What Are the Dynamical Variables in Quantum Mechanics of Time?

In summary, time serves the same role in both non-relativistic quantum mechanics and Newtonian mechanics as a dynamical variable or parameter. However, there is no sensible way to construct an operator for time in quantum mechanics. Generalized coordinates and momenta make up the set of dynamical variables, with positions and conjugate momenta in Hamiltonian mechanics and positions and velocities in Lagrangian mechanics.
  • #1
Amir
26
0
does anyone know?
time = ?
 
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  • #2
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
Originally posted by chroot
Time plays the exact same role in (non-relativistic) quantum mechanics as it does in Newtonian mechanics.

That's true.

It's just a dynamical variable.

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
Originally posted by chroot
It's just a dynamical variable.
no t hat, remember?
 
  • #5
Eek, you're right.

- Warren
 
  • #7
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
Originally posted by chroot
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

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
Oh by the way...
A "dynamical variable" satisfies an equation of motion in classical mechanics
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
Perimeter for what?
 
  • #11
Originally posted by chroot
Is a generalized coordinate an example of a dynamical variable?

Yes, generalized coordinates and generalized momenta together make up the set of dynamical variables.
 
  • #12
Originally posted by Amir
Perimeter for what?

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
Originally posted by Tom
Yes, generalized coordinates and generalized momenta together make up the set of dynamical variables.
Great, thanks for clearing that up. I won't louse it up again. :wink:

- Warren
 
  • #14
oppsss brain to hand signaling problem ...
so is t constant, or relatively constant ?
 
Last edited:
  • #15
Originally posted by Tom
Yes, generalized coordinates and generalized momenta together make up the set of dynamical variables.

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

in Lagrangian mechanics, its positions and velocities instead.
 

1. What is the quantum mechanics of time?

The quantum mechanics of time is the study of how time behaves at a microscopic level, as described by quantum mechanics. It involves understanding the nature of time, its properties, and how it interacts with other fundamental forces and particles.

2. How does quantum mechanics explain the flow of time?

According to quantum mechanics, time is not a fundamental physical quantity, but rather emerges from the interactions between particles and fields. The flow of time is described as a continuous and irreversible process, where the future state of a system is determined by its current state and the laws of quantum mechanics.

3. Can quantum mechanics explain the concept of time dilation?

Yes, quantum mechanics can explain time dilation, which is the phenomenon where time appears to pass slower for objects moving at high speeds or in strong gravitational fields. This is due to the relationship between time and space, as described by the theory of relativity.

4. How does quantum mechanics affect our perception of time?

Quantum mechanics challenges our traditional understanding of time as a linear and continuous concept. It suggests that time may be non-linear, with the potential for multiple timelines or parallel universes to exist. Additionally, the concept of quantum entanglement suggests that events in the past, present, and future may be connected, blurring our perception of time.

5. What are the implications of quantum mechanics of time for the universe?

The quantum mechanics of time has significant implications for our understanding of the universe. It suggests that time may have a beginning and an end, and that the laws of physics may have been different in the early stages of the universe's formation. Additionally, it raises questions about the ultimate fate of the universe and the possibility of time travel.

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