# Quantum mechanics of time?

1. Jan 28, 2004

### Amir

does anyone know?
time = ?

2. Jan 28, 2004

### chroot

Staff Emeritus
Time plays the exact same role in (non-relativistic) quantum mechanics as it does in Newtonian mechanics. It's just a dynamical variable.

- Warren

3. Jan 28, 2004

### Tom Mattson

Staff Emeritus
That's true.

Nope, it's a parameter. A "dynamical variable" satisfies an equation of motion in classical mechanics, and its expectation value satisfies the same equation in nonrelativistic quantum mechanics (NRQM). Also, an operator can be constructed for any dynamical variable in NRQM, but there is no sensible way to construct an operator whose eigenvalue is time.

4. Jan 28, 2004

### lethe

no t hat, remember?

5. Jan 28, 2004

### chroot

Staff Emeritus
Eek, you're right.

- Warren

6. Jan 28, 2004

### Tom Mattson

Staff Emeritus
Last edited by a moderator: Apr 20, 2017
7. Jan 28, 2004

### chroot

Staff Emeritus
I'm aware that time is not an observable, has no corresponding operator, and so on, of course. I just goofed up and forgot the definition of the phrase "dynamical variable."

- Warren

8. Jan 28, 2004

### Tom Mattson

Staff Emeritus
Right, but I think we're talking over a lot of people's heads here. Rather than type out the math (still haven't mastered LaTeX), I posted a link to a reference.

9. Jan 28, 2004

### chroot

Staff Emeritus
Oh by the way...
How does a dynamical variable then differ from a generalized coordinate (or velocity, or whatever)? Is a generalized coordinate an example of a dynamical variable?

- Warren

10. Jan 28, 2004

### Amir

Perimeter for what?

11. Jan 28, 2004

### Tom Mattson

Staff Emeritus
Yes, generalized coordinates and generalized momenta together make up the set of dynamical variables.

12. Jan 28, 2004

### Tom Mattson

Staff Emeritus
No, it's not "perimeter", it's "parameter". In both classical mechanics and NRQM, the dynamical variables can be considered functions (dependent variables) of the parameter, time (the independent variable).

In relativity, position gets demoted to the status of a parameter as well.

13. Jan 28, 2004

### chroot

Staff Emeritus
Great, thanks for clearing that up. I won't louse it up again.

- Warren

14. Jan 28, 2004

### Amir

oppsss brain to hand signaling problem .....
so is t constant, or relatively constant ?

Last edited: Jan 28, 2004
15. Jan 28, 2004

### lethe

in Hamiltonian mechanics, yes, positions and conjugate momenta make up the dynamical variable.

in Lagrangian mechanics, its positions and velocities instead.