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Someone once told me that if, in theory, we could know the position and motion of all the particles in the universe, we could use that data to run time backwards, and work out everything that had come before. That means the current state of the universe effectively encodes all of history.

Is this theory reasonable?

I have two main concerns, so it would be great if you could address these in your answer:

  • Due to entropy, information is lost over time. I believe that means the same state could be arrived at by two different histories. (For example, once a glass of water is still or frozen, we don't know if it was poured 100 years ago or 10,000 years ago.) If that is true, I don't see how we could determine history from state alone.

  • From A Brief History of Time (Stephen Hawking) I got the impression that time was symmetrical: it acted the same regardless of which way it was running. So if the universe is deterministic going forwards, that would also mean it is deterministic going backwards. Was Hawking correct about time symmetry, or did I just misunderstand him?

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  • $\begingroup$ I would be more inclined to believe Stephen Hawking rather than the un-named "somebody"... Your 2 objections seem to adequately dispose of the "theory". What more is there to say? $\endgroup$ – sammy gerbil Jul 30 '16 at 19:12
  • $\begingroup$ My opinion is that if it's not physically posible to do something, in this case trace the motions and positions all the way back, then this is a philosophical question, not a physical one. We don't know for sure that the universe was deterministic in the past, as we can only see a small part of it, ( or what we believe is a small part, we just don't know :) $\endgroup$ – user108787 Jul 30 '16 at 19:21
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    $\begingroup$ The universe is not deterministic "going forward": you cannot predict the outcome of a measurement in quantum mechanics. This is discussed in the PSE page you linked. $\endgroup$ – valerio Jul 30 '16 at 19:47
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    $\begingroup$ Have a read of this, based on retrocausality and related to your question: bbc.com/earth/story/… $\endgroup$ – user108787 Jul 30 '16 at 20:01
  • $\begingroup$ Time is not symmetrical. Time is that which the clock shows and a monotonously increasing series of time values is not the same as a monotonously decreasing one. The universe is deterministic in the sense that one can locally reverse its dynamics, but this doesn't extend to the global solution. What you were told about being able to predict the future from the present is wrong, even in classical physics (see non-integrability) and even more so in quantum mechanics. The final lid on this is put on by relativity: one can never "catch" outgoing massless waves, they are lost irreversibly. $\endgroup$ – CuriousOne Jul 30 '16 at 20:17
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Two things to think about. Is physics (i.e., the description we understand of the universe) deterministic, and then is is time symmetric? The answer to the first is yes, and the second is no. This answers treats both because tHey are Intrinsically related to the question of whether the universe would evolve back to the same if we reversed time. Clearly, if it was time symmetric but not deterministic, nothing would ever go back to the same.

This covers it all, though some of it summarily. But I try to describe and answer this using physics, and identify what may not be well known or accepted physics. There is lots of good physics to cover.

The basic answer seems to be that it is deterministic (in a strange but well understood way even in quantum physics), but not time symmetric (both microscopically and macroscopically).

At its basics the universe is deterministic, though in practice that's a different question. The question of whether the universe is deterministic was asked and had a number of answers in 2013, see Is the universe fundamentally deterministic?

The answer that emerges there, and the answer backed by known physics, is that basically it is deterministic, if we believe the currently best known physics, the Standard Model and General Relativity (GR). That is at a microscopic level plus relativity. It ignores the possibility that unknown physics such as Quantum Gravity would say otherwise, since we don't have a theory for Quantum Gravity yet. Clearly it also ignores what may be found at much higher energies than we have been able to measure things at, in what would be called Beyond the Standard Model'. Also, GR may allow closed timelike curves (CTC), which would also imply a breakdown of causality (which requires nothing faster than light, in the physics we know). For causality reasons most physicists think CRCs are not possible, except in regions separated from us by event horizons such as inside black holes so that we would not be affected. There are some strange GR solutions that allow CRCs, but they seem to not be physically possible. That does remain a controversy. This is not philosophy, it is pure physics, and with that possible exception the universe is causal and deterministic (I know, an exception is an exception, we just don't know about those yet)

