The Quantum Thomist

Musings about quantum physics, classical philosophy, and the connection between the two.
Is Thomism really refuted by modern science? (Further Response)

Why Is There Something, Rather Than Nothing? (Part 3)
Last modified on Sat Dec 8 22:33:38 2018

Before my brief break, I was writing a series on a recent article by Sean Carroll. This is taking me several posts to respond to it fully, so I am going one section at a time. My first post gave an introduction to the topic, and covered Carroll's own introduction. My second post discussed his first main section, where he established his definitions and described the scope of his discussion. Now we ask what do we mean by "Something" and "Nothing."

This is a topic of some importance. The main criticism levied against physicists who attempt to address this topic is that they don't start with Nothing as the philosophers understand it. They might start with a quantum vacuum, or gravity, and say that the universe can arise from those. That obviously doesn't answer the question, but merely pushes it back. We have to ask what explains the quantum vacuum, or gravity. Indeed, it is impossible for the physicist use physics to get to Something from Nothing. Why? Because the physicist assumes that there are various laws and regularities governing the material universe. He has two goals: 1) to discover what those laws are, and 2) to uncover the consequences of those laws. So a physicist might well say, "Given these laws of physics, a universe such as the one we live in is bound to emerge," but he cannot go much further than that. Perhaps the physicist can reduce the laws of physics to some deeper principle, such as symmetry, but that is still not to explain why those symmetries hold and not some others. We are able to construct numerous consistent physical theories based on different symmetries. So why would these symmetries given the universe and not others? It is at this point that the physicist needs to hand over to the philosophers (whether professional, amateur, or even the physicist himself squatting in somebody else's department).

To his credit, Professor Carroll understands this point. He distinguishes the question into two parts. Firstly, why there is stuff (matter, energy and so on), and secondly why there is anything at all. Answers are often made to answer the first question, but these have little relevance to the second question. Yet it is this second question that people want to be answered.

Carroll continues to discuss the various progressions in physics. Newton imagined an absolute space and absolute time that passed indefinitely into the past. Special and general relativity combine space and time into demanding a universe which began with a singularity (could that represent the transaction from something to nothing?)

But quantum mechanics is the big change. For one thing, the philosophy of quantum mechanics is unclear. One thing that all agree on is the centrality of the wavefunction. But what is this? Carroll lists the Everett multiple worlds formulation as an example of a theory where the wavefunction is everything. There are also approaches such as the De-Broglie/Bohm approach where there are additional degrees of freedom in addition to the wavefunction. Carroll will focus on the wavefunction as describing everything approach.

Certainly he has some justification for this; De-Broglie/Bohm famously struggles with relativity. But this is the first point where I might question Carroll's approach. There are many interpretations besides the two that he mentions; by focussing only on one of them risks missing something important if that interpretation turns out to be incorrect. After all, the Everett interpretation with its branching universes is wholly unintuitive, and still begs the question of why the universe would behave in that way.

But of course (and this is the point that I keep making), we need to move beyond quantum mechanics. Quantum mechanics is a compromise between the philosophy of classical mechanics and the philosophy of quantum field theory (which I believe to be Aristotelian). Quantum mechanics itself is not Aristotelian, because some of its premises are taken from mechanism. Among these is the idea that there is a fixed number of particles. In field theory, we no longer think that way.

Carroll indeed abandons the particle interpretation entirely. The focus of field theory, he writes, is on fields which permeate all space, rather than positions of individual particles. This statement has, I think, the merit of being partially true and partially false. Even though we see fields spreading through all space, the focus is on individual excitations of those fields. These excitations are (usually) localised (the exceptions are unbound unrenormalised massless particles such as bare photons -- although note that by localised I don't mean that they exist at a single point as in classical physics but that their amplitude at any given moment in time is spread over a small volume), and thus take on some properties which we associate with particles. These excitations are the primary object of study in field theory. Thus we can think of field theory as a study of particles, just not the same sort of particles that are studied in classical mechanics. This is, of course, how I usually approach it.

The vacuum in quantum field theory plays an important role. This is defined as the lowest energy state. One might think that the lowest energy state is one in which there are no excitations, and thus no particles, and thus qualifies as nothing. However, this isn't the case. Naively, one might might question whether the lowest energy state is a zero energy state. However, in non-gravitational quantum physics, all we measure are energy differences, so it is not clear that it is possible to uniquely define an point of absolute zero energy. This might change when we introduce gravity. But more importantly, there are various structures in the quantum vacuum that exist in even the lowest energy state. Carroll lists a few examples. I will add the topological structures in the gluonic field, such as monopoles, instantons, vortices, and so on.

The gluonic field is the field that drives the strong nuclear force, and is responsible for holding the nucleus of the atom together (among other things).

A topological invariant is a quantity which doesn't change under continuous changes in the vacuum. For example, we might think about the number of times something encloses something else. Consider a ball and a balloon (which is fully sealed up). We can either place the ball inside the balloon, or outside it. We label all the states where the ball is outside the balloon with the number zero (mathematically, this number is referred to as the Pontryagin index or winding number). We label all the states where the ball is inside the balloon with the number one. This number describes the number of times the balloon is wrapped around the ball. We can move the two objects around, deform the shape of the balloon, and by processes such as this transform from any one winding number zero state to any other winding number zero state. And equally from any winding number one state to any other winding number one state. But we can't get from a winding number zero state to a winding number one state by just moving things around. We have to burst the balloon to get the ball outside it.

