that if we set set up an experiment in a particular way and repeat it enough times, there will be a certain frequency of clicks on a particular detector. There is no need in this interpretation to suppose that real-electrons and real-photons even exist (that would be an open and unanswerable question). Abstract electrons and photons are merely useful conceptual tool to predict clicks on a detector.

Hard realists, conversely, believe that there is no meaningful distinction between abstract-electrons and real-electrons. Physics can tell us about the ontology of real-electrons.

Some structural realists will say that we can't know from the physical description what electrons and photons really are (except, I assume, that there are such things as real-electrons and real-photons). But we do have analogous knowledge about their interactions, because abstract-electrons relate to abstract-photons in the same way that real-electrons relate to real-photons.

Personally, I agree that neither instrumentalism nor hard realism are tenable, and we need a middle position. Instrumentalism doesn't explain why physics makes its predictions so well; and maybe even would suggest that its mere coincidence that physics makes such good predictions. To my mind, this makes it distinctly inferior to softer and harder forms of realism. If it can't explain, it can't add to our understanding. (Of course, even if it can explain, that doesn't make the explanation true, as there might be some other model which explains just as well or maybe better.) As someone sympathetic to hylomorphism, I accept that real substances are a mixture of form and matter. I don't believe that physics can tell us anything about the actual nature of matter (beyond that there is such a thing), and this in itself rules out hard realism. However, I would say (although I don't intend to defend it here) that physics can give us at least a partial understanding of the form, certainly for compound objects. Compound objects aren't just the sum of their parts, so can't just be reduced to the relationships between those parts. I agree with the structural realist that relationships between the abstract objects can provide useful knowledge of the relationships between the real objects. But I would personally adopt an intermediate position between structural realism and hard realism. But Professor Feser is a structural realist, and I don't dispute that we can have at least a partial knowledge of real relations, so that's a sensible place to adopt for this discussion.

The center of my argument concerns symmetry. Symmetries presuppose relationships between two objects. So if we can derive at least partial knowledge of real-relationships from our knowledge of the abstract-relationships, then we can also derive at least partial knowledge of real-world symmetries from our knowledge of symmetries in the abstraction. So if there is a symmetry in the abstraction inconsistent with the notion of an objective simultaneity, so there must by a symmetry in reality inconsistent with the notion of an objective simultaneity. And if simultaneity is only a subjective rather than object notion, you can't have an objective notion of the now, and presentism is false.

Professor Feser's response to this is that I have misunderstood structural realism. It's far more abstract than my argument requires. There are various things "structure" can mean. The more abstract the conception of structure, the less metaphysical relevance the physics has. What tends to be preserved through theoretical revolutions in physics are mathematical equations. Professor Feser cites the example of Fresnel's and Maxwell's equations concerning the nature of light. Fresnel used these equations to interpret light as an elastic solid. Maxwell thought of it in terms of a non-localised electromagnetic field. So the equations cannot by themselves tell in favour of these interpretations.

Likewise special relativity's mathematical form is consistent with B-theories of time. But William Lane Craig interprets it according to Lorentz rather than Einstein/Minkowski's geometrical interpretation. Or Zimmerman proposed there is a privileged slicing of space-time corresponding to the present, but physics is methodologically unable of detecting it. Or Tooley's attempt to merge special relativity with a growing block theory of time. And so on.

Professor Feser isn't endorsing any of these positions, but merely saying the mathematics itself can't help us choose between them. If there are solid objections to one or more of those interpretations, that doesn't mean there isn't another interpretation consistent with some A-theory that survives those objections. The mathematics alone can't tell us. And, in Professor Feser's version of structural realism, the mathematics by itself is all the physics gives us confidence in.

The relationship between space and time

In my original argument, I then draw an analogy between Lorentz transformations and rotations. Rotations map between neighbouring points in space, and nobody doubts that those neighbouring points exist in reality. Lorentz transformations are mathematically similar, and map between neighbouring points in time.

Professor Feser suggests that the obvious response is that this confuses between the representation and the reality. Are we just treating time as another spatial dimension? I respond no; there are differences: the minus sign in the metric is least important. There is the need for time ordering when calculating amplitudes, and the positivity of energy. These last two suggest that there is a direction and objective succession in time that is lacking in space.

But Professor Feser thinks that I missed the point here. My argument, he claims, raises both space and time alike into eternity. This makes space-time a kind of Platonic abstract object that is both spaceless and timeless, which is very unlike our ordinary conceptions.

Professor Feser mentions that direction and succession aren't enough to define time. The integers have the same property, but that doesn't make counting integers temporal.

Causal relations

Professor Feser supposes that I will reply that causal relations between events in a series makes them temporal. But what remains of causality when ordinary notions of space and time are replaced by coordinate systems?

If points in time are as equally real as points in space, then a stick’s going from rest to motion is like it’s being red at one end and green on the other. The latter is not a change but just the having of different attributes at different spatial parts, and it is hard to see how the former amounts to a true change either, as opposed to merely the having of different attributes at different temporal parts. And if we replace our ordinary notion of space no less than our ordinary notion of time with the idea of points in an abstract coordinate system, the result is something even less like change in the ordinary sense. But without change in the ordinary sense (which, Cundy agrees, entails the actualisation of potential) what becomes of causality in the ordinary sense? We don’t seem to be talking about change or causality at all as we consider the coordinate systems Cundy is describing, but simply noting different aspects of a kind of Platonic object.

Fallacy of equivocation

Professor Feser raises the point that physicists often use the same words as common usage, but assign a different meaning to them. "Time" in the ordinary sense means something different to "Time" as the physicist uses it. The same principle applies to concepts such as space, change and causality. The mathematical representation drains the concept of its meaning.

What's the link between abstraction and reality?

Now we come to the crux of my argument. My argument is that the symmetries in the abstract representation must also reflect symmetries in reality. The symmetries basically define what interactions are possible. The strength of those interactions is determined by the physical constants, but whether the the interactions are possible or impossible is determined by the symmetry requirements alongside the need for renormalisability/mathematical consistency. We can construct physical theories with whatever symmetries we like. We can use Galilean relativity instead of Einstein's relativity; once again, that will be expressed in terms of a set of symmetries constraining the action. The theory developed from that would be self-consistent, mathematically reasonable, and from the point of view of the theoretician perfectly reasonable. It would be wrong, of course, in the sense that it would make incorrect predictions of reality and fail the experimental test. But there is no reason from the perspective of theoretical physics why the universe has to be that way.

So why do we need to construct the theory using Lorentz symmetry rather than the symmetries that underlie Galilean relativity in order to correctly describe what happens in reality? The obvious reason is that reality also reflects a symmetry which is the analogue of Lorentz symmetry in the representation. Recall that the transformations underlying the symmetries are among those things that can be directly mapped from reality to representation and back again. If Lorentz symmetry in the representation, essentially a rotation between spatial distances and temporal durations, requires a four-dimensional space-time, then the analogue of Lorentz symmetry that we know must exist in reality would also require a four-dimensional space-time.

Professor Feser's response to this is that I underestimate how abstract the mathematical representation is. I seem to be arguing that I can read off the equal reality of past, present and future events from the mathematics itself. But that's reading too much into it. An additional, metaphysical, argumentation is needed to reconstruct the same conclusion in reality. But then its this metaphysical argument that does the work. Professor Feser again notes that the models of Craig, Tooley and so on are perfectly consistent with the mathematics, but draw very different metaphysical conclusions. Independently motivated metaphysical considerations can and should guide the interpretation of the mathematics. But the mathematics alone isn't enough to determine a metaphysical conclusion.

Empirically detectable or in reality?

Professor Feser maintains that the most special relativity rules out is a privileged reference frame that's empirically detectable. To jump from this to ruling out a privileged reference frame in reality requires assuming verificationism or a similar philosophy, i.e. that only those things empirically testable are meaningful. However, we have good reasons to reject verificationism, and there is no empirical basis for it. Alternative philosophical positions have independent grounds to affirm presentism.

Thus the choice isn't between science and presentism, but between a philosophy used to interpret the science, and another rival philosophy. The difference between these philosophies boils down to metaphysics and epistemology, which are both both pre-cursors to science rather than things which can be derived from science.

Potentialities for future outcomes

What about my claim that adopting presentism entails there are aspects of the mathematical representation which don't correspond to things in reality? Suppose that we say that only the present exists in actuality. But within the present there are potentialities for generating future outcomes, including the range of observations made by different observers in special relativity.

A mathematical representation can correspond to reality in one respect, while in another respect the feature is a mere artifact of the mathematics. So the empirical success of relativity's mathematical representation doesn't necessarily mean that all temporal points are real, in the same way we regard all spatial points are real.

Analogy with Euclidean geometry

Physics representation of space is constructed in two separate mappings. Euclidean geometrical space has tremendous usefulness. It has features which remain invariant under different choices of coordinate systems. Does this combination of invariance and usefulness mean that Euclidean space corresponds to the true structure of the universe? No. Euclidean geometry wouldn't be as useful if it didn't capture something about reality. But only something, but not much. The relationship between the structure of a mathematical representation and the structure of reality is loose.

So why do I maintain that the combination of invariance and usefulness of Minkowski space corresponds to the true structure of the universe?

Change in the B-theory?

I claim that change is possible in a dynamic B-theory. At one time state A is actual and state B exists potentially. At a slightly later time, state B is actual, and state C is potential.

Professor Feser compares this to a stick that's red at one end and green at the other. We can't say that the stick is changing its colour. One part of it is actually red, and the other part actually green. There is no change from red to green. He states that the B-theory makes a things attributes essentially like this, even if it doesn't fully specialises time. Potentiality doesn't give way to actuality any more than it does in the stick example. There is no process, but the eternal co-existence of different states. The B-theory fails to capture real change and causation. Everything is already actual.

Common sense notions of time and space?

In my previous post, I criticised some arguments that Professor Feser used. He argued (as I presented it) that you can have rotations in space, but nothing equivalent between space and time. I pointed out that a Lorentz transformation is, effectively, a rotation between space and time. The mathematical difference between rotations and Lorentz transformations in Minkowski space-time (I neglect complications when we advance to general relativity) is solely to accommodate the minus sign in the metric.

Professor Feser replies that I didn't address what he wrote. He was discussing out pre-theoretical or commonsense notions of time and space. Obviously, the presentation of time and space used in special relativity isn't pre-theoretical. Thus I am accused of a fallacy of equivocation, confusing between the physicists representation of time and the commonsense notion of time referring to reality.

Does Professor Feser mean to suggest the common sense notion of time is true over the notion used by physicists? No. Here merely makes the point that to compare them you first need to fully define the common sense conception of time. Whether physics is consistent with it is another question. But the further physics departs from it, them greater is the danger of an equivocation.

Collapse distinction between time and eternity?

Does the four dimensional view of space-time collapse the distinction between time and eternity? I argued that it maintains it. This follows from the distinction between the subjective notion of the present seen by things in time, and the God's view from a perspective outside time of all the universe together.

Professor Feser sates that this is merely stating that time will appear to pass and there will appear to be a unique present from the observer's subjective point of view. This isn't contentious. The question is whether this appearance corresponds to anything in reality outside the subjective point of view. The question isn't whether in a B-theory time merely seems not to collapse into eternity, but whether it really does.

Are there truths which cannot be captured in tenseless terms?

I argued that tense is a real part of the four dimensional universe, only I argued that it is subjective rather than objective. For everything in the universe there is a past, present and future. But which moment is the present depends on our position in time.

As before, Professor Feser states that I am confusing between how things seem to be to us, and how they really are. Is tensed language necessary to describe how the universe really is from an objective sense? I seem to be arguing that it is only subjective. So I don't accept that tense is a real part of the four dimensional universe.

Is my position the moving spotlight?

Professor Feser argued that we cannot eliminate the notion of temporal passage from the mind itself. I agree. But I argued that this argument only attacks the static version of B-theory (which denies both an objective present and an objective temporal passage, while affirming the reality of four-dimensional space-time), not the dynamic version (which denies an objective present, but accepts an objective temporal passage, i.e. an objective distinction between past and future, while affirming an objective four-dimensional space-time).

Professor Feser argues that my position collapses into the moving spotlight position. The moving spotlight view affirms the reality of four dimensional space-time, but accepts both the objectivity of the present and the passage of space time.

So expressed in this way, there is a clear distinction between the static version of B-theory, the dynamic version of B-theory, and the moving spotlight models. I reject the moving spotlight theory primarily because it adds an unnecessary and ad-hoc assumption to the dynamic version of the B-theory. But Professor Feser thinks that I need to adopt it to make my position coherent. It's worth quoting him in full.

Cundy’s position is therefore ambiguous. On the one hand, his affirmation of the equal existence of past, present, and future moments of time and his characterisation of tense and presentness as “subjective” seem to imply a B-theory. On the other hand, his Aristotelian-Thomistic commitment to the reality of change as the actualisation of potential and his affirmation of the ineliminability of temporal passage seem to point to an A-theory. It appears to me, then, that Cundy may really be a “moving spotlight” theorist without realising it, or at least that adopting a version of the moving spotlight theory might be the best way for him to make his various commitments cohere

Response to Professor Feser

Verificationism

Professor Feser is correct that verificationism is very problematic. For example, we can consider virtual particles. In a Feynman diagram expansion, for example, the electromagnetic interaction is mediated by photons. This isn't a literal description of what happens. The Feynman diagrams are computed in an unrenormalised energy/momentum basis, which isn't physical. Even if we can switch to a similar description in a renormalised space/time basis (which would be similar to the histories in the consistent history interpretation), there are numerous Feynman diagrams each leading to the same possible result, and all we can say is that each of them is a possible sequence of events which happened, and we can't know which one happened in practice. Some of those paths lead to outcomes with probability zero. Those paths are possible in the sense that they are allowed by the individual final causes of the particles at each moment of time, but impossible in the sense that the outcome has probability zero from calculations of all the paths to that outcome. (These statements don't contradict if you regard notions of possibility as contingent on various premises, and two different notions of possibility can only be compared if those premises don't contradict.) But nonetheless, the interpretation of electron-electron scattering that either one electron spontaneously emitted a photon which was absorbed by the other electron affecting the motion of both electrons, or there was some more complicated process involving multiple photon emissions and perhaps also some electron/positron pair creation and annihilation, remains the most natural interpretation of quantum field theory. This process isn't empirically observable. We can't observe the intermediate photons. If we did observe them, i.e. they interacted with a detector, they would no longer be intermediate. Why then do I call this interpretation most natural? Because the theoretical framework describes the interactions in terms of electron and photon creation and annihilation (or generation and corruption in Aristotle's language). The theory correctly predicts frequency distributions to an exceptionally high accuracy. Why is the theory so successful? The obvious reason is that the possible processes it describes are processes that occur in reality, even if they can't be directly empirically confirmed.

I've still here relied on empirical data to say that the theory is correct. Does that mean I have subtly embraced verificationism? I think if we interpret verificationism this way, and rejected that verificationism, then everything would become suspect. After all, as Aquinas noted, "all our knowledge originates from sense. " But there are things whose existence is directly observed, and other things whose existence is inferred (perhaps after numerous steps) from what is directly observed. I would take verificationism to state that only statements concerning those things which are directly observed (or whose denial would amount to a contradiction) are meaningful. Clearly my interpretation of QFT goes beyond what is directly observed. But I still regard it as meaningful.

As indeed would be my description of God as the termination of a cosmological argument. The starting point of the cosmological argument is empirical: "It is evident to our senses that some things are in motion." Or "There exist contingent beings." Or "There exist beings with an efficient cause." These statements cannot be proved from reason, but are deduced from observation. Nonetheless, statements about the conclusion of the argument (namely God) are certainly meaningful.

So what about my statement

The statement of relativity is that coordinate systems must be relative to each other, and that there is no absolute coordinate system. This I take to be so deeply enshrined in physics that I don't think that anybody can rationally challenge it.

Is this dependent on the idea that only statements about what is directly observed are meaningful? I don't think so.

Coordinate systems themselves cannot be directly observed. They are part of the representation, artificially created during the mapping from reality to representation. I'm discussing the representation here, not reality. In strict verificationism, my statement itself would be meaningless.

There are two ways in which we might approach this statement.

The first is because the coordinate systems are arbitrarily imposed. They are not part of reality. But we nonetheless use the theories constructed from those coordinate systems to make successful predictions concerning reality. The way to reconcile this is to say whichever coordinate system we choose will ultimately lead to the same prediction. This means three steps:

1. mapping from reality to initial state in the representation (in QFT the choice of creation operators and their basis to apply to the vacuum state);
2. the calculation of future possibilities (in QFT, the Hamiltonian evolution of the Fock state);
3. mapping back from representation to reality (in QFT, we use a comparison Fock state constructed by applying other creation operators in a given basis to the vacuum operator, which is then applied to the result of step 2 to compute a total amplitude covering all possible paths, which is converted into a probability, which is then compared against an experimental frequency distribution).

This first argument means that only the product of the three steps is independent of the coordinate systems, i.e. the Hamiltonian might take a different mathematical form in different coordinate systems, if the way we construct the initial and comparison final states compensates for this difference.

Consider the two cases.

1. There is something corresponding to an absolute coordinate system preferred in reality.
2. There is nothing corresponding to an absolute coordinate system preferred in reality.

What physical theories might arise if we start from these assumptions? In the second case, we would be forced into a theory where the choice of coordinate system was arbitrary, as we do. This is also possible in the first case; obviously if all choices of coordinate systems give the "right" result (by "right" I mean empirically successful), then so would the one which reflects reality. But if the first proposition is true, there is another option: namely that we would have to choose the coordinate system representing the preferred frame in reality in order to make the "right" predictions. In that case, if we chose the incorrect coordinate system, we would get the wrong result, and the theory would be ruled out through falsification.

