The Quantum Thomist

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Does the Mentaculus disprove efficient causality?
Last modified on Sun Apr 11 18:53:11 2021

A little while ago, a commentator asked me to respond to a paper by Dan Linford entitled The Kalam Cosmological argument meets the Mentaculus. This post is my response.

I imagine that most readers will be familiar with William Lane Craig's revival of the Kalam Cosmological argument.

  1. Everything that begins to exist has a cause.
  2. The universe began to exist.
  3. Therefore the universe has a cause.

Further argumentation shows that this cause must be God, as classically understood (or some vague approximation to the classical understanding). This is not an argument I myself use, for various reasons which I don't want to go into here. But one of Linford's objections to this argument is relevant to the various Aristotelian versions of the Cosmological argument, so it is worth taking a little time to respond to that part of the paper.

The objection arises from an attempt to evade the second premise of the Kalam argument, from a bouncing universe scenario. The cosmological standard model, based on classical general relativity, has the universe beginning at an initial singularity. The universe at that point is with very low entropy. The universe then expands and simultaneously entropy increases. The end fate of the universe is not completely clear. It might be open, i.e. the universe expansion continues forever; flat, where the expansion comes to a stop at infinite time; or closed, where the universe collapses back into another singularity. At the moment, as far as I am aware (although I am not a cosmologist and thus not an expert on this), the evidence favours a flat universe. But it wouldn't take much for some additional physical effect we don't know about currently to affect the calculation and shift everything to a closed universe. It is a possibility.

The bouncing universe model supposes that instead of collapsing into a fresh singularity, the universe will only approach the singularity, and then start expanding again. So you start from a low entropy state, the universe expands and entropy increases, then the universe contracts, and at this point entropy starts to decrease, until again you have a very small low entropy universe. Then this triggers the expansion process, and so on ad infinitum.

One of Craig's responses to the bouncing universe scenario is to tie the direction of time to the increase in entropy. In this case, at the bounce, you don't have the universe being reborn, but two independent universes being simultaneously created. If the point of lowest entropy is at time t = 0, then from one perspective, our universe has time greater than zero and increasing, while the other universe has time less than zero, and growing more negative. However, this way of putting it is misleading, because the direction of time is related to the increase of entropy. So what you get in reality is two separate universes with time positive and increasing. If you go backwards in time in both universes you come to the moment when t = 0, and this counts as a beginning to the universe. Thus even a bouncing universe still has a beginning, and we can still apply the Kalam argument. At least, that is one way in which Craig has responded to the possible bouncing universe scenario.

Linford is responding to this response by Craig. He thinks that he has found a problem with it, and that's what his paper is about.

The first question is whether the passage of time is reductive or not reductive. By reductive, I think he means that it reduces to some physical phenomena. Craig's statement that the direction of time corresponds to the direction of increasing entropy can be interpreted as a reductive theory of time. In particular, Linford appeals to a particular philosophy of time associated with Albert, Loewer, and Papineau, which is termed the Mentaculus. Linford claims that this is the best way of proposing a reductive theory of time, and thus if the passage of time is reductive, then this model is probably true. But the Mentaculus construction also denies that there is efficient causality at the microscopic level. It is thus not true that everything that begins to exist has a cause; and the argument is that if Craig's defence of the second premise to the Kalam argument is successful, then he indirectly undermines his first premise. Linford concludes that if time is reductive, then the Mentaculus model is correct, and if the Mentaculus argument is correct, then not everything has an efficient cause. If true, this obviously has consequences for all cosmological arguments, not just the Kalam argument.

Linford's argument can be presented as:

  1. If the direction of time is reducible, then, probably, not all events have efficient causes
  2. If, probably, not all events have efficient cause then the first premise of the Kalam argument is false.
  3. So, if the direction of time is reducible then the first premise of the Kalam argument is false.
  4. If the direction of time is not reducible, then the direction of time does not necessarily correspond to the entropic arrow of time.
  5. If the direction of time does not necessarily correspond to the direction of the entropic arrow of time, then: a) the interpretation of the interface (between two bouncing universes) as a beginning without a physical cause is unjustified; and b) the claim that events on one side of the interface cannot be the efficient cause of events on the other side of the interface is unjustified.
  6. If (5a) and (5b) then Craig and Sinclair's interpretation of bounce cosmologies is unjustified.
  7. So, if the direction of time is reducible then Craig and Sinclair's interpretation of bounce cosmologies is unjustified.
  8. The direction of time must be either reducible or not reducible.
  9. Therefore the Kalam cosmological argument is unjustified.

I intend in this post to focus on steps 1-3, and their discussion of efficient causation. I am not going to discuss the rest of the argument, since that isn't really relevant for my own work. The Aristotelian Cosmological arguments are not threatened by bouncing universes, since they don't rely on the premise that the universe had a beginning.

The argument as presented by Linford

Theory of time

As stated above, Linford bases his work on that of Albert, Loewer, and Papineau. His argument consists of two parts. Firstly to show that, in this construction, the direction of time is reducible in a particular way. Secondly that given this reducibility of time, efficient causation can be eliminated in some circumstances.

The starting point is the claim that the best microphysical theories do not distinguish the past from the future. His distinction between microphysical and macrophysical theories is related to the fundamentality of the theory. By microphysical, he means our current most fundamental theories, which would be the standard models of particle physics and of cosmology; what lies beneath them is as yet unproven. I will subsequently just refer to the standard model of particle physics as the Standard Model, since cosmology only indirectly affects this theory of time. The macrophysical level is obtained from the microphysical by a process of averaging or course-graining. This is not unreasonable. It is how we do move from one layer of physics to another, at least in certain respects. It is how we convert from a theory of quarks, leptons and gluons to one of atoms and molecules; or from a theory of atoms and molecules to gases and liquids as a whole. The other approach involves taking various limits and approximations; for example when we move from quantum physics to classical physics. But as we move to larger systems, the quantum effects become less important, and the quantum to classical transition is less of an approximation. Thus I think that the assumption that the macrophysical physics is an averaging over some microphysical states has justification.

