>> I recall Bruce giving an example of an irreversible process, but I can't recall the details. AG
> Probably a FAPP irreversible process.
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Why do you say it's irreversible in principle? Wouldn't the time-reverse of that just be a photon traveling towards an atom and being absorbed, which is permitted by the laws of physics given a different set of initial boundary conditions?
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"The time invariance of the laws means that a photon coming in from outer space is consistent with the laws. But that cannot be the same photon."But "reversibility" as physicists define it has nothing to do with actually causing the same system to reverse itself, it's a more abstract notion that you could have a different system obeying the same dynamical laws whose behavior over time would be a perfectly time-reversed mirror of the first system's behavior. If you think it's about a single system evolving one way for some period of time and suddenly reversing itself so that its subsequent behavior looks like a reversed version of its initial behavior, that's just a misunderstanding of the concept.
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Are you defining "process" as a *pattern* of behavior which can be duplicated with different bits of matter, or as something that refers to some specific bits of matter, so that reversing a process would require doing it to the same bits of matter that underwent the original process? I think if a physicist talked about a "process" being reversible or not, they would be referring to the pattern-based notion. For example, take the process of a rogue planet coming close to a planetary system and getting captured by its gravitational interactions with the star and the planets in the system. With a pattern-based notion of process, that process is reversible in the sense that one could have a different star and different planets with identical masses, where the initial conditions were such that the planet got ejected from the system in a perfect time-reversed version of the behavior of the first system.
> But when physicists say that a given system's dynamics are "reversible" doesn't this generally involve an appeal to different initial boundary conditions?
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> The same happens with quantum mechanics. There is a Poincare recurrence, given by the exponential of the Euclideanized action. However, there is an additional phase, which defines the quantum complexity and the recurrence time on that is the exponential of the Poincare recurrence time. Quantum complexity is interesting, and I think it involves the Hilbert-Polya conjecture concerning the Riemann zeta function and the zeros being mapped to the eigenvalues of a Hermitian operator. In this case the recurrence is a vast period of time, as long as the stability of the de Sitter manifold of the cosmos.
On Friday, August 5, 2022 at 6:14:42 PM UTC-5 Bruce wrote:
On Sat, Aug 6, 2022 at 7:54 AM Jesse Mazer <laser...@gmail.com> wrote:
Why do you say it's irreversible in principle? Wouldn't the time-reverse of that just be a photon traveling towards an atom and being absorbed, which is permitted by the laws of physics given a different set of initial boundary conditions?
The laws of physics are invariant under the time-reversal operation. That does not imply that irreversible processes are impossible. Brent has pointed out that sending a photon out into an expanding universe is a process that is irreversible in principle. The time invariance of the laws means that a photon coming in from outer space is consistent with the laws. But that cannot be the same photon. The idea that you can surround everything with a perfectly reflecting mirror, so that all emitted photons are returned, is just a fanciful diversionary tactic -- no such reflective surrounds exist. Besides, reflecting photons back is not a process reversal in an expanding universe. The red shift induced by the expansion means that the returning photon inevitably has lower energy than the emitted photon.
Bruce
It is the case of a billiard ball impacting another vs a set of racked billiard balls. If I were to take a video of a billiard ball impacting another, framed this in the center of mass of the balls and mask any perception of the rotation of the balls, the video run backwards and forwards would by very similar. There would be nothing to distinguish the forwards and backwards video. It is perfectly time reverse invariant. Now consider the racked balls impacted by the cue-ball. It is pretty easy to see which is forwards in time, as we do not expect balls to rush inwards and align themselves in an ordered set and eject another. However, if the table were "perfect," it had frictionless surface and the balls reflected off the sides perfectly, if we wait long enough it will return to its original state. This is Poincare recurrence. You have to wait a lot longer than the duration of the universe so far.
The same happens with quantum mechanics. There is a Poincare recurrence, given by the exponential of the Euclideanized action. However, there is an additional phase, which defines the quantum complexity and the recurrence time on that is the exponential of the Poincare recurrence time.
Quantum complexity is interesting, and I think it involves the Hilbert-Polya conjecture concerning the Riemann zeta function and the zeros being mapped to the eigenvalues of a Hermitian operator. In this case the recurrence is a vast period of time, as long as the stability of the de Sitter manifold of the cosmos.
In effect we have limitations on what we can observe and account for, but ultimately the universe may have an accounting of quantum information, at least for unitary systems and quantum gravitation with Petrov types that have Killing vectors. When it comes to the universe at large, that may be a different matter. Such ideas may turn out to be false.
LC
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On 8/21/2022 4:22 AM, Lawrence Crowell wrote:
On Friday, August 5, 2022 at 6:14:42 PM UTC-5 Bruce wrote:
On Sat, Aug 6, 2022 at 7:54 AM Jesse Mazer <laser...@gmail.com> wrote:
Why do you say it's irreversible in principle? Wouldn't the time-reverse of that just be a photon traveling towards an atom and being absorbed, which is permitted by the laws of physics given a different set of initial boundary conditions?
The laws of physics are invariant under the time-reversal operation. That does not imply that irreversible processes are impossible. Brent has pointed out that sending a photon out into an expanding universe is a process that is irreversible in principle. The time invariance of the laws means that a photon coming in from outer space is consistent with the laws. But that cannot be the same photon. The idea that you can surround everything with a perfectly reflecting mirror, so that all emitted photons are returned, is just a fanciful diversionary tactic -- no such reflective surrounds exist. Besides, reflecting photons back is not a process reversal in an expanding universe. The red shift induced by the expansion means that the returning photon inevitably has lower energy than the emitted photon.
Bruce
It is the case of a billiard ball impacting another vs a set of racked billiard balls. If I were to take a video of a billiard ball impacting another, framed this in the center of mass of the balls and mask any perception of the rotation of the balls, the video run backwards and forwards would by very similar. There would be nothing to distinguish the forwards and backwards video. It is perfectly time reverse invariant. Now consider the racked balls impacted by the cue-ball. It is pretty easy to see which is forwards in time, as we do not expect balls to rush inwards and align themselves in an ordered set and eject another. However, if the table were "perfect," it had frictionless surface and the balls reflected off the sides perfectly, if we wait long enough it will return to its original state. This is Poincare recurrence. You have to wait a lot longer than the duration of the universe so far.
The same happens with quantum mechanics. There is a Poincare recurrence, given by the exponential of the Euclideanized action. However, there is an additional phase, which defines the quantum complexity and the recurrence time on that is the exponential of the Poincare recurrence time.Is that in some thermodynamic limit? There is no chaos in QM so I would expect the recurrence time to be bounded by that. Do you have a reference?
Brent
> I do not think much of this idea that the universe is sentient.
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