Is it possible to construct a theory which requires a particular coordinate system, and is wrong in any other coordinate system (even if the mathematical form of the time evolution operator changes depending on which coordinate system was chosen)? This is actually pretty difficult. Aristotle's own physics is possibly our best hope for a counterexample. Aristotle's physics accurately describes the motion of a particle in a fluid after it has reached terminal velocity. There is thus a preferred reference frame; that of the fluid. It's natural to calculate in this reference frame. But I don't think we are forced to: we could choose a different coordinate system, construct the theory in that coordinate system, and use it to successfully describe the path of the particle. The theory would be far more complicated in the other coordinate system; but it ought to be possible. And, of course, there would be no way of saying which coordinate system corresponded to the preferred frame in reality, because they would all lead to the same predictions. It's likely that the theory would be simpler in the coordinate system corresponding to the absolute frame in reality, but "It's likely" isn't proof, and "simpler" is too ill-defined to be useful.

So while in principle the statement that there is nothing corresponding to an absolute coordinate frame in reality might lead to a physics which requires an absolute coordinate frame in the representation, in practice I can't think of how it would work (which isn't the same as saying it can't work). So either a reality with or without an absolute coordinate frame would lead to a same principle "there is no absolute coordinate system [in the representation] and this is so deeply enshrined in physics that I don't think that anybody can rationally challenge it."

I have gone to more detail, but this is the argument I used to support my statement in the original post which I cited above.

Does this argument prove that there is no absolute coordinate frame in reality? Clearly not. For in this sense, both reality with and without an absolute reference frame lead to the same restriction on the physical representation; so we can't say which of the two premises is falsified. So I think my statement which Professor Feser cited is justified, but it isn't an argument against Presentism.

But then, at that point in my post, it wasn't intended to be. I was just setting the scene. To get directly from this argument to "Presentism is false" would require verificationism, but I wasn't taking that step. Instead, this is merely a first step in an argument from this statement, alongside other premises, to indirectly suggest that presentism is false, which (I believe) avoids verificationism.

I mentioned two ways in which we could interpret the statement. The one above is what I meant in my post at that point in the argument; and I accept it doesn't rule out presentism. I went on to discuss the second way in the next section of my original post.

I stated that for most theories we could represent the theory in any coordinate system we choose, and it would in principle lead to the same predictions. But this comes at the cost that the mathematical form of the time evolution operator would differ from one representation of the theory to another. But there is a small class of possible theories where the mathematical form of the time evolution operator is the same no matter which coordinate system you choose. This is when the time-evolution operator (or, more technically, its associated Lagrangian/action) has a symmetry with respect to the transformation corresponding to the changes between coordinate systems. Suppose we find that the physical theory which makes correct predictions requires such a symmetry. What does that imply?

In my own work, I regard the time-evolution operator as a description of how God sustains the universe. It describes the possible changes God could induce, and assigns an amplitude/probability to each possibility. Those possibilities are restricted to the substances potentia and by its final causes. I think if you accept theism -- that God is active in sustaining the universe by actualising potentia while respecting the substance's formal and final causes -- and that physics provides a description of how the universe evolves, then this is a natural conclusion to draw. The symmetries of the time-evolution operator then reflect God's own omnipresence and timelessness. Thus (and obviously there is far more detail needed which I've provided elsewhere), if God exists, we can expect the laws of physics to be roughly as we observe; while if God does not exist, we can have no such expectation (and there are good reasons to suspect they would be different).

So now lets return to the two statements I presented above:

1. There is something corresponding to an absolute coordinate system preferred in reality.
2. There is nothing corresponding to an absolute coordinate system preferred in reality.

For statement 1, we would expect the predictions of the theory to be independent of the coordinate system. But there is no good reason to expect the time evolution operator to take the same mathematical form regardless of the coordinate system. This doesn't happen, for example, in Aristotle's physics, nor Newtonian physics, or a physical theory where electromagnetic waves are carried by an aether. You might say "It's possible that the true theory would have the symmetry even if there is an absolute coordinate system in reality." Maybe its possible. But it isn't required. It's just one possibility out of perhaps an infinite number of options.

But statement 2 implies there is a symmetry in reality. If there wasn't such a symmetry, not all things corresponding to coordinate systems would be equivalent, implying there is some preferred coordinate system. For example, suppose we have 3 interacting objects. Z sits at the point in real-space-time which is mapped to the origin of my coordinate system in my present. Two others, X and Y are the same spatial distance from the origin. In one reference frame, X appears simultaneous with me. In another reference frame, Y appears to be simultaneous with me. If there were no absolute temporal reference frame, I couldn't say that one of these objects was objectively simultaneously with me. Thus there can be no difference in how Z would interact with either X or Y. Since the time-evolution operator represents the interactions between these substances, there should be no difference in the mathematical form of the part of operator describing Z's interactions with X and describing Z's interactions with Y. In other words, we expect the time evolution operator to have a symmetry corresponding to the lack of preferred coordinate frame in reality.

So option 2 must lead to a physical theory as we observe it (at least with respect to Lorentz invariance). Option 1 might, but this is very unlikely, isn't the case in the leading theories which were naturally developed from presentism (Aristotle's physics, Newton's physics, and non-relativistic quantum wave mechanics), and isn't what you would naturally expect from such theories. One would naturally expect the time evolution operator to reflect the symmetries associated with Galilean relativity (where the mapping of the temporal coordinate is the same regardless of the velocity or location in space).

So to get from "the time evolution operator satisfies Lorentz symmetry" to "Presentism is false" isn't verificationism, but a form of falsification. We accept "Presentism is true" as the premise; ask ourselves "What laws of physics would that premise imply?" and then "Do those laws of physics correspond to what we see in reality?" We then repeat the process for the premise "Presentism is false." Not-presentism implies the theory should have Lorentz symmetry (or the extensions to Lorentz symmetry used in general relativity). Presentism doesn't make that implication. But we find that Lorentz symmetry is required for the theory to make successful predictions. Whether this makes presentism false or merely highly improbable (improbable computed from the proportion of possible theories consistent with presentism which have Lorentz symmetry or its extensions) depends on how seriously you take the argument that were presentism true, you would expect the time evolution operator to reflect the symmetries of Galilean relativity. But either way, this gives a strong argument against Presentism.

So this way of interpreting the statement does lead to an argument against presentism, but doesn't need to assume verificationism to do so.

I also note that there is a false dichotomy in Professor Feser's argument. He states its either physics doing the work of disproving presentism (which, in his view, requires verificationism), or independent grounds. But the argument could also be based on the combination of independent grounds and physics, neither one nor the other doing the legwork, but the two working together. This is the approach taken by falsification. You start by calculating the physical consequences of any metaphysical world view -- which doesn't require any empirical physical input -- and then compare each set of consequences against the actual physics. So we start with grounds independent of physics -- the different metaphysical models -- but use physics to judge between them.

Structural realism

Professor Feser stated that his structural realism states that physics reveals mathematical relations without telling us about the intrinsic nature of the underlying entities. There is, of course, a sense where this is true. Quantum electrodynamics informs us how electrons interact with photons. It's success is good evidence that the theoretical constructs representing electrons and photons correspond to particles which exist in the real world. But it doesn't tell us what electrons and photons actually are. And given that there are aspects of real electrons and photons which can't be abstracted (since our abstractions are never identical to the real thing), I don't think we can ever know fully what electrons and photons really are.

When we get to compound objects, effective field theories and into condensed matter theory, I think we can know some more. Here their underlying matter isn't the fundamental particle or prime matter, but the electrons, quarks, photons, gluons, and so on which we do represent. We use use effective field theory, constructed using symmetry considerations, to establish their structure and properties. Their colour, how they react under tension and compression, how sound waves or heat passes through them, and so on. These properties don't just describe how the particles relate to external particles (or forces), but also their internal structure. Again, we can confirm that structure and those properties through experiment. But again, this doesn't and cannot give a complete answer of what the compound objects are; their intrinsic nature.

But physics does provide a partial knowledge of real-electrons, real-photons and so on. It gives us good reasons to believe that there are such particles, for example. To reasonably dispute this one would have to come up with some alternative theory that makes the same predictions that doesn't require such particles. Can I say such a theory is impossible? No. But it would be extremely difficult to produce.

This seems to be the avenue that Professor Feser is taking. Professor Feser concentrates on the interpretation of the equations. What survives are the equations. But they don't tell us the correct interpretation of those equations.

There is some truth in this. Professor Feser's example of the Fresnel and Maxwell interpretations of the nature of light is out of date. The physics has moved on since that time. The Lagrangian which leads to Maxwell's equations in classical physics is still part of the standard model; but the principle of least action needed to derive the equations from the Lagrangian has gone (at least its now derived from the path integral formulation of quantum physics and is only an approximation to the real world).

But, of course, the numerous different interpretations of quantum physics provide an alternative example Professor Feser could have used. These (mostly) lead to the same mathematical formulae. Deciding between them is a matter of how one interprets the probabilities that arise from quantum physics theory; how one deals with the non-local correlations that arise from quantum physics, and so on. To an extent its a matter of personal prejudice. Of course, I have my own favourite, but clearly other people disagree with me.

But just because we don't know which interpretation is true, we can say for certain that many interpretations of the physics are false. Both Fresnel's and Maxwell's interpretations of the nature of light are false (at least not wholly true), because they rely on an underlying classical framework. The equations those interpretations are either derived from or imply aren't an accurate description of reality. Obviously to give an interpretation that is consistent with contempoary physics requires getting back into the mess of interpreting quantum field theory, which I don't want to revisit here.

