I How is the arrow of time defined?

[nikkkom]

You are basically envisioning a solution which describes Minkowski spacetime which has some distribution of quantum fields in the "far past" that has a supply of muons and no (or very few) electrons and antineutrinos; and you are saying that in the "far future", there will be few if any muons left and a much larger number of electrons and antineutrinos. But it seems obvious that there will be another valid solution, the exact time reverse of this one, in which there is a large number of electrons and antineutrinos in the "far past", and where the initial conditions are set up just right (as they must be, for this solution to be the exact time reverse of the one I just described) for those electrons and antineutrinos to collide with each other and form muons, creating a large supply of muons in the "far future". So in this solution, muons reconstitute more than they decay.

All true, I'm not disputing it.

My point is that the observed physical world realizes only the first possibility.

If you set up many independent non-interacting systems, half of which are "muon-dominated" (let's describe them as "impenetrable box with a few muonic hydrogen atoms") and other half are "electron-dominated" (box with ordinary hydrogen + sufficiently energetic muon and electron antineutrinos), very soon all of them will become electronic. Not one of "electronic" boxes will have muonic hydrogen in it.

Since boxes don't interact, how do they "know" that they are all in the "forward-time" solution of the physical laws?

 

[PeterDonis]

My point is that the observed physical world realizes only the first possibility

Sure, but so what? Again, we aren't talking just about our particular solution. We're talking about all possible solutions. And since all possible solutions include solutions where, for example, muons reconstitute instead of decay, the obvious answer to "why do muons decay in our observed world" is that we happen to live in a solution in which that is the case. In other words, it's not the laws, it's the initial conditions (or whatever it is that distinguishes our solution from all the other possible ones).

If you set up many independent non-interacting systems, half of which are "muon-dominated" (let's describe them as "impenetrable box with a few muonic hydrogen atoms") and other half are "electron-dominated" (box with ordinary hydrogen + sufficiently energetic muon and electron antineutrinos), very soon all of them will become electronic. Not one of "electronic" boxes will have muonic hydrogen in it.

Remember, once again, we're talking about all possible solutions of the laws, and we are assuming that the laws are time symmetric. So what you have described is, once again, one particular solution in which there is some asymmetry in the initial conditions, which means that there will be another solution with a corresponding asymmetry in the final conditions. You've made the asymmetry in the initial conditions harder to see by the way you describe things, but that doesn't matter; the fact that you've described a solution with an obviously asymmetric final state (all electronic boxes) means that there must be a corresponding time reversed solution with a similarly asymmetric initial state.

To resolve your apparent "paradox", we can just take that time reversed solution, evolve it to the point corresponding to the state you describe (half muonic boxes, half elelectronic boxes), and ask, what happens next? Since the half muonic, half electronic box state is unstable, what will happen to it? There are only two possibilities. One is that the half and half state is not actually the "initial" state of the system you described; it must have arisen from a state in the past with even more muons. That means that, in the time reversed solution, the half and half state will evolve into a state with even more muons in it, because the trajectories of all the electrons and antineutrinos in the initial state were lined up just right. If this is true, it implies that the "half and half" state you describe could only have arisen from a state in which there were originally all muons in both of the boxes; that would be the correct initial condition.

The other possibility is that, in the "time reversed" solution, the half and half state evolves into another "all electronic" state--in other words, that this "time reversed" solution is actually identical to the original solution you described, which is in fact time symmetric! If this is the case, then the "half and half" state must have been produced, in the original solution you described, from a previous "all electronic" state, by an appropriate arrangement of the electrons and antineutrinos to produce muons. In fact, this initial "all electronic" state must be the same as the final "all electronic" state you describe, except with all of the velocities of the electrons and antineutrinos reversed (so that they will evolve into the half and half state).

 

[nikkkom]

Sure, but so what? Again, we aren't talking just about our particular solution. We're talking about all possible solutions.

I am talking about actually observed experimental results.
Physics attempts to explain and predict observed experimental results. The observed experimental results are that there is time asymmetry. Among all possible solutions, we overwhelmingly observe those where muons decay.

It does not matter to me that among all possible solutions, time-reversed ones exist. I don't argue against that. I'm asking why they are not realized 50% of the time, as they naively should be. What is causing that?

 

[PeterDonis]

It does not matter to me that among all possible solutions, time-reversed ones exist. I don't argue against that. I'm asking why they are not realized 50% of the time, as they naively should be.

Because the "naive" expectation is not what you think it is. We don't live in an ensemble of all possible solutions. We live in one particular solution. That particular solution happens to have various time asymmetric properties. So the obvious, "naive" answer to why we observe those time asymmetric properties is that they are the properties of the particular solution we live in.

Even if we want to say that the set of all muon experiments we have run realizes some "ensemble of solutions", rather than one particular solution, we still can't say that that ensemble is fully representative of all of the possible solutions. We don't know what constraints the time asymmetry of the overall global solution we live in puts on the local "solutions" that can be realized in our experiments; and the fact that, so far, all of the laws appear to be time symmetric (except for a few cases in the weak interactions), strongly indicates that the time asymmetry in our experimental results is due to time asymmetry in the initial conditions we can realize.

 

[nikkkom]

We don't know what constraints the time asymmetry of the overall global solution we live in puts on the local "solutions" that can be realized in our experiments;

That's the part I agree with: we don't know why this is happening.

and the fact that, so far, all of the laws appear to be time symmetric (except for a few cases in the weak interactions), strongly indicates that the time asymmetry in our experimental results is due to time asymmetry in the initial conditions we can realize.

This can also indicate that we did not yet discover the time-asymmetric part of the laws of physics.

 

[PeterDonis]

This can also indicate that we did not yet discover the time-asymmetric part of the laws of physics.

Yes, this is possible. But the OP of this thread assumed that the laws are time symmetric, so that is the context I have been using.

 

[timmdeeg]

It seems even more weird to think of a time reversed solution of coalescing black holes emitting gravitational waves thereby or of the time reversed solution of the oxihydrogen reaction.

 

[PeterDonis]

It seems even more weird to think of a time reversed solution of coalescing black holes emitting gravitational waves thereby or of the time reversed solution of the oxihydrogen reaction.

It seems weird to us, yes. But both of these are valid solutions.

 

[Edgar L Owen]

All,

As to the source of the arrow of time a known corollary of relativity is that everything continually moves through combined space and time at the speed of light. Call this the STc Principle or STc for short. This is a fundamental principle that makes relativity much easier to understand. It also solves the arrow of time problem and puts the arrow of time on a firm physical basis produced by relativity itself.

Since STc tells us that everything is continually moving through time at c everything has to be at one and only one position in clock time and moving in one and only one direction.

So a proper understanding of relativity itself solves the arrow of time problem.

The notion of entropy as the source of the arrow of time is incorrect for two obvious reasons. 1. Entropy varies widely throughout the universe and clock time rates have nothing to do with those variations. 2. Entropy states are NOT fundamental because they depend entirely on the prevailing mix of fundamental forces. Eg. the maximum entropy state of a universe of attractive gravity will be the minimum entropy state of a universe of repulsive gravity and vice versa. Therefore entropy states are derivative rather than fundamental, and entropy cannot be the source of the arrow of time.

Edgar

 

[PeterDonis]

everything continually moves through combined space and time at the speed of light.

This is a common pop science statement (Brian Greene likes it, for example), but it's not a good description of the actual physics because it often leads to misconceptions. We've had a number of previous threads here on this (none too recently, though).

Since STc tells us that everything is continually moving through time at c everything has to be at one and only one position in clock time

This is one of the misconceptions. The concept of "clock time" does not apply to lightlike objects (objects like light rays that move on null worldlines, not timelike worldlines). But the actual physics does include lightlike objects, so this interpretation won't work.

Entropy varies widely throughout the universe and clock time rates have nothing to do with those variations.

This doesn't matter; all that matters is that the direction of increasing entropy matches the direction of increasing clock time (for objects moving on timelike worldlines).

Entropy states are NOT fundamental

This doesn't matter either unless you think the arrow of time is fundamental. But we don't know that that is the case. Physical laws don't appear to have any fundamental arrow of time built into them.

the maximum entropy state of a universe of attractive gravity will be the minimum entropy state of a universe of repulsive gravity and vice versa.

