How is the arrow of time defined?

[hailzeyy]

Physical processes do not require an arrow of time to be defined. Then how does one know for certain that time is unidirectional, that there is a past, present and future?

 

[Chalnoth]

Sean Carroll has written a lot of excellent stuff on this. Short version: it's all about entropy.

He wrote a book on it, "From Eternity to Here: The Quest for the Ultimate Theory of Time," and has a number of videos and essays posted online.

Here's an hour-long talk he gave, for example:


And an FAQ on his blog:
http://blogs.discovermagazine.com/cosmicvariance/2007/12/03/arrow-of-time-faq/

 

[rootone]

Physical processes do not require an arrow of time to be defined. Then how does one know for certain that time is unidirectional, that there is a past, present and future?

Because we don't see the dead arising from their graves, or new born infants being absorbed by their mother.

 

[PeterDonis]

Physical processes do not require an arrow of time to be defined.

This is not quite true. There are some processes involving the weak interaction that are not time symmetric. But it is true that these processes aren't involved in the ordinary everyday observations we make that indicate that there is an arrow of time.

how does one know for certain that time is unidirectional, that there is a past, present and future?

Let me turn this question around: what would your everyday experience be like if time were not unidirectional? The arrow of time is a fact of our everyday experience: we remember the past but anticipate the future. The question is how we explain this everyday fact in terms of our fundamental theories of physics. Our best current explanation is that forming a memory of something requires an increase of entropy, so the events we remember took place when entropy was lower than it is when we retrieve the memory. So the arrow of time we perceiver is the arrow of increasing entropy.

As for how entropy can increase if the physical laws involved are time symmetric, our best current explanation is that it is a matter of initial conditions: our universe started out in a very low entropy state, and entropy has been increasing ever since because that is the natural thing to happen when you start with a low entropy state.

 

[SleepDeprived]

"As for how entropy can increase if the physical laws involved are time symmetric, our best current explanation is that it is a matter of initial conditions: our universe started out in a very low entropy state, and entropy has been increasing ever since because that is the natural thing to happen when you start with a low entropy state."

Does that mean that if another universe started out different than our with respect to its entropy state, it's possible that time can move forward or backward?

 

[Stephen Tashi]

Let me turn this question around: what would your everyday experience be like if time were not unidirectional?

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.

 

[backward]

If somehow time reversed direction and we went into our past (this is different from time travel through closed time like circuit), we would not notice anything strange because as we go back in time our corresponding memory also will be lost. So we will feel exactly like when we were there at that point of time. If time again changes direction and we come back to the present, this will feel exactly as if time had always maintained the same direction.

 

[PeterDonis]

Perhaps the processes that implement our consciousness only have a "forward" direction in time

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.

 

[PeterDonis]

If somehow time reversed direction

Can you describe a way that this could happen, consistent with the laws of physics?

 

[Chalnoth]

This is not quite true. There are some processes involving the weak interaction that are not time symmetric. But it is true that these processes aren't involved in the ordinary everyday observations we make that indicate that there is an arrow of time.

These interactions don't follow T symmetry, but do follow the slightly different CPT symmetry exactly. There is a significant difference between those two symmetries, but it makes no conceptual difference as it relates to the question in the OP. We can say that all known physical laws are exactly time-symmetric just by stating that we mean CPT symmetry rather than T symmetry.

 

[OCR]

If somehow time reversed direction and we went into our past (this is different from time travel through closed time like circuit), we would not notice anything strange because as we go back in time our corresponding memory also will be lost. So we will feel exactly like when we were there at that point of time. If time again changes direction and we come back to the present, this will feel exactly as if time had always maintained the same direction.

There are some ideas, or interpretations... that seem to imply what you stated...
Basically a newer interpretation, here ... of an older one, here .

 

[backward]

Can you describe a way that this could happen, consistent with the laws of physics?

For all we know it may be happening without our knowledge. After all, barring some processes in weak interactions etc there is nothing to prevent time from going backwards.

 

[PeterDonis]

there is nothing to prevent time from going backwards.

You're missing my point. What does "time going backwards" mean? Can you describe a scenario, consistent with the laws of physics, in which "time goes backwards"? It's not enough just to make a vague general statement. You need to give the specifics.

 

[PeterDonis]

There are some ideas, or interpretations... that seem to imply what you stated...

Do they? These interpretations of QM involve "advanced waves", which can be interpreted (if we are willing to tolerate some wiggle room in interpretation) as "waves going backward in time". But the claim backward is making is about "time going backwards". That doesn't seem like the same thing.

 

[backward]

You're missing my point. What does "time going backwards" mean? Can you describe a scenario, consistent with the laws of physics, in which "time goes backwards"? It's not enough just to make a vague general statement. You need to give the specifics.

It means that just as you can and often go back in space cordinates, you go backwards in time coordinate. This is allowed by the laws of Physics with some exceptions. I cannot think of a specific physical process which would trigger time-reversal. So, it is a general statement. Only point I wished to make is that if somehow time reversed direction in our lives, we would fail to notice it.

 

[backward]

For one thing, antiparticles have been interpreted as particles going backwards in time.

 

[Chalnoth]

For one thing, antiparticles have been interpreted as particles going backwards in time.

Well, no. The correct statement is that a matter particle moving forward in time is the equivalent to an anti-matter particle moving backward in time. If you wanted to, you could just as easily describe a matter particle moving backward in time, which would behave like an anti-matter particle moving forward in time.

In other words, this is a statement of symmetry, not a statement about the time direction of any particular particle. In fact, you can reverse the time direction of any microscopic reaction and get a valid reaction (and if you also swap the particles with anti-particles, you're guaranteed to get identical properties of the reversed reaction).

The way to understand the fact that time seems to have a direction is through entropy, not looking at microscopic particles. The Sean Carroll links I posted above do a pretty good job at introducing the subject.

 

[PeterDonis]

It means that just as you can and often go back in space cordinates, you go backwards in time coordinate. This is allowed by the laws of Physics

No, it isn't. That is not what time reversal symmetry means.

Time reversal symmetry means that, if we have a valid solution to the laws of physics that describes some process, then the time reverse of that process is also a valid solution to the laws of physics. For example, one solution to the Newtonian laws of gravity is an object starting from rest at a given height above a large mass and accelerating downward towards the mass. The time reverse of this is an object decelerating upward away from the mass until it comes to rest at a given height. But in both cases, everything goes in the same direction in the time coordinate; nothing in a single solution "turns around" and goes in the opposite direction in the time coordinate.

 

[OCR]

... if we are willing to tolerate some wiggle room ...

Wiggle room? ...wiggle room, really?? ...you're joking!

Ten snakes, all at the same time, could crawl though this mess ! ...

"At the same time" ... is even an interpretation with wiggle room ...

 

[julcab12]

According to them. In QM arrow of time is determined statistically.. In configuration of particles in space, nothing in theory precludes that in the next step -- particles may become arranged in a way which embodies lower entropy. If you look at only that single event in which the entropy of the system has decreased, you will not be able to tell if time was running forward or backwards. ODOH. Entropy-decreasing events are improbable. As particle evolves-- through more and more steps by statistical probability, there are so many more states for which the entropy increases than states for which entropy decreases, so statistically entropy will increase as the system evolves. Its pretty hard to determine by looking at just one change step you may not be able to tell the time’s arrow, but if you keep looking at more and more steps, it will become clear that entropy increases, and that will tell you the actual arrow of time without a doubt.

.. In LQG--In the area of thermodynamical quantities in equilibrium. Dynamics can be expressed as correlations between variables, and does not need a time to be specified.

 

[nikkkom]

It's a really difficult subject.

As I see it, the problem can be formulated as: why when you go forward in time particles have hard time colliding (most of the time they miss), while if you go backward in time they somehow find themselves exactly where they need to be to interact. E.g. muon decay, seen backwards, looks like this: electron and e-antineutrino collide, turn into W-, and this W- magically happens to be just in the right place to collide with a very convenient mu-antineutrino passing by, and turn into muon.

One may say "it's natural for particles to usually miss each other". Well, it looks natural to us only because we are conditioned by all our experience since birth to see exactly this behavior as normal.

Possibly, both behaviors are okay (they are not nonsensical), the "reversed" one only looks weird to us. This is not the difficult question.

The question is, why they are _different_, while laws of physics are _time-symmetric_?

 

[PeterDonis]

The question is, why they are _different_, while laws of physics are _time-symmetric_?

Because the laws being time symmetric is not the same as the individual solutions being time symmetric. Time symmetric laws can have time asymmetric solutions, as long as the solutions occur in pairs that are time reverses of each other. We happen to live in one particular time asymmetric solution, so we consider that kind of time asymmetry as "normal" and the opposite kind, the kind in the time reverse of our solution (which must exist if the laws are time symmetric), to be "weird".

 

[nikkkom]

I know what spontaneous symmetry breaking is :)

This still isn't a satisfactory explanation. With EW symmetry breaking, we have an explanation why vacuum is not symmetric under it: it's easy to read off the Higgs potential that it has a minimum away from zero field state.