So what about special relativity? Obviously, I should be reluctant to challenge people such as William Lane Craig, Zimmerman or Tooley, who possess far better minds than my own. But I think there is a subtlety in my argument which Professor Feser is missing. My argument doesn't rely on the interpretation of special relativity. It relies on the interpretation of special relativity as it is used in quantum field theory. Quantum field theory isn't the same as classical special relativity. Classical special relativity basically reduces to saying that we need to use the Lorentz transformations to map between the observations of observers travelling in different inertial frames. The Lorentz transformation corresponds in the real world to a change of velocity for the observer. Quantum field theory states that the Laws of physics themselves (at least the Lagrangian which gives rise to the Hamiltonian operator which describes how quantum states evolve in time, with those quantum states used to compute the probabilities for various outcomes) have an underlying Lorentz symmetry. This is a far stricter requirement. One can easily write down theories where Lorentz transformations are needed to map between different inertial frames without requiring the Lagrangian satisfies Lorentz symmetry.

All valid interpretations of quantum physics thus need to say that Lorentz symmetry is a fundamental part of the theory. Any interpretation that denies this (at least until we get into quantum gravity, where Lorentz symmetry is replaced by the more general Riemann symmetries associated with general relativity; which doesn't undermine my point) is invalid. One can have interpretations of classical special relativity which minimise or ignore the importance of Lorentz symmetry. Hence the alternative interpretations of Craig, Zimmermann, and so on. But not relativistic quantum field theory.

But does this help me? My own interpretation of quantum physics can be started from the fundamental premise of theism: God didn't just create the universe, but actively sustains it (or one could work backwards from physics to offering an empirical validation of the fundamental causal principles to the various causal arguments that Professor Feser has defended so well to the conclusion that God sustains the universe; but for the purpose of this post its easier to start with God). God has an active role in actualising potency (while the real particles have a passive role). At some point then, the physical description of how the universe evolves will reduce to a description of how God sustains the universe. As Professor Feser agrees, God is timeless, in the sense that He is causally connected to every point and moment in the universe without Himself being subject to change or the passage of time. God is omnipresent. Consequently, we cannot say that God is travelling through the universe at a particular velocity. Or that He prefers one velocity to another, which for the purposes of this discussion amounts to the same thing. God will interact with all particles the same no matter their velocity or direction of travel. Consequently, the mathematical form of the operator which describes the amplitude that God will actualise potentia A rather than potentia B for a given particle (where I use particle to denote the things that exist in the real world, whatever their intrinsic nature might be) would be independent of the particle's velocity. Hence we can expect Lorentz symmetry. God's timeless nature means that for God there is no objective moment of time which He points to and says "that's my present," which seems to contradict the notion that there is an objective present. (William Lane Craig, for example, defends the view that God is timeless without creation and temporal after creation, which ties in with his interpretation of special relativity. He needs his interpretation to deny God's timelessness after creation; a timeless God would be inconsistent with his interpretation of special relativity.)

Or, alternatively, we can work backwards through this argument, and state that given Lorentz symmetry, whatever is responsible for determining whether potentia A rather than potentia B becomes actual in practice must be timeless and omnipresent.

Obviously, not everyone will agree with this interpretation. But whatever interpretation is adopted, if it is to be at all satisfying, it needs to have some explanation of why this particular potentia is actualised rather than another. (Arguably, only the pilot wave, Everett, and my own interpretations can do this.) And that explanation will also have to explain why Lorentz symmetry rather than some other symmetry, such as the symmetries behind Galilean relativity, constrains the Lagrangian that describes the interactions in the abstraction which represent the real-world interactions between particles. The obvious, and I think only, explanation is that Lorentz symmetry in the abstraction corresponds to a symmetry in whatever it is in the real world that leads to potentia being actualised. Just as the rotational symmetry in the abstraction corresponds to a rotational symmetry in the real world.

My argument was that since a Lorentz transformation is essentially just a rotation between spatial and time coordinates (applicable to both past and future times), the symmetry this implies a 4-dimensional universe in the abstraction, which suggests that the corresponding real world symmetry also implies a 4-dimensional universe, at least in the view of whatever it is that "decides" which potentia should be actualised. Time translation symmetry is also relevant, and plays the same role.

Obviously this argument assumes a whole bunch of stuff which Professor Feser also objected to. I will get to that below. But here I just want to make the point that while there are multiple viable interpretations of relativistic quantum field theory which differ in many respects, there are certain points of agreement shared by all valid interpretations. The importance of Lorentz symmetry in the theoretical abstraction is one of those points. Can we interpret this importance in different ways? Whatever interpretation we adopt needs to explain why Lorentz symmetry is so important. Not every potential explanation would imply the correct physics. Some would imply the incorrect physics. These should be ruled out. As stated above, I think there is a strong argument, for example, that any interpretation involving Presentism would implies the geometry that underlies Galilean relativity. It doesn't explain why Lorentz symmetry is so important, and thus should not be preferred over those theories which do explain that fact. We have to ask what physical theories naturally flow from the metaphysics. I don't think there is much question that presentism fits far more comfortably with Galilean relativity than Einstein's relativity. Until Einstein, people assumed presentism, and that's why it was incorporated into Galilean relativity without much thought, and why Einstein's relativity came as such a big surprise. But equally, denial of an objective present easily explains why we have the symmetries which underlie the standard model. The physics follows naturally from this metaphysics. While a different set of symmetries follow naturally from presentism, leading to an incorrect physics.

Obviously "most comfortably" and "most naturally" aren't proofs. But I think the burden shifts to advocates of presentism to derive the laws of physics from their metaphysics (plus whatever other minimal set of assumptions that they need).

That there are multiple valid interpretations of the mathematics doesn't invalidate my argument if they all lead to the same conclusion on this point. There might also be invalid interpretations (either self-inconsistent, or inconsistent with the theory, or require some metaphysical absurdity such as denying causation) of the mathematics which don't lead to the same conclusion, but we needn't waste time considering those.

As far as I am aware (and I would welcome correction), Professor's Craig, Zimmerman and Tooley don't present valid interpretations explaining the symmetries of relativistic quantum field theory because they aren't interpretations of relativistic quantum field theory, but merely classical special relativity. Whether they are valid or invalid interpretations of classical special relativity is beside the point.

The relationship between space and time

Professor Feser's next objection is that I make space-time a Platonic abstract object, both spaceless and timeless. Quite how I do this I'm not sure. Certainly the representation of space and time is an abstract object. That's why its called a representation. We couldn't analyse it otherwise. But this doesn't mean what it represents is an abstract object. The mapping to the representation takes locations from real space and moments in real time and relates them to points in the representation. We can lay out a grid of rulers in real space, with appropriate identical clocks at each vertex to measure time, and use them to convert each point into a set of four numbers. These numbers would correspond to the numerical representation. That the real points can be represented as numbers doesn't make real space abstract.

But, of course, I'm not just discussing points, but also transformations. In abstract space, a rotation is a mathematical operation. But there is also an equivalent physical observation that rotates in real space. In abstract space, a Lorentz transformation is a mathematical operation. It too has a real space transformation which corresponds to it: travelling with a different (but constant) velocity. In abstract space, the Lorentz transformation mixes spatial and temporal coordinates. As stated, one can simulate the coordinate grid in real space using rulers and clocks. We would need two such grids to simulate the Lorentz transformation, one co-moving with respect to the other. It's obvious that the spatial coordinates measured on one grid of rulers will differ from those measured on the other grid. The grids might overlap at the starting time, but at any subsequent time their origins will move relative to each other. The transformation merely allows us to convert an event from one set of coordinates to another. The formula will work just as well in real space as it does in abstract space.

It's less obvious, of course, that the clocks in the two grids will show the same time at the start, but different times thereafter. This is because we only experience speeds much less than the speed of light, and any difference is too small to be noticed. Nonetheless, time dilation has been observed using exceptionally precise atomic clocks. Each tick of a clock at a particular point on the grid correspond to an event. We have two grids of rulers, and two sets of clocks, but we can identify events from each grid when two clocks tick together as they pass each other.

Of course, that we observe time dilation doesn't by itself mean that we can abandon presentism. It shows that two people's personal clocks which agree at the start would disagree later, even though the clocks are identical. In particular, observer A might define the present by saying its when all the clocks on his grid record the same time as his own clock. But then, when he checks the clocks in the other grid, he will see that they record different times compared to his own clock (even though they all agreed at the start). And how different they are from his grid's clock will vary from one location to another. In particular, he will read observer B's personal clock, and see that other clocks on observer B's grid will show different times at his present. Or he could record the times on his grid's clocks when observer B's clocks all agree, and see that these points, representing the present for observer B, are at different times on his own clocks. In other words, the events which B regards as being the present aren't the same as the events that A regards as being in his present.

A and B have different opinions about which set of points are in the present.

But this still isn't enough to disprove presentism. You could say that the laws of physics are different on A's grid and B's grid, causing their clocks to tick at different rates, even though they appear to be identical. Then you calculate those laws of physics, and show that the laws governing A's clocks are simpler, or some other measure that gives reason to say that A's measure is objectively the present. For example, if there was an aether (as was believed before special relativity), and A was stationary with respect to that, you could argue that A's experience should be preferred over B's.

