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The arrow of time

  1. Sep 14, 2009 #1
    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?
     
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  3. Sep 14, 2009 #2

    PeterDonis

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    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.
     
  4. Sep 14, 2009 #3

    A.T.

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    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.
    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.
     
  5. Sep 14, 2009 #4

    Dale

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    The http://en.wikipedia.org/wiki/T-symmetry" [Broken] is actually pretty decent. Gravity is attractive in forward or reverse, as Peter described.
     
    Last edited by a moderator: May 4, 2017
  6. Sep 14, 2009 #5

    DrGreg

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    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?
     
  7. Sep 19, 2009 #6
    Cheers. Freely moving inertia and gravitational drag are interchangeable if you ignore cause and effect? Weird!
     
  8. Sep 19, 2009 #7

    Dale

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    Huh? What does that mean?
     
  9. Sep 19, 2009 #8

    JesseM

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    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).
     
    Last edited: Sep 19, 2009
  10. Sep 19, 2009 #9
    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.
     
  11. Sep 19, 2009 #10

    atyy

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    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.
     
  12. Sep 20, 2009 #11

    Saw

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    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…
     
  13. Sep 20, 2009 #12

    atyy

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    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
     
  14. Sep 20, 2009 #13

    atyy

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    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.
     
  15. Sep 20, 2009 #14

    Dale

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    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.
     
  16. Sep 20, 2009 #15
    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?
     
    Last edited: Sep 20, 2009
  17. Sep 20, 2009 #16

    atyy

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    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.

    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.
     
  18. Sep 20, 2009 #17

    Saw

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    I cannot but agree with it. Could you please tell Brian Greene and David Deutsch and dozens of clever physicists about that?
     
  19. Sep 20, 2009 #18

    PeterDonis

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    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).
     
  20. Sep 20, 2009 #19

    PeterDonis

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    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.
     
  21. Sep 21, 2009 #20

    Dale

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