His example, which I will discuss below, is related to Newtonian mechanics, which I agree is time symmetric in the sense that he needs.

With regards to quantum field theory, he discusses two objections to the idea that there is no direction in how the theory treats time. The first is related to wavefunction collapse. In the standard Copenhagen interpretation, it is easy to see why people might view wavefunction collapse as a barrier to time reversibility. You find a particle coming into a detector in a superposition state; it interacts with the detector which forces it to collapse into an eigenstate of a particular basis determined by the detector, and it leaves the detector in a definite eigenstate of that basis. You never see the reverse process happening, i.e. the particle entering the detector in a definite eigenstate, and leaving it in a superposition. In this sense, wavefunction collapse is not time reversible. Linford objects to this by saying that he doesn't find objective collapse interpretations of quantum physics particularly promising. A better response (from his point of view) would be to indicate that he does believe that there is a direction of time at the macrophysical level, as I will discuss below, and when the particle encounters the detector the system moves briefly from the microphysical to the macrophysical, giving the illusion of a temporal direction.

The second objection he responds to is a bit more technical. There are three discrete symmetries related to the Standard Model action. The first of these is parity, P, which is basically the process of converting x into -x in every spatial direction. It is a bit like holding the whole universe in a mirror, and declaring that it looks exactly the same. The second is charge conjugation, C, which involves the conversion of particles to anti-particles. The second is time reversal symmetry, T, which is what we are interested in and which involves changing t into -t. It is a bit like holding the universe in a temporal mirror, and declaring that it looks exactly the same. What Linford wants to claim is that the microphysical laws as a whole are time reversal symmetric. Showing that the action is invariant under T is a necessary but not sufficient condition for this, since there is more to how quantum field theory operates than just the action, although the action is a significant part of it.

Every viable action we know of is invariant under CPT. That means that it is time reversible, but only if you simultaneously convert particles into anti-particles and reverse parity. (As usual, when someone says "it is, but …" they mean that it isn't.) Most parts of the theory are invariant under CP and T individually, but there is one aspect, related to some theoretical (but not practical) freedom in how you merge together the electro-weak and strong nuclear aspects of the standard model, which breaks these symmetries. This means that T symmetry is violated in nature, and the microphysical theory is not time symmetric.

Linford's response to this that one can define as an effective time reversal operation one that takes a specific sequence of states, {S1,S2,S3,…,SN} and then convert it to another sequence of states {S*N,…,S*3,S*2,…,S*1}, which is said to be the time reversal of the first sequence. Linford defines time reversal invariance of physics as the proposition that the time reversal operation returns a sequence of events that is explainable and permissible in terms of the original laws. And this definition of time-reversibility does apply to the standard model action. The second point that he makes is that such violations at the level of quantum field theory play little role in the macrophysical experience of time irreversibility, i.e. that you can't unfry an egg. This is also true, but I think that it is irrelevant to the main claim on which his argument rests, which is that there is no temporal asymmetry at the microphysical level.

Onto the Newtonian example. Consider a ball in a vacuum bouncing off a wall. The wall is on rollers, and everything is frictionless and elastic so there is no loss of energy to heat. When the ball bounces off the wall, the wall must begin moving. So we have 1) The ball is moving and the wall is at rest. 2) The ball collides with the wall. 3) The ball is moving in the opposite direction, and the wall is also moving. We can reverse time, and start with 3*) the ball and wall are moving; 2*) the ball collides with the wall; 1*) the ball is moving and the wall is at rest. This reversed sequence of events is just what you would get from applying Newtonian laws to the state 3*. In this sense Newtonian mechanics works just as well running time backwards as it does forwards.

Phase space is the space of possible microphysical states. After the averaging process that gives us the macrophysical world, we can't say precisely which microphysical state the system is in. Instead we have a small range or region of possibilities. But the size of this region of possible microphysical phase spaces is not constant in time. As we move forwards in time, applying the macrophysical version of the laws of physics, it grows larger. This introduces some time-irreversibility at the level of the macroscopic physics. This is true even though at the microphysical level physics is time reversible.

The size of the phase space region is termed the entropy. The amount of entropy characterising a system has observable macrophysical consequences. Work can be done when a system is out of equilibrium; you can take advantage of the natural flow from a non-equilibrium to an equilibrium state to do something useful such as powering a piston or a generator. As the process tends towards an equilibrium state, the less work you can get out of it.

We can consider our records of the past. These require a relationship between the present time, the time the record was created, and a time prior to that. There are a large number of trajectories from higher entropy regions that could create macrophysical records indistinguishable from our own. To ensure that the record we possess did not randomly fluctuate into existence, we need to be confident that the recording device was in the correct state to record the past accurately. But to be sure of this, we need a record of the state that the recording device was in just before it recorded the event, and so on. This regression can only terminate if there was an original state with very low entropy, i.e. only one possible state for the first recording device to be in.

So now we come to the Mentaculus hypothesis. This is based on three principles: firstly the fundamental dynamical physical laws, L. Secondly, the hypothesis that the universe began in a low entropy state M(0). And then there is the statistical hypothesis. M(0) refers to a macrophysical state of the universe. There are numerous different microphysical states which could give that same macrophysical state. Since we only observe the macrophysical state, we don't know which of these states is the correct one, so we should assign each of them a uniform probability. A consequence of this is that we can apply the laws of physics to each of these microphysical states, extrapolate them forwards in time, work out which macrophysical states they each belong to, and that will give us a phase space distribution for the current state of the universe, M(t). We can narrow this down a bit based on current observations.

Every formalisable proposition p concerning the state of the physical world is assigned an objective probability by the Mentaculus: P(p|LM(0)M(t)). Every macrophysical temporal asymmetry can be recovered from one feature of this only: that it depends on the low entropy initial state, M(0).