But, of course, the mathematical form of the laws of physics measured by A and measured by B turn out to be same. Every experiment and observation they perform within their inertial frame gets the same results.

In other words, there is no measurement or observation we can make which can distinguish whether A's understanding of the present or B's understanding of the present is the objective present (or whether neither of them are). Neither can we appeal to God. Since God is timeless, as St Peter (arguably), Augustine, myself, and I think Professor Feser would agree (though Professor Craig would disagree), God relates to every moment of time in the same way, and thus can't single out one set of locations/moments in space and time as being simultaneous with each other. This is the basis of my statement that the notion of the present isn't objective, but only subjective.

This converts my argument from the abstraction to reality. Is it the same conception of space and time as the common understanding? In one sense, it's hard to see why not. We are all familiar with rulers and clocks as measures of distance in real space and durations in real time. I don't see why the conception of space and time used here is any less common-sense than another. Of course, in another sense, it isn't, because time dilation isn't something in our common experience. We simply don't travel at speeds close enough to light speed to notice it. But regardless of whether we measure it, its still a part of the real world, has been measured, and is still consistent with our low speed observations. The question is how we extrapolate from our low speed observations to light speed. There are objectively right and wrong ways of doing that. The Lorentz transformations might not be intuitive; but that doesn't make them wrong.

I think from this way of expressing my argument also shows why Professor Feser accuses me of verificationism. The argument can perhaps be expressed as

1. Observer A's conception of the present (as those points simultaneous to him) differs from observer B's conception of the present. (Empirical fact.)
2. There can be no experiment we can do for any observer A which shows that his conception of the present corresponds to an objective present in preference to observer B.
3. There can be no theoretical reason to regard any observer A's conception of the present as corresponding to an objective present.
4. There can be no theological reason to regard any observer A's conception of the present as corresponding to an objective present.
5. Any objective feature of the real world would lead to either empirical, theoretical or theological evidence that it exists.
6. Thus either there is no objective present, or we can never have a reason to accept is such a thing.

I've argued enough for the first 4 premises. I think the argument is sound, or at least can be made so without too much tinkering. I suspect that premise 5 is what makes Professor Feser particularly uncomfortable. I can't speak for all his objections to it, but if nothing else I suspect that he would add that we also need to exclude metaphysical evidence.

But then, how do we know our metaphysics is correct? There are competing metaphysical theories. I personally agree with almost all of Professor Feser's metaphysics (at least as published in his textbook); the philosophy of time is (I think) the only point where we differ in any significant way. Maybe he would argue that makes my views inconsistent; maybe they aren't. But we do differ on this one point.

So how do we judge which metaphysical theory is correct? I can only think of two ways: logical consistency, and consistency with observation. Suppose for the sake of argument that both his view and mine are logically consistent (I'll get to his objections concerning causality below). Then we are just left with consistency with observation. If so, then metaphysical evidence reduces to either empirical evidence or (if we need to connect different observations) theoretical evidence.

Can't we just say that if both metaphysical theories are consistent with the evidence, then we should just leave the question of if there is an objective notion of the present open? That's the approach I would naturally take. But I'm not convinced that Presentism is consistent with the evidence (or at least it doesn't constrain possible theories as well as the dynamic block theory), as discussed above.

Professor Feser is quite correct to say that direction and succession aren't enough to define time. But I never argued that they were. I stated that they are necessary components of the definition of time. I don't claim they are sufficient to fully define time. I do claim they are a sufficient distinction between time and space to not undermine the various important metaphysical concepts (such as causality) which require a difference between time and space. They might not be the only distinction between time and space, but its the minimum required to not introduce a contradiction with the rest of Aristotelian metaphysics.

Additional qualities are still needed to define time (such as it is a measure of change in real-world objects). Those qualities would distinguish time from an integer sequence. For example, time is continuous, while an integer sequence isn't (although this too isn't sufficient to define time, merely another part of time's definition which distinguishes it from the sequence of integers.) Since I was discussing what distinguishes time from space, I was justified in concentrating on these two qualities.

Causal relations

Professor Feser raises the comparison between a stick (stick A) that is red at one end and green at another and a temporal change. I'll use the example of a green stick that transforms into a brown stick (stick B) at a later time to make the parallel with stick A clearer. I and Professor Feser would both say that the green stick is among the causes of the brown stick B. But that doesn't hold for the red and green ends of stick A. Is this inconsistent?

I agree that on a static block theory, where the only difference between space and time is that minus sign in the metric, the analogy would be solid and raise a genuine problem. I, however, don't defend this theory, but advocate for a dynamic block theory which maintains an objective succession and direction.

So what makes a relationship a causal relationship? I would say three key things:

1. There is a relationship.
2. There is an objective distinction between cause and effect, where the cause is objectively prior to the effect.
3. The cause in some respect explains the effect, i.e. from just knowledge of the cause, you can accurately predict something about the effect (even if that prediction isn't complete or perfectly precise).

In the case of the two sticks, in both cases there is a relationship. Whether one can predict the colour of one side of stick A from knowledge of the other side or the later or earlier colour of stick B from knowledge of the other state is a matter of the physics, biology or human nature. Let's suppose for the sake of argument that we can. The distinction between the two cases then reduces to whether one state, the cause, is objectively prior to the other state, the effect. I don't believe (and I don't believe that Professor Feser does either) that every causal chain for every type of causality has to be temporal. But there does need to be an objective sense as to which link of the chain is the cause and which the effect. An objective direction underlying the relationships in the chain.

Is this the case for either of the two sticks in the dynamic block theory? For stick A, clearly not. There's no objective priority between left and right in space; you can't say one is before the other. But for stick B, there is. This is because there is an objective succession and direction in time. The earlier state of the stick is objectively prior in the sequence of events to the later state. Thus we can objectively label the earlier state as the cause and the later state as the effect.

A dynamic block B-theory thus doesn't undermine efficient or final causality in the same way that a static block B-theory would.

Fallacy of equivocation

Does time in the ordinary sense (time-O)mean something different to Time as the physicist (time-P) uses it? But what does time in the ordinary sense mean? I'm reminded of a quotation from St Augustine (Confessions, 11.14),

For what is time? Who can easily and briefly explain it? Who even in thought can comprehend it, even to the pronouncing of a word concerning it? But what in speaking do we refer to more familiarly and knowingly than time? And certainly we understand when we speak of it; we understand also when we hear it spoken of by another. What, then, is time? If no one ask of me, I know; if I wish to explain to him who asks, I know not.

This is the problem: we all experience time's passing, but when it comes to explaining what it is, then it becomes difficult. I would dispute then that there is a single ordinary conception of time, or if you asked different people, they would come up either with different answers, or trivial answers which don't really mean anything, or no answer at all.

But what of the physicists account of time? Here again, I don't think you will find consensus or a single definition. Many physicists will, for example, relate the passage of time with the second law of thermodynamics. I disagree with that; I think the passage of time is fundamental to the universe's structure, and needs to be inputted into our equations rather than something that arises out of it.

But I think the most physics based physicist definition is time is that which is measured by a clock. Don't forget: physicists (except perhaps those too wrapped up in string theory) are always looking back to experiment: that's what makes us different from mathematicians (alongside perhaps a propensity to take mathematical shortcuts ahead of full rigour, as many mathematicians would claim). The experimental physicists definition of something is then the definition which everyone else in the field ultimately has to use. That clock could be many things: based on the oscillations of a caesium atom, or the swings of a pendulum, or the rising and setting of the sun, or the human heartbeat. All of these ultimately measure the same quality. The theoretician, of course, converts each of these measures into a number which is then mapped to the abstract representation. Is this definition verificationism, defining time in terms of what can be measured? That's not the sense in which I mean it. Time is an objective feature of the real world. Clocks happen to be the instrument which we use to measure that feature. For example, we can also say "Length is that which is measured by a ruler." This doesn't make real-world lengths dependent on rulers. It just states that a) length is a real feature of the world; and b) we can use rulers to measure it. The use of rulers doesn't change the fundamental nature of length, which is prior to any measuring tool. But even so, rulers are one of the ways we can measure length.

I personally don't think that which is measured by a clock. is too different from a reasonable definition of time-O. Professor Feser's definition of time is that it is the measure of change with respect to succession. The clock has succession, and is also a physical object which undergoes change, so the clock definition describes many specific examples of his definition. The clock definition incorporates notions of succession, past, present, future, and so on. I think to make Professor Feser's objection more precise, I will take time-O to mean this experimental/real world definition, and time-P to refer to the abstract representation of the theoretical physicist.

The question is then, is time as represented by the theoretical representation equivalent to time defined as that which is measured by a clock? No. It's only a partial representation of it, capturing some aspects but not all. The coordinate system definition doesn't capture temporal directionality. And there is clearly difference between any abstraction and something existing in reality (I mean this analogously, I wouldn't describe time as a thing, and the word existing in this context is only analogous to the sense used when saying a table exists). And perhaps some other differences as well. There is a one-to-one relationship between time-O and time-P (if there wasn't, calculations in the model won't produce accurate real life predictions) in some aspects, while other aspects of time-O aren't captured by time-P. And, I suppose that one could say that there are aspects of time-P which are mere artefacts of the calculation method, and which don't correspond to anything in time-O.

So the question then becomes: does my argument involve aspects of time where there is a one-to-one mapping between time-P (where conclusions drawn from the representation will carry over to reality, even if expressed in a different form in reality), or an aspect of time-O absent in time-P, or an aspect of time-P absent in time-O. The second option is obviously incorrect. I would say it's part of the one-one mapping. My argument is based on symmetries, which are present in the theoretical model, but also in reality. This is obvious for rotational and translation symmetry. Rotations can be expressed in both reality and the abstraction. Lorentz transformations also can be expressed in the abstraction and correspond to changes in velocity.

But if the transformations in the abstraction correspond to things in reality, what about the symmetries? In the abstraction, these concern the invariance of the action under those symmetries. The action is an abstract concept. However, it is related to the Hamiltonian, the operator which describes how Fock States and their associated amplitudes change over time, which can also thus be said to be constrained by the symmetry. Changes over time certainly also exist in reality. Fock states count how many particles exist in each state, which also exist in reality. Amplitudes are perhaps the weakest part here; in my preferred interpretation they parametrise our uncertainty concerning the state and location of the particles (ultimately predicting a frequency distribution). But even so, this is still a predictor for things that exist in reality. So the symmetry concerns things which have analogues in reality. And we have to ask why does the abstraction need to respect this symmetry in order to produce accurate predictions? There must be something in reality which imposes this constraint.

What's the link between abstraction and reality?

So, what additional metaphysical assumption am I making in this argument? I suppose it is that if a symmetry is needed to constrain the action in order for the theory to make accurate predictions, that symmetry must also have an analogue in reality.

For example, suppose that changes in reality are brought about by God actualising potentia in line with the being's final causes. The being has many final causes. God has a free choice about which one to actualise. This leads to indeterminacy. But God is also rational, and we expect there to be the same chance that He makes the same decision in the same circumstances. This allows us to predict frequency distributions. The symmetries constraining the action would then represent whether God regards two circumstances to be "the same" in the sense that they lead to the same chance of a particular action. The transformations underlying the symmetries map between different circumstances which God regards as the same.

This is one example with one metaphysical model and philosophy of physics. One can accept other models. How the metaphysical assumption enters into the explanation would obviously differ in different models. But however you explain why some events occur rather than others, something which is represented by the symmetry will have to be part of that explanation. Otherwise there is no reason why the symmetry would occur in the abstraction.

The mathematical representation is abstract, but its still connected to reality. Professor Feser underestimates the degree to which it is in this one to one relationship with reality: not just the particles and their motion; not just the initial and final states, but also transformations such as rotations and translations in space in the abstraction have direct analogues in reality. Likewise the Lorentz transformation maps between two different inertial frames. Two observers travelling at different velocities. People travelling at different speeds is also a feature of reality. Likewise locomotion (movement of particle from one location to another) exists in reality with a direct analogue in the abstraction. The symmetries role is to link the transformations which exist in both the abstraction and reality with the explanation of why a particle moves to one particular place rather than another. And reality will have such an explanation.

Yes the mathematical representation is abstract. Yes, there are aspects of it which we should not naively assume are also aspects of reality. But there are also parts of the representation which are in a direct one-to-one relationship to reality. Here we can consider the representation, and draw conclusions about reality. If this were never true, the theory wouldn't be capable of making successful empirical predictions. So if we draw a conclusion from the representation, we have to ask whether it concerns an aspect of the representation that has a direct analogue in reality. If it doesn't, we should regard the claim that the conclusion also applies to reality as dubious. If it does, then an analogue of that conclusion might also apply to reality; one would need a good argument to suppose that it doesn't. I have raised arguments suggesting that the symmetries underlying my argument do have direct analogues in reality. It's up to critics of my view to provide arguments suggesting that they don't.

After all, even Aristotelian philosophy is a highly abstract representation of reality. Our concept of potentia represents something analogous to it in reality. An Aristotelian philosopher will draw conclusions from that concept. But those conclusions are drawn from the representation. Why think they also apply to reality? Because there is a direct relationship between the concept of potentia and the aspect of reality it represents. And I think it quite reasonable to apply those conclusions to reality. But what if a critic states that this underestimates how abstract the representation of reality in terms of potentia is? I'm sure Professor Feser would be able to answer that critic. But his answer would probably also apply to those aspects of the mathematical representation which directly map either to reality or to the concepts of Aristotelian metaphysics. Can he consistently defend his drawing of conclusions from the abstractions of Aristotelian Metaphysics while attacking these particular aspects of the abstractions behind the mathematical representation of quantum field theory.

Empirically detectable or in reality?

I think that saying that most special relativity rules out is an empirically detectable reference frame misses the point. Firstly, my argument is not based on special relativity, but relativistic quantum field theory. Secondly, the argument concerns the symmetry of the action, which ultimately means the probability that certain events occurred. If the action didn't have the Lorentz symmetry (for example if it had the Galilean symmetry that corresponds most closely with presentism), you would calculate a different probability distribution.

To my mind, metaphysical theories ought to be tested by their internal coherence, but also by how well they explain the mathematical structure of physical theory. So the metaphysics provides some fundamental principles. From those we deduce a philosophy of physics. From that we deduce a physical theory. Perhaps not constrain it perfectly, but enough to outline its general structure. The defender of presentism needs to explain, in terms of their metaphysics, why the action of the physical theory is constrained by Lorentz symmetry rather than (for example) a Galilean symmetry. As I understand him, Professor Craig argues that God is timeless before creation, and temporal after creation. By temporal, he means that there is a three dimensional universe updating in time. This maps to a E³ <⊗> E¹ geometry. Certainly a three dimensional Euclidean space certainly; I'm not sure how he would treat time but if it is to be treated geometrically it would have to be a Euclidean line. E³ naturally maps to a symmetry under SO(3). Time is separate from space in this philosophy. So how do you derive an SO(3,1) symmetry from the underlying metaphysical presupposition? The Lorentz transformation mixes present and past coordinates, which ought not to be possible in presentism. On the other hand, a dynamic block universe naturally leads to a symmetry between different inertial frames, or under SO(3,1).

So my argument isn't that only those things empirically testable are meaningful. My argument is that a metaphysical proposition is meaningful if

• It is internally consistent, containing no self-contradictions; and
• it is consistent with various physical theories, n implying predictions inconsistent with empirical observation, and m implying predictions consistent with empirical observation, with n much smaller than m.
• while its rivals either
  • imply theories all of which contradict experiment, or
  • are consistent with various physical theories, N implying predictions inconsistent with empirical observation, and M implying predictions consistent with empirical observation, with N either comparable to or larger than M.

My argument is thus closer to being based on falsification rather than verificationism.

Potentialities for future outcomes

Likewise I don't claim that the empirical success of relativity's mathematical representation implies all temporal points are real. I claim that we need to explain why the mathematical form of the time-evolution operator needs to be constrained by certain symmetries rather than others if it is to correctly predict real-world results. I also claim that the best explanation for this is that those symmetries reflect reality. A symmetry is an invariance under certain transformations. If the symmetry reflects reality, then that transformation must also be reflected in reality.

This isn't the same argument as saying that the mathematical representation is empirically successful, therefore that mathematical representation must correspond to reality in all its respects. There are similarities between the two arguments. They both emphasise the importance of the theory being empirically successful. But I only reference some of the representations respects, namely the symmetries. And I don't naively map from the representation to reality. I ask "Given this theory of time in reality, what symmetries could that imply, how would those symmetries be manifest in the mathematical representation, and is the corresponding theory empirically successful?"

And I don't argue from special relativity by itself, but relativistic quantum field theory. Relativity is a key component of that, but the key thing is how the Lorentz symmetry is used to constrain the quantum field theory action.

Analogy with Euclidean geometry

The analogy with Euclidean geometry breaks down because

1. The three dimensional Euclidean spatial metric is included within the Minkowski space-time metric. It's symmetries also constrain the action. So using Minkowski space-time explains why Euclidean space works so well. But you cannot make a reverse argument from Euclidean space and a single "real" moment of time to Minkowski space-time. I can use the same arguments to imply the reality of a Euclidean space. I don't do so because that's not in dispute.
2. Euclidean space-time is the infinite speed of light approximation of Minkowski space-time. The speed of light isn't infinite, but it is very large. So Minkowski space-time explains why the Euclidean space-time is useful.
3. Of course, all this is the zero gravity/zero curvature approximation to reality. I don't discuss quantum gravity since a) we don't know precisely what that theory is; and b) adding space time curvature adds additional local symmetries, but doesn't deny the global symmetries of relativistic quantum field theory that are the basis of my argument.
4. The relationship between the structure of Euclidean space-time and reality is loose because Euclidean space-time is merely the infinite space time and zero gravity approximation to the correct theory. The relationship between Minkowski space-time and reality will also be loose because its the zero gravity approximation to the correct theory, but that doesn't affect my argument. Professor Feser, however, wants to suggest that the relationship with reality is loose for a different reason, namely that the representation contains one feature (the reality of temporal points) which is merely a mathematical argument. This isn't the same reason he provided to explain the looseness of Euclidean space time. The analogy thus isn't helpful to illustrate his point.

