The Quantum Thomist

Musings about quantum physics, classical philosophy, and the connection between the two.
Why Is There Something, Rather Than Nothing? (Part 3)

Why Is There Something, Rather Than Nothing? (Part 4)
Last modified on Sat Jul 13 18:31:10 2019

I have been sporadically 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. My third post discussed the definitions of "something" and "nothing". Carroll was a bit more reasonable here than many of his fellow atheists, who managed to get something out of nothing only by redefining the word "Nothing" to mean "Something."

But now we start to get to the heart of Carroll's argument. Carroll is trying to argue that the universe can be reduced to a Brute fact, i.e. something which need not be as it is but just happens to be that way. So he is asking whether the universe requires something external to itself to explain its existance.

Physical considerations

Carroll starts by assuming that quantum mechanics is the correct theory of nature, hoping that even if it is not true, whatever the true theory is will share the same feature. I myself constantly highlight the differences between quantum mechanics and quantum field theory. If you make this distinction, then it is clear that quantum mechanics is not the true theory of nature, because it is inconsistent with special relativity. However, most of the philosophers of physics, at least out of those that I have read, focus on quantum mechanics and all but ignore field theory. One justification they give for this is the belief that quantum field theory is just quantum mechanics generalised to also include fields. I disagree, and think that the differences between the two and their philosophical consequences are far more profound than that. That's something I discuss in detail elsewhere. However, some people use the phrase "quantum mechanics" to mean all of quantum physics, both mechanics and field theory. If Professor Carroll is doing the same thing, then I would only quibble about his terminology. That certainly seems to be what he intends: he states that his argument is valid in both quantum mechanics and in relativistic field theory. The problem is that he uses equations and results that are taken from quantum mechanics? Do they truly generalise to field theory?

He introduces a quantum state, and demands that the dynamics of the state are governed by a differential equation in terms of the Hamiltonian operator,

Schroedinger equation

He claims

This equation applies to the dynamics of any isolated quantum system, including relativistic quantum field theories and presumably quantum gravity; all one has to do is specify the right Hilbert space and Hamiltonian. (We assume the universe is isolated, or else we should be including whatever influences it as part of the universe.)

Now let us first of all look at that assumption in the last sentence. He assumes that the universe is isolated. But consider also his definition of the universe earlier in the article.

I'm using "universe" here to refer to the entirety of physical reality. No judgment is implied about whether things other than physical reality can be usefully said to exist.

And also bear in mind his earlier definition of God.

Creation: There is something apart from physical reality, which brings it into existence and/or sustains it. This hypothetical entity is often identified with God in the literature, but there is not necessarily any strong connection with a traditional theistic conception of the divine.

So God is defined as explicitly not being part of the universe. So either Carroll is assuming (not proving, but assuming at the start of his argument) that God doesn't influence the universe (which no theist would accept), or he is contracting himself about whether or not God is part of the universe.

This is a common mistake made by atheists. Most people in the contemporary world think of the laws of physics as operating independently of God (God might be their origin, but no more than that). So a scientific explanation is a rival to a theological explanation. This is a hangover from the beginnings of modern science in the late medieval, Renaissance and early modern era, where the mechanistic picture came to be the dominant philosophy of physics, first spawning deism and then atheism. Most of the rest of mechanism is now known to be false (its premises contradict quantum physics), but this idea remains, even though the reasons that it was originally proposed are long since rejected, and nothing put in their place. The problem is that a theist doesn't think of the laws that underlie physics in the same way. This is not a question of the mathematical form of the laws, or the predictions made from them, but the philosophy behind them. Theists believe that God is continually acting in the universe. He uses secondary causes, which each type of matter (baring miracles) acting in regular ways, and these secondary causes can be understood with just reference to material substances. But they are merely tools used by God, and ultimately reflect God's nature. For the theist, a scientific explanation is a description of how God did it.

I have no objections to someone who reasons against this theist interpretation: someone who starts from atheistic principles, and deduces our current best laws of physics, or starts from theism, and shows that one reaches a different set of laws. Then, at least, we can debate. But that isn't what is done; like here one just gets an assumption without justification that the atheist understanding of science is correct.

But I think that a more serious issue here is that he has his physics wrong. It is certainly true in quantum field theory the Hamiltonian operator is identical to the time evolution operator. But it doesn't act directly on the quantum state. Instead, we use the exponential of the Hamiltonian in the time evolution. For a small time period δt, we instead use

QFT time evolution equation

Where the Hamiltonian operator is decomposed into various creation and annihilation operators (this means that when considering more than just an infinitesimal time step, one has to be careful of how one performs the integration over time, since those operators don't commute with each other, but that goes beyond the scope of what I am discussing here). This exponential is important because when we expand it in a power series, it is interactions in the higher order terms of the expansion that lead to all the loop effects and virtual particles which make the predictions of quantum field theory different from those of quantum mechanics. Naively, one might just say "Why not just expand the exponential in δt, take the limit as the time difference goes to zero, and you are left with the quantum mechanical expression?" But this is incorrect. The limit required to reconstruct the differential operator is only valid if the Hamiltonian operator represents a continuous evolution. However, it involves the creation and annihilation of various particles, a discontinuous process. Quantum mechanics assumes that particles are not created or destroyed (it only considers single particle Fermion states and mean field potentials), and under this assumption one can derive the Schroedinger equation from the QFT time evolution operator. But the assumption is ultimately unphysical (which is why quantum mechanics is only an approximation to the true quantum physics). Thus one cannot just apply the Schroedinger equation to a relativistic theory.

The second important difference between quantum mechanics and quantum field theory is that in quantum mechanics the quantum state represents only a single particle, and in quantum field theory it is a Fock state counting the number of particles in each different possible state. Thus what the state represents depends on which theory you are discussing. Carroll starts by using the quantum mechanics form of the time evolution, but in a few paragraphs he is going to use his state to represent the state of the universe -- which implies that he should be discussing quantum field theory.

The solutions of the Schroedinger equation are that the (quantum mechanical) wavefunction rotates with a speed of rotation proportional to an Energy eigenstate of the Hamiltonian operator.

time evolution

Any quantum mechanical state can be expressed as a superposition of these energy eigenstates, and thus which constantly rotate in time. This is a process which has no beginning or end. (Indeed, the quantum mechanical Schroedinger equation is time symmetric). Carroll uses this to suggest that all quantum states evolve eternally in both the past and the future. Thus, he argues that almost any quantum mechanical universe is necessarily eternal (I will get to the "almost" part in a moment). The big bang is not truly a start of time (as it is in classical general relativity). To quote Carroll,

As far as physics is concerned, such a universe would be completely self-contained, existing perpetually without any external cause. One can still question whether or not an uncaused eternal universe is intellectually satisfying, but there is no physical or cosmological obstacle to its existence.

The problem occurs, once again, when we try to apply this reasoning to quantum field theory. The time evolution of the standard model is not time symmetric (it is instead symmetric under time reversal, the same operation with respect to space which is called parity, and charge conjugation which is transforming all particles into anti-particles, which is known as CPT symmetry). Thus we see that the quantum states cannot be thought of as having that same time evolution as in quantum mechanics; instead there is a constant creation and destruction of particles. The single particle states are not the eigenstates of the Hamiltonian, and one needs to be careful in replacing the exponential of the Hamiltonian operator with the exponential of its Energy eigenvalues because of its construction from non-commuting operators and the importance of time ordering. Secondly, even in quantum mechanics, the continuous (and time symmetric) wavefunction evolution is not the only thing going on; there is also the rather mysterious wavefunction collapse which breaks time reversal symmetry. Thus one cannot conclude from quantum mechanics that the universe extends indefinitely in both directions.

Moreover, the classical theories of Newtonian mechanics (which corresponds with Schroedinger mechanics) and special relativity (which corresponds to the standard model) are both consistent with an eternal universe. In classical physics, it is only when we introduce curved space time and general relativity that we see the necessity of an initial singularity. Why should we then be surprised if the analogue to the classical big bang is absent in quantum theory in flat space time, which is all that Carroll analyses? We would need to have and analyse a theory of quantum gravity in a Riemann geometry to make any statements about any beginning to the universe in quantum physics.

Carroll suggests an exception to his perpetual universe, namely the state with zero energy. This is when Carroll transmutes his quantum state to cover the entire universe, and posits

Wheeler deWitt

This is the Wheeler-DeWitt equation, which arises in various attempts to quantise gravity, and has one obvious problem: it implies a completely static universe. I believe the idea in this equation is that the negative enegy of gravity cancels out the positive energy associated with matter. The issue is, of course, that the straight-forward attempt to quantise gravity, and thus the derivation of this equation, is mathematically inconsistent.

Carroll's proposed solution to this is to suggest that time is an emergent property; that the Hilbert space of the universe can be factorised into two parts, one of which contains a clock part of the universe, and the other is (at the level of the Lagrangian) compensating for it but (at the level of the ground state) the symmetry is spontaneously broken so it doesn't fulfil this function in practice. [Spontaneous symmetry breaking is when there are several different states with the same minimum energy described by the Hamiltonian. These states can be mapped onto each other by one of the symmetries of the system. However, in practice, nature must choose one of them. This means that while the symmetry exists in the Hamiltonian operator, it is broken by the actual distribution of matter in the universe. In this case, there would be some symmetry in the universe linking the two parts of the Hilbert space to ensure that overall at the level of the Hamiltonian the combination is time-independent, but in practice the symmetry is spontaneously broken, meaning that time evolution emerges from the system].

Such an emergent time need not extend perpetually into the past, so has been used to posit a finite universe. The idea would be that physics would descrbe a universe in two parts; the first (without the spontaneous symmetry breaking) containing no time or change, the second a time evolution. (One example of this would be the Hartle-Hawking model). People who advocate this claim that the temporal universe (something) emerges from the part of the universe without time (nothing) -- although this is misleading, because the phrase "emerges" implies a temporal sequence, which can't be the case when one side of the business is timeless. The temporal part of the universe emerges from the laws of physics without any external cause.

So Carroll concludes that either in the case of an eternal universe, or a Hartle-Hawking model, there is no reason why the universe needs a cause independent of physical reality. He makes an additional point about energy conservation, supposing that the energy either must go somewhere in time or (if the total energy is zero) the universe could have a beginning.

So what should we make of this argument? Firstly, he assumes that the universe is governed by the Wheeler-deWitt equation, which has its problems. I highlighted a few of them on the way, in particular that it is based on the principles of quantum mechanics rather than quantum field theory. Another is that in gravity, energy is measured as a component of the stress energy tensor. In quantum physics, energy is the eigenstate of the Hamiltonian operator. These are two different definitions. So saying that gravitational curvature can be thought of as a negative contribution to the stress energy tensor is not obviously relevant to energy as it is defined in quantum physics. It is in no way clear that the universe is governed by this equation. Secondly, he ignores the arguments that the universe cannot stretch indefinitely backwards in the past, for example from the second law of thermodynamics, or the observational evidence for an initial singularity. His argument from the conservation of energy misses the point -- those who posit a beginning to the universe would suppose that the laws of physics (including the conservation of energy) break down at the moment of creation. Energy is created along with time.

But the biggest problem in saying that the universe emerges from the laws of physics is that the laws of physics themselves both need explanation and are not something which can provide the causal (meaning substance efficient causality) explanation that we need. The laws of physics are either a description of the interactions between different physical substances (from an atheist/deist perspective), or a description of the interactions between different physical substances which result from God's continual guiding of the universe in the absence of special providence (from a theist perspective). Being merely a description, they cannot be a cause of anything; they merely describe causes. Carroll states

The question is not whether a universe could pop into existence out of nothingness, but whether a universe with a beginning can be entirely described by an appropriate set of laws of physics without the help of any external cause. The answer is that, by itself, the existence of an earliest moment to time is no obstacle to describing the physical universe in completely consistent, self-contained terms.

But this ignores the role of the laws of physics. In the Hartle-Hawking model, these provide the explanation of how the temporal part of the universe emerges, but where do these come from? After all, the laws of physics are not part of physical reality, and thus not part of the universe as Carroll defined it. They describe the evolution of physical reality. Since they do not describe their own evolution, they cannot be part of physical reality, and are thus not part of the universe in the same way that matter and energy are. Thus the laws of physics -- or whatever sits behind them (which, as a theist, I would identify with God; it certainly must share all the attributes traditionally ascribed to God) -- themselves in the Hartle-Hawking are the external cause that Carroll claims doesn't exist. And if the laws of physics demand (as they do) that every thing that changes its state has an efficient cause (a substance), then one cannot both claim to have a universe arising from those same laws without anything external and the first substances arising without a cause.

Principle of sufficient reason

Next, Carroll anticipates an objection by discussing the principle of sufficient reason. The principle of sufficient reason basically posits that the termination of the chain of explanation cannot be something contingent (i.e. which need not exist in some different state), but only necessary. There are two definitions of necessary found in the literature. The first is logically necessary which means that there is a logical contradiction in something not existing. The second means something which exists but is incapable of change (in Aristotlean terms, this would be a being of pure actuality). For something in this second sense, one cannot deduce its existence through logic alone, but if one induces its existence through (for example) its effects, then no further explanation is required because it cannot be in a state other than what it is.

Carroll's objection to the PSR is that it relies on a causal view of physics. The dichotomy presented by those who support the PSR is that we have a choice between saying that everything contingent requires an explanation and a state of irrational anarchy. Carroll proposes that there is a middle ground, one which denies causal relations in physics, but thinks of it in terms of impersonal, unbreakable patterns. He also claims that this is what modern physics describes.

But I struggle to see what Carroll means by impersonal, unbreakable patterns, that avoids both anarchy and sufficient reason. As I have argued, modern physics is consistent with, perhaps even implies, Aristotlean efficient causality, where every effect (a substance) emerges from a cause (another substance). This is ensured by the conservation of energy and momentum. Immediately we get a causal/powers understanding of physics. Perhaps by "unbreakable patterns" Carroll means an empiricist understanding, where physics is merely a description of observed regularities. But then either those regularities are truly unbreakable, in which case they are more than just our observations and imply some explanatory regress, or they are not, in which case they just happen to occur most of the time, and we are reduced again to anarchy. While quantum physics is indeterminate, it is not anarchy, because the possible decays still follow various selection rules and conservation laws. But these same selection rules and laws, and the consistent, unchanging amplitudes, imply rational explanation, which again leads us back to the PSR.

Next Carroll argues against the idea of a necessary being, but here he brings in an argument from Hume against a logically necessary being. As I discussed, the concept of a necessary being as needed by the PSR is weaker than this, so Hume's argument is an irrelevance, only arguing against the definition that classical theists wouldn't use.

So Carroll concludes this section by arguing that while we are welcome to search for a greater being or specific purpose behind the universe, or for a reason why we have these laws of physics rather than another, but he states that there is no logical reason why such an entity must exist. The universe could just be as a brute fact.


As I have shown, while up to this point Carroll's article hasn't been too bad and I agreed with much of it, his argument in this section has been problematic. His argument from physics contained mistakes. He transposes equations and ideas from quantum mechanics into quantum field theory where they are invalid. He neglects the effect of curved space time on quantum physics; where he does discuss quantum physics he uses speculative and unproved theories that don't prove his point in any case. His response relies on physics being an active agent in bringing about the universe are. But whatever the laws of physics are, they are something external to the material reality, i.e. outside the universe. Thus any physical account of the origin of the universe denies that the universe itself can just be a brute fact. His argument against the PSR involves invoking a middle ground between the two extremes of PSR rationality and a wholly irrational universe. But it is not clear quite what his proposal suggests. He does not seem to be aware of substance causality.

But most importantly, his argument does not justify his conclusion. He concludes with the statement

But there is no logical or empirical reason why such an entity [extra universal cause] must exist; the universe can just be.

But to prove this statement, one needs to discuss every possible argument why such a cause must exist, and show it to be lacking. Carroll has discussed three such arguments: from physics, a cosmological argument based on the PSR, and an ontological argument leading to a logically necessary being. But even if successful (which he wasn't) these don't exhaust the possible arguments. He accepts the laws of physics; there are metaphysical arguments based on the existence of physical law in the first place for an explanation behind that law. He neglects the Aristotelian argument from accidental and essential series (demonstrating that there isn't an infinite sequence of explanations for at least some causal sequences). He neglects the argument from thermodynamics (the universe isn't in equilibrium). He confuses the need to explain the universe (which in my view is nonsensical) with the need to individually explain all the things in the universe. As soon as you state that "the universe can just be" you are avoiding the main issue. He admits the existence of a termination of the sequence of explanations (since he believes the universe to just be), but rejects the classical arguments about why such a termination must possess the divine attributes. He even neglects the "What caused God?" argument so beloved of the new atheists. This, of course, has no effect against the God of classical theism (defined as the termination of the chain of causality, a necessary being which cannot be explained further; when applied to this definition of God the question becomes self contradictory), but is powerful if we suppose that the sequence of explanation terminates with something contingent. Any point you stop the explanatory sequence except God is just arbitrary. You cannot be sure that there is nothing beyond it, and, given that if it is contingent then it could be in some other state, and if it could be in some other state then given enough of an opportunity it would have been in some other state, then there is cause to suppose that that being is not the termination of the sequence of explanation.

So I don't believe that Carroll has made his case in this section. Next time, "Why this particular universe?"

Why Is There Something, Rather Than Nothing? (Part 5)

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