No such thing is obvious with time asymmetry.

 

[PeterDonis]

I know what spontaneous symmetry breaking is :)

I wasn't talking about spontaneous symmetry breaking. Our expanding universe is a time asymmetric solution of the laws of GR; there is a corresponding time asymmetric solution describing a contracting universe. Neither one arises by spontaneous symmetry breaking. But they're still a pair of time asymmetric solutions that are time reverses of each other.

 

[nikkkom]

In the GR solution which is a contracting Universe muons would still usually decay, not "spontaneously reconstitute" from electrons and antineutrinos. Time asymmetry would not be reversed.

 

[PeterDonis]

In the GR solution which is a contracting Universe muons would still usually decay, not "spontaneously reconstitute" from electrons and antineutrinos.

Not once the temperature got high enough during the contraction. From the standpoint of GR, we just have a "cosmological fluid" whose proportion of muons relative to electrons and antineutrinos varies with temperature, and the temperature varies with time, and that variation in the contracting solution is the exact time reverse of the variation in the expanding solution.

You could also look at a much more detailed solution that includes QFT as well as GR, so you have to include not just the usual GR description of the matter and radiation present in terms of perfect fluids, but the detailed QFT description of all the fields and their states. Then you would find that there would be a contracting universe solution in which the initial conditions were such that the inverse reaction of electrons + antineutrinos -> muons happened in the exact time reversed way that the forward reaction of muons -> electrons + antineutrinos happens in our expanding solution. Of course this contracting solution would not look "normal" to us, since inverse decay would predominate over decay; but there would also be another contracting solution with different initial conditions, such that the muon decay looked "normal" (muon decay predominating over inverse) in the contracting universe; and there would be an expanding solution that is the time reverse of that one, in which the initial conditions were such that the inverse of muon decay predominated during the expansion, and this expanding solution would not look "normal" to us. But in all of this, the underlying laws are still time symmetric; you just have to look more carefully at what the "time reverse" of a given solution means.

 

[nikkkom]

Not once the temperature got high enough during the contraction. From the standpoint of GR, we just have a "cosmological fluid" whose proportion of muons relative to electrons and antineutrinos varies with temperature, and the temperature varies with time, and that variation in the contracting solution is the exact time reverse of the variation in the expanding solution.

You could also look at a much more detailed solution that includes QFT as well as GR

Actually, I would prefer to have a simpler picture. Namely, to go from GR to SR.

There is no obvious reason to link arrow of time with the expansion of the Universe. Physics in flat Minkowski space, which is time translation invariant, exhibits the same time asymmetry between past and future: muons decay, not reconstitute.

 

[PeterDonis]

There is no obvious reason to link arrow of time with the expansion of the Universe.

I didn't say we had to. In fact the examples I have given show the opposite, that as far as valid solutions of the laws are concerned, there is no reason why the "arrows of time" associated with different processes (expansion vs. muon decay, in my example) must be linked. Any such link (or more properly "correlation") is a property of a particular solution, not of the overall set of solutions.

Physics in flat Minkowski space, which is time translation invariant, exhibits the same time asymmetry between past and future: muons decay, not reconstitute.

In other words, you are now claiming that there is no valid solution of the laws that corresponds to a Minkowski spacetime in which muon decay goes in reverse. Can you back that up with actual math? I strongly doubt it, since you have already said the inverse reaction to muon decay is physically possible.

 

[nikkkom]

In other words, you are now claiming that there is no valid solution of the laws that corresponds to a Minkowski spacetime in which muon decay goes in reverse.

Not at all. I'm just saying that in Minkowski spacetime, for some reason muons far more often decay than "reconstitute", when you go in "future" time direction. Of course they can, and sometimes they do "reconstitute".

 

[PeterDonis]

I'm just saying that in Minkowski spacetime, for some reason muons far more often decay than "reconstitute", when you go in "future" time direction.

And what is your basis for this claim? It can't be based on what we actually observe, because we are not talking about our particular solution of the laws; we are talking about all possible solutions of the laws. So you must be claiming that there is no valid solution of the laws in which muons reconstitute more than they decay in Minkowski spacetime. I am asking if you can back up that claim. Can you?

Perhaps it will help if I describe such a "reconstituting" solution. 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.

The only basis I can see for the claim of yours that I quoted above is to somehow show that the "reconstituting" solution I just described is not a valid solution, without using any time asymmetric laws. Can you?

 

[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.