# What is Time reversal symmetry: Definition and 17 Discussions

T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal,

T
:
t

t
.

{\displaystyle T:t\mapsto -t.}
Since the second law of thermodynamics states that entropy increases as time flows toward the future, in general, the macroscopic universe does not show symmetry under time reversal. In other words, time is said to be non-symmetric, or asymmetric, except for special equilibrium states when the second law of thermodynamics predicts the time symmetry to hold. However, quantum noninvasive measurements are predicted to violate time symmetry even in equilibrium, contrary to their classical counterparts, although this has not yet been experimentally confirmed.
Time asymmetries generally are caused by one of three categories:

intrinsic to the dynamic physical law (e.g., for the weak force)
due to the initial conditions of the universe (e.g., for the second law of thermodynamics)
due to measurements (e.g., for the noninvasive measurements)

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1. ### I Born rule: time running forwards and backwards?

Can the Born rule be understood as time running both forwards and backwards simultaneously? The probability ##P_{i \rightarrow f}## that an initial quantum state ##\psi_i## is measured to be in final quantum state ##\psi_f##, after evolving according to the unitary time-evolution operator...
2. ### I Time Reversal Symmetry in Classical Physics

I try to justify time-reversal symmetry in a very simple classical problem; Free Fall. The position, ##x##, and the velocity, ##v## are obtained versus time from the equation ##-g=\ddot x##. So, if we consider the primary conditions as ##t_0,x_0,v_0## it is clear that...
3. ### I Time reversal symmetry in physics

It is said that Newton's laws of motion or laws of Quantum Mechanics posses time reversal symmetry but the second law of Thermodynamics does not. What I understand by the first part of the sentence is the following. The dynamical state of a system changes with the increase of time. The state at...
4. ### Why is it said that magnetism breaks time reversal symmetry?

It is known that Maxwell equations have the time reversal symmetry. I.e. by changing t by -t, J by -J (which can be understood as the charges going in the opposite direction when time is reversed, which makes sense), E to E and B to -B, the equations are still satisfied. However, it is also...
5. ### A Time reversal symmetry and Bloch states

Hello! The time reversal operator, ##\hat{\Theta}## transforms a Bloch state as follows: ##\hat{\Theta} \psi_{nk}=\psi^*_{nk}##. How does one proceed to prove the condition that ##\psi_{nk}## and ##\psi^*_{nk}## must satisfy in order for our system to be time reversal invariant? Thanks in advance!
6. D

### A Asymmetry parameter while relating proper time with distance

In special relativity, we know, (proper time)^{2} = - (proper distance)^{2}. But, in Causal Dynamical Triangulations (CDT), they introduce an asymmetry parameter \alpha as, (proper time)^{2} = - \alpha (proper distance)^{2} [Q. 1] Can you please explain me about, why we need to introduce \alpha...
7. ### B Time reversal symmetry in topological insulator

Hi all My question: I have read: Topological Insulators: Dirac Equation in Condensed Matters But also I have read: Observation of a Discrete Time Crystal Is it different situations ?
8. ### I What breaks time reversal symmetry in ferromagnets

I am told that in ferromagnets, time reversal symmetry is broken. However, I don't know any hamiltonian terms in solid that can break time reversal symmetry. So is there a hamiltonian term I don't know or is there any subtlety in ferromagnets?
9. ### Time-Reversal Symmetry Explained

I completely have no idea what time-reversal mean. Why does, by substituting -t into an equation and if the result is the same as the original equation, then the equation is said to be time-reversal symmetry? Also, what does that 'symmetry' mean there? An even function?
10. ### Effect of TRS potential on Topological insulator (QSH)

Hi every body, I faced a paradox. The topological insulator is robust against a potential that does not breaks the TRS. But in the original work of Kane-Mele (PRL 95, 146802), the "staggered sublattice potential" that does not breaks the TRS,, makes zigzag ribbon trivial insulator (figure 1 in...
11. ### Does time reversal symmetry imply hermicity of s-matrix?

If the probability for a state α prepared initially to be in a state β at a later time is given by: S_{\beta \alpha} S_{\beta \alpha}^* and for a state β prepared intitially to become a state α is: S_{ \alpha \beta} S_{ \alpha \beta}^* then in order for the two to be equal (by...
12. ### Time reversal symmetry in Topological insulators of HgTe quantum Wells

Hi everyone, While reading about the BHZ model used to describe HgTe quantum well topological insulators, I read at many places that the effective Hamiltonian (which is a 4 x 4 matrix) can be written in block diagonal form and the lower 2x2 block can be derived from upper 2x2 block as...
13. ### Time Reversal Symmetry & Magnetic Field: Charges Explained

Talking about charges. If someone claims that in his work time reversal symmetry is conserved, does that equal to say he/she is not imposing a magnetic field?
14. ### Time reversal symmetry breaking

We know velocity/momentum and magnetic field both are odd to time-reversal operation. Then how is the time-reversal symmetry broken in quantum Hall effect since magnetic field is always coupled with velocity/momentum?
15. ### Time Reversal Symmetry: Particle Motion

Hi there! You have a particle moving to the left as time goes on. Now if you reverse the time the particle will move to the right. Does it mean that the system is not symmetric under time reversal?
16. ### Time reversal symmetry breaking in EM

I have come across a problem I am trying to understand, and hoping someone here has some insight. Basically, when writing down different solutions for an EM field from given sources, there seems to be a problem from the standpoint of time symmetry. From my understanding, if you reverse time, the...
17. ### Time Reversal Symmetry Question

Ok, so if you have two electrons near one another, they will start to repel one another and separate as time goes on. Now if you reverse time, they will move towards one another. But it is said that antimatter can be viewed as matter going backwards through time. Now if this is true, this would...