×
Well done. You've clicked the tower. This would actually achieve something if you had logged in first. Use the key for that. The name takes you home. This is where all the applicables sit. And you can't apply any changes to my site unless you are logged in.

Our policy is best summarized as "we don't care about _you_, we care about _them_", no emails, so no forgetting your password. You have no rights. It's like you don't even exist. If you publish material, I reserve the right to remove it, or use it myself.

Don't impersonate. Don't name someone involuntarily. You can lose everything if you cross the line, and no, I won't cancel your automatic payments first, so you'll have to do it the hard way. See how serious this sounds? That's how serious you're meant to take these.

×
Register


Required. 150 characters or fewer. Letters, digits and @/./+/-/_ only.
  • Your password can’t be too similar to your other personal information.
  • Your password must contain at least 8 characters.
  • Your password can’t be a commonly used password.
  • Your password can’t be entirely numeric.

Enter the same password as before, for verification.
Login

Grow A Dic
Define A Word
Make Space
Set Task
Mark Post
Apply Votestyle
Create Votes
(From: saved spaces)
Exclude Votes
Apply Dic
Exclude Dic

Click here to flash read.

Newton's force law $\frac{d {\bf P}}{dt} = {\bf F}$ is derived from the
Schr\"odinger equation for isolated macroscopic bodies, composite states of
e.g., $N\sim 10^{25}, 10^{51}, \ldots$ atoms and molecules, at finite body
temperatures. We first review three aspects of quantum mechanics (QM) in this
context: (i) Heisenberg's uncertainty relations for their center of mass (CM),
(ii) the diffusion of the C.M. wave packet, and (iii) a finite body-temperature
which implies a metastable (mixed-) state of the body: photon emissions and
self-decoherence. They explain the origin of the classical trajectory for a
macroscopic body. The ratio between the range $R_q$ over which the quantum
fluctuations of its CM are effective, and the body's (linear) size $L_0$, $R_q
/L_0 \lesssim 1$ or $R_q/ L_0 \gg 1$, tells whether the body's CM behaves
classically or quantum mechanically, respectively. In the first case, Newton's
force law for its CM follows from the Ehrenfest theorem. We illustrate this for
weak gravitational forces, a harmonic-oscillator potential, and for constant
external electromagnetic fields slowly varying in space. The derivation of the
canonical Hamilton equations for many-body systems is also discussed. Effects
due to the body's finite size such as the gravitational tidal forces appear in
perturbation theory. Our work is consistent with the well-known idea that the
emergence of classical physics in QM is due to the environment-induced
decoherence, but complements and completes it, by clarifying the conditions
under which Newton's equations follow from QM, and by deriving them explicitly.

Click here to read this post out
ID: 172047; Unique Viewers: 0
Unique Voters: 0
Total Votes: 0
Votes:
Latest Change: June 3, 2023, 7:32 a.m. Changes:
Dictionaries:
Words:
Spaces:
Views: 8
CC:
No creative common's license
Comments: