The illusion of time
nature.com
nature.com
Time is lodged into almost all of physics because the only way we can do something useful (not being God and not knowing the absolute equations sans-units) is to compare present values to previous-present values. That division sign wedged into every relative unit of measure - kg, sec, meter, etc - is basically a way of saying "as compared to". Present as-compared-to the-previous-present. What-is-now ÷ the-remembered-now. Universe-at-Planck-Tick #145 ÷ Universe-at-Planck-Tick #144
All of the universal constants come down to comparing a present state to a previous-present state and noticing that the delta between them is a consistent value. I don't think this is really news to many, but it helped to make physics and the some of the exotic math behind it make more sense to me.
I think about time in a similar manner. The delta between point A and point B is the mutation state and point A is the initial state that was mutated into B.
Here is a rather long interview I found (and only skimmed to confirm its mostly relevant): https://www.edge.org/conversation/the-end-of-time
> All of the universal constants come down to comparing a present state to a previous-present state
The problem with this as you state it is that it is not relativistically invariant; there is no absolute "present" for the universe as a whole.
However, a more restricted version of this, where the notion of "present" is not applied to the whole universe but only to a single observer's worldline, works fine.
And if God played chess, what would be his next move? We entertain the absolute/omniscient perspective to discover answers in our simplest of games, where truth appears relative because our access to information is finite.
I'm always a fan of applying that strategy to the bigger games. Physicists might benefit if they did the same, but I understand we are at the point where philosophical assumptions form the basis for many axioms.
Along any particular person's worldline, God's "next move" is whatever the next thing is that that person experiences.
For the universe as a whole, there is no well-defined "next move", for the same reason there is no well-defined "present".
Put another way:
My writing this comment is changing the state of our universe. I'm writing it because I perceive the state change. If time is solely illusion then there would be no difference in the state between Tick #145 and Tick #146, but there is and it is this comment, which means that the universe (or at least our universe) is dependant on something that you all say doesn't exist.
I'm not saying you're all wrong, but it is a pretty surprising thing if it's true and modal realism is false.
If that was the case there would be nothing to take it from state N to state N+1 because (as per your definition) there's nothing in-between states.
An explosion occurred at the narrow end of the box/horn. We, the Earth, the Sun, solar system, Milky Way, everything we can see are the particles flying away from the explosion. The path we're tracing are the world lines. Indeed, these can be seen as tunnels, and we are a charged force propagating through them.
We perceive time as a cross section of the cube/horn. But things slow down where they gather. And so the actual cross section would be very lumpy. But not to our limited perception.
The Youtube channel PBS Spacetime did some of the best explorations of ideas in this area that I've heard:
https://www.youtube.com/watch?v=GguAN1_JouQ
So no, space and time are not "measurements/perspectives" that are fundamentally distinct from "a bunch of molecules".
Also I never said space was measurement/perspective, I said time was. You believe what you want to believe, but maybe stick to a single scenario in the future. I'll say it again, a cup of coffee just sitting there is distinct from time.
Duration is as much a measurement/perspective as displacement, this is an observation which led to Special Relatively. If time can be called an illusion, so can position.
Time flows and is irreversible, this is what makes it special, and it is the denying that the flow and irreversibility are inherent properties of time that constitutes "dispelling the illusion".
In other words, saying that "time is an illusion" is saying "time is just like space".
In what sense? Normally people use that word in a sentence such as “time flows like water”, but water is made of discrete molecules and has momentum, which doesn’t generally ever sound like the subsequent sentence, whatever that happened to be at the — ah ha — time.
> and is irreversible
The funny thing is, thermodynamics is the only law of physics which say that and last I checked nobody knew (or agreed) why, as thermodynamics is inevitable from the other laws but the other laws don’t imply a direction for time.
Of course, there’s also the difference of it acting like imaginary (sqrt(-1)) space…
I think you need to be precise with language for this sort of thing, and avoid similies everywhere, or you’ll run into the same sort of problems quantum physicists have with “observations collapse the wave function” being misunderstood as “conscious minds collapse the wave function”.
There's also cosmology, which says there has to be a direction to time because of how the universe turned out as a result of the Big Bang, inflation, and everything that followed.
The question is where does this structure originate? Is there a fundamental thing "time" that has direction, irreversibility, a moment of now, memory of the past?
It doesn't appear so. Instead it seems that most of these properties emerge for complex systems.
If the universe was a box of gas there would be none of the above. So we conclude that time direction, memory, irreversibility, etc... are features of particular configurations of matter that we experience. A universe with the same laws of physics but without these features is conceivable, so they are not fundamental.
If updown was a special named dimension and you took a single 2-space+1-time slice of the universe at fixed radius from the Earth, your argument wouldn’t really be different, only words and phrases like “sitting still”, which is inherently about the dimension being removed, because it’s convenient for us.
And that’s ignoring questions like “can particles have momentum if there is no time?” which might actually be important in the unlikely event that I understand what a black hole’s singularly does to time.
Regarding the last question, if I understood forces correctly, it's that they remain in motion until an equal or greater force stops them right? Why do we need time for that out of curiosity?
A fascinating book on this topic is "Philosophy in the Flesh" by George Lakoff:
Momentum has a direct influence on Einstein field equations, and I don’t know enough maths to follow GR (just two A-levels) so I have no idea if that “direct” influence is still present at a no-more-future boundary condition.
My insufficient maths skills are, amongst other things, why I don’t trust my understanding that a black hole singularity really is a no-more-future boundary condition.
I don't believe that mental experiment proves what you think. If you freeze time, there wouldn't be anyone that could make observations. You might as well choose one fixed point in the universe, eliminating space considerations, and think about its whole story from the beginning to the end of time; that would be as real as a frozen universe.
I think of reality as a goo of vibrating stuff, encompassing all matter and energy. Matter creates space, and the vibrations of change create time.
I did not say they are interchangable, I said if one is an illusion, so is the other.
I also claimed that your notion of "physical manifestation" is not a meaningful distinction. Or at least, it's not easy to make it into a meaningful distinction that is compatible with what we know about the laws of physics.
It iis incorrect to claim that nobody really understands black holes. There are aspects of them that we don't understand, but we understand fairly well how a massive amount of coffee would turn into a black hole (a structure in space and time).
Also space and time are really not on different epistemological or ontological footing anymore.
We also should distinguish a particular instance of coffee and the concept of coffee itself, just as we should distinguish a particular time interval from the overall notion of time. A time interval then is a chunk of metric between two endpoints that would be marked, for example, by molecules doing something like ticking. It's a relative configuration of gravitational and matter fields.
Your concrete cup of coffee is likewise a configuration of matter and gravitational fields. Ontologically they really aren't that different if you take general relativity seriously.
Your perspective seems to be somewhat pre GR. Sort of Kantian: Time is not a category of reality but a category of our perception of reality. The work of Rovelli et.al. is two steps further. In GR time no longer has a distinguished foundational meaning in (and in that way it is like coffee). It's constructed from physical fields that describe its structure. The thermal time hypothesis goes one step further by making the "time field" (which is the metric, which is the gravitational field) be emergent. It's not the only theory to do so. Jacobsons GR from black hole entropy is conceptually similar.
In any case, the cup distorted spacetime even when it wasn't big enough to form a event horizon, so that it still does it after being squashed proves nothing for the issue at hand.
If you take out time, you can't point to the coffee: you'd be stuck not-pointing!
So time is a perspective in the same way that thinking of a cup of coffee as an object is a perspective. Both exist as something that can be observed in reality, and you're the one that clumps several billions of observed phenomena (changing molecules) into something observed (either a cup, or a second, depending on what you fixate upon).
I, too, think the word "illusion" is grotesquely overused in this area. It's a sophomoric equivocation between the denotation of illusion as being something that isn't there in the sense that it appears to be and the connotation of illusion as something that doesn't exist, and then getting high and going "whoooaaaaa" as you try to straddle the two things.
Time clearly exists. Less clearly, but very well established, is that physics has already told us that our common sense ideas about time are already special cases, so we already know it isn't what we think it is. Equally well established is that we're not done understanding time yet. So the idea that time may not be what we thought it was is not so much "whooooaaa" as "duuuuhhhhh".
Personally I find thinking about it and learning about it to be plenty interesting enough without the "illusion" word getting stuck in there, and indeed, if anything, spraying the word "illusion" around like rockets in a Quake deathmatch just makes it harder to understand what is being said.
Why doesn't this break the rules of causality? I found this answer on Quora (https://www.quora.com/Is-chronological-order-of-events-prese...) but I don't understand it.
In other words, we only see this for independently occurring events, which both happen before a light signal could have travelled from the location of one event to the other.
Now for the distortions in time perception, it does matter as to who the viewer is. Everyday you wake up you experience energy that’s being radiated from the Sun that’s roughly 8 minutes away (at the speed of light).
And yet, there’s cosmic events which have released energy that have happened millions and millions of years ago which have yet to reach us because we are so far away. So from our perspective the Sunlight from today is an older event than the truly much older supernova explosion that has yet to reach our planet. That which when we finally detect it, it will be a “new” event which again is much older than our Sun.
Certainly from the human perspective, these events in sequence look causal. But our perception of time is finite and our mind is constructing the order of those events. But the human perspective is subject to the limitations of our sense of scale, our faulty sense impressions and our faulty logic in reconstructing those events.
At the scale of molecules, the distances between the molecules of air, the rubber of the balloon and the metal of the pin are vast. It is impossible to perceive, looking at a subset of molecules of air within the balloon far from the site of the pinprick, why the molecules of metal interacting with the molecules of rubber have any effect on the molecules of air around them. There is no correlation.
Going deeper, at the intra-atom scale, it is difficult to fathom an incontrovertible connection between cause and effect when two atoms interact, as mostly empty space encounters mostly empty space. That their nuclei are close enough to influence each other is determined probabilistically, not deterministically. The odds that any two atoms interact is quite small. The probability improves with their relative number and density in a given volume of space and gives us some measure of reliability that we treat as causality.
Electrons are more like continuous clouds surrounding the atom.
> The picture of an atom being mostly empty stems from the childhood of atomic structure analysis, where most of the atom's extension was found to be transparent for alpha rays, and the early models explained that by pointlike nuclei and electrons. Similarly the picture of a proton or neutron being essentially empty apart from three quarks embedded in it arises because deep inelastic scattering shows that protons are essentially transparent for very energetic electrons, except when the latter meet an almost pointlike quark. But both pictures are quite limited: We don't think glass doesn't occupy space because it is transparent for light.
https://www.mat.univie.ac.at/~neum/physfaq/topics/touch.html
No, it isn't. In loop quantum gravity, which is the theory discussed in the article, "causal sequences" are more fundamental than spacetime itself, so even when you dig down to the level at which spacetime disappears, causality is still there.
https://en.wikipedia.org/wiki/The_End_of_Time_(book)
Its interesting, the but the picture of reality that it conjures up is ultimately a bit of a stretch, in my view. Kinda creating a bunch of new problems just to try and get rid of the time problem. If it was a code refactoring, it would strike you as a questionable one.
http://blog.rongarret.info/2014/10/parallel-universes-and-ar...
It's actually pretty obvious once you understand how entanglement and measurement are related, i.e. the are the same physical phenomenon.
Conveniently enough, this direction of time coincides with the one where the fusion of hydrogen atoms into helium in the Sun emits radiation (rather than the alternative direction where the Sun absorbs from the space exactly the radiation required to fission helium atoms to obtain hydrogen), the one where separated gases mix (rather than the alternative direction where mixed gases separate spontaneusly), coffee gets cold (rather than hot), etc.
(Edit: fusion/fission are atomic processes not properly accounted for in classical mechanics but I hope you understand what I mean. If there is a classical arrow of time there is no need to explain it again from a quantum point of view.)
https://en.wikipedia.org/wiki/Feynman_sprinkler
My guess is that if you really could carry this argument through without reference to the asymmetry of entanglement that it would be a major breakthrough in the philosophy of science.
The classical laws are time reversible, so the time reverse of a solution that describes, for example, two gases mixing together, is also a solution (and would describe the two gases separating themselves spontaneously).
The usual classical argument for why we don't observe the time reversed solutions is that they would require such precise initial conditions that in practice they never happen.
Which is fine as long as you recognize that that's your opinion, not an established fact.
Of course stars aren't the only things that would absorb photons in this manner, but they'd absorb a lot more than other objects, and you could probably do something with the spectrum as well.
No, it doesn't. If it did, then flashlights would behave differently depending on what you were pointing them at.
This isn't an explanation, it's just a restatement of the problem. The radiation process itself is time reversible: the case where the sun emits and your eye absorbs, and the case solution where your eye emits and the sun absorbs, are both valid solutions of the equations describing the physical laws. Saying that the eye has to absorb radiation to see it just restates the fact that, in our actual universe, we do in fact see the sun by our eyes absorbing radiation--i.e., that that solution of the laws is the one we live in. It doesn't explain why that solution of the laws, and not the time reversed one, is the one that's actually realized.
Yes, I know. It wasn't meant to be an explanation, it was meant to be a very specific and narrow response to a very specific comment. The full explanation is in the article I linked to above, which is too long to reproduce in an HN comment.
I'll take a look. I see that it's several years old; if I have comments, should I post them there, or here?
I think the point is also valid that has been raised by others in this subthread, that the argument about emission vs. absorption of radiation is also valid classically, so it doesn't explain why you need to bring in quantum entanglement for an explanation.
What you mean is that you don't like the classical explanation (as you said in your other response to me upthread). That's not the same as "can't".
In the classical GR picture, at a BH (black hole) event horizon there are no timelike worldlines that leave the BH; inside the horizon there are no lightlike ones that leave the BH either. All worldlines are thus directionally constrained and any object can only march further inwards towards the gravitational singularity. This is a feature of a BH metric.
It isn't that much of a stretch to have a classical BB (big bang) metric constrain all worldlines to march outwards from the gravitational singularity. Shazam: the arrow of time is then set by global geometry.
QM isn't even needed for half of the BH information loss problem to manifest itself: if you drop a spherical shell of mass M into a Schwarzschild BH or two spherical shells each of mass M/2 into a Schwarzschild BH, at late times who can know this? In the classical case, no BH evaporation means no information lost (it's just locked up somewhere else); but if we allow complete evaporation then we have to have stored that information somewhere. Non-evaporating growing black hole has a clear arrow-of-time due to global asymmetry; evaporating black hole formed by collapse should in principle be fully time-reversible. QM just sharpens the picture by providing a mechanism for evaporation, bringing in unitarity and other features, and letting us drop in collections of particles into arbitrary black holes such that a no-hair black hole can hide an awful lot of quantum numbers inside. It also gives us hope for a structure that replaces the gravitational singularity.
Likewise in the BB case, we'd like to avoid marching back to a gravitational singularity so we can bring in a similar QM structure to replace it (although you can do that with "throat" models fully classically, see slide 17 at https://www.slideshare.net/seanmcarroll/what-we-dont-know-ab... and refs therein). Similarly, we expect there to be an enormous number of quantum numbers in the hot dense phase of the universe, and unitarity, and so forth.
In these cases the thermodynamic arrow of time is the set of transformations that leave the equilibrium state unchanged. We can do that in the classical regime as well as the quantum one, given some additional symmetries (including but likely not limited to translation invariance and Gallilean boost invariance) and keeping well away from the ultrarelativistic limit. With a small positive cosmological constant, much of the early universe gas can be constrained to remain at essentially the same comoving coordinates as its daughter products that collapse into structures like galaxies, although things get ugly in the infinite temperature limit.
Statements arguing that the arrow of time is driven by increasing quantum correlations are great slogans, certainly enough to help focus theorists' attention, but I think they do not capture a required feature of an expanding FLRW universe's early epochs.
Not only isn't it "much of a stretch", this is exactly how the idealized Friedmann-Robertson-Walker spacetimes in GR work. They have an initial singularity which is to the past of all events in the spacetime, which is the time reverse of the way in which the black hole singularity is to the future of all events inside the horizon.
However, there are also time reversed versions of the FRW spacetimes, which have a final singularity instead of an initial one--just as there are time reversed versions of black holes (white holes), where the singularity inside the horizon is initial, not final (and where nothing can travel from outside the horizon to inside). So you still need to explain why we observe the "forward" versions of these solutions, but not the "reversed" ones.
Right. You could have at least read all the way down my comment. :-)
> So you still need to explain why we observe the "forward" versions of these solutions, but not the "reversed" ones.
I don't think so; that's just the cosmic variance problem: we're apparently in the DE-dominated era of an expanding universe rather than in some other era in the same universe or in a non-expanding universe.
If you start travelling an arbitrary great circle on Earth you'll experience significant temperature changes on most GCs; if you happen to pass through one of the polar regions and can't remember anything before that then until you are near the equator you'll be very tempted to conclude that the past is colder than the present. Conversely if you happen to cross the equator on a GC that takes you into a polar region, and you forget everything before the equator crossing, you'll be very tempted to say that everything freezes in the future. There's no time reversal at play here, just a memory horizon that is tempting to extrapolate through.
What's this mean? I think it means that RW spacetimes have an implicit choice of gauge in them that we hate to really think about because it is so convenient to foliate them.
Isn't this just a restatement of the problem? Or are you saying that those other solutions also exist, they're just in different universes from the one we live in?
> I think it means that RW spacetimes have an implicit choice of gauge in them that we hate to really think about because it is so convenient to foliate them.
Hm. Since the standard foliation is picked out by a symmetry of the solution (the standard foliation is the one in which each spacelike surface is homegeneous and isotropic), I suppose it could be termed an "implicit choice of gauge". But the same gauge choice would be implied by a contracting FRW spacetime, so I don't see how it picks out one direction of time vs. the other.
The gauging here is simply in picking out an appropriate slicing or threading. As you say, with mild assumptions, we seem to be offered a highly useful and effective one on a plate.
Now we can focus on what I think we haven't agreed.
Let's take a page out of perturbative cosmology and think of a second (explicit) gauging, wherein each hypersurface in the observed(observable)/perturbed universe is matched uniquely to a hypersurface in the model/background. Let's also ignore uniqueness problems that might arise in the deep dS era or before the very early universe (we could evolve to a static equilibrium and lose observational means of checking the hypersurface matching) and pretend that in introducing inhomogeneities perturbatively we don't run into any problems selecting the families of hypersurfaces to associate with t=const.
Let's also not argue about whether we run into problems if we define a background and do observations in the perturbed spacetime rather than determine the background from observations; for easiness, let's take the former approach, and talk about model vs observed rather than background vs perturbed.
The question, in a nutshell, is whether the observed systems at the scale of galaxies and smaller should have their entropy grow or shrink in the same way as the model. Informally, when the model is collapsing, do we expect the observed to have many more instances of e.g. blocks sitting still on a flat but not perfectly smooth surface accelerate along the surface; do we expect to see a mug milky coffee separate and eject the milk; do we expect to see omelettes evolve into whole eggs -- observations these dominating any observations of dissipative (classical) processes like friction slowing a sliding block to a standstill, and so on?
That is, is the observed matter's thermodynamic arrow of time determined by whether the model is expanding or collapsing? If there are no perturbations at all (we observe only the model), then we can agree that the answer is "yes", right? But if the observed has evolving structure, and the perturbations' entropy decreases or increases exactly like the model's, is the answer still "yes"? If so, then is the question of whether we're in an expanding or contracting spacetime merely "make your own choice, the physics doesn't care"?
Let's consider unaligning the arrows: in a collapsing background, can we have observed systems in which Boltzmann entropy is increasing? If there is interacting content in the background, what happens in the presence of these incompatible arrows of time?
In the collapsing dust background we have an initial configuration with a large coarse-grained entropy, and marching "forward" in time we see the Boltzmann entropy decreasing, with the momenta of the matter content of the background finely tuned so that it arrives in a small region of phase space. Our problem is when we define that small region as having lower entropy. Perturbations of the collapsing dust check the decrease in entropy in general; as an example we can add in matter that collapses into a black hole.
Conversely, in an expanding FLRW background, can we find theoretical support for perturbations which evolve to lower Boltzmann entropy? How common can systems like that really be? Where in spacetime can they safely interact with the content of the background, given the latter has more degrees of freedom?
By implicitly choosing to keep the Boltzmann arrows of time compatible in the background/model and in the perturbed spacetime/observed universe, we sweep these questions under the rug.
This is the implicit (and here, third) gauging, wherein we pick out and totally order hypersurfaces by their coarsest-grained Boltzmann entropy.
> Or are you saying that those other solutions also exist, they're just in different universes from the one we live in?
I'm not sure we should trust that the RW metric should be always-expanding or always-contracting. Here I'll note that you omitted Lemaître's initial. :-)
What evidence conflicts with us being in one region of a reproducing cosmology where we have possibly many (unobserved but not necessarily in principle unobservable) hot dense phases and many cold sparse phases, where the one that we can see (back to the surface of last scattering) is only relatively low entropy? Where's the beginning of the universe in that? Maybe there isn't one.
Things get even messier if we take a Hartle-Hawking or Page-Wooters view of time as non-fundamental and use that as a basis for considering that the universe may not have had a beginning.
> Isn't this just a restatement of the problem?
Possibly, but even if it's "just" that, I think it probably helps to consider the statement of the problem from different angles.
I don't see any reason why these two would have to be connected, since the FRW model as it is used in cosmology is only supposed to describe the average behavior of matter on very large distance scales. It certainly is not intended to describe, for example, a cup of hot water on my kitchen table cooling as it exchanges heat with the surrounding air.
> in a collapsing background, can we have observed systems in which Boltzmann entropy is increasing?
Why not?
> In the collapsing dust background we have an initial configuration with a large coarse-grained entropy, and marching "forward" in time we see the Boltzmann entropy decreasing
If you choose the initial configuration precisely enough, yes. But again, in an actual collapsing universe you most likely would not have such a precisely chosen initial configuration, since such a configuration would have to be extremely smooth, i.e., it would have to have an extremely small variation in density. Our actual universe is nothing like that--it's highly clumped. A collapsing universe with lots of clumps separated by empty space would not collapse into a "big crunch" state in the very small volume of phase space you describe. Its "big crunch" state would be very different--lots and lots of inhomogeneities being magnified by the collapse.
(Roger Penrose discusses this kind of model in, IIRC, The Emperor's New Mind, in the context of proposing his "Weyl Curvature Hypothesis", which says that an "initial" state is one with zero, or at least very small, Weyl curvature. The "big bang" state of our own universe was like that. But the "big crunch" state of a universe that is clumped like ours as it collapses would have very large Weyl curvature--diverging to infinity as the final singularity was approached. A "real" black hole final singularity would be similar--look up "BKL singularity" for an actual known solution to the Einstein Field Equation of this kind.)
(Note, btw, that in an idealized FRW solution, the Weyl curvature is zero everywhere. So in a universe that exactly realized such a solution, the issues described above cannot arise. But of course, as I said, our actual universe is not a precisely idealized FRW solution; that's only an approximation valid on large distance scales.)
> This is the implicit (and here, third) gauging, wherein we pick out and totally order hypersurfaces by their coarsest-grained Boltzmann entropy.
I see. I agree that, in general, we cannot prove that such a gauging even exists. I'm not sure whether anything significant in our current cosmological models depends on assuming that it does.
> I'm not sure we should trust that the RW metric should be always-expanding or always-contracting.
I'm not sure what you mean. If you are referring to the fact that there are also solutions which start with a big bang, expand, then recollapse into a big crunch, that's true; these solutions are their own time reverses.
> What evidence conflicts with us being in one region of a reproducing cosmology where we have possibly many (unobserved but not necessarily in principle unobservable) hot dense phases and many cold sparse phases, where the one that we can see (back to the surface of last scattering) is only relatively low entropy?
This looks like an eternal inflation model. AFAIK at least some such models are consistent with what we know.
Yes, and the particular one I was thinking about was Carroll & Chen arXiv:hep-th/0410270.
Rather than an expanding cosmology < (t-axis horizontal; x vertical) or an expanding and recollapsing <>, they have something closer to ><, which close to what I had in mind with, "... RW metric [might not be] always-expanding or always-contracting". Of course <> fits that too.
I'm not sure we're really disagreeing on anything now - I think that we agree that while the homogeneity-on-every-slice constraint is a useful picture for many things, it's not really useful for distinguishing the ends of time of e.g. a collapsing universe with three crucial epochs: one that's smooth and low entropy, one that's lumpy and higher entropy, and one that's even higher entropy, exactly (as you wrote) because that's not what the standard model can yield on its own; you need to perturb around the model, for instance. Once you're doing that, you're not doing physics in the model sensu stricto. But surely for a question like this we want to depart from homogeneity on every slice?
For smoothness I just assume that reheating after inflation does that and we get clumping after baryogenesis. For a recollapsing universe (with eventual galaxies), if you can give me a sketch of a mechanism for dismantling late-epoch structure into something reasonably similar to the dark ages in our universe, I'd go away and have a think about think about how to distinguish the different ends of time. But otherwise, I agree '"big crunch" state would be very different--lots and lots of inhomogeneities being magnified by the collapse' and argue that distinguishes the two ends of time sufficiently that a thermodynamic arrow of time points towards increasing entropy.
> If you choose the initial configuration precisely enough
Yes, that's the kernel of the argument.
> > in a collapsing background, can we have observed systems in which Boltzmann entropy is increasing?
> Why not?
Let me try to tighten the wording: in a collapsing universe where the entropy the entropy at one end of time is higher than the entropy at the other, can we have long-lived mutually-interacting systems where one is decreasing in Boltzmann entropy as it gets closer to the higher-entropy end, while the other is increasing in Boltzmann entropy as it gets closer to the higher-entropy end? Or does the one with more DOF's "correct" the other?
Agreed. :-)
> in a collapsing universe where the entropy the entropy at one end of time is higher than the entropy at the other, can we have long-lived mutually-interacting systems where one is decreasing in Boltzmann entropy as it gets closer to the higher-entropy end, while the other is increasing in Boltzmann entropy as it gets closer to the higher-entropy end?
I don't see why not. The only constraint the second law imposes is that net entropy has to increase; it certainly doesn't forbid one of a pair of interacting systems from decreasing in entropy, as long as the other's entropy increases at least as much.
Maybe you don't. But you need something more than Newtonian mechanics. It's possible that GR is enough. I don't understand it well enough to be able to say one way or the other. But I'm skeptical. In particular, this registers on my bogometer:
> In these cases the thermodynamic arrow of time is the set of transformations that leave the equilibrium state unchanged. We can do that in the classical regime as well as the quantum one, given some additional symmetries...
I'd want to see that argument developed in more detail. I can see how GR might provide an arrow of time for the universe, but not for the sugar dissolving in my coffee.
Try a pool table simulation -- rack up the balls (which picks out low-entropy initial conditions) and smack one of them really hard with the cue ball. The balls will spread out; entropy decreases. Now throw the simulation into reverse: the balls will return to the racked-up configuration. Entropy is reversed!
But if you randomly drop balls onto the pool table to start with, almost all the configurations of the balls will be very different from the racked-up configuration: they will be in high entropy. If you then smack a ball with the cue ball, the entropy doesn't change at all. Play this back in reverse, and you get the same thing: entropy stays essentially the same.
If you drop a spoon-and-sugar into a cup of coffee, the initial configuration of the sugar is all clustered very close to the spoon and far from most of the coffee. It will generically evolve to higher entropy, where the sugar and coffee are much more mixed, and (if you stir) the region around the spoon is not much different from the regions far from the spoon. If we look close enough early on, we'll see overdensities and underdensities of sugar at many scales; indeed, we could even see sugar crystals forming "spontaneously".
You can do this cosmologically too: start with a low-entropy configuration of a fixed amount of matter at the narrow end of an expanding universe, and the latter end will generically have a lot of empty space (which is very high-entropy). Depending on the matter, when looking more closely sufficiently close to the low-entropy condition we may see overdensities and underdensities and those can drive structure formation (it's the normal explanation for structure formation, in fact).
(We could sprinkle in a bit of Penrose for clarity: if the matter of the early universe is evenly distributed, although it seems like it is in high Boltzmann entropy, since we can swap matter here for matter there without drastically changing structure formation, the gravitational entropy is very low. We can't push together a bit of matter here or pull apart a bit of matter there without changing later macrostates.)
That is, the thermodynamic arrow of time arises not from the laws of physics, but from a particular -- and highly non-generic -- configuration that evolves according to them towards a high-entropy equilibrium state.
If you don't start with a low-entropy configuration, then time-symmetric laws of physics don't give you macroscopic time asymmetry (Loschmidt/Zermelo); you need something to break the symmetry (e.g. a law that is (spacetime) position-dependent), and that something will probably also set the direction of the thermodynamic arrow of time.
You are trivializing a very deep question: https://en.wikipedia.org/wiki/Superdeterminism
I wonder if the "we project" part is the author's choice of words or Carlo Rovelli’s. It is not explained and therefore has not definitive meaning.
If you take reality to be right here, right now (what else could it be?), time cannot exist, it just helps us map change.
And even well before that:
For what is time? Who can easily and briefly explain it? Who even in thought can comprehend it, even to the pronouncing of a word concerning it? But what in speaking do we refer to more familiarly and knowingly than time? And certainly we understand when we speak of it; we understand also when we hear it spoken of by another. What, then, is time? If no one ask of me, I know; if I wish to explain to him who asks, I know not. Yet I say with confidence, that I know that if nothing passed away, there would not be past time; and if nothing were coming, there would not be future time; and if nothing were, there would not be present time. Those two times, therefore, past and future, how are they, when even the past now is not; and the future is not as yet? But should the present be always present, and should it not pass into time past, time truly it could not be, but eternity. If, then, time present — if it be time — only comes into existence because it passes into time past, how do we say that even this is, whose cause of being is that it shall not be — namely, so that we cannot truly say that time is, unless because it tends not to be?
—Augustine of Hippo, Confessiones lib xi, cap xiv, sec 17 (ca. 400 CE)
Which means it's impossible to construct a wormhole to the past, since the past doesn't exist. But GR does theoretically allow for certain configurations of space to bridge different time frames.
"There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy." - Shakespeare
"If you take reality to be right here, right now (what else could it be?)" - can't disagree!
But, after that, things start to get self-referential in tangled ways - "time cannot exist, it just helps us map change" - but 'change' requires time! And 'mapping' is a mental act that involves change!
I can't help but feel that if these apparent contradictions were ironed out, the answer to 'what is time?' would be close by.
Or, all memory is faulty, and that's all we've got of the past? In that sense, this might be true.
At least, as it appeared in the comments on HN.