Timeline for What's the intuitive reason that phase space flow is incompressible in Classical Mechanics but compressible in Quantum Mechanics?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 5, 2018 at 14:07 | comment | added | Cosmas Zachos | I'm not sure I understand radioactive fluid stuff, and I don't want to stand between you and your intuition. As WP emphasizes, compressible means failure of the material derivative to vanish because the divergence of the velocity fails to vanish. Probability is conserved, of course, but not in every comoving cell, where it may concentrate in or diffuse out of. As in my other answer linked, the efflux amounts to the integral of the difference between the MB and the PB over such a cell. | |
| Jul 5, 2018 at 9:04 | comment | added | jak | So formulated differently, is the QM phase space flow compressible in the usual sense (gas vs. fluid) or more like in the radioactive fluid vs water case? I would be really interested to hear @CosmasZachos opinion | |
| Jul 5, 2018 at 9:03 | comment | added | jak | Thanks! Maybe the terminology is somewhat unfortunate here. What I was thinking of is like the difference between water and a radioactive fluid. The number of water molecules stays the same over time and therefore the volume occupied by the water. In contrast, for the radioactive fluid molecules decay and over time a smaller and smaller volume is occupied. However, "compressible" really seems like the wrong word here. It's more like "self-compressing" (or expanding) over time. The crucial question now, of course, is what is really going on in QM. | |
| Jul 5, 2018 at 8:32 | comment | added | sagittarius_a | A crompressible flow still fulfills a continuity equation. What makes a flow incompressible is only the fact that the divergence of the velocity field is zero. | |