There is another factor to account for, and two items to explain. First, account for entropy and thermodynamics, then about wave function collapse and the measurement problem. Both of those are still a bit controversial, but there is some semi-consensus that is emerging. That is the next two paragraphs. The third is simply a misunderstanding by laymen that quantum physics is not classically deterministic i.e., the uncertainty principle. That also is explainable and physicists agree that quantum physics is deterministic, eg, the Schrodinger, Dirac, and all other quantum physics (in quantum mechanics and in quantum field theories) all predict the quantum physics we see; the simplest way to see it's to understand that in QM the wave function is perfectly predictable. @Bush explains below that it is not if position or momentum is predictable but whether the wavefucntion (or other quantum equivalents) are deterministic. They are. In overall quantum physics that comes from the fact that all the evolution equations we know for the standard model are unitary. That's the technical term for information is conserved. Black Hole physics seems to contradict it with the horizon, but even Hawking has agreed that information is conserved, and people are trying to solve the 'paradox'. See Hawking's latest described simply, and the reference to his June Phys Rev Letters at http://phys.org/news/2016-06-hawking-team-soft-hair-theory.html

For entropy and thermodynamics it's simpler. Those are simply statistical macroscopic observation we have to make when detailing the evolution of all the quantum fields everywhere in the universe can not be computed. It's a practical and smart way to deal with the largeness, but it is our lack of knowledge we compute in entropy, not the universe.

As for wave function collapse not being unitary, or breaking the quantum physics laws, the well understood (not by laymen) answer is that if you include the evolution of the measuring apparatus, it is unitary and there is no collapse, just interactions that make the original wave function decohere. It appears to collapse if we caused it, but it simply interacted with us unitarily.

So the symmetry going back in time can ignore all of that, and and simply be answered by whether quantum physics is time symmetric, plus the additional issue of initial conditions in the large. On time symmetry, it is known that physics is not. The weak force breaks time symmetry, and CP symmetry. The CP symmetry breaking has been known, it is why there are only left handed neutrinos. (CP symmetry may also be broken, very very weakly, by the strong force, there are physical observations that hint at it, but it is not clear, and it has never been measured to be so). CPT symmetry (T is time symmetry) has never been found to be broken, so when CP is broken so is T. It is complicated but it seems to be so, and it is hoped that the CP breaking will explain why there are more particles than antiparticles in the universe, still an unsolved issue. See on T symmetry at https://en.m.wikipedia.org/wiki/T-symmetry and a lot of references there and elsewhere. The weak force is not time symmetric.

The final argument is the question of why are we evolving forward? Macroscopically it is thought now that it has to do with the initial conditions of the universe and entropy. That it was created in a low entropy state, and the evolution microscopically to a state of higher and higher entropy is the reason for the direction of the time arrow. Well, macroscopically it seems reasonable, but is that inherent in the universe or our perception? Physically there is still arguments going back and forth and it is sometimes described as philosophy. The time arrow exists in microscopic physics in the weak force, but is is totally unclear how that manifests itself in macroscopic physics and entropy.

But taking that into account then the answer is that if you run the universe backwards from where it is right now somerhing would be different. Microscopically, the weak force time asymmetry would change some of the evolution, and macroscopically the initial conditions would make it go towards a higher entropy rather to back to a small entropy.

Lots of physics in that (which has physical, real effects) but some unknowns people call philosophy, and which may or may not have physical effects.

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    $\begingroup$ Wait, physics is deterministic? The Schroedinger equation sure is, but as you go on to say, who knows about wave-function collapse? $\endgroup$ – lemon Jul 30 '16 at 21:34
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    $\begingroup$ My answer explains it. It is simply the interaction with the measurement apparatus. Include the wave function (pretty complex) of the two and there is no collapse. The evolution is always unitary, i.e. Causal, i.e. deterministic. $\endgroup$ – Bob Bee Jul 30 '16 at 22:30
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    $\begingroup$ But that's not accepted mainstream physics... $\endgroup$ – lemon Jul 31 '16 at 6:41
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    $\begingroup$ Yes it is. Read real physics. I understand the confusion. Unitary means deterministic at the quantum level. The indeterminacy is when one tries to determine classical parameters like position and velocity. The wavefunction is the basic physics and evolves from deterministic quantum physics. The indeterminacy is trying to predict classical quantities which are, by quantum physics, probabilistic. That comes from the wave or field type nature of reality, according to quantum theory. I'll post a reference a little later today when I have more time. $\endgroup$ – Bob Bee Jul 31 '16 at 17:33
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    $\begingroup$ There are lots of writings and papers on this. The understanding has been sharpened by the whole idea of decoherence, in interactions with the environment. When you look at the system w/o considering it is interacting with the environment, it looks like it looses coherence, i.e., it becomes a mixed state. Consider the system and the environments, and the wavefunction for the whole is coherent and follows unitary evolution. When you break it up into the two each is entangled wiTh the other and is now a mixed state. The rest is philosophy. See en.m.wikipedia.org/wiki/Quantum_decoherence $\endgroup$ – Bob Bee Jul 31 '16 at 19:31
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Consider an arbitrary superposition state with n eigenstates. In our perception of time, let's call this 'forward time', when that superposition state is measured, it collapses to an eigenstate. Which eigenstate is chosen may or may not be determined by the measurement process. But consider this: the superposition told you a lot about the system it was in because it was a linear combination of n eigenstates, but after measurement, the quantum state consists of only one eigenstate, which could be the eigenstate of any number of systems.

Now let's consider this process through 'backward time'. You start with a quantum state that consists of one eigenstate. Is there enough information for this quantum state to transform into the arbitrary quantum state mentioned previously? All the literature I've read suggests no, there is not enough information. A quantum measurement is time asymmetric for this reason.

This problem is rather deep and not fully understood at this time. I don't remember Hawking addressing this problem in his book, and this is a serious issue that any determinism proponent must address. Looking at the conclusion of A Brief History of Time, Hawking says:

The unpredictable, random element comes in only when we try to interpret the wave in terms of the positions and velocities of particles. But maybe that is our mistake...

Here he addresses the effect of the Uncertainty Principle on determinism. I'd say he certainly leaves determinism up for debate, even without addressing the quantum measurement problem.

To make the point of my answer clear: you based your question on the assumption that the universe is deterministic going 'forward' in time, but that is not an assumption that can be made. Considering there are time-asymmetric processes at the elementary particle level, whether the universe in 'backwards' time is deterministic will be an even more difficult question to answer.

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    $\begingroup$ The equations of quantum theory are time reversal invariant in the sense that CPT symmetry has to be fulfilled. This has nothing to do with the measurement process, which is simply open in nature rather than closed and unitary. All the theory tells us is that we can not reconstruct the past completely any more than we can predict the future completely. That's no different from classical mechanics. $\endgroup$ – CuriousOne Jul 30 '16 at 20:11
  • $\begingroup$ I think the measurement problem is deeper than the connection with classical mechanics you suggest, but that's beyond the scope of this discussion. You're right: an example from classical mechanics would have sufficed. Still, I'll leave my answer here to encourage discussion. $\endgroup$ – B. Bush Jul 30 '16 at 20:17
  • $\begingroup$ One could even leave the measurement process out of it, really. The crux is that even with a unitary transformation there are entire classes of pasts that are compatible with most given presents (there are cases where we start with a unique state and end up on a unique state, of course, that's just not true in general), so even though we can reverse the dynamic of any (sufficiently) closed system (e.g. in spin echo experiments), we still don't know where "the rest" came from. $\endgroup$ – CuriousOne Jul 30 '16 at 20:24
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No, the universe is not deterministic when looking backwards. The determination of position and velocity of a particle can NEVER (by the Heisenberg uncertainty principle) be known at any time, so neither forward-time nor backward-time "predictions" of a particle trajectory are absolute.

If you can't absolutely predict a particle, a universe is out of the question.

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