Thus the direction of time is reducible to the presence of the initial state of the universe in the Mentaculus. The argument is that if we had knowledge of the present macrophysical state of the universe alone, then there would be numerous possible trajectories for the possible evolution of the microstates extending into both the past and the future. The overwhelming majority of these trajectories for both the past and the future evolution of the universe would lead to an equilibrium state, due to time asymmetry at the microphysical level. However, due to the assumption that the universe began in a low entropy macrophysical state, we can filter out those present microstates which imply a high entropy past, and discard them. However, the future trajectories remain unbounded, so the overwhelming majority of them will be directed towards a high entropy state, and thus we have the emergence of the second law of thermodynamics. To discard most of the microstates that could lie behind our presently observed macrostate, those that imply a high entropy past, to enforce consistency with a low entropy initial state, while not doing something similar for those states which imply a high entropy future, breaks the temporal symmetry. The flow of time is a breaking of temporal symmetry; and if the flow of time is reducible to physical phenomena, and this time asymmetry in the Mentaculus is the only physical breaking of temporal symmetry, then the experienced flow of time must emerge from the asymmetry in the Mentaculus. Thus the source of all our experiences about the arrow of time and its direction emerges from the smaller size of the phase space in the past.

Efficient causality

So now we come to efficient causality, as explained by Linford (this is a summary of his argument; and not one I myself would make).

Efficient causality is time asymmetric, since causes generally come before their effects. If all physical time asymmetry is reducible to the Mentaculus, then that means that asymmetry in efficient causality will also be reducible to the Mentaculus. On the other hand, at the microphysical level, for an individual event, there is no objective distinction between which events make up the events past and its future. Thus there is no distinction between causes and effects, which eliminates the possibility of efficient causality which presupposes a temporal asymmetry.

This doesn't apply so much at the macrophysical level. Here there is a difference in the amount of information you need to predict the past from knowledge of the future state compared to predicting the future based on knowledge of the past state. The Mentaculus is a macrophysical concept, so we are allowed to have efficient causality at the macrophysical level. This is why we naturally perceive there to be causality in the universe. But in the microphysical world, events merely happen.

This is distinct from the sort of causal scepticism attributed to David Hume and associated with an opposition to metaphysics. This approach is not anti-metaphysical; instead it states that we should read our metaphysics off our best science. Efficient causation is important for macrophysical events, and required for our best science. Linford's argument doesn't deny all efficient causation; indeed it demands that we accept efficient causation at the macrophysical level. What it denies is the idea that everything that comes into existence has a cause. Some changes require a cause (including the standard examples of causation, since they are macrophysical), but there are other changes which don't.

Equally, this is not the view that quantum indeterminism demonstrates that efficient causation is inapplicable to microphysical processes. That's a separate argument which Linford doesn't discuss. I have responded to it elsewhere.

If it is true that microphysical events don't have a cause, then it is false that all events have a cause, and thus one of the premises of the Kalam argument is incorrect, and thus the argument as a whole fails.


Linford states that objections must either a) challenge the premise that the Mentaculus construction of the reducibility of time is probably true; or b) challenge the argument that if not all events have efficient causes invalidates the Kalam argument. He seems to take a) for granted (which is a pity, because that is what I am going to attack), and focuses on b). Here he looks at a response by Craig to a similar argument from Quentin Smith. Smith argued that vacuum pair creation is a counter-example to efficient causality because there are no prior events which necessitate it. Craig responded, in my view reasonably but missing out a few details, that the vacuum causation might be spontaneous but cannot be said to be uncaused because it only occurs if various physical conditions are present. Linford argues that this sort of response would not work against his objection. Linford does not deny that there are certain physical configurations required for an event, but only that one can't make the distinction about whether such configurations are in the event's past or future. Moreover, when Craig claims that God is both explanatory prior to and temporarily simultaneous with the creation of the universe, this model does not require that causes are explanatory prior to or simultaneous with with their coming into being. (My own feeling is that Linford has made a mistake here. His whole argument concerns temporal priority, while Craig was referring to explanatory priority. They are two different things.)

Linford uses an example from general relativity to illustrate this. There is nothing at the microphysical level to distinguish between a particle following a geodesic and collapsing into a gravitational singularity (a black hole) compared to a particle being emitted from that singularity and following a geodesic. (Again, I am a bit nervous about this. General relativity is a macrophysical theory under Linford's categories and thus, by his arguments, does have time asymmetry; the microphysical theory would be quantum gravity, and we don't know enough about that to say how it treats the direction of time. You can't apply general relativity to quantum particles.)

I will just highlight one more sentence in his response to objections,

Since early modernity, the explanatory categories that we utilise when we plumb nature's depth have been repeatedly revised and have been shown to be far removed from the categories relevant for explanations in the manifest image or in the spacial sciences. With Galileo, we had to give up the Aristotelian demand that uniform motion requires a cause, and some have argued that quantum mechanics forces us to give up a demand for deterministic causation. Perhaps physics has simultaneously shown us that we need to give up irreducible causation and offered a new set of explanatory criteria for fundamental explanations.

While it is true that many people rejected Aristotelian causation at the time of Galileo, such a rejection was not necessary. Firstly, Aristotelian causation does not concern the motion of an object, but a moving object. It is fairly easy to argue that inertial motion is a type of natural motion, i.e. that the cause of a particle in whatever location and momentum state it is in at time t+1 was that same particle in whatever location and momentum state it was in at time t. The particle having the final cause of moving to another location according to its philosophy. (Obviously this has to be modified a little in the face of quantum physics, and become a bit more nuanced when we think of special relativity, but we are discussing classical mechanics.) I agree that quantum mechanics forces us to deny deterministic causation, but Aristotle's efficient causation need not be deterministic. And as I have discussed repeatedly, contemporary physics fits very nicely with Aristotle's vision of causality, as long as one has an accurate understanding of what Aristotle proposed, and not base you rejection on a straw man caused by trying to interpret Aristotle through a modernist lens.

But, in any case, that's the end of Linford's discussion of objections. I have cited it mainly to show that he did not consider the objections I list below.

Further details

I want to also mention something noted by Barry Loewer, in his paper Two accounts of laws and time, which was among the background reading I needed to do to prepare for this post. Loewer distinguished between between what we might call the Platonic view of the laws of nature (my terminology, not his) and the Humean view. He uses the work of Tim Maudlin as an exemplar of the Platonic view. The Humean view does not mean a full acceptance of everything that Hume wrote, but merely the account that the laws of nature are mere descriptions of conjunctions or regularities. The fundamental entities in the universe, things like particles, fields and so on, together with the categorical properties and relations instantiated by them. Aside from the basics of raw geometry, everything else in the universe can be reduced to this "Humean mosaic". Fundamentally, that is all there is; everything else is derived from it. These entities lack causal powers, so there is no fundamentally necessary connection between spatio-temporality non-overlapping events in non-overlapping portions of space time. Like everything else, the laws of physics emerge from study of the fundamental entities.

The Platonic view, on the other hand, sees the laws of physics having a existence, separate from the entities and properties that form the Humean Mosaic, in some abstract third realm. They have an effective power to act on the things in the universe. So the laws provide us with a connection between non-overlapping events. For example, a classic mechanistic understanding of physics would be Platonic.

Two alternative views of the laws of nature would be the Aristotelian and the Thomist (or scholastic). These agree with the Platonist that the laws of nature have their own individual existence (in a sense) which transcends individual particles. However, rather than existing by themselves in some abstract third realm, they subsist in particulars. The Aristotelian account would have them subsisting within concrete objects, but disagrees with the Humean account because these are related to the underlying universals that the entities are dependent on, and because they imply that those entities have causal powers which do provide us with an objective causal connection between different events. The Thomist account would add that the laws could also subsist within a mind, and will point to the mind of God in particular. The Thomist account doesn't deny the Aristotelian belief in inherent causal powers, but will say that God is necessary to explain those powers, and to actualise any potency implied by those powers.

In any case, Loewer states that the idea that the flow of time is ultimately reducible, and thus the whole structure of the Mentaculus, fits very nicely with a broadly Humean account of the laws, and seems to require such an account. The idea that the flow of time is not reducible, but is fundamental to the pre-physical structure of the universe, sits more comfortably with a Platonic view of the laws of physics. I should add that the Aristotelian and Thomist views of the flow of time again sits somewhere between these two views. Time is (in these views) a measure of change, so if you don't have any material entities (or even immaterial entities) to change then you can't have the passage of time. But it is not something that emerges from the entities themselves, but instead is a universal connecting everything in the universe. The same flow of time subsists in each individual particular. (In the context of relativity, we would have to say that time can be experienced as flowing at different rates for individual particulars, but they all experience it flowing in the same direction, and they all experience it flowing.) Thus time is not reducible to the entities of the Humean mosaic, but it is a universal subsisting in each of those entities (against a Humean account) so without them there would be no flow of time (against a Platonic account).

So the idea behind the Mentaculus carries this additional assumption: that a Humean understanding of the laws of nature (which might not be specifically Hume's understanding, but something in the same family) is correct. This premise is obviously going to be rejected by theists, because theists, as a general rule, reject the Humean understanding of the laws of nature. Thus in this sense, it could be suggested that Linford's argument is circular: he responds to an argument for the existence of God by drawing on premises, one of which is generally seen as being inconsistent with the more philosophically sophisticated understandings of God.

The standard argument against the Humean understanding of the laws of nature is that in it it fails in one of the two tasks which the laws are meant to achieve, in that it fails to explain why the universe operates according to those laws. The Platonic explanation is straight-forward: it gives the laws themselves causal efficacy. The Aristotelian interpretation is that the laws describe inherent causal powers, and the Thomist that the laws describe both inherent causal powers and (ultimately) God's acts in the universe. In each case, there is an explanation of why nature behaves in a manner consistent with its laws. But the Humean cannot fall back on any such explanation, because he rejects all notions of causal connections (at least in the sense that most people would apply that time). He cannot use laws to explain the nature of the physical particles in the universe and their interactions, because (according to him) laws emerge emerge from the physical particles. But he also has nothing else in the place of the laws to provide the explanations. All the Humean has is brute matter, which acts in determined ways but without any reason. Events just happen, and that's the end of it.

Loewer responds to that objection by saying that it fails to distinguish between a metaphysical explanation and scientific explanation. So saying that the laws metaphysically don't actually explain everything does not mean that they can't be invoked (for example) in a scientific explanation of why an uranium nucleus has the tendency to decay and emit alpha particles. I don't think that this response is adequate. The scientific explanation should ultimately be derived from the metaphysical explanation. The goal isn't just to explain uranium decay in terms of various scientific laws (which deal with abstract representations of the uranium atom), but why those scientific laws mirror what happens in concrete reality. The Humean claims that there is nothing in concrete reality which can explain the causal connections seen in scientific law. But that just leaves the success of science as some brute fact which is only achieved for no reason at all. If metaphysics is meant to explain being as being, then this is no metaphysics at all (and I am not sure that Hume would disagree with that statement). Any metaphysics which explains why science is successful must be preferable to one which states that there can be no such explanation.

A second objection to the Humean account arises from non-local effects in quantum physics, such as the Einstein-Polaski-Rosen paradox, and shown by the experimental violation of Bell's inequalities and related theorems. Unless we posit a non-local entity (as in the Pilot wave interpretation of quantum physics), there is clear correlation between disjointed space time events, which (whatever does explain it) cannot be reduced to the categorical properties of the individual particles. Obviously this creates problems for most metaphysical ideas which emerged in the era when classical physics seemed to be dominant, but I struggle in particular to see how it can be easily reconciled to a Humean account of the laws in which everything is reducible to the categorical properties of individual particles. (But I am just throwing this out there for comments; I still need to think it through a bit more.)

So one good reason for rejecting the Mentaculus account of the flow of time, and its consequences for efficient causation, is that it relies on a metaphysics which is both controversial and problematic, and in particular not a metaphysics that most theists would accept.

I should also comment that Loewer's account of the Mentaculus assumes that the underlying microphysics is deterministic. He states that it can be adapted to indeterminate laws of physics, but fails to go into any details.

Comments and response

The first comment to make is that the model that Linford adopts is that his paper is ultimately a response to a discussion around whether the bouncing universe model undermines the Kalam cosmological argument. However, the construction of the Mentaculus assumes the second law of thermodynamics, namely that entropy is always increasing. We start from a low entropy state, and as time increases move to a high entropy state. However, in the bouncing universe model, the universe starts in a low entropy state, expands, and then reaches a maximum (which will be short of the maximum possible entropy which is reached at infinite time), contracts, and then returns to another low entropy state. Under the assumption that the microphysical laws are fully time reversible, it must be possible to take that final low entropy state (let's call it M(∞), reverse time, and get to the present day. This would be true at the microphysical level; but since the macrophysical dynamical laws are derived from the microphysical laws it must be true for those as well. The present microphysical state is constrained because it must have a past trajectory that leads to a low entropy state. In the bouncing universe model, it must also be constrained because the future trajectories of the present microphysical state must also lead to a low entropy state. In other words, we could just as easily assign every proposition in the natural world an objective probability P(p|LM(t)M(∞). This probability is of equal merit to the one that Linford uses, P(p|LM(0)M(t)). There is no objective reason for preferring one over the other. The macrophysical time asymmetry disappears. If you tie the low entropy state at the end of the bounce to no more than being an artefact of the universes contraction under general relativity, and thus try to claim that all future trajectories must collapse into it; then you can also apply that same argument to the period of initial expansion and say that all past trajectories of our current state must collapse into it (and so we are not discarding those which lead to a high entropy past since no trajectories lead to a high energy past in this general relativistic model). The asymmetry contained within the Mentaculus again disappears, and thus the Mentaculus is no explanation of temporal asymmetry and the whole project fails. This objection of course, is only valid in a bouncing universe model. It does not apply in the flat or open universes which were assumed in the works that developed the Mentaculus. I suppose that you can also get around it by saying that you can choose to use either M(0) or M(∞) based on which side of the entropy maximum you are in, but then you are introducing another premise into the construction of the Mentaculus, namely that the flow of time is in the direction of increasing entropy. If you do that, it collapses to the model of temporal reducibility which is assumed to be used by Craig and Sinclair. The Mentaculus is no longer the correct way of looking at the flow of time, and the arguments against efficient causality which assume the truth of the Mentaculus account of the flow of time have not been shown to hold.

My second introductory comment is to once again beg people to please recognise the distinction between event and substance causality. The cosmological arguments, both the Kalam and Aristotle's, require substance causality, i.e. the notion that we can point to one or more objects in particular physical states as the cause of another object in a given physical state. There is no need for these arguments to make the assumption that events have physical causes; they might do, but could also be spontaneous and the cosmological arguments would still work just as well. Event causality is when you search for a physical cause of an event, or cite an event as a cause for something physical. I have argued often enough that quantum physics is inconsistent with event causality (at least if, as I believe, one of the indeterministic interpretations of it is correct), but substance causality is perfectly consistent with it, and it could be said that quantum physics implies some form of substance causality. That does not mean that quantum events have no cause; only that that they do not have a physical cause, in the sense of something representable in physics, so within space and time. In any case, throughout this paper, Linford continually refers to event causation, and never substance causation. I don't think that this is a major drawback for his argument. His paper can easily be adapted to refer to substance causation alone. But it is just something which irks me, so I had to make this point.

The next comment to make is to question whether the Aristotelian can accept that the direction of time is reducible to some underlying physics. In this respect, Professor Feser's recent post is worth reading. In this post, he warns against treating the physical abstractions used in the sciences as though they were concrete reality. And relating metaphysical conclusions to abstractions, rather than the underlying reality. I think that it is easy to see that Linford's argument, and the whole Mentaculus project in general, falls into this error. The Mentaculus isn't even a scientific abstraction; it is an abstraction of an abstraction. It can thus be argued, and I think cogently, that this is too far divorced from reality for us to draw any useful conclusions from it.

I should add that Professor Feser might well have had me in mind when he wrote that post, since his response to my post on time was at the top of his further reading list. I really ought to get round to responding to his post at some point, but I will just say here that my own position is probably in the middle between the complete rejection of scientific abstraction as being useful for metaphysics on the one hand, and the confusion of abstraction with reality on the other. I agree that reality is not the same thing as the abstraction. And I agree that metaphysics is prior to physics, and should be based on reality rather than the abstraction. I believe that the correct abstraction (and, of course, our current best theories provide only an approximation, albeit a very good one, to that) is in a one-to-one mapping with at least part of reality. There is more to reality than is caught by the sciences (since scientific abstraction doesn't describe material causation, or that which needs to be united with a form to make a concrete object). But our metaphysical theory ought to be consistent with the physics. Part of this involves looking at a physical object, and identifying its formal and final causes, and how efficient causality applies to it, how we can relate its possible changes in terms of act and potency. That is to say, taking the general metaphysical principles, and showing that they have analogues in our best physical theories. The fact that metaphysical principles apply to real objects as a whole, and that some aspects of those real objects are in a one to one mapping with the scientific abstraction, then we might expect to find some analogues of the underlying metaphysical principles in our physical theory. Since we know in what respects the metaphysical principles apply to reality, and what aspects of reality are captured by the scientific representation, then we have a good idea to expect what metaphysical principles would have an analogue in the abstraction. If we can't find such an analogue, then it might just mean that we are not smart enough to see it, or it might mean that the abstraction doesn't correctly model the relevant part of reality, or it might mean that the scientific abstraction is wrong, or it might mean that we are working from the wrong metaphysical model. Thus when we have two competing metaphysical theories, and one of them fits in nicely with our scientific abstraction, and the other one doesn't, then we have good grounds to prefer one theory over the other. If one of the metaphysical theories implies things about reality which contradict the predictions of the scientific abstraction, while the other is perfectly consistent with it, then that gives us even better grounds for preferring one metaphysical theory over the other. This principle is at the heart of my argument of why we should accept a broadly Aristotelian or Thomist framework over a mechanistic or Humean one.

So does this caveat let the Mentaculus argument off the hook? I'm not so sure that it does. Firstly, the Mentaculus itself is far too much of a generalisation. It comes from an averaging procedure. It is not in a one-to-one relationship with (aspects of) reality. Thus it is not the sort of theory which we can use to test different metaphysical ideas about the direction of flow of time in reality. What about the claim that the microphysics cannot distinguish between past and future? If true (and I will argue below that it isn't), this does not prove that in reality there is no distinction between past and future.

What we have is a mapping between physical time and a geometrical line segment (using pre-relativistic physics for simplicity of explanation; the relativistic version of this argument is more complicated because you have to discuss the temporal and spatial mappings together, but the arguments below are unaffected by this extra complexity). Let's call the present time t = 0, and the start of the universe t = t-N (which is negative) and the end of the universe t = tN (this could, of course, be at infinity). What we are doing is mapping each moment of time in reality to a point on the line. What Linford is claiming is that the laws of physics, the equations that describe how things change, are invariant under the global transformation t → t' = -t (perhaps conducted concurrently with other transformations). What this means is that we map the start of the universe to a time t' = -t-N, and then have our time variable decrease as we head into the future. There is still a direction to time and, since this is a global transformation, it remains the same direction at all times. The transformation used by Linford to conclude the notion of time reversal symmetry is only applicable to the abstraction. There is no evidence that there is something corresponding to it in reality. But we would need something corresponding to the time reversal transformation in reality in order to say that the transformation represents something in reality; and we need that to be able to apply Linford's arguments about causality to physical reality. Thus it can be argued that any conclusions drawn from this symmetry only apply to the abstraction, but not reality. If the abstraction can't distinguish between past and future, it does not mean that reality cannot make the distinction.

But suppose that there is a direction of time in reality, even at the microphysical level. Is this going to be captured by the mapping of time onto a geometrical line segment? No, because a geometrical line segment has no directionality. Thus if, after we come up with the final theory of physics and find that it has no time directionality at the microphysical level (I'm not claiming that that will be the case; just setting up a hypothetical), we then have a good reason to suppose that the lack of time directionality in the theory reflects that the direction of time is some part of reality which is not capable of being captured by the abstraction. It might be, of course, that we have to put the directionality of time into the dynamics of the theory in order to make the correct predictions. If so, that's fine, and it would provide good evidence that time in reality has a direction even at the microphysical level, and consequently that you can distinguish between cause and effect. But if not, it says nothing about whether time in reality flows from past to future, since those who claim that it does so flow could say that it is a feature of reality cut out by the mapping of time to a line segment.

So what does it mean to say that the equations governing the laws of physics are symmetric under time reversal? It just means that if X can change into Y, then it is also true that Y can change into X (or, more precisely, that some Y' can change into some X'), with the same probability. In each case, you can still have something changing into something else, i.e. a distinction between cause and effect. So the time-reversibility of the laws of physics is irrelevant to the question of whether time has a direction, even in the abstraction, and even less so in reality.

But where does this leave Craig and Sinclair? If we are arguing that there is a direction in time in reality which may or may not be captured by the mapping from reality to the scientific abstraction, does this mean that time is not reducible to some physical effect such as the increase in entropy? My goal in this post is just to defend efficient causality at the microphysical level, so I will let Professor Craig speak for himself; he is more than capable of doing so. If I were to do so, I would probably argue along the following lines. Instead of the direction of entropy increase determining the direction of time, it is instead a necessary reflection of the direction of time at the microphysical level. So the direction of time is there at the microphysical level in reality (and perhaps also in the microphysical abstraction, but that is less important), but maybe it isn't obvious at the microphysical level, particularly when it comes to the universe before the big bang (in a bouncing universe scenario) which we can't observe. But if you have reasons to argue that the macrophysical direction of time tied in with the direction of entropy increase is always correlated with the microphysical direction of time (in reality, even if it is absent in the abstraction), then you can use the direction of entropy flow as evidence that the direction of time at the microphysical level, or even (if we may be bold enough to make this jump) in microphysical reality reverses at the entropy minimum. Certainly the modern proofs of the second law of thermodynamics that I am aware of assume a temporal direction at the microphysical level, so I think from this that there is good reason to argue that entropy increase is correlated to temporal succession at a more fundamental level. Even the Mentaculus assumes a direction of time at the microphysical level, since it states as a premise that the microphysical phase space increases in time. This makes little sense unless there is a more fundamental direction of time prior to the discussion of phase spaces and their sizes.

I should state that Linford anticipates this response in his section 3.2, but his response is not particularly well-founded.

For example, consider a world consisting of a vast collection of Newtonian particles at thermodynamic equilibrium. Because the world is at equilibrium, the entropy will have some constant value. Nonetheless, the entropy will fluctuate around the average, and there will be some finite probability for fluctuations of arbitrary size. Given enough time, the system with fluctuate to a microscopically small entropy.

Equilibrium means that the system is stable in time. Yes, there will be small fluctuations at the microscopic level, but there will always be the tendency in the system for those fluctuations to decrease if they become too big. One way to think about this is to think about flows in phase space. Each flow represents a trajectory which describes how the system can evolve under some fixed laws. Such flows, in many physical systems, have a tendency towards or away from various fixed points, which is a point in the phase space where, if the system is in the associated state and you apply the laws then it will remain in that state. Fixed points are distinguished by the behaviour of systems close to those points. A relevant fixed point sucks any neighbouring state into it. An irrelevant fixed point pushes any neighbouring state away from it. A mixed fixed point is a combination of the two. There are also things like fixed orbits, and chaotic systems. In a chaotic system, there are no relevant fixed points (so two neighbouring states can diverge by an arbitrary amount), but most chaotic systems of physical relevance develop attractors, where the system becomes trapped in what resembles a sort of fuzzy fixed orbit. If a system is in equilibrium (at the macrophysical level), it is either in a relevant fixed point, or a relevant fixed orbit, or an attractor. That means that there is a tendency for systems that deviate from equilibrium to move back into it, not away from it into a low entropy state. This is even more true in a quantum system. If there is a single trajectory that allows the system to escape the attractor in the deterministic system, you can be certain that in a quantum system some fluctuation would move the system off that path and back onto a trajectory which leads into the attractor. Entropy is not going to be reversed by chance. (In the bouncing universe model, entropy is reversed because the universe itself undergoes gravitational collapse, space time is condensed, forcing everything into a small phase space. It is not the model proposed here by Linford.)

So now let us turn to the Mentaculus itself, and the actual physics. This is the claim that it is always possible to define a probability for any statement based on the laws of physics, the phase space of microphysical states at the start of the universe, and the current phase space of microphysical states. To my mind this is a trivial statement, but it is not one that is especially meaningful. To be meaningful, it would need to be argued that this is the only way in which we can usefully extract the probability of various physical propositions. That we can think about time in this way is one argument that the direction of time is correlated with the increase in the size of the phase space (or entropy increase). But it doesn't prove that it is the only way in which we can think about the direction of time. For example, I can assign a probability for any physical proposition given the knowledge of the laws of physics, the current microphysical phase space of the universe, and the assumption that the direction of time at the microphysical level. Those are, essentially, the assumptions that go into the calculation of a matrix element or cross section in quantum field theory; the method was developed for the microphysical level, but can also be applied at the macrophysical level.

So I don't think that we can use the Mentaculus to tell us anything profound about the philosophy of time.

So what about the claim that quantum field theory is invisible to the direction of time, and thus is inconsistent with the notion of efficient causality?

The direction of time enters into quantum field theory in three places. There is the CP violation in the action; the phenomena of wavefunction collapse; and there is the time ordering of the path integral. Two of these are mentioned by Linford, but only CP violation is discussed in detail, so I will start there.

As Linford discusses, the standard model action is only invariant under CPT symmetry, not each of these individually. It is not time reversible. Linford avoids this by redefining time reversibility of physics as a whole to mean that if there is a change X→Y which is permitted by the laws of physics, then there is also a change Y*→X* which is also permitted with the same probability, and where X* is conjugate to X in the same sense that Y* is conjugate to Y (in this case, conjugate is defined in terms of the CP transformations). This is also true in classical mechanics. To get a Newtonian system to run backwards, you have to reverse the momentum of all the states, so time reversibility strictly requires that you construct conjugate physical states (the difference is that in classical physics, switching the direction of the particle's velocity and thus momentum is natural when switching the direction of time; while a CP transformation is not so obviously linked to time reversibility). The problem comes when he tries to apply this to say that there is no distinction between cause and effect. That lack of distinction would only be the case were X* = X and Y* = Y. As it is, we can say that if we have X at one moment of time and Y at the next, we can be confident that X is the cause and Y the effect because the laws of physics do not permit the transformation of Y into X (at least, not with the same probabilities; we might need to repeat the experiment a large number of times if we need to measure frequencies). Similarly, if we have states X* and Y*, then we can be sure that Y* is the cause and X* the effect, because the laws of physics only allow us to transfer from Y* to X* (at least, with the given probability). Linford's argument for the breakdown of efficient causality at the microscopic level assumes one definition of time reversibility; while his discussion of CP violation leads him to a different definition.

There is a related point which Linford raises later in his paper, based on a remark by Earman. Even if the laws of physics are not time-reversible, how do we know which direction is correct? The answer to this seems to me to be obvious. The direction of time is a global phenomena. It doesn't change depending on where or what you are in the universe. It doesn't vary according to the scale of the phenomena (not just microphysical against macrophysical, but how macrophysical you are). It is also not simply a matter of the abstraction. We perceive the arrow of time to flow in one particular direction. Therefore it flows in that some direction for everything, including at the microphysical level of the standard model. What we identify as the past is the past universally. What we identify as the future is the future universally. Again, I think that in this objection Linford and Earman are focusing too much on the finer details of the abstraction, and ignoring the broader view of reality itself. Once you identify which end of the line segment represents the start of the universe, and which the end, then all the events, and in particular the physical states, are in a definite temporal order, and thus you can say which came first in time and thus which is the cause and which is the effect. And, as stated above, to fix which point of the line segment represents the start of the universe, all we have to do is look beyond the abstraction and appeal to our own conscious awareness of the passing of time. Even though our awareness is at the macrophysical level, there is still a single ordering of events at the microphysical level, and that must be consistent with the ordering in the macrophysics.

So then we have wavefunction collapse. I would agree that this is a bit more controversial, since there are interpretations of quantum physics which avoid wavefunction collapse, such as the pilot wave interpretation which Professor Craig himself prefers. But that is very much a minority view. The most popular interpretations of quantum physics are the Copenhagen, Everett multi-worlds, and consistent histories interpretations. Copenhagen has wavefunction collapse; the multi-world interpretation has branching of the multiverse (which implies a loss of information in a single universe); and consistent histories, while not following precisely wavefunction collapse, still has irreversible macroscopic changes at a measurement. So I don't think that it is fair to dismiss the interpretations that involve time asymmetric wavefunction collapse, or something that plays a similar role, without giving some justification.

The point is that Linford is presenting an argument against efficient causality. If that argument is to be persuasive, then all its premises must be correct beyond doubt. One of those premises is that the correct interpretation of quantum physics is one in which there is no wavefunction collapse. Since there is no consensus about the correct interpretation of quantum physics, a defender of efficient causality can easily say "But I find the indeterminate interpretations of quantum physics more promising," and thus escape the force of Linford's argument. If you are trying to prove that something is false, you should not leave behind potential loopholes like this.

Thirdly, we have time ordering. I have rarely seen philosophers of physics take much note of this, which is unfortunate, because it is a crucial part of quantum field theory. It is needed in any calculation. When you calculate a propagator (connecting an initial and final state), the order in which you place the creation and annihilation operators makes a difference. The correct order, the one that gets the answer in agreement with experiment, is to use time ordering. You can find this described in any standard textbook in quantum field theory; for example I am looking at Peskin and Schroeder, sections 2.4 for a Bosonic field and 3.5 and 4.7 for Fermion fields, or section 9.2 for the path integral formulation, along with numerous other places in the book. Now if you have to introduce a time ordering operator into the abstraction, on top of the various time symmetric mappings and constructions, to get it to make predictions that correspond to reality, then that suggests that in reality the succession of physical states is ordered in time. And this is at the microphysical level. There is, of course, still the question of which direction should be regarded as going into the past and which as travelling in the future. The requirement for time ordering doesn't answer that. But I addressed it above.

Thus Linford has not provided sufficient argumentation to demonstrate that physics at the microphysical level is time symmetric in the sense that he needs to undermine the notion of efficient causality.


The first thought is that this argument is not at all relevant to the Aristotelian, since in Aristotle's philosophy, time is not reducible to the direction of entropy or some other similar macroscopic effect. Instead time is the measure of change. Since change happens at the microscopic as well as the macroscopic level, the arrow of time must exist at the microscopic level. Albert, Loewer, and Papineau's whole argument is thus somewhat irrelevant. The Aristotelian would not say that time is reducible in the sense that they require. And thus the Aristotelian can follow the second horn of Lingard's dilemma, without any adverse effects to their own cosmological arguments. The claim would be that Albert, Loewer, and Papineau's central premise that the direction of time is reducible to macroscopic effects is irrelevant.

But, even taken on its own terms, the argument has its problems, and I don't think it works as advertised. The construction of the Mentaculus is sufficient to show that there is some connection between the direction of increasing entropy and the direction of time, but it is not sufficient to show that the direction of time is reducible to the Mentaculus. There are other, equally valid, ways of looking at the world which make different assumptions about the origin of the direction of time. His denial of efficient causality in the microphysics fails because the quantum field theory description is not time symmetric in the sense that he needs for his argument to work. And in all of this, he is guilty of confusing the abstractions with reality.

Is God a failed Hypothesis? Part 12: The Patriarchs

Reader Comments:

1. Michael Brazier
Posted at 14:51:59 Monday April 12 2021

Bouncing universe?

I see another issue with the bouncing universe model - the idea that a collapsing universe must have a decreasing entropy. That's not logically necessary, and considering that the entropy of black holes increases with their mass, one can easily conceive a collapsing universe in which all the matter is driven into a single black hole by the collapse. Such a universe would have a very high entropy, not a very low one.

2. Daniel J Linford
Posted at 03:48:44 Tuesday May 18 2021

Thanks for the reply!

Thank you for your long reply to my paper! I am very pleased to see that you offered a long, thoughtful, and quite detailed reply to my paper. I think that what you argued is interesting and would encourage you to think about elaborating on your post and submitting it as a paper to a journal. Perhaps that would encourage a scholarly exchange between us somewhere other than the blogosphere.

Having said that, allow me to offer a few replies. I won't reply to all of the points that you raised against my paper, but you have given me a lot to think about.

First, you argued that the Mentaculus is committed to Humean supervenience, that is, the thesis that the physical world is fundamentally only a distribution of qualities across space-time without, as Hume would put it, any necessary connections between distinct existences. First, while some of the defenders of the Mentaculus have also defended Humean supervenience and have even defended the Mentaculus in virtue of their commitment to Humean supervenience, the Mentaculus, itself, does not entail Humean supervenience. In fact, Barry Loewer -- who you cited -- has more recently provided a revised Neo-Humean view that is not committed to Humean supervenience.

Moreover, there are authors -- e.g., Mach, McTaggart, and Kuhn -- who thought that although there is no fundamental direction of time, there are necessary connections of the sort that Neo-Humeans deny. (I do not claim that Mach, McTaggart, and Kuhn are committed to the Mentaculus.) The view that there is no fundamental direction of time is compatible with there being necessary connections between distinct existences because the relationship of efficient causation is only one kind of necessary connection. Unlike efficient causation, other relationships of necessary connections can be symmetric with respect to time. (You mention that you think quantum mechanics is likely indeterministic. I disagree, but I'm most attracted to the Everettian interpretation. Despite what you said about that interpretation, the Everettian interpretation involves the view that the wavefunction evolves deterministically.)

Second, you explained that, according to the Mentaculus account, the flow of time is explained by the entropy gradient. That's not quite right. What the Mentaculus account claims is that the direction of time -- which is not the same thing as the flow of time -- shares a reductive explanation with the second law of thermodynamics. And that this reductive explanation of macrophysical time asymmetries can be expressed in terms of a low entropy boundary condition. Of course, folks who think that time flows in some metaphysically thick sense will likely think that the flow of time picks out the direction of time. But, in that case, the low entropy boundary condition will not determine the direction of time.

Third, you sometimes recognize that I am offering a dilemma and then other times seem to be saying that I'm committed to there being no microphysical direction of time. Instead, I'm offering a dilemma for someone like Craig, who endorses a view of absolute time on which -- according to *Craig* -- the direction of time has no important relationship to the entropy gradient. It's only on the first fork of the dilemma -- on which the direction of time shares a reductive explanation with the entropy gradient -- that there is no microphysical efficient causation.

Fourth, you provided a reply to one of my arguments from section 3.2 of my paper. But I don't really understand your argument. My example of a Newtonian universe at equilibrium was supposed to show that, on views like Craig's that involve absolute time, the alignment of the direction of time with the entropy gradient is not a necessary feature of the world. If time is absolute, then, conceivably, the entropy could decrease into the future and we can even cook up examples in which that occurs. Since the time that I published this paper, I have since discovered that Craig makes the same point in one of his own papers and even provides an example similiar to the example that I offered.

Fifth, at one point, you argued that we could place the low entropy boundary condition in the future just as easily as we could place the low entropy boundary condition in the past. I don't quite understand what you were trying to argue. If there is no absolute direction of time -- as supposed on the first arm of my dilemma -- and the direction of time is explained by the Mentaculus -- or something quite similar -- then the condition that picks out the past direction just is the low entropy boundary condition. Perhaps I'm missing something.

Anyway, I enjoyed your post and I'm glad that you responded to my paper. I look forward to hearing more from you.

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