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3
votes
4answers
127 views

Understanding intuition behind time translation in classical mechanics

In V.Arnold book "Mathematical Methods of Classical Mechanics" he says that invariance with respect to the time for isolated systems means that "the laws of nature remain constant", i.e., if $\phi(t)$ ...
-2
votes
1answer
52 views

Time difference between all particles and waves [closed]

Since all elementary particles and waves were created simultaneously in the big-bang (t0) would there be any time difference between any interacting elementary particles and/or waves after t0? I'm ...
3
votes
1answer
78 views

How does time-translation symmetry morph into evolution in time?

I am reading Ballentine's textbook "Quantum Mechanics: A Modern Development". In it he transitions from discussing time-symmetry to discussing evolution (of the state) in time. I'm finding it ...
0
votes
1answer
34 views

What does “Real-time” mean?

In the context of describing Real-time dynamics of Lattice gauge theories, have they specifically mentioned real-time in order to differentiate it from imaginary-time. Or does it have any other ...
0
votes
2answers
66 views

QM: Time evolution with $H = H(t)$

In order to calculate time evolution in QM we use Schrödinger equation \begin{align*} i \partial_t |\psi\rangle_t = H(t) | \psi\rangle_t. \end{align*} If $H\neq H(t)$ then \begin{align*} i \partial_t ...
1
vote
2answers
65 views

Do we suspect that any 2 seemingly identical experiments actually change under the passage of time?

For example, let's say that I set up 2 consecutive identical experiments where I know that the conditions are exactly the same (go through whatever difficulties you need to). The only thing I can't ...
4
votes
4answers
2k views

Which Schrödinger equation is correct?

In the coordinate representation, in 1D, the wave function depends on space and time, $\Psi(x,t)$, accordingly the time dependent Schrödinger equation is $$H\Psi(x,t) = i\hbar\frac{\partial}{\...
4
votes
1answer
930 views

Time evolution in quantum mechanics

We know that an operator A in quantum mechanics has time evolution given by Heisenberg equation: $$ \frac{i}{\hbar}[H,A]+\frac{\partial A}{\partial t}=\frac{d A}{d t} $$ Can we derive from this ...