Winding numbers also appear in physical systems. In particular, the possible states of the gluonic field can be split into different sub-sets with different winding numbers. These winding numbers are associated with various structures in the field, or the topological objects. The point is, once these structures are present, you can't get rid of them by continuous transformations. You can move the instantons, vortices and monopoles around, you can add in additional pairs of structures with winding number plus and minus one (thus preserving the total winding number), but ultimately you can't get rid of them. The lowest energy state which can be reached by a physical process won't be a state where nothing exists.

As Carroll notes, it might be that the most symmetric vacuum (i.e. without any structures, winding number zero) is not the minimum energy state. In this case, the system would naturally prefer one of the states with non-zero winding number. Thus some people people argue, there is something rather than nothing because nothing is unstable, if we allow us to be able to define nothing as a symmetric false vacuum state. But this has nothing to do with the universe, since it does not explain why there are fields at all in which there can be vacuum states, symmetric or otherwise.

Carroll also dismisses the relevance of quantum fluctuations (such as an electron and positron popping out of the vacuum for a short period of time). This picture is sometimes used, with justification from the uncertainty principle, interpreted to mean that there can be a small fluctuation of energy in a short period of time. I have always disagreed with this: All QFT processes satisfy the conservation of energy and momentum at the level of creation and annihilation processes. A fluctuation of this type would violate that. Such disconnected diagrams don't play any role in a perturbative expansion, and there is no reason to suppose that they could be non-perturbative effects. Carroll notes another reason for rejecting this: a true vacuum state (or a true state of nothing) would be stable, while if these particles could emerge it would imply an unstable state, and thus not nothing.

Then there are issues from quantum gravity. Firstly, most theories of quantum gravity treat space and time as a quantum object, which runs against our classical intuition. The notion of empty space and space filled with stuff blurs. Instead, space-time itself becomes stuff.

Secondly, there is the issue of whether quantum gravity implies a beginning of the universe. Classically, an initial singularity is guaranteed, and this is supported by the overwhelming evidence for inflation and a big bang. However, quantum effects certainly will make the classical arguments break down, and might mean that it is possible to avoid the initial singularity. However this is all still very much uncertain.

The only additional point we need to ask is whether we can say even this much. I am not convinced that trying to quantise space and time is the best way of combining general relativity and quantum field theory. I discuss that possibility in detail in chapter 15 of my book.

But broadly speaking, I agree with Carroll here. Most attempts by physicists to answer this question have always started with something that isn't nothing. That isn't acceptable.

Why Is There Something, Rather Than Nothing? (Part 4)

Reader Comments:

1. CM
Posted at 08:34:18 Sunday December 9 2018


I am having trouble getting my comment posted (probably because of some error on my part) so hopefully all three versions of this comment don't get posted. Nonetheless I want to try one last time to get it posted. I know my question isn't exactly on topic (doesn't have to do with Carroll specifically) but it is close enough to post here I hope.

My question is about a form of the cosmological argument, namely the Kalam. One part of this argument is the idea that the universe is past finite, it had a beginning. This seems false in light of this paper called, "Quantum no-singularity theorem from geometric flows" - a r x i /abs / 1705.00977 (spaces added because I couldn't get comment to post without them) I was hoping you could comment and tell me if this paper undermines the case for the beginning of the universe, or only one method of demonstrating its beginning (the Hawking-Penrose singularity theorem namely). I know there are other attempts to show the universe had a beginning (Borde Guth Vilenkin theorem, or Aron Wall's "The generalized Second Law Implies a Quantum Singularity theorem") but was unsure if they would fair better against the argument in the paper I linked.

In short, does this paper refute the idea that the universe had a beginning? Finally, if it does show that the universe can't have a singularity, could it still be past finite in time, even without a singularity (unless I am wrong the Hartle Hawking model is something like that - past finite but with no singularity)? Basically, could it be the case that there is no singularity, but there is still a finite amount of time in the universe's past? That would seem sufficient for the universe "coming into being" even if that coming into being wasn't at a point of infinite mass etc (given that it isn't eternal into the past).

It seems to me that one of the strongest arguments for why there must be a creator is that the universe had a beginning, so I thought I would ask and see if the Kalam (as defended by Craig and others) is defeated. I know that the Thomistic arguments don't need a beginning of time, but nonetheless it seems problematic for naturalism if there was a beginning and thus at least some evidence for theism. Thank you for your time reading over my complex (and possibly confused) question. Being an undergrad in physics these papers are not totally out of my reach but still challenging so I thought I would ask for clarification. Thanks for your time and God bless.

2. Nigel Cundy
Posted at 17:06:07 Sunday December 9 2018

Reply to CM

Thanks for your comment. It did actually get through yesterday, but obviously there is some problem with the posting here which I need to look at.

I have had a look at the paper, but need to think about it before I respond.

3. Scott Lynch
Posted at 04:35:03 Monday December 10 2018

Unrelated Comment

Did you see Dr. Feser’s most recent post on his blog? I’d love to see you do a blog series reviewing the book (at least as it pertains to physics and chemistry) when it comes out.

4. Nigel Cundy
Posted at 18:21:52 Monday December 10 2018

Aristotle's revenge

Yes, I'm looking forward to Aristotle's revenge. I'm not sure that I will buy it as soon as it comes out, but it will move to the top of my list.

5. Nigel Cundy
Posted at 12:49:45 Tuesday December 18 2018

Response to CM

I do personally have problems with some forms of the Kalaam argument. It's advantage is its simplicity,

  1. Everything that begins to exist has a cause
  2. The universe began to exist
  3. Therefore the universe had a cause
  4. This cause is God

Obviously each of these steps, particularly the last one, are backed up by considerable further argumentation, which I don't want to go into here since it is off-topic. My main concern with the argument is that the universe is not a thing. Thus there is a bit of a jump from saying that everything that comes into existence has a cause to the universe would have a cause if it had come into existence. The arguments used to demonstrate that things have causes to support premise 1 might not apply to the universe as a whole. That's one reason why I prefer cosmological arguments that rely on chains of individual beings as causes and effects, such as that of Aristotle. However, I think there is still some merit in the Kalaam argument, and if used properly should be possible to resolve this problem; it just needs to be properly expanded (which would, unfortunately, remove its simplicity and main appeal).

But, you are right that the Kalaam argument relies on premise (2), and as it is used today this is based on various scientific theories, including the classic Hawking-Penrose singularity theory. This has an obvious weakness that it refers to classical general relativity rather than some quantised general relativity. Classical general relativity is merely an approximation to the quantum theory, albeit one which in almost all circumstances you would never notice the difference, but we know that the approximation will break down at some points. And unfortunately, the point we are interested in, the initial singularity, is almost certainly one of those. It might be that some similar theory will survive in the quantum theory, and until we know what that quantum theory is we can't be sure.

Which brings me to the paper you referenced. Firstly, I should note that I am not an expert in the area of quantum gravity (my speciality is in the standard model of particle physics), so be a bit wary of what I say. However, I read through the paper, and was not convinced by it. Indeed, I am surprised that it got through peer review in its current form (although perhaps a revised version was published which wasn't submitted to the archive). Firstly, the paper contained several typos, which made it harder to read. The definition of \rho fails to include the measure of the integration. The symbol h (not h_{\alpha\beta}) is used without definition -- I assume that it means the determinant of h. Between equations 24 and 25 a less than or equals sign seems to magically become a greater than or equals sign. The definition of bounded from below in equation (20) seems to be wrong. Equation (23) didn't seem to follow from the definitions in (22) and (16b), and as far as I could tell would seem to concern the spectrum of $\theta^2$ rather than $\theta$ -- to say that the spectrum of $\theta^2$ is bounded from below isn't too controversial. They should have provided a reference for the theorem that they used to derive equation (25): it wasn't obvious to me. Their use of the Schroedinger equation in section VI didn't strike me as the right way of doing it; their solutions were derived in the case when the curvature of space time is zero, which won't be the case at the initial singularity. And so on. Most significantly, the paper was based around the quantisation of rho -- the determinant of the metric, while most approaches to quantum gravity that I am aware of quantise the components of the metric tensor, or something related to them, rather than its determinant. So I am not sure that it can be generalised to all approaches to quantum gravity.

As I said, this paper is a little bit outside my area of expertise, so there might be something which I am missing, and my struggles might just be related to my own lack of intimate familiarity with this field (I am familiar with the basics of GR and some of the various approaches to quantise it, and know enough to read a paper in the field, but can't bring to mind all the important background theorems and knowledge that a true expert would know immediately). We must be prepared for a paper showing that quantum gravity avoids the various singularity theorems -- but I don't think that this paper is it.

Of course, the singularity theorems are not the only reason why we might postulate a beginning to the universe. There is strong experimental evidence for the big bang/inflation model of cosmology. The second law of thermodynamics comes into play as well (if the universe had existed for an infinite time in the past, then it would be in a state of statistical equilibrium; the universe is not in a state of statistical equilibrium, therefore it hasn't existed for an infinite time in the past), although there might be issues here from GR if the universe continually collapses and then re-expands (although I personally don't believe that this is an issue -- open universes are a possibility, so eventually in the cycle one would expect to hit one, but again this veers outside my area of expertise so there might be something I don't know).

So I don't think that there is yet strong evidence against that premise of the Kalaam argument. However, neither is the evidence used to support that premise quite watertight, and until we have a theory of quantum gravity and somebody works out its implications, there is always going to be an element of doubt that future physics might invalidate its premise, particularly since, while the argument relies on our best available physics (as my own work does), it (unlike my work) applies that physics to a point where we expect that those theories will break down. By all means use the Kalaam argument, but don't base your faith on it and back it up with more rigorous cosmological arguments.

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