And, of course, I do answer why symmetry and empirical success, and in particular the empirical failures of the symmetries which are most naturally implied by presentism, suggest something about the true structure of the universe.

Change in the B-theory

Professor Feser here fails to distinguish between the static and dynamic block versions of the B-theory. The objective direction of time but not space explains why we can say a potentiality at one time can give way to an actuality at the next time, but not make the same argument with respect to space where neither end of the stick proceeds the other in an objectively-ordered causal sequence.

Common sense notions of time and space?

I responded to this argument above.

Collapse distinction between time and eternity?

I'll need to go into more detail here to describe what Professor Feser means by eternity.

In his blog post, Professor Feser wrote,

What is really going on, I argued, is that mathematical representations of the sort Cundy has been describing essentially desiccate both time and space. It’s not that they drag time down into the world of concrete spatially located objects, making movement through time literally like forward movement through space. It’s rather that they raise space and time alike up into eternity. They make of space-time a kind of Platonic abstract object that is spaceless no less than it is timeless, or at any rate is like neither time nor space in the ordinary conceptions of those things.

In Aristotle's revenge, he wrote

As with other abstractions -- universals, propositions, possible worlds etc. -- the mathematical representation of time and space has a timeless or eternal quality. But that is precisely because it is an abstraction, and not because of anything to do with time and space itself. It has no tendency to show that time and space don't really have the qualities that common sense attributes to them, any more than the timeless or eternal character of universals like dogginess shows that individual dogs are timeless or eternal. &hellips; When we identify space and time with the static four dimensional space-time of mathematical physics, we are essentially collapsing the distinction between time and eternity. Or rather, we are changing the subject, and talking about some eternal Platonic object rather than talking about space and time.

While he defines time as

When a banana goes from being green to being yellow, the greenness is lost and the yellowness is gained, but the banana itself persists. Time, on the Aristotelian analysis, is just the measure of change with respect to the succession of such gains and losses. … Time, again, is the measure of change with respect to succession.

He goes on to note that neither change alone nor succession alone can be identified with time. It requires both succession and change in substances (the procession from potentiality to actuality).

I don't see an equally clear definition of eternity in Aristotle's Revenge (which is almost certainly my fault for just skimming the text in my re-read rather than his), but from the earlier quotes it seems to indicate something like an abstract concept, residing outside of time and space, in which there is no changes in or of substances.

Firstly, I don't identify the mathematical representation of time with the reality of time. My argument is that certain symmetries important to the mathematical expression of physics can only be explained if those symmetries are also important in reality.

Secondly, how I have presented time in reality doesn't differ greatly from Professor Feser's. I used the example of clocks rather than bananas, but again there is the notion of change and succession. I have repeatedly emphasised the importance of the objectivity and reality of temporal succession to the philosophy I present. And I certainly accept that that succession is with respect to changes in real world objects, whether those are clocks or bananas.

The difference is merely one of language. Professor Feser will say that a certain state is potential now, in the present, and will become actual in the future. I say that a certain state is potential simultaneously with this thought of mine, and will be actual simultaneous with my next thought (after, if we are not at the same location, defining simultaneity within my own frame of reference). The point is I can still regard time as the measure of change in succession. There is change. There is temporal succession. The temporal succession distinguishes between what it was changed from and what it changed into.

There is no doubt that Professor Feser's description is more succinct. But ultimately they convey exactly the same data, and correspond to exactly the same experiences. How then can Professor Feser say his view is more common sense than mine?

Consider, for example, how we regard events in the pass. Take the assassination of Julius Caesar. Brutus moves the knife. Caesar dies. There is change in both the movement of the knife and within Caesar. At one moment of time, the knife was actually in Brutus' hand and potentially in Caesar's body. A later moment of time, it was actually in Caesar's body. I can't regard either of those moments as now, because I live over two thousand years later. But I can recognise that there was reduction from potentiality to actuality. I can still say that Caesar was potentially a corpse at the time just before he was stabbed, and also potentially a living man having received a fright (had the conspirators drawn their knifes, but then decided at the last moment not to attack him). That's how I explain the sequence of changes that happened then, and outline the causes and their effects.

So when we consider events in the past, we think in terms entirely analogous to how I describe time. I say states are not potential or actual absolutely, but only potential at one time and actual at another. It's just necessary to specify the time alongside whether the state is potential or actual. This applies equally to past, present and future. Obviously we don't know which states will be actual and which potential in what is to us the future, but that's just a limitation of our knowledge. It's epistemological ignorance rather than ontological fact. At least, just as reasonable to argue that as the presentism position that the future is unreal ontologically. More reasonable, in some respects, because there's no difference in how we regard potentialities in our past, our present and our future. While still not collapsing time into eternity; it's merely that the same concepts can be applied at each time, while still maintaining the distinction between past, present and future. We say on the Ides of March, 44BC, certain states were potential then later that day became actual. Those potentialities and actualities are assigned particular times. At this moment of time, one state was actual and others potential. Five seconds later, one of those potentialities had become actual, and other states had become potential, describing the next set of possible changes.

Those events aren't in my present, but Brutus and Caesar did regard them as their present. So the potentialities were simultaneous with certain thoughts of Brutus and Caesar, and were actualised simultaneously with later thoughts of Brutus.

So, if we happily think about the past in this atemporal way, why is it unnatural to use the same language to describe what is to us the present (or the future), but will tomorrow become our past? Why should we privilege one way of expressing our experience of time as common sense over another which is equally naturally used in a different context if they aren't distinguishable from each other empirically?

We then distinguish them from metaphysical premises, and how well those different systems explain the physical theories that describe reality. Appealing to common sense views of time isn't good enough, since what's common sense to one person is seen as bizarre by another. Professor Feser's definition of time equally well applies to the dynamic block theory's understanding of time as it is in presentism. The notion of eternity is equally inappropriate in both systems. We aren't going to decide which view is right through arguments such as this.

This response would not, of course, be valid in static block theories of time which deny its objective succession. Then you would have change without succession, and would require a different definition of time. The static block B-theory does conflate time and eternity, as Professor Feser states in Aristotle's revenge; but the reason it does so isn't applicable to the dynamic block B-theory.

Are there truths which cannot be captured in tenseless terms?

Professor Feser stated that I confuse between how things seem to be to us and how they really are. I agree there is a distinction between how things seem and how they are. A classical example is when you look at a circular table from an angle and it appears elliptical. It seems to be elliptical; it really is circular. Of course, this is resolved by adding the context of the observation. It appears elliptical from this angle. It appears circular from another angle. With the context in place, the two observations don't contradict, and you can use them to calculate what its actual shape is in its own reference frame.

But how do we judge what something really is? We only have four tools:

1. Logical consistency
2. Empirical observation
3. Metaphysical necessity
4. What can be reasoned (e.g. via deduction or falsification) from the three points above.

My view is that the notion of the present is subjective. Professor Feser's view is that there is an objective truth that one moment of time is the present. How do these two views line up with the various options above? Both views are logically consistent. Both views can be reconciled with our immediate experience. The two views entail different metaphysical world views. In my view, it isn't a major difference; everything else in Professor Feser's scholastic metaphysics (a brilliant exposition of Thomistic metaphysics) maps into the dynamic block theory, with either no or insignificant modifications. But that in itself doesn't mean that either view is wrong, unless it implies either self-contradictions or contradictions with other areas of natural philosophy or empirical science. I imagine that Professor Feser would argue that presentism is superior to the dynamic block theory due to the metaphysical implications. But his main argument is that denying the objectivity of the present contradicts the notion of causality, while I claim that causation only requires an objective temporal direction and succession, among other things unrelated to the philosophy of time. I didn't see where Professor Feser argued that specifically the notion that there is an objective present is required to identify one thing as a cause, another as an effect, and the relationship between them. So here again we cannot choose between the two models of reality. But my claim is that presentism fails on the final point. It implies a set of symmetries which when mapped into the physical representation of reality would constrain the action in such a way that it would lead to predictions inconsistent with experiment. While the static block model implies symmetries consistent with the action which gives correct predictions.

This objection thus can also be raised against Professor Feser. It seems, to many people, that the notion of the present is objective. That doesn't mean that it is really so.

Is my position the moving spotlight?

Finally, Professor Feser suggests that my position might be the moving spotlight model. There are certainly some similarities. They are both four dimensional models. They both acknowledge that past, present and future can have some reality. That we can't talk about actual existence and potential existence without context, but only say that at a given time these possible states are actual and those states are potential, with which states are actual and which potential changing over time. Denote A(t) as the set of actual states, and P(t) the set of potential states, at a given time t. Then consider the three data points

• A(my past), P(my past)
• A(my present), P(my present)
• A(my future), P(my future)

The causal relationships between P(my past) and A(my present) (and so on) are the same in presentism, the moving spotlight, and dynamic block theories.

Both the moving spotlight and the dynamic block theories say that these should all be given the same metaphysical status. Presentism states that the second point has a different status to the first and last points.

