The Arrow of Time: The Laws of Physics and the Concept of Time Reversal

[A-wal]

I definitely remember reading something official that said the laws of physics don't distinguish between the past and the future. I thinkit might have been A Brief HistoryOf Time. You could run it backwards and it would still work just as well. But now I've thought about it, there's something I can't resolve. Take two objects in space that are static relative to each other. They would gravitate towards each other. Now if time was running backwards then they would be moving away from each other. So gravity would be a repulsive force. But that doesn't work because if time was running backwards on Earth, we would still be pulled towards the planet, not pushed away. In other words it would work in freefall/at rest, but not when accelerating against gravity. How can it be both repulsive and attractive at the same distances?

 

[PeterDonis]

If we want to consider what would happen if time was running backwards, we need to first specify at what time we "start" things running backwards.

Suppose we pick time t = 0, the time at which the two bodies are mutually at rest, to start running time backwards. Then we have to know how, in the original scenario with time running forwards, the objects *got* to the point where they were at rest relative to each other at time t = 0. If they were moving freely, then if we start at some time t << 0 and run time forwards, the two bodies must have been moving *away* from each other, gradually decelerating, until they came to mutual rest at t = 0. So if we run time backwards from t = 0, we will see the objects accelerating *towards* each other--the time reverse of them moving away from each other but decelerating to mutual rest at t = 0.

Or, we could pick some time t >> 0, and run time backwards from there. Then we would see the objects moving away from each other, yes, but they would be *decelerating*, not accelerating, as time ran backwards, until they came to mutual rest at t = 0. And the law of gravitation talks about the *acceleration* of the bodies: it says each body's acceleration vector points towards the other. That is true in the time-reversed scenario just as it is in the time-forward scenario. So there's no problem.

 

[A.T.]

Take two objects in space that are static relative to each other. They would gravitate towards each other.

But do you understand how the properties of the time dimesion cause them to gravitate towards each other? Once you do, you will see that they will gravitate towards each other regardless their individual direction in time. If you stick tape around the neck of a bottle, it is always diverted towards the thicker part of the bottle. It doesn't matter which way around the bottle you stick it.

Now if time was running backwards then they would be moving away from each other.

Depends what you mean by "time" and by "backwards ". You seem to think about reversing the coordinate time (observes time). This is most probably not what the text meant. But if you treat the advance in proper-time as movement along the time dimension then the orientation of that axis is arbitrary. Forwards and backwards in time are just like right and left in space.

 

[Dale]

The http://en.wikipedia.org/wiki/T-symmetry" is actually pretty decent. Gravity is attractive in forward or reverse, as Peter described.

 

[DrGreg]

Film someone throwing a ball high in the air and then catching it when it falls. Then run the film backwards. Ignoring the throw and the catch, while the ball is in the air, can you tell if the film is going forwards or backwards?

 

[A-wal]

Cheers. Freely moving inertia and gravitational drag are interchangeable if you ignore cause and effect? Weird!

 

[Dale]

Huh? What does that mean?

 

[JesseM]

Cheers. Freely moving inertia and gravitational drag are interchangeable if you ignore cause and effect? Weird!

Yeah, what do you mean by "freely moving inertia"? If you throw a ball upwards, it's still accelerating in the downwards direction, since its velocity upwards is continually decreasing as it goes up. And if all collisions are perfectly elastic (ignoring the fact that some kinetic energy is converted to heat in collisions, which increases entropy and is thus statistically unlikely to happen in reverse, though not forbidden by the fundamental laws of physics) then a ball falling down from a certain height will bounce against the Earth and go back up to exactly the same height, then fall and bounce over and over forever in a way that looks the same backwards as forwards.

A basic rule of thumb is that any time a given process would seem bizarre or unlikely in reverse, it's because the process involves an increase in entropy, so it's really the second law of thermodynamics that makes it unlikely in reverse (and the second law of thermodynamics is itself thought to trace back to the low-entropy initial conditions of the universe immediately after the Big Bang, the reason for which is still not well-understood although there are a few hypotheses).

 

[A-wal]

Huh? What does that mean?

It means I worded it badly. I meant that if you reverse the situation of two objects moving away from each other under their own inertia while slowing down due to gravity and then moving towards each other, then reverse it and inertia > gravity before t0 before it's reversed and gravity > inertia "before" t0 after it's reversed.

 

[atyy]

It means I worded it badly. I meant that if you reverse the situation of two objects moving away from each other under their own inertia while slowing down due to gravity and then moving towards each other, then reverse it and inertia > gravity before t0 before it's reversed and gravity > inertia "before" t0 after it's reversed.

When people say if a situation satisfies Newton's laws, then its time reverse also satisfies Newton's laws, that is a little sloppy, and maybe that's confusing you here. The less sloppy statement is that if a situation satisfies Newton's laws, then a situation in which time AND the momenta of all the particles are reversed will also satisfy Newton's laws.

 

[Saw]

The less sloppy statement is that if a situation satisfies Newton's laws, then a situation in which time AND the momenta of all the particles are reversed will also satisfy Newton's laws.

And, well, Atyy, an even less sloppy statement would be that if the momentum (m•v) of a particle changes, it is because it has suffered an interaction that has changed its velocity. If, in particular, the direction has been reversed, then you’ll get the same phenomenon in opposite direction. Full stop. You don’t need to add that the direction of time has been reversed.

Because… if you do, what does it mean? You know, concepts are created to play some function. The concept of “time reversal”, which function does it play? If I say that in this experiment time is still flowing forwards, that is useful: I convey the idea that, while we made it, all processes in the rest of the universe kept happening and will be shaped by the nature of their corresponding interactions. But if you say that in our simple experiment, “time has reversed”, what does that mean? May it be that just because our ball bounced off the floor (its velocity changed), I may also be growing younger?

Well, this is a truism, but just because it is, let’s not forget what it means. If the concept of “time reversal” only means that the effects of any interaction in a system can be undone by applying another interaction that restores things to the original state of the system, I would rather call it “effects reversal”.

“Time reversal”, in my opinion, is just a way to thrill and prepare the reader for more exciting emotions like “time travel”, but that’s another story…

 

[atyy]

And, well, Atyy, an even less sloppy statement would be that if the momentum (m•v) of a particle changes, it is because it has suffered an interaction that has changed its velocity. If, in particular, the direction has been reversed, then you’ll get the same phenomenon in opposite direction. Full stop. You don’t need to add that the direction of time has been reversed.

Law of physics in forward time: F=dp/dt

Same law with reverse time and momentum: F=[d(-p)/d(-t)]=dp/dt

Reverse momentum without reversing time: F=[d(-p)]/dt
Gravity has become repulsive: -F=dp/dt

 

[atyy]

“Time reversal”, in my opinion, is just a way to thrill and prepare the reader for more exciting emotions like “time travel”, but that’s another story…

F=-dp/dt would not be stay the same under time and momentum reversal if F also contained p. For example there is no time reversal in the presence of friction F=kp, where k is a constant and p is the momentum of the body.

If there is friction and F=kp, then energy is not conserved. This is the cheater's way of showing that time reversal is related to conservation of energy.

It also means that although we see lack of time reversal, ie there is friction in everyday life - as far as we know, there is no friction at a fundamental level. The existence of friction in everyday life is related to the second law of thermodynamics. This means that the second law of thermodynamics is not "fundamental", but is somehow related to our inability to follow the motion of all fundamental particles.

 

[Dale]

Time reversal is not as confusing as some of the last few posters make it out to be. Many quantities of physics involve time, some involve even powers of time (force, acceleration, energy) some involve odd powers of time (velocity, momentum). When we say something like "Newton's laws are time reverse symmetric" it simply means that they only involve even powers of time. This, in turn, means that for any system which obeys Newton's laws, the time reversed system (playing the movie backwards) also obeys Newton's laws. It has nothing to do with time travel.

 

[A-wal]

This is what I'm talking about:

If we want to consider what would happen if time was running backwards, we need to first specify at what time we "start" things running backwards.

Suppose we pick time t = 0, the time at which the two bodies are mutually at rest, to start running time backwards. Then we have to know how, in the original scenario with time running forwards, the objects *got* to the point where they were at rest relative to each other at time t = 0. If they were moving freely, then if we start at some time t << 0 and run time forwards, the two bodies must have been moving *away* from each other, gradually decelerating, until they came to mutual rest at t = 0. So if we run time backwards from t = 0, we will see the objects accelerating *towards* each other--the time reverse of them moving away from each other but decelerating to mutual rest at t = 0.

Or, we could pick some time t >> 0, and run time backwards from there. Then we would see the objects moving away from each other, yes, but they would be *decelerating*, not accelerating, as time ran backwards, until they came to mutual rest at t = 0. And the law of gravitation talks about the *acceleration* of the bodies: it says each body's acceleration vector points towards the other. That is true in the time-reversed scenario just as it is in the time-forward scenario. So there's no problem.

That's why it's still attractive when it's time reversed in free-fall/at rest as well as when you're accelerating against gravity like on Earth. You all keep saying Newtons laws. Does that mean it doesn't work in general relativity under extreme gravity?

 

[atyy]

Time reversal is not as confusing as some of the last few posters make it out to be. Many quantities of physics involve time, some involve even powers of time (force, acceleration, energy) some involve odd powers of time (velocity, momentum). When we say something like "Newton's laws are time reverse symmetric" it simply means that they only involve even powers of time. This, in turn, means that for any system which obeys Newton's laws, the time reversed system (playing the movie backwards) also obeys Newton's laws. It has nothing to do with time travel.

I hope this is equivalent to what I said? Newton's laws can be a second order differential equation or two first order differential equations, and in both cases initial (or final) conditions on position and momentum are needed. In time reversal, the final conditions become initial conditions, and the momentum initial condition gets reversed by definition of time reversal. I thought A-wal was confused by forgetting to reverse the momentum initial condition. In any case, A-wal seems to have understood PeterDonis's point.

This is what I'm talking about:That's why it's still attractive when it's time reversed in free-fall/at rest as well as when you're accelerating against gravity like on Earth. You all keep saying Newtons laws. Does that mean it doesn't work in general relativity under extreme gravity?

There is no arrow of time in general relativity either. In physics, the only arrow of time comes from the second law of thermodynamics (with a small caveat on the weak interactions) which says that the change in entropy is *monotonic* in time. By convention, the direction in which entropy increases is called the future.

 

[Saw]

Time reversal (...) has nothing to do with time travel.

I cannot but agree with it. Could you please tell Brian Greene and David Deutsch and dozens of clever physicists about that?

 

[PeterDonis]

This is what I'm talking about:That's why it's still attractive when it's time reversed in free-fall/at rest as well as when you're accelerating against gravity like on Earth. You all keep saying Newtons laws. Does that mean it doesn't work in general relativity under extreme gravity?

It works the same way in GR. You'll note that my explanation, which you quoted, didn't specify a particular set of laws; I just described what would be observed (and for the case I was describing, Newton's Laws and GR give the same answer, since the Earth's gravity is so weak that the GR corrections to Newton's Laws are negligible).

 

[PeterDonis]

...for the case I was describing, Newton's Laws and GR give the same answer, since the Earth's gravity is so weak that the GR corrections to Newton's Laws are negligible.

Oops -- I was getting muddled. The OP's scenario, which I described, starts with two objects at rest relative to each other in empty space, so the Earth's gravity doesn't come into it, just the gravity of the objects themselves. The predicted behavior of the objects under GR vs. under Newton's Laws would still be pretty similar, but I can't say for certain that all of the GR corrections would be negligible. In any case, the basic principle about time reversal does hold in GR.

 

[Dale]

I cannot but agree with it. Could you please tell Brian Greene and David Deutsch and dozens of clever physicists about that?

Sure, next time I talk to them I will mention it.

 

[JesseM]

I cannot but agree with it. Could you please tell Brian Greene and David Deutsch and dozens of clever physicists about that?

I've read plenty of Brian Greene and David Deutsch and I've never seen them equating time reversal symmetry with time travel, although they do both discuss the possibility of time travel separately since certain solutions in GR allow closed timelike curves (for example, the Godel metric and traversable wormholes). If you think they have equated the two at some point, could you give a quote from one of their books?

 

[Dale]

You all keep saying Newtons laws. Does that mean it doesn't work in general relativity under extreme gravity?

GR and SR are also time-reverse symmetric. Thermodynamics is not time-reverse symmetric, nor is the standard model where time-reverse asymmetry is usually called a "CP-violation" and is usually associated with the weak nuclear force.

 

[Saw]

I've read plenty of Brian Greene and David Deutsch and I've never seen them equating time reversal symmetry with time travel, although they do both discuss the possibility of time travel separately since certain solutions in GR allow closed timelike curves (for example, the Godel metric and traversable wormholes). If you think they have equated the two at some point, could you give a quote from one of their books?

Actually, I didn’t say they “equate” the two things. I said:

“Time reversal”, in my opinion, is just a way to thrill and prepare the reader for more exciting emotions like “time travel”, but that’s another story…

It appears that “time reversal” is not only that. Posts above point out that the concept does have other useful functions, which I accept. I was mistaken in that respect. What remains, then, is whether some authors use “time reversal” as a theoretical background to later introduce and make it easier to swallow the idea of “time travel”.

As to whether BG and DD, in particular, make that connection:

- DD in The Fabric of Reality, Penguin books, dedicates Chapter 11 to demolishing the idea that “time flows”. In the course of this discussion, he occasionally leans on the “time-reversibility property of the laws of quantum physics” (page 283). As a conclusion of the Chapter and as a way to link with the following one (Chapter 12, titled “Time travel”), he says “Time travel may or may not be feasible, but we already have a reasonably good theoretical understanding of what it would be like if it were (…)”. It is true, however, that his main argument seems to be that different universes (his “multiverse”, as purportedly required by quantum phenomena) are different times. For the rest, I do not understand the text really well. If you do, I’d like to hear your view. But maybe this is off-topic and off-forum. Where could that be discussed? QM forum?

- My apologies to BG. He deals with the time symmetry of the laws of physics in Chapter 5 of The Fabric of he Cosmos and with time travel in Chapter 15. But he makes no express connection between the two things. On the contrary, in page 145 he makes the sensible comment that the expression “time reversal” might be better worded as “event order reversal”, i.e., reversal of events happening “in time”.

Anyhow, for a comment in the line of the one I made but without my mistake, see http://discovermagazine.com/1992/oct/timereversal140.

 

[A-wal]

I just want to check I've got this right. It's a bit off topic but still concerning time. Black holes when viewed from the outside have an event horizon where time stops. But the closer you get to the black hole, the smaller it becomes because of length contraction. Someone who is approaching a black hole will see the event horizon retreat towards the singularity until the singularity's all that left. You could ague that the event horizon is the edge of the singularity then? I heard relative velocity effects the size of the horizon? Presumably it makes it smaller the faster your moving? Then an object in motion relative to the black hole could move into the event horizon and come out of it again from the perspective of someone who's at rest relative to the black hole? That doesn't sound right! They'd have to be further away of course so maybe the object flying past would look further away because of length contraction and therefore be outside the horizon? I must be close.

(and the second law of thermodynamics is itself thought to trace back to the low-entropy initial conditions of the universe immediately after the Big Bang, the reason for which is still not well-understood although there are a few hypotheses).

Sounds interesting. What are they?

 

[Austin0]

Hi It appears to me that all physical processes are inherently irreversible.
The negatively entropic process of the formation of the egg , is just as irreversible as the positively entropic process of its smashing on the ground.
That all motion is irreversible . To reverse the motion of a single particle in any meaningful sense would require reversing the motion of every particle in the universe.
The arrow of motion moves inexorably forward.

As the poet put it

" The moving finger writes and having writ moves on..."

 

[atyy]

Hi It appears to me that all physical processes are inherently irreversible.
The negatively entropic process of the formation of the egg , is just as irreversible as the positively entropic process of its smashing on the ground.
That all motion is irreversible . To reverse the motion of a single particle in any meaningful sense would require reversing the motion of every particle in the universe.
The arrow of motion moves inexorably forward.

As the poet put it

" The moving finger writes and having writ moves on..."

Yes, but the arrow of time is usually differently defined. An egg forming and an egg unforming - both would require reversing equal numbers of particles to reverse. The thermodynamic arrow is that we only see one of the two processes.

 

[JesseM]

Actually, I didn’t say they “equate” the two things.

OK, but you suggested they made a connection between the two, responding to DaleSpam's comment that "Time reversal (...) has nothing to do with time travel" by asking someone to tell Deutsch and Greene that, as if they were saying time reversal symmetry does have to do with time travel.

As to whether BG and DD, in particular, make that connection:

- DD in The Fabric of Reality, Penguin books, dedicates Chapter 11 to demolishing the idea that “time flows”. In the course of this discussion, he occasionally leans on the “time-reversibility property of the laws of quantum physics” (page 283). As a conclusion of the Chapter and as a way to link with the following one (Chapter 12, titled “Time travel”), he says “Time travel may or may not be feasible, but we already have a reasonably good theoretical understanding of what it would be like if it were (…)”.

This is just saying that time-reversal symmetry can be seen to support the philosophical view known as eternalism, where spacetime is viewed as a whole with time as just a dimension in spacetime and every event in it equally real, no preferred set of events in "the present" which is flowing forward as in presentism (the relativity of simultaneity is also often taken to support eternalism over presentism). And eternalism may make the idea of time travel easier to understand, since there is no objective sense in which the past has "ceased to exist", it's just that historical events are at a different position in spacetime than we (the ones remembering them) are. But there's no way that believing in eternalism suggests we should believe time travel is possible; that depends on whether the laws of physics allow it, as Deutsch says in chapter 12:

Taken literally, Einstein's equations predict that travel into the past would be possible in the vicinity of massive, spinning objects, such as black holes, if they spun fast enough, and in certain other situations. But many physicists doubt that these predictions are realistic. No sufficiently rapidly spinning black holes are known, and it has been argued (inconclusively) that it may be impossible to spin one up artificially, because any rapidly spinning material that one fired in might be thrown off and be unable to enter the black hole. The sceptics may be right, but in so far as their reluctance to accept the possibility of time travel is rooted in a belief that it leads to paradoxes, it is unjustified.

Even when Einstein's equations have been more fully understood, they will not provide conclusive answers on the subject of time travel. The general theory of relativity predates quantum theory and is not wholly compatible with it. No one has yet succeeded in formulating a satisfactory quantum version — a quantum theory of gravity. Yet, from the arguments I have given, quantum effects would be dominant in time-travelling situations. Typical candidate versions of a quantum theory of gravity not only allow past-directed connections to exist in the multiverse, they predict that such connections are continually forming and breaking spontaneously. This is happening throughout space and time, but only on a sub-microscopic scale. The typical pathway formed by these effects is about 10^–35 metres across, remains open for one Planck time (about 10^–43 seconds), and therefore reaches only about one Planck time into the past.

Future-directed time travel, which essentially requires only efficient rockets, is on the moderately distant but confidently foreseeable technological horizon. Past-directed time travel, which requires the manipulation of black holes, or some similarly violent gravitational disruption of the fabric of space and time, will be practicable only in the remote future, if at all. At present we know of nothing in the laws of physics that rules out past-directed time travel; on the contrary, they make it plausible that time travel is possible. Future discoveries in fundamental physics may change this. It may be discovered that quantum fluctuations in space and time become overwhelmingly strong near time machines, and effectively seal off their entrances (Stephen Hawking, for one, has argued that some calculations of his make this likely, but his argument is inconclusive). Or some hitherto unknown phenomenon may rule out past-directed time travel — or provide a new and easier method of achieving it. One cannot predict the future growth of knowledge. But if the future development of fundamental physics continues to allow time travel in principle, then its practical attainment will surely become a mere technological problem that will eventually be solved.

It is true, however, that his main argument seems to be that different universes (his “multiverse”, as purportedly required by quantum phenomena) are different times. For the rest, I do not understand the text really well. If you do, I’d like to hear your view. But maybe this is off-topic and off-forum. Where could that be discussed? QM forum?

Yes, much of the book is about the many-worlds interpretation of quantum mechanics which I only have a rough conceptual understanding of, I don't really understand the part about other universes being equivalent to other times...the QM forum would be a good place to ask about this.

- My apologies to BG. He deals with the time symmetry of the laws of physics in Chapter 5 of The Fabric of he Cosmos and with time travel in Chapter 15. But he makes no express connection between the two things. On the contrary, in page 145 he makes the sensible comment that the expression “time reversal” might be better worded as “event order reversal”, i.e., reversal of events happening “in time”.

A good way of thinking about time reversal symmetry is that if you take a movie of a system and play it backwards, there should be nothing in the fundamental laws of physics that prevents the existence of a separate system which, when viewed in the normal forward direction of time, behaves precisely like the reversed movie of the first system. In the Standard Model of quantum mechanics, time-reversal symmetry is replaced by charge-parity-time symmetry, which basically means that if you take a movie of a system and play it backwards while also reversing the labels of particles and antiparticles (relabeling each electron in the original system as a positron in the reversed movie, for example) and taking the mirror image of the movie along all three spatial axes (flipping left for right and up for down and forward for backward), then the resulting backward/relabeled/flipped movie should describe a physically allowable forward time-evolution for a different system.

 

[JesseM]

Hi It appears to me that all physical processes are inherently irreversible.
The negatively entropic process of the formation of the egg , is just as irreversible as the positively entropic process of its smashing on the ground.
That all motion is irreversible . To reverse the motion of a single particle in any meaningful sense would require reversing the motion of every particle in the universe.
The arrow of motion moves inexorably forward.

As I said in my previous post, time reversal symmetry doesn't mean actually reversing the motion of the particles that make up a given system, it just means that there is nothing in the fundamental laws of physics to forbid a separate system whose forward behavior exactly resembles the first system's backward behavior (and time-reversal symmetry also says nothing about the practicality of intentionally creating such a system, it just says that the laws of physics don't make such a thing absolutely impossible, as is true of macroscopic reversals of the second law which are extremely improbable statistically but not forbidden by the laws of physics).

 

[JesseM]

I just want to check I've got this right. It's a bit off topic but still concerning time. Black holes when viewed from the outside have an event horizon where time stops. But the closer you get to the black hole, the smaller it becomes because of length contraction. Someone who is approaching a black hole will see the event horizon retreat towards the singularity until the singularity's all that left.

No, that's not true at all--if you know where the event horizon is located, then you can know you've crossed it at some finite value of your own proper time, prior to the time you get crushed by the singularity (likewise if some light is suspended right on the horizon, there will be some finite value of your proper time when you detect that light). Where did you get this idea about length contraction?

Sounds interesting. What are they?

The most popular ones have to do with the idea of our universe having "inflated" from a tiny region of some preexisting universe (which could itself have inflated from a small region of an earlier one and so forth, the idea of eternal inflation), and because the inflated region is much larger than the original tiny region it expanded from, an original tiny region whose entropy is not too much lower than the maximum entropy for a region of that size (so it can plausibly arise as a random statistical fluctuation) can give rise to a large region with fantastically low entropy for its new size (despite this, the inflationary process would apparently nevertheless represent an increase in entropy for the combined system of the previous universe and the newly inflated universe). Here's a quote on this from Brian Greene, p. 318 of his book Fabric of the Cosmos:

Although we don't have an unassailable understanding of what the universe was like during such a preinflationary era, let's see how far we can get if we assume that things were in a thoroughly ordinary, high-entropy state. Specifically, let's imagine that primordial, preinflationary space was riddled with warps and bumps, and that the inflaton field was also highly disordered, its value jumping to and fro like the frog in the hot metal bowl.

Now, just as you can expect that if you patiently play a fair slot machine, sooner or later the randomly spinning dials will land on triple diamonds, we expect that sooner or later a chance fluctuation within this highly energetic, turbulent arena of the primordial universe will cause the inflaton field's value to jump to the correct, uniform value in some small nugget of space, initiating an outward burst of inflationary expansion. As explained in the previous section, calculations show that the nugget of space need only have been tiny--on the order of 10^-26 centimeters across--for the ensuing cosmological expansion (inflationary expansion followed by standard big bang expansion) to have stretched it larger than the universe we see today. Thus, rather than assuming or simply declaring that conditions in the early universe were right for inflationary expansion to take place, in this way of thinking about things an ultramicroscopic fluctuation weighing a mere twenty pounds, occurring within an ordinary, unremarkable environment of disorder, gave rise to the necessary conditions.

What's more, just as the slot machine will also generate a wide variety of nonwinning results, in other regions of primordial space other kinds of inflaton fluctuations would also have happened. In most, the fluctuation wouldn't have had the right value or have been sufficiently unoform for inflationary expansion to occur. (Even in a region that's a mere 10^-26 centimeters across, a field's value can vary wildly.) ... Remember from Chapter 6 that Boltzmann suggested that everything we now see arose as a rare but every so often expectable fluctuation from total disorder. The problem with Boltzmann's original formulation, though, was that it could not explain why the chance fluctuation had gone so far overboard and produced a universe hugely more ordered than it would need to be even to support life as we know it. ... The tremendous advantage of the inflationary incarnation of Boltzmann's idea is that a small fluctuation early on--a modest jump to the favorable conditions, within a tiny nugget of space--inevitably yields the huge and ordered universe that we are aware of ... A jump to lower entropy within a tiny nugget of space was leveraged by inflationary expansion into the vast reaches of the cosmos.

Sean Carroll and Jennifer Chen proposed an interesting variation on this idea where we "start" from a generic spacetime called a "de sitter vacuum", then project its dynamics both forward and backward in time (in order to both predict its future state and 'retrodict' its past state), and they argue that we'd find inflating regions giving rise to new universes in both the forward and backward direction, with the entropy of the 'multiverse' as a whole increasing eternally in both directions with no upper bound. Carroll gives a short explanation of the idea in this entry from his old blog (he's currently part of a group blog called cosmic variance), with the original paper where he and Chen proposed the theory available here, and an easier-to-read essay on the theory written as an entry for the ""Gravity Research Foundation Essay Competition" being available here.

 

[A-wal]

I read somewhere that an observer moving towards a black hole would never reach the event horizon until they reached the singularity. I thought it was here but maybe not. It stuck in my mind because I've never heard that before and it did kind of seem to make sense for the event horizon to be relative and not a fixed radius. Is that not right then? What about for an observer moving quickly past the black hole? Surly length contraction would mean that the event horizon moves inwards as you approach it and move into a stronger gravitational field? Isn't it the equivalent of how you can go faster than light from the perspective of the distance in your original frame? So you can escape the event horizon using it's radius from another frame but that frame will see you as outside the event horizon in the same way as your original frame won't see you moving faster than c?

Interesting thought about a “blown up singularity”: The biggest thing in the universe is the big bang singularity because it covers the edge of the entire universe :)

Friction isn't time reversible. Is that because if it's run backwards friction would still cause it to heat up rather than cool down, or am I oversimplifying?

Thanks for the info and links on inflation.

 

[Saw]

(…) time-reversal symmetry can be seen to support the philosophical view known as eternalism, where spacetime is viewed as a whole with time as just a dimension in spacetime and every event in it equally real, no preferred set of events in "the present" which is flowing forward as in presentism (the relativity of simultaneity is also often taken to support eternalism over presentism). And eternalism may make the idea of time travel easier to understand, since there is no objective sense in which the past has "ceased to exist", it's just that historical events are at a different position in spacetime than we (the ones remembering them) are. But there's no way that believing in eternalism suggests we should believe time travel is possible; that depends on whether the laws of physics allow it, as Deutsch says in chapter 12 (…).

Well, that’s what I meant when I said that time-reversal symmetry (TRS) is sometimes used as a way to “prepare the reader’s mind to accept time travel” (TT). It’s not that the authors who reason that way think that one thing inexorably leads to the other, but they do suggest that the former is a pre-condition for the latter: just by having TRS you do not get TT, but if you do have TRS then it’s “easier to understand that” some other phenomena (eg: wormholes) make TT possible. One could put it this way: TRS is not the only law of physics that is necessary to discuss on TT, but it’s one of the laws of physics that make the very discussion about it intellectually acceptable. The same would apply to the relativity of simultaneity.

A good way of thinking about time reversal symmetry is that if you take a movie of a system and play it backwards, there should be nothing in the fundamental laws of physics that prevents the existence of a separate system which, when viewed in the normal forward direction of time, behaves precisely like the reversed movie of the first system. In the Standard Model of quantum mechanics, time-reversal symmetry is replaced by charge-parity-time symmetry, which basically means that if you take a movie of a system and play it backwards while also reversing the labels of particles and antiparticles (relabeling each electron in the original system as a positron in the reversed movie, for example) and taking the mirror image of the movie along all three spatial axes (flipping left for right and up for down and forward for backward), then the resulting backward/relabeled/flipped movie should describe a physically allowable forward time-evolution for a different system.

I agree with this definition. But if TRS means only this, then we would be obstructing the logical path for making the above mentioned connection with TT. I mean, with this definition, the result of TRS is always new events, which have happened later, in a subsequent time. However, those who make the (weak) connection mentioned above between TRS and TT suggest that the same original past events, thanks to TT (eg: wormholes) are recovered and this is easier to understand in the light of the eternalism somehow supported by TRS, because those events have “not ceased to exist”, they are somewhere waiting for us in the “block universe”, even if (to avoid damage to causality) we have to place this “somewhere” in another world or universe. But this TRS that supports eternalism that supports TT, isn't it another TRS having nothing to do with your precise definition?

 

[Austin0]

Yes, but the arrow of time is usually differently defined. An egg forming and an egg unforming - both would require reversing equal numbers of particles to reverse. The thermodynamic arrow is that we only see one of the two processes.

I assume you are talking about entropy as it is applied in thermodynamics and not that the breaking egg is the reverse of the forming egg.
There is no question that as it applies in that context, it is a valuable and valid concept which provides clearly defined parameters and quantified measurements within limited or closed systems.
But taken out of that realm and applied to the universe as a closed system
do you think the principle or parameters are as clearly defined?
From what I have read it seems to rest largely on interpretations and assumptions regarding the ultimate fate and original beginning of the system.
You have an expanding mass of gas , clearly increasing entropy. In fact a classical example. Then at a point in time gravity becomes the dominant factor and the volume begins to decrease , an apparent increase in both organization,differentiation and the potential for the release of energy .
So how do you interpret this?? It would appear to be comparable to the classically negatively entropic process of creating thermal or pressure differentials in a system.
Yet I have read interpretations of this as as being positively entropic.
?
To me the universe appears to be in a state of entropic flux with the arrow pointing all over the place depending on local conditions . What is the entropy of a black hole?

 

[Dale]

Austin0, everyone agrees that the laws of thermodynamics are not time-reverse symmetric. That is why everyone was so careful to say "Newtons laws" etc. above, in order to specify that we were only talking about laws of physics that are time-reverse symmetric.

The fact that thermodynamics is not time-reverse symmetric does not change the fact that a planet orbiting clockwise is every bit as valid a solution to Newtons laws as a planet orbiting counterclockwise and that one is the time-reverse of the other. You do not have to reverse the course of the entire universe in order to be able to clearly state that Newton's laws are time reverse symmetric.

 

[JesseM]

I You have an expanding mass of gas , clearly increasing entropy. In fact a classical example. Then at a point in time gravity becomes the dominant factor and the volume begins to decrease , an apparent increase in both organization,differentiation and the potential for the release of energy .
So how do you interpret this?? It would appear to be comparable to the classically negatively entropic process of creating thermal or pressure differentials in a system.
Yet I have read interpretations of this as as being positively entropic.
?

For one thing you have to take into account that as a cloud of gas contracts under its own gravity, the potential energy of all the particles decreases and is converted into kinetic energy, which means that even though there is a smaller range of available position-states, there is a higher range of available momentum-states--and the "entropy" of a given macroscopic state is determined by the total number of precise microscopic states compatible with that macroscopic states, with each distinct microscopic state corresponding to a precise specification of each particle's position and momentum (although in quantum mechanics the precision is limited by the uncertainty principle).

It turns out, though, that the increase in available momentum states as a cloud contracts is not sufficient to explain how the contraction can represent an overall increase in entropy--John Baez discusses this in detail on this page. He gives a hint about the true answer here, I think I remember someone saying that a fair amount of the energy lost as the gas cloud collapses is converted into photons (or just electromagnetic waves if we're talking about classical physics), so that the entropy of the collapsed cloud plus the photons is higher than the entropy of the original diffuse cloud. If that's not what Baez meant by the hint, though, someone please correct me!

 

[JesseM]

Austin0, everyone agrees that the laws of thermodynamics are not time-reverse symmetric. That is why everyone was so careful to say "Newtons laws" etc. above, in order to specify that we were only talking about laws of physics that are time-reverse symmetric.

The fact that thermodynamics is not time-reverse symmetric does not change the fact that a planet orbiting clockwise is every bit as valid a solution to Newtons laws as a planet orbiting counterclockwise and that one is the time-reverse of the other. You do not have to reverse the course of the entire universe in order to be able to clearly state that Newton's laws are time reverse symmetric.

To say the laws of thermodynamics are not time-reverse symmetric is potentially a little misleading though--after all the laws of thermodynamics are directly derived from more fundamental laws in statistical mechanics, and those laws are themselves time-symmetric (or CPT-symmetric in QM). It might be more clear to specify that if you impose a low-entropy boundary condition on the beginning of the universe (or on the initial state of the system for whatever time window you wish to study), while placing no such low-entropy boundary condition on the future, then entropy will tend to increase as predicted by the second law. However, if you chose the initial conditions of a system randomly from the set of all possible microstates available to the system, then in this case thermodynamics would be totally time-symmetric--the probability of seeing a given decrease in entropy would be exactly the same as seeing the probability of an increase in entropy by the same amount (because although it's unlikely that a system starting out at some high entropy E will spontaneously decrease to lower entropy E', it's equally unlikely that a randomly-chosen initial state would happen to have an entropy as low as E' in the first place!). And if you choose a low-entropy boundary condition for a system's final future state and then "retrodict" its earlier history using the same time-symmetric laws, in this case the second law would work backwards, with decreases in entropy being much more likely than increases.

 

[Dale]

To say the laws of thermodynamics are not time-reverse symmetric is potentially a little misleading though

dS/dt > 0 is not time-reverse symmetric, no if's and's or but's. Thermodynamics may not be a "fundamental law", but its equations are clearly and unambiguously not time-reverse symmetric.

 

[PeterDonis]

dS/dt > 0 is not time-reverse symmetric, no if's and's or but's. Thermodynamics may not be a "fundamental law", but its equations are clearly and unambiguously not time-reverse symmetric.

Yes, but JesseM is correct that the *reason* we observe that law to hold is not any asymmetry in the fundamental laws. It's just that our past has a low-entropy boundary condition--the universe we live in started out in a very low entropy state--whereas our future does not.

As for *why* we impose that low-entropy boundary condition on our past, it looks like that has already been discussed in these forums--see https://www.physicsforums.com/showthread.php?t=48076".

 

[JesseM]

dS/dt > 0 is not time-reverse symmetric, no if's and's or but's. Thermodynamics may not be a "fundamental law", but its equations are clearly and unambiguously not time-reverse symmetric.

Are you talking about thermodynamics or statistical mechanics though? In statistical mechanics, if you pick a microstate randomly from a system's phase space and it happens to be a low-entropy one, then if you use the dynamical laws to project it forwards it's very likely to be in a higher-entropy state in the future, but it's equally true that if you use the dynamical laws to project it backwards and find the state at earlier times, it's very likely to have been in a higher entropy-state in the past too (and for a large system, very likely means overwhelmingly likely). So without any special choice of early boundary conditions, statistical mechanics is totally time-symmetric in this sense.

 

[Dale]

I am talking about thermodynamics. But the point remains that not all laws of physics are time reverse symmetric. Newtons laws are, as are GR and SR. Thermodynamics and the standard model are not. You can also do the same analysis for other laws of physics regardless of if they are a fundamental law, for example, Ohm's law is not time reverse symmetric, but Hooke's law is. You don't need to go to first principles, you can simply look at the equations and the quantities associated with each law and determine the symmetry.

 

[JesseM]

I am talking about thermodynamics. But the point remains that not all laws of physics are time reverse symmetric. Newtons laws are, as are GR and SR. Thermodynamics and the standard model are not. You can also do the same analysis for other laws of physics regardless of if they are a fundamental law, for example, Ohm's law is not time reverse symmetric, but Hooke's law is. You don't need to go to first principles, you can simply look at the equations and the quantities associated with each law and determine the symmetry.

Agreed, but I think it is a good thing to know that all fundamental laws are believed to be either T-symmetric or CPT-symmetric (and violations of T-symmetry in a CPT-symmetric theory like the Standard Model only crop up in certain esoteric areas of particle physics), so any time you have a non-fundamental law which is not time-symmetric, you can bet that the reason for it has to do with the fact that this approximate law is dealing with a situation where entropy is increasing, so that it's just a special case of the asymmetry in the second law of thermodynamics. For example, I couldn't tell you the exact connection between the asymmetry of Ohm's law and entropy increase, but I'm confident it must be there (something to do with resistors dissipating the energy of the current as heat, presumably).

 

[Dale]

Agreed, but I think it is a good thing to know that all fundamental laws are believed to be either T-symmetric or CPT-symmetric

I also agree.

I couldn't tell you the exact connection between the asymmetry of Ohm's law and entropy increase, but I'm confident it must be there (something to do with resistors dissipating the energy of the current as heat, presumably).

Yes, exactly. In a resistor energy always goes from low entropy electrical energy to high entropy thermal energy, never the reverse. But you can see the asymmetry directly from the Ohm's law equations without any knowledge of how those equations relate to entropy and thermodynamics.

 

[atyy]

Yet I have read interpretations of this as as being positively entropic.

Yes.
http://arxiv.org/abs/0812.2610
Statistical mechanics of gravitating systems: An Overview
T. Padmanabhan

What is the entropy of a black hole?

Yes, classical black holes are a problem for thermodynamics. Apparently quantum mechanics saves the day.
http://arxiv.org/abs/gr-qc/9702022
Black Holes and Thermodynamics
Robert M. Wald

 

[ernestpworrel]

I definitely remember reading something official that said the laws of physics don't distinguish between the past and the future.

I've read something similar. What this actually means is that the entropy of the microsystem increases in either direction. Take the case of ice cubes. They start out as fully formed cubes with low entropy. They gradually melt into a pool of water which means the entropy has increased. However, there had to have been a pool of water in the first place for the ice cubes to form, which means evolution from a state of high entropy to one of lower entropy. You have high-entropy water becoming low-entropy ice becoming high-entropy water. So the water had higher entropy on both sides of the ice cube state. Of course, entropy is still conserved in the macrosystem.

The rest of your post had to do with time reversal. Physical laws allow time reversal in that they do not favor any particular direction in time, which is called time-reversal symmetry. Everyone else has done a good job explaining this.

 

[A-wal]

I read somewhere that an observer moving towards a black hole would never reach the event horizon until they reached the singularity. I thought it was here but maybe not. It stuck in my mind because I've never heard that before and it did kind of seem to make sense for the event horizon to be relative and not a fixed radius. Is that not right then? What about for an observer moving quickly past the black hole? Surly length contraction would mean that the event horizon moves inwards as you approach it and move into a stronger gravitational field? Isn't it the equivalent of how you can go faster than light from the perspective of the distance in your original frame? So you can escape the event horizon using it's radius from another frame but that frame will see you as outside the event horizon in the same way as your original frame won't see you moving faster than c?

I take it that's not right then? The event horizon is the same radius in all frames? That's not very relative.

 

[Austin0]

Austin0, everyone agrees that the laws of thermodynamics are not time-reverse symmetric. That is why everyone was so careful to say "Newtons laws" etc. above, in order to specify that we were only talking about laws of physics that are time-reverse symmetric.

The fact that thermodynamics is not time-reverse symmetric does not change the fact that a planet orbiting clockwise is every bit as valid a solution to Newtons laws as a planet orbiting counterclockwise and that one is the time-reverse of the other. You do not have to reverse the course of the entire universe in order to be able to clearly state that Newton's laws are time reverse symmetric.

HI Sorry if I went slightly off the general thrust of this thread.
I do have question in line with the concept.
As I understand Thermodynamics , including entropy, it itself does not propose any fundamental concepts but is a generalized, statistical description of the workings of other
physical principles and forces.
The conservation of mass and energy, the kinetic interactions of particles, intermolecular forces,[Van der Wall etc] and at extreme ranges various QM effects.
If ,at the fundamental level, all these individual interactions and forces are time-symetric, what principle would lead to the aggregate results not also being time-symetric.
More specifically ,friction, heat dissappation etc are simply intermolecular tranfers of kinetic energy correct??
Is it quantum uncertainty that makes this movie not run backwards equally well?
Thanks

 

[Dale]

If ,at the fundamental level, all these individual interactions and forces are time-symetric,

They are not all time-symmetric (T symmetry), they are charge-parity-time-symmetric (CPT symmetry). Although some people like to say that the T asymmetry (more commonly known as a CP violation) is minor, it nonetheless establishes a fundamental arrow of time.

what principle would lead to the aggregate results not also being time-symetric.

All of the laws of physics are incomplete descriptions. They require additional information, called boundary conditions, in order to describe a physical situation. Asymmetries can arise from the boundary conditions, even with symmetric laws. Thermodynamics essentially does a statistical analysis of all possible boundary conditions to make its asymmetric conclusions.

Is it quantum uncertainty that makes this movie not run backwards equally well?

It is uncertainty, but I would include general measurement uncertainty and incomplete descriptions of systems and not limit it to quantum uncertainty.

 

[JesseM]

I take it that's not right then? The event horizon is the same radius in all frames? That's not very relative.

The word "frames" is not very clear in general relativity--in the context of SR it's usually used to refer to the particular set of coordinate systems known as inertial frames, so a given inertial observer will have a unique "rest frame", but in GR there is no similar set of preferred global coordinate systems in curved spacetime, you are free to use pretty much any type of coordinate system imaginable (with arbitrary coordinate values for the radius of a physical object like a black hole) according to the principle of "diffeomorphism invariance", discussed a bit http://www.aei.mpg.de/einsteinOnline/en/spotlights/background_independence/index.html . If we want to speak in coordinate-independent terms, though, we can just talk about proper time along the worldline of an observer falling into a black hole, and all coordinate systems will agree in their prediction about the proper time when the event horizon is crossed, which is a finite value and is also prior to the proper time when the worldline ends at the singularity (also at a finite value of proper time).

 

[A-wal]

Yea my terminology is a bit off. I use the word frame to mean the strength of the gravitational field as well. But I was also asking about whether relative velocity to the black hole would effect the radius of the event horizon. The proper version of being in a different frame. So the radius is the same regardless of length contraction either from relative velocity or gravitational field strength? I know this hasn't got much to do with the original topic but I'm getting to that.

 

[JesseM]

Yea my terminology is a bit off. I use the word frame to mean the strength of the gravitational field as well.

What do you mean by "as well"? I didn't say anything about frame being used to represent strength of field, a "frame" always refers to some kind of spacetime coordinate system which allows you to assign position and time coordinates to any event.

But I was also asking about whether relative velocity to the black hole would effect the radius of the event horizon.

But the "radius" of anything can only be defined in terms of the coordinates of some spacetime coordinate system...for instance, if one end of an object is at x=10 meters in your coordinate system, and the other is at x=15 meters, then the object would be 5 meters long in this coordinate system. As I said, in GR you can use absolutely any coordinate system (did you look at the article on diffeomorphism invariance), and any object should be able to have any length under the right choice of coordinate systems. So if you want to ask meaningful questions about the length or radius of something, you first need to specify what type of coordinate system you want to use.

 

[A-wal]

Okay I think we're having a breakdown in communication here. I think of a different frame as a frame which is time dilated/length contracted relative to another frame, whether it be from a difference in relative velocity or from a difference in gravity.


Yes I read the article and it didn't tell me anything I didn't already know. In fact it didn't say anything that I hadn't figured out before I started checking out the official stances on these concepts, although there are some good links on that page.


I read or heard somewhere that the event horizon recedes when it's approached, which I'd never heard before and it got me thinking.

If the event horizon recedes then it could mean that nothing can cross the event horizon in any frame which makes sense. If your observing something approaching a black hole then you will never see it reach the horizon. How close have you got to be? Right along side it? If you can't cross the event horizon in any frame then it would mean that both in falling and outside observers see exactly the same thing but measure it differently because they're in different frames, meaning the event horizon and the singularity are the same thing basically. Time stops at the event horizon for external observers and at the singularity for falling observers right? How close do you have to be to be classed as falling in? It suggests to me that the event horizon can't be crossed in any coordinate system.