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The theoretical symmetry of physical laws under the transformation of time reversal, that is t -> -t.

4 votes
1 answer
92 views

Is it legal to add two physical quantities that behave differently under time-reversal, pari...

In physics, can we legally add two physical quantities that behave differently under time-reversal or parity? For example, let $\vec{a}$ and $\vec{b}$ are two observables. Let $\vec{a}$ flips sign und …
Solidification's user avatar
2 votes
2 answers
638 views

Does it make sense to say that the action is even or odd under time reversal?

The action of a system in mechanics is an integral over time defined as $$S[x(t)]=\int\limits_{t_1}^{t_2}L(x,\dot{x},t)dt.$$ Here, the time $t$ is integrated making the left hand side depend only on t …
Solidification's user avatar
4 votes
0 answers
81 views

Cases of various time symmetries

Is it possible to cook up three physically relevant examples where the Lagrangian has explicit time dependence but the system still has one of the following? time-reversal invariance, time transla …
Solidification's user avatar
2 votes
1 answer
581 views

Why does the subclassification of fields under parity require the quantum theory?

The fields of relativistic field theory (scalars, vectors, tensors, and spinors) are all defined via their transformation properties under the restricted Lorentz group (which excludes discrete spaceti …
Solidification's user avatar
0 votes
1 answer
57 views

Square of the Feynman amplitude for $a +b\to c+d$ and its reverse

In quantum field theory, if a process $a +b\to c+d$ is allowed by a certain interaction Lagrangian (hermitian), the reverse process, $c+d\to a+b$, must also be allowed (as far as I understand) by the …
Solidification's user avatar
9 votes
1 answer
3k views

Why is time-reversal represented by an antilinear and antiunitary operator? [duplicate]

Operators related to physical transformations in quantum mechanics are usually unitary and linear except time-reversal which is both antiunitary and antilinear. What is the explanation for this differ …
Solidification's user avatar