But, the moving spotlight, presentism, and growing and shrinking block theories all say that there is an objective time which is the present. In other words, you ought to equate my present with the present. The dynamic block theory denies that there is a coherent notion of the present. There is only the subjective my present. It shares this with the static block theory. And on this account it differs from the moving spotlight theory.

Do Professor Feser's objections to the moving spotlight theory apply to the dynamic block theory? These are the objections he raises in Aristotle's revenge

1. The moving spotlight view might imply time travel is possible. Of course, this depends on what we mean by time travel. We all travel gradually into the future as part of the normal succession of time. But usually time travel refers to a sudden discontinuous jump into the past or the future. But there is no reason why this should be allowed by physical law; indeed the very symmetries which I argue are the main reason for supporting the dynamic block theory forbid it (excluding science-fiction additions to physics).

   Even if time travel is metaphysically possible in a moving spotlight or block theory of time, that doesn't show that it is metaphysically required that it should be physically possible.

   What about time reversal, i.e. we suddenly start finding ourselves going into the past rather than the future (perhaps against the flow of everything else)? The objective succession of time, important in both the moving spotlight and dynamic block theories, prevents this.

2. The moving spotlight theory spatialises time. I have argued why this is not true in the way it would be metaphysically dangerous above.

3. The moving spotlight theory implies that some events are past, present and future all at once. If there is some event E at a given time t, then when the spotlight falls on it it is present, but when the spotlight was before t, E would be in the future, and likewise likewise after t, E would be in the past. Since all these times are equally real, E must be all of past, present and future in the same sense, which is impossible.

   However, this argument depends on there being an objective notion of the present. If there is an objective succession but only a subjective present, then you can't say that an event is in the present simpliciter, but only that it later than, earlier than or simultaneous relative to some other event. So the conclusion has to be re-expressed as that E is earlier than one time, simultaneous with another time, and later than a third time, which clearly doesn't entail a contradiction.

4. The series of events along which the spotlight of the "now" is said to move is supposed to contain all events. But the arrival of the spotlight on each moment is itself a series of events. This requires a higher-order series of events, and to explain that would require a further series, leading to a vicious infinite regress.

   The dynamic block theory doesn't single out a moment as objectively now (doesn't require a spotlight), so this objection isn't applicable.

Thus the difference between the dynamic block and moving spotlight theories mean that these objections aren't applicable, or fail for other reasons. Professor Feser also states that the moving spotlight falls to other issues in the static block theory, but I have already argued that the dynamic block theory evades any valid objections.

I also agree that if you accept an objective present, then presentism makes more sense than the other A-theory models. Going back to my formulation above, there seems to be little sense in saying that there is an objective metaphysical equality between

• A(the past), P(the past)
• A(the present), P(the present)
• A(the future), P(the future)

when there is an objective metaphysical difference between past, present and future.

Conclusion

This was a long post, both in word-count, and the time it has taken me to prepare it. And, frankly, I was flattered that Professor Feser responded to me. However I don't think Professor Feser's objections hit the mark. He failed to adequately realise the differences between the static block (where his objections do have force) and my own dynamic block theories. And I don't think he fully appreciated the thrust of my argument. I'm not producing the usual objection from special relativity. I agree that special relativity by itself doesn't disprove presentism. It merely teaches us how to map between different inertial frames. But I'm arguing from how special relativity affects the description of motion in quantum physics. In particular how that description is constrained by symmetries. And in particular that we can deduce what those symmetries ought to be from our philosophy of time. And that the symmetries implied by the static block model are correct, while those implied by presentism aren't. And I don't think that Professor Feser adequately addressed those arguments.

But no doubt he would disagree, and he is a far better philosopher than I am.

Reader Comments:

1. Michael Brazier

Posted at 18:22:51 Friday July 24 2026

I am not convinced that introducing "time has an objective direction" really answers all the objections to a B-theory of time. For the objection from causality, for instance, it seems to miss the point.

The relation between the stages of a banana - green when plucked, turning yellow and then brown - is causative; the yellowness is initially a potential of the green banana, and the brownness is a potential of the yellow banana once the yellowness becomes actual. But this means more than the colors appear in that order, and that the sequence is predictable. Take a flagpole; one can easily predict that the flagpole's base will be thicker than its tip, because flagpoles are meant to stand vertically and support their own weight under gravity. That constraint entails a clear sequence in thicknesses along the flagpole's length, and allows one to tell which end is which. It couldn't be mounted upside down without falling over. But the base isn't among the causes of the tip. The flagpole's ends exist, in that sense, independently of each other.

A dynamic block theory seems to liken the banana to the flagpole. Since the moments at which the banana is green, yellow and brown are equally real, they are all parts of the banana's total existence. And they would always appear in that order, not in reverse. But it seems possible that like the flagpole's ends, the banana's stages exist in some sense independently; they are linked structurally, but not causally. An occasionalist, for instance, would say that God is the immediate cause of every stage of the banana.

So causation can't be reduced to predictability and temporal order. But then just assuming an objective direction in time isn't enough to defeat the objection.

The basic problem IMO is that both the God's-eye view of the B-theories and the man's-eye view of the A-theories have strong evidence in their favor -- B-theories from the reality of Lorentz symmetries as proved by experiments, and A-theories from our immediate experience as temporally bound agents, prior to every theory. The true philosophy of time has to account for both, somehow.

2. Nigel Cundy

Posted at 13:09:41 Sunday July 26 2026

Does "time has an objective direction" answer causality objection?

Dear Michael,

Thanks for your comment. And I'm certainly grateful to hear of objections or needed clarifications.

My argument was only that "time has an objective direction" is a necessary condition to have a meaningful theory of causality. Not that it is sufficient. I agree one also needs a workable theory of potency, and perhaps other things as well. The difference between my own view and Professor Feser's is that I deny that you need an objective notion of the present to have a meaningful theory of causality or a useful theory of act and potency. To argue against my model, you need to argue that the objective present is a necessary premise to a workable theory of causality (or whatever your objection is centred around), or one of the pre-requisites to that theory such as a useable theory of act and potency.

Consider the example of the banana. I will assume for the sake of this argument that bananas only go from yellow to brown (I'm afraid my knowledge of bananas doesn't extend much beyond they are good to eat when yellow and not so much when green or brown).

Let tY be the time when the banana is yellow and tB the time when the banana is brown.

Then, from the perspective of the dynamic block theory, I would argue that at time tY the banana has, among its potencies, a brown banana. At time tB the banana has among its potencies a rotten banana, but it doesn't have a yellow banana. Along with the direction of time, this establishes the causal sequence from yellow banana to brown banana to rotten banana. We can add the full theory of act and potency to the dynamic block theory without any problems.

But consider what happens if we try to do this in the static block theory. In this theory, there has to be an underlying symmetry between past and future in every objective or metaphysical sense, since for that symmetry to be broken would imply an objective distinction between past and future. (The symmetry applies to the underlying metaphysics, whether particles in what we view to be the future are in different states to those particles in what we view to be the past isn't the sense which I'm discussing, but rather the underlying fundamental laws of physics and more importantly the principles which lie behind or explain those laws.) So the static block theory has three options (that I can see):

1. Say that the banana at tB has the potency to become a yellow banana in addition to its potency to become a rotten banana, since it could "become" a yellow banana in a backwards running time.
2. Say that there is a parallel second sense of potency, referring to possible changes in the past, with underlying distinction between the two senses of potency. So in sense A (forward time) the banana at tB has the potential to become a rotten banana, and in sense B (backward time) the banana at tB has the potential to become a yellow banana. But ultimately these two senses have no metaphysical difference because time lacks an objective direction.
3. Suppose that the theory of potency is too tied up with listing could happen in the future, which since this implies a direction of time is inconsistent with the defining characteristics of the static block theory, and abandon the notion altogether, effectively denying the relation between cause and effect.

Options 1 and 2 deny causality by not being able to distinguish between cause and effect (given the static block theorist also denies they can be distinguished by the direction of the flow of time). Option 3, which I think is the usual approach taken by static block theory advocates, reduces to your flagpole example (at best). But the reason the static block theorist has to deny any useful notion of potency is precisely because they deny the objective direction of time. The dynamic block theorist has the fourth option listed above, where potentialities refer to possible future changes only, precisely because they accept there is an objective distinction between future and past. But nowhere does assigning limited potencies to a banana at each moment of time require that there is an objective notion of the present. I did not need to specify whether tY and tB are in my past, present or future, only that tB is later than tY. I'm sure there are some bananas for which they are in my future as I write this, and your past as you read it, but nonetheless we can both assign the potency to become brown to the banana at tY and deny that the banana at tB has the potency to become yellow. That we identify the present to be different times doesn't come into it.

The basic problem IMO is that both the God's-eye view of the B-theories and the man's-eye view of the A-theories have strong evidence in their favor -- B-theories from the reality of Lorentz symmetries as proved by experiments, and A-theories from our immediate experience as temporally bound agents, prior to every theory. The true philosophy of time has to account for both, somehow.

But I argue that the dynamic block theory achieves this. It satisfies the arguments from relativistic QFT (which includes Lorentz symmetries) supporting the block theory, and its notion of a subjective present fully accounts for our subjective experiences as temporally bound agents.

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