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Excluding Thermodynamic's arrow of time, all mathematical descriptions of time are symmetric. We know the arrow of time is real and we know the equations describing physics are real so is there any insights into what breaks the symmetry between real time and the mathematical description?

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I'll let someone else answer but I believe magnetic fields are key here. – Fire Mar 31 '13 at 4:29
You should read… . – Yvan Velenik Mar 31 '13 at 7:36
The thermodynamic arrow of time is the breaking of time symmetry. – Nathaniel Mar 31 '13 at 12:11
Coarse graining breaks the reversibility (never heard that this is called time symmetry) of the microscopic laws. I guess by mathematical description you mean the micriscopic laws which are reversible and by real time the irreversibility of the macroscopic effective laws we observe. – Dilaton Apr 1 '13 at 23:53

You seem keen to exclude the thermodynamic arrow of time, but as far as I know that is the only source of time asymmetry.

As Ross mentioned in his answer, the collapse of the wavefunction has been presented as a time asymmetric process. However I would guess most people now view even this as fundamentally time symmetric. If you believe in decoherence the wavefunction collapse is just another example of the thermodynamic arrow of time.

There remains the (basically philosophical) problem of why humans experience time to flow in a single direction, but this too may simply be because the thought process inevitably follows the thermodynamic arrow of time.

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My knowledge is quite limited in this interesting problem, but I think you may also define an arrow of time using universe expansion, by saying "time increases as universe expand". This cosmological definition of the arrow of time is not, I think, related to the thermodynamic arrow of time. – Bru Mar 31 '13 at 11:50
I wouldn't be too sure the expansion of the universe is unrelated to thermodynamics: – John Rennie Mar 31 '13 at 11:58
Thermodynamics is technically not excluded because it is a form of classical mechanics to the extend that the laws of physics that are symmetric in time can be used to derive the laws of thermodynamics which are not symmetric in time. That is why I asked about the mechanism. – user4884 Mar 31 '13 at 18:57
Actually, the Standard Model isn't symmetric under time reversal. CP violation gives rise to T-violation. – user1504 Apr 1 '13 at 18:28
John, on the assumption that CPT symmetry holds any CP violation implies the violation of time symmetry, on top of that T violation in B decays has been explicitly observed. – dmckee Apr 5 '13 at 15:52

Actually, it's not true that our laws of physics are symmetric under time reversal. The Standard Model of particle physics isn't.

In fact, it's been strongly suspected since the 1960s that the laws of physics can't be invariant under the operation of time reversal. There is a very reliable theoretical result called the CPT theorem which says that any reasonable quantum field theory must be invariant under the combination of charge reversal (C), parity reversal (P), and time reversal (T). We have known since the 60s that the laws of physics are not invariant under CP reversal (reverse charge and parity); these violations have been experimentally observed, in the physics of Kaons and B-particles. So the CPT theorem implies that any correct physical model must predict the violation of T-symmetry. This symmetry has to be violated in a way that exactly compensates for the violation of the CP symmetry.

Direct violation of T-symmetry has recently been observed by the BaBar experiment.

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+1 because this shows up that the assumption "all mathematical descriptions of time are symmetric" is wrong. I cannot see off hand though how one could define an arrow of time from this symmetry breaking. – anna v Apr 1 '13 at 19:14
@anna v. All mathematical descriptions of time do not have to be symmetric. We know Newtonian mechanics is time symmetric and Thermodynamics is time asymmetric. How can laws that are symmetric in time be used to derive laws that are asymmetric in time if some mechanism did not brake that symmetry. The standard model is not classical, is not mechanical and you can have time independent wave functions. I thought the Standard Model was based on symmetries not mechanics as viewed in classical physics. – user4884 Apr 1 '13 at 22:34
@user4884: annav is quoting the first sentence of your question; you're the one who asserted that all mathematical descriptions of time are symmetric. The point of my answer is that this assumption is erroneous. – user1504 Apr 1 '13 at 22:47
@annav I agree that it's not completely obvious how to turn the usual standard model data into a time orientation for spacetime. But the lack of T-symmetry shows that this data is there implicitly. The Lorentz transformations in Standard Model's symmetry group must be proper and orthochronous. – user1504 Apr 1 '13 at 22:50
user1504 . The only way I can see an arrow of time might appear is in following the steps that Lubos is pointing out on how to get classical fields out of quantum mechanical ones here:…, concentrating on the CP violating components. – anna v Apr 2 '13 at 4:40

There are books on this subject. All the answers I have seen focus on one of two things: the thermodynamic arrow or the quantum collapse. I have not seen any good answer for translating quantum collapse into the large scale world. The thermodynamic argument is quite subtle if you dig into it. From any point in time that entropy is not a maximum, entropy (with huge probability) should increase in both directions.

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Regarding Translating Quantum Collapse into the large scale world: A wave function with classical properties was successfully isolated in the motion of binary stars. and my profile where it was reported at Anna Astronomy News. – user4884 Apr 2 '13 at 12:56

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