What do you mean by "attractive gravity" and "repulsive gravity"?

 

[Edgar L Owen]

Hi Peter,

My understanding is that clock time does apply to photons but that the comoving clocks of photons just have no velocity in time. That's completely consistent with STc since all their combined c spacetime velocity is through space..

The question is whether STc is true or not, not whether it's "pop science". I think the evidence is that it is true and is fundamental.

Any proposal that entropy is the source of the arrow of time must suggest an actual mechanism for why this is true. I know of no possible mechanism. STc does provide a very simple mechanism consistent with relativity itself.

Quantum decoherences do have a fundamental irreversible arrow of time built in and everything actually happens at the quantum level. Only classical level laws are time independent.

Repulsive gravity eg. the cosmological constant. The point is that the measure of entropy depends on the prevailing mix of forces and changes with that mix rather than being fundamental.

Edgar

 

[PeterDonis]

My understanding is that clock time does apply to photons

Your understanding is incorrect. For the concept of "clock time" to apply to photons, you would have to be able to use proper time, i.e., Minkowski "length", as an affine parameter on their worldlines, as you can on timelike worldlines. But you can't, because photon worldlines are null--their Minkowski length is zero.

but that the comoving clocks of photons just have no velocity in time

Again, this is a common pop science notion, but it doesn't work when you actually try to do the math. This notion does not recognize the fundamental physical difference between timelike worldlines and null worldlines. See above.

I think the evidence is that it is true

Please give references (textbooks or peer-reviewed papers) to support this statement. Otherwise it is just your personal opinion and is out of bounds for discussion here at PF. Please review the PF rules.

Any proposal that entropy is the source of the arrow of time must suggest an actual mechanism for why this is true. I know of no possible mechanism.

I described one earlier in this thread: it's due to the time asymmetry of initial conditions.

Quantum decoherences do have a fundamental irreversible arrow of time built in

Reference, please?

Repulsive gravity eg. the cosmological constant.

What do you think the minimum entropy state is in the presence of a cosmological constant? (For example, in a de Sitter universe.) And what do you think the minimum entropy state is in the presence of "attractive gravity" (by which I assume you mean a universe with ordinary matter and energy present).

 

[Edgar L Owen]

Peter,

It's accepted science that quantum processes in which exact decoherence values are randomly chosen from probability distributions are not time reversible to the probability distributions from which they were randomly chosen. And everything actually happens at the quantum level. Therefore it's clear that real world processes are not time reversible. I'm surprised you'd even doubt that.

The maximum entropy state in a purely attractive gravity universe (assuming no other forces and no initial expansion for illustrative simplicity) is a collapse to a single universal black hole. The maximum entropy state in the same universe with only repulsive gravity is an unending expansion and even distribution of all matter. The minimum entropy states are the reverse. If gravity is reversed entropy states reverse. Therefore it's forces not entropy states that are fundamental and entropy can't be the source of the arrow of time because time runs in the same direction in both universes. As I said in a 4 force expanding universe like our own the min and max eventual entropy states are not clear.

Saying that the proper time of photons is zero is completely consistent with light like world lines having zero interval length.

If you think that STc is mathematically inconsistent please explain why.

Edgar

 

[PeterDonis]

It's accepted science that quantum processes in which exact decoherence values are randomly chosen from probability distributions are not time reversible to the probability distributions from which they were randomly chosen.

Yes, I know. But it's also accepted science that quantum mechanics is unitary, and unitary necessarily implies time reversible (because any unitary mapping is one to one and invertible). So you have yourself a conundrum here: either QM is not unitary, or something is missing from your statement above.

AFAIK nobody has come up with a workable way to make a quantum theory that is not unitary. So that leaves option 2. The thing that is missing is that you are looking at probability distributions instead of states. If you look at states, everything is reversible, and entropy increase is a matter of selecting improbable initial conditions (improbable compared to thermal equilibrium).

The maximum entropy state in a purely attractive gravity universe (assuming no other forces and no initial expansion for illustrative simplicity) is a collapse to a single universal black hole.

You are wrong here in two ways. First, "collapse to a single universal black hole" is not a valid description of the Big Crunch singularity that will occur at the end of a universe with attractive gravity which has zero expansion at some moment of time.

Second, while many physicists did believe at one time that a black hole was the maximum entropy state for an isolated static system with attractive gravity (note that such a system cannot be the entire universe), that was before the discovery of Hawking radiation. When you add Hawking radiation to the mix, it turns out that the maximum entropy state for this type of system is Hawking radiation escaping outward to infinity from a black hole that has fully evaporated. (At least, according to our best current understanding; we won't know for sure until we have a full theory of quantum gravity.)

The maximum entropy state in the same universe with only repulsive gravity is an unending expansion and even distribution of all matter.

Remember that here we are talking about de Sitter spacetime; and what you describe here is not the "end state" of that spacetime, it is its state at all times. The apparent "expansion" in this spacetime is actually something of an illusion, caused by a particular choice of time slicing. One can choose another slicing in which the spacetime is static--unchanging with time--at least inside the cosmological horizon.

The minimum entropy states are the reverse.

For de Sitter spacetime, the "reverse" is the same, as noted above. Another way of putting it is that de Sitter spacetime is time symmetric. This is counterintuitive, but true.

For attractive gravity, as noted above, when you add Hawking radiation to the mix the final state turns out to be not much different from the initial state, at least when considering an isolated static system. But we know our universe as a whole is not an isolated static system. So none of this really applies to our universe.

Saying that the proper time of photons is zero is completely consistent with light like world lines having zero interval length.

No, it isn't, because proper time has to be an affine parameter, and one of the requirements for that is that each event on the worldline has to be labeled with a unique value of the parameter. But on a photon's worldline, every event is labeled with the same length number, namely zero. In other words, you can't use the length to distinguish between events on a photon worldline, but you have to be able to do that in order to treat the length as a proper time.

You are coming close to a warning here, since what I have just said is part of the basic mathematical framework of relativity. I strongly suggest that you take a step back and consult some references.

If you think that STc is mathematically inconsistent please explain why.

It's up to you to provide a reference if you think it's mathematically sound and has evidence in its favor. I haven't seen any reference or any math from you on it, so I have nothing to go on.

 

[PeterDonis]

Here is an interesting paper on this topic by Sean Carroll and Jennifer Chen:

https://arxiv.org/pdf/hep-th/0410270v1.pdf

A layman's description of the contents is on his blog here:

http://www.preposterousuniverse.com/blog/2004/10/27/the-arrow-of-time/

But the paper is worth reading since it is not restricted to the specific model he describes in the blog post; it also discusses other more general issues related to this thread's topic.

 

[Edgar L Owen]

Peter,

The unitarity of quantum processes simply means that the sum of all probabilities of an event must equal 1. i don't see why that implies any time reversibility of quantum processes. Please explain.

You say I should look at states rather than probability distributions. But one state follows another via a random choice from the possibilities of the previous. Are you implying quantum choices are not made randomly? If they are I don't see how they are reversible. One can't reasonably consider a succession of states without considering the process that transforms one to the next, and that process is random not deterministic. Therefor I don't see how it could be time reversible.

Re Hawking radiation from a universal black hole. That depends 1. on whether space itself contracts to the size of the universal black hole. One could reasonably suspect that might happen since space originally inflated from essentially no volume after the big bang. 2. If space itself is contracting then eventually there will be nowhere for the Hawking radiation to go and the collapse will be complete.

Thanks for the Sean Carroll link. One question I have re the supposedly minimum entropy state of the immediate post big bang universe is if everything is at essentially the single point space occupied and particles don't even exist yet then how can entropy even be characterized?

But accepting that it was minimal assume that the previous big crunch state was a universal black hole with maximum entropy. Now assume the big bang was a black hole white hole transition in which gravity reversed from attractive to repulsive. In this scenario entropy also reverses and we automatically get both the improbable minimum entropy state of the big bang universe and inflation at the same time. This is of course speculative but this scenario would explain some important things if true.

Edgar

 

[PeterDonis]

The unitarity of quantum processes simply means that the sum of all probabilities of an event must equal 1.

No, it means that the time evolution of quantum states is realized by a unitary operator. (Typically this operator is expressed as $\exp \left( - i \hat{H} t \right)$, where $\hat{H}$ is the Hamiltonian.) Since a unitary operator is one to one and invertible, the time evolution of quantum states is reversible. The sum of all probabilities being 1 is a consequence of this, but it is not the only implication of unitarity.

one state follows another via a random choice from the possibilities of the previous.

No, it doesn't. It follows by a unitary transformation. The random choice only comes in under collapse interpretations, and those are just interpretations. No collapse interpretations, such as the MWI, make all of the same predictions for experimental results.

Re Hawking radiation from a universal black hole.

What do you mean by a "universal black hole"? What mathematical solution of the Einstein Field Equations are you referring to?

That depends 1. on whether space itself contracts to the size of the universal black hole.

If you are talking about a "Big Crunch" in a closed universe here, black holes are not possible in such a universe. Such a universe has no spatial infinity, and black holes--event horizons--are only possible if there is a spatial infinity, since that's how the event horizon is defined.

if everything is at essentially the single point space occupied and particles don't even exist yet

No such state occurs in any models actually used in cosmology. The immediate "post Big Bang" state was a state of hot, dense, rapidly expanding plasma, full of particles. Just before that, while inflation was in progress (in models with inflation, such as Carroll's), was a rapidly expanding state in which the inflaton field was in a "false vacuum" state and no Standard Model particles were present (because all of the other quantum fields were in "true vacuum" states).

how can entropy even be characterized?

The inflaton field is a scalar field (at least in most models, including Carroll's), and the Standard Model fields are spinor and vector fields (except the Higgs, which is scalar). All of these fields have well-defined entropy.

assume that the previous big crunch state was a universal black hole

Again, what do you mean by "a universal black hole"? What mathematical solution of the Einstein Field Equations are you referring to? I'm not aware of any cosmological model that includes anything like this. If it's your own personal model, personal theories are off limits for discussion on PF; you would need to give an acceptable reference (textbook or peer-reviewed paper).

Now assume the big bang was a black hole white hole transition in which gravity reversed from attractive to repulsive.

In the standard white hole (the past singularity of the maximally extended Schwarzschild solution), gravity is attractive, not repulsive. So I don't know what you're talking about here.

 

[julcab12]

Again, what do you mean by "a universal black hole"? What mathematical solution of the Einstein Field Equations are you referring to? I'm not aware of any cosmological model that includes anything like this. If it's your own personal model, personal theories are off limits for discussion on PF; you would need to give an acceptable reference (textbook or peer-reviewed paper).

I think he's referring to the weyl curveture hypothesis were the main assumption is that black hole singulaties i.e initial-final singularities formed in a universal gravitational collapse.. but didn't hold nowadays ( CCC version back in the days ). S=1/4 . kc^3 A/Gℏ-- due to recent discoveries. In fact what we see is that the expansion of the universe is accelerating and that the expansion should continue indefinitely.

"Penrose now believes that at the end of the universe all information will have been destroyed via black hole evaporation. The universe, consisting of nothing but radiation, will then have no concept of time or history, and so will "reset" itself by forgetting about its large entropy content. At that point there will be nothing to distinguish the universe from its pre-Big Bang state. Thus, a new Big Bang will occur, possibly with a different set of fundamental physical constants; then another, and another after that, for all eternity." Quite poetic nonetheless.

In the standard white hole (the past singularity of the maximally extended Schwarzschild solution), gravity is attractive, not repulsive. So I don't know what you're talking about here.

... Maybe the hypothetical Schwarzschild's calculations of negative solution -- square root inside the horizon which is a representation of white hole. In addition, White holes appear in Einstein's field equation specifically in the Einstien Rosen Picture.. It is still hypothetical.

 

[PeterDonis]

I think he's referring to the weyl curveture hypothesis were the main assumption is that black hole singulaties

No, the Weyl curvature hypothesis had to do with initial singularities: the hypothesis was that initial singularities, like the one in idealized FRW spacetimes, should have zero Weyl curvature. It was a way of picking out what spacetime models would be applicable to the universe in cosmology. It had nothing to do with black holes. Nor even with white holes: the white hole singularity in the maximally extended Schwarzschild spacetime has infinite Weyl curvature, not zero, so it can't possibly satisfy the WCH.

