# Thread: quantum arrow of time

1. If you are conversant with arrow of time which is the idea that everything happens progressively in a particular direction of time,that is forward mostly in macroscopic systems.

I have read and there is still a hole in my knowledge about how particles can violate this time direction. Mostly I ωαηт to know how it was proved theoretically and experiments that has gone on. So please preview this quantum violation which says if time were reversed particles will behave in a way that still make sense unlike our everyday life. I understand how that can happen but don't get how it was predicted and anything mathematical that can prove so.

2.

3. It has something to do with antimatter-type properties, like opposite charge or opposite spin or something.

An antiparticle with an opposite spin is indistinguishable from a particle of regular matter going backwards through time.

I'm pretty sure there's more to it than that, but I'm not an expert either.

4. Originally Posted by merumario
If you are conversant with arrow of time which is the idea that everything happens progressively in a particular direction of time,that is forward mostly in macroscopic systems.

I have read and there is still a hole in my knowledge about how particles can violate this time direction. Mostly I ωαηт to know how it was proved theoretically and experiments that has gone on. So please preview this quantum violation which says if time were reversed particles will behave in a way that still make sense unlike our everyday life. I understand how that can happen but don't get how it was predicted and anything mathematical that can prove so.
It is my understanding that the arrow of time arises because transition probabilities are real-number values that are greater than or equal to zero. Because transition probabilities change sign under time-reversal, they cannot be interpreted as transition probabilities in a time-reversed system, thus distinguishing the forward time direction from the reverse time direction. Because transition probabilities are the result of a measurement, they are strictly classical. By contrast, a quantum mechanical wavefunction is complex-number valued and does not have the same constraint as classical probability under time-reversal. Therefore, quantum systems are time-reversible. The unitary evolution of a quantum system is also a mathematical statement of the absence of an arrow of time. However, note that in practice, a quantum wavefunction is conditional upon a given classical past (the initial condition), and this provides an arrow of time to the quantum mechanical system.

5. Originally Posted by KJW
It is my understanding that the arrow of time arises because transition probabilities are real-number values that are greater than or equal to zero. Because transition probabilities change sign under time-reversal, they cannot be interpreted as transition probabilities in a time-reversed system, thus distinguishing the forward time direction from the reverse time direction.
Most interesting. I never thought of that.

6. Originally Posted by Markus Hanke
Originally Posted by KJW
It is my understanding that the arrow of time arises because transition probabilities are real-number values that are greater than or equal to zero. Because transition probabilities change sign under time-reversal, they cannot be interpreted as transition probabilities in a time-reversed system, thus distinguishing the forward time direction from the reverse time direction.
Most interesting. I never thought of that.
If we consider the rate equation for a first-order chemical reaction:

then the rate constant is a measure of the transition probability for the chemical change, and is a positive real number. Covariance demands that transforms the same way as , and therefore changes sign under time-reversal. It is important to note that the time-reversed rate equation does indeed describe the time-reversed system, but the time-reversed system can no longer be interpreted in terms of probability. What this means is that the time-arrow of the second law of thermodynamics does not conflict with the general covariance of general relativity as a description of a system. But when we start to introduce notions of causality based on transition probabilities, we do conflict with general covariance. I believe the above provides some clarification of the apparent conflict between the arrow of time and the symmetry of the laws of physics.

7. It is perhaps ironic that quantum physics is more consistent with general relativity than classical physics.

8. Considering this further, consider the microscopically reversible reaction:

with rate equations:

(Note the symmetry between and )

If considers the reaction starting from pure and proceeding to a point that is still well before equilibrium so that , then in spite of the microscopic reversibility, the probability of past transforming to future is different to the probability of future transforming to past . Therefore, the notion of microscopic reversibility is not the same as temporal reversibility because microscopic reversibility still only refers to the transformations in the forward time direction.

9. Merumario, there is another aspect of this in terms of relativistic quantum theory which I feel causes most of confusion. The Dirac equation which is equation of motion for spin 1/2 fermions is 4-dimensional matrix equation. Its solution are bispinors - 4D vectors is spinor space. Its components each represent different thing. First two components of Dirac spinor represent basically wavefunction (in sense that its square is probability density) of electron with spin 1/2 and electron with spin -1/2. This is all good and energy of these states are positive. The other two components of bispinor are positron "wavefunction" representin probability amplitude of positron ith spin 1/2 and spin -1/2. Positron is nothing fancy it is just electron with positive energy. Hovewer problem is that Dirac equation predicts that these solutions have negative energy. Since evolution operator looks like this

(this is operator that evolves state vectors in time, there is no need for you to understand its meaning), then when you put in negative energy it formally seems like state is evolving backwards in time. This particular problem with Dirac equation was solved by second quantisation which is basicaly a transition from quantum mechanics to field theory. There are no fundamental issues like this in QFT because both electron and positron states have positive energy. Only thing that prevails is that electron annihilation operator has positive energy in Fourier spectrum whereas positron annihilation operator has negative energy in Fourier spectrum and vice versa for creation operators but these are just formal aspects nothing fancy going on.

Similar shenanigans happens in nonrelativistic field theory of solid state. There a hole (missing electron from valence band) has also formally negative energy and sometimes physicists refer to hole as electron propagating backwards in time. Hovewer this is just a silly jargon. Again. Nothing fancy going on.

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