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## Main Question or Discussion Point

What is more fundamental and why, the postulated time symmetry of QM tie evolution or the time asymmetry of the CPT theorem?

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What is more fundamental and why, the postulated time symmetry of QM tie evolution or the time asymmetry of the CPT theorem?

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atyy

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The time reversibility of QM is more fundamental - it is basically guaranteed by unitary evolution of the wave function. The time asymmetry of CPT is more a matter of definition as to what we mean by time reversibility. It is not so much different from the fact that in classical physics, to reverse time, one has to also reverse the direction of velocity. Here is Sean Carroll's explanation.

http://preposterousuniverse.com/eternitytohere/faq.html [Broken]

**Don't the weak interactions violate time-reversal invariance?**

Not exactly; more precisely, it depends on definitions, and the relevant fact is that the weak interactions have nothing to do with the arrow of time. They are not invariant under the T (time reversal) operation of quantum field theory, as has been experimentally verified in the decay of the neutral kaon. (The experiments found CP violation, which by the CPT theorem implies T violation.) But as far as thermodynamics is concerned, it's CPT invariance that matters, not T invariance. For every solution to the equations of motion, there is exactly one time-reversed solution -- it just happens to also involve a parity inversion and an exchange of particles with antiparticles. CP violation cannot explain the Second Law of Thermodynamics

http://preposterousuniverse.com/eternitytohere/faq.html [Broken]

Not exactly; more precisely, it depends on definitions, and the relevant fact is that the weak interactions have nothing to do with the arrow of time. They are not invariant under the T (time reversal) operation of quantum field theory, as has been experimentally verified in the decay of the neutral kaon. (The experiments found CP violation, which by the CPT theorem implies T violation.) But as far as thermodynamics is concerned, it's CPT invariance that matters, not T invariance. For every solution to the equations of motion, there is exactly one time-reversed solution -- it just happens to also involve a parity inversion and an exchange of particles with antiparticles. CP violation cannot explain the Second Law of Thermodynamics

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Wouldn't this suggest counterintitively that QM is more fundamental than QFT? or does it rather point to some discrepancy between the two since after all QFT from wich the CPT symmetry is derived is based on QM with unitary time evolution.The time reversibility of QM is more fundamental - it is basically guaranteed by unitary evolution of the wave function. The time asymmetry of CPT is more a matter of definition as to what we mean by time reversibility. It is not so much different from the fact that in classical physics, to reverse time, one has to also reverse the direction of velocity.

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atyy

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By QM I included QFT. Unitary time evolution holds in QFT also.Wouldn't this suggest counterintitively that QM is more fundamental than QFT? or does it rather point to some discrepancy between the two since after all QFT from wich the CPT symmetry is derived is based on QM with unitary time evolution.

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That was my point when saying "after all QFT from wich the CPT symmetry is derived is based on QM with unitary time evolution".By QM I included QFT. Unitary time evolution holds in QFT also.

So Carroll's argument is that the important symmetry is the whole CPT and there's no point splitting it into CP violations and T-violation?

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atyy

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No, he just means that for the purposes of the second law arrow of time, unitary time evolution guarantees that the second law is not fundamental within the quantum mechanical framework.That was my point when saying "after all QFT from wich the CPT symmetry is derived is based on QM with unitary time evolution".

So Carroll's argument is that the important symmetry is the whole CPT and there's no point splitting it into CP violations and T-violation?

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I see. That makes sense.No, he just means that for the purposes of the second law arrow of time, unitary time evolution guarantees that the second law is not fundamental within the quantum mechanical framework.

Is that in general seen like a problem for QM or for the second law? I mean, is the second law as fundamental as it used to be(I'm thinking of the famous Eddington quote on the second law)?

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atyy

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For a long time the second law has not been fundamental. Still Eddington's quote holds true.I see. That makes sense.

Is that in general seen like a problem for QM or for the second law? I mean, is the second law as fundamental as it used to be(I'm thinking of the famous Eddington quote on the second law)?

Anyway, for how the second law may arise within quantum mechanics, try looking at http://arxiv.org/abs/1007.3957 or http://arxiv.org/abs/1402.3380, which contain good pointers to other papers.

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Sorry, I'm not following what you mean by this.For a long time the second law has not been fundamental.

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atyy

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In classical mechanics and in quantum mechanics, the dynamics are deterministic in a way that given full knowledge of the state at any one time, the entire past and future are known. In contrast, the second law tells us that the future is more uncertain than the past. So the second law and classical and quantum mechanics are in contradiction if we consider both to be fundamental. The majority point of view has been to take the classical and quantum dynamics as fundamental, and consider the second law to be emergent or an accident of the initial conditions.Sorry, I'm not following what you mean by this.

(Here we ignore the Copenhagen interpretation, in which a definite or irreversible macroscopic outcome is fundamental.)

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Ok, thanks.In classical mechanics and in quantum mechanics, the dynamics are deterministic in a way that given full knowledge of the state at any one time, the entire past and future are known. In contrast, the second law tells us that the future is more uncertain than the past. So the second law and classical and quantum mechanics are in contradiction if we consider both to be fundamental. The majority point of view has been to take the classical and quantum dynamics as fundamental, and consider the second law to be emergent or an accident of the initial conditions.

(Here we ignore the Copenhagen interpretation, in which a definite or irreversible macroscopic outcome is fundamental.)

So on this particular point you think the majority pov differs from the Copenhagen pov that highlights the contradiction, right?

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atyy

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No, it just means that all the statements hold only for the part of quantum mechanics in which the time evolution is completely governed by unitary time evolution.So on this particular point you think the majority pov differs from the Copenhagen pov that highlights the contradiction, right?

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Is the time parameter in the time evolution operator required to be continuous? It would seem that for interacting systems is not required.No, it just means that all the statements hold only for the part of quantum mechanics in which the time evolution is completely governed by unitary time evolution.

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atyy

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I'm not sure. My guess is that it is not, since lattice gauge theory is usually formulated in discrete time and loop quantum cosmology also has discrete time.Is the time parameter in the time evolution operator required to be continuous? It would seem that for interacting systems is not required.

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