Penrose now believes that at the end of the universe all information will have been destroyed via black hole evaporation.

That is not the WCH. It's a separate idea.

Maybe the hypothetical Schwarzschild's calculations of negative solution -- square root inside the horizon which is a representation of white hole.

I don't know what you're talking about here. The mass of the white hole in the maximally extended Schwarzschild spacetime is positive; it's the same as the mass of the black hole (since they're both part of the same solution).

White holes appear in Einstein's field equation specifically in the Einstien Rosen Picture..

That's part of maximally extended Schwarzschild spacetime, yes.

It is still hypothetical.

No, it's unphysical, at least in the opinion of practically all physicists. Real black hole spacetimes do not include the white hole, or the Einstein-Rosen bridge; the presence of the non-vacuum region containing the object that originally collapsed to form the hole makes a big difference.

 

[julcab12]

No, the Weyl curvature hypothesis had to do with initial singularities: the hypothesis was that initial singularities, like the one in idealized FRW spacetimes, should have zero Weyl curvature. It was a way of picking out what spacetime models would be applicable to the universe in cosmology.

Im quoting Penrose Diagram or his assumption of a crunch scenario which is unlikely now.. He assumes the entire history of a closed universe starts from a uniform low entropy BB with Weyl=0 and ends with high entropy Big crunch. representing the congealing of many black holes---with weyl → ∞.

I don't know what you're talking about here. The mass of the white hole in the maximally extended Schwarzschild spacetime is positive; it's the same as the mass of the black hole (since they're both part of the same solution).

.. I am referring to the non real mathematical artifact -- Kruskal–Szekeres coordinates. And yes it is not real. But i ve read somewhere "
A white hole model that fits cosmological observations would have to be the time reverse of a star collapsing to form a black hole. To a good approximation, we could ignore pressure and treat it like a spherical cloud of dust with no internal forces other than gravity. Stellar collapse has been intensively studied since the seminal work of Snyder and Oppenheimer in 1939 and this simple case is well understood. It is possible to construct an exact model of stellar collapse in the absence of pressure by gluing together any FRW solution inside the spherical star and a Schwarzschild solution outside. Spacetime within the star remains homogeneous and isotropic during the collapse.

It follows that the time reversal of this model for a collapsing sphere of dust is indistinguishable from the FRW models if the dust sphere is larger than the observable universe. In other words, we cannot rule out the possibility that the universe is a very large white hole. Only by waiting many billions of years until the edge of the sphere comes into view could we know." -- http://www.math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html

 

[PeterDonis]

A white hole model that fits cosmological observations would have to be the time reverse of a star collapsing to form a black hole.

And we would have to be inside the non-vacuum region occupied by the exploding matter, yes.

we cannot rule out the possibility that the universe is a very large white hole

Not just based on the observation that the universe is expanding and that its matter density appears to be uniform on large scales, no. But the article you quote does not take into account the fact that the expansion is accelerating (it was written in 1997, when that part of our current best-fit cosmological model was still not fully established). There is no way to get accelerating expansion in a white hole model; the expansion in such a model can only decelerate.

 

[Stephen Tashi]

Perhaps the processes that implement our consciousness only have a "forward" direction in time, so we think time goes in that direction because our processes of thought go that way.

As far as we can tell, this isn't the case; the processes that implement our consciousness do not involve any of the particular aspects of the weak interaction that are known to be time asymmetric.

What is the interpretation of "As far as we can tell"? I think you mean that as far as we can imagine a mathematical model of physical processes that implement consciousness, we imagine them to be time symmetric. On the other hand "as far a we can tell" from direct experience, we do distinguish between a past and a future.

 

[PeterDonis]

I think you mean that as far as we can imagine a mathematical model of physical processes that implement consciousness

No, I mean as far as we can tell about the actual physical processes that go on in our brains, they don't involve any of the aspects of weak interactions that are known to be time asymmetric. It's all basically electromagnetism, which is known to be time symmetric.

"as far a we can tell" from direct experience, we do distinguish between a past and a future.

Yes, but that doesn't tell us whether the underlying physical laws are time asymmetric. It just tells us that something is time asymmetric. That something could just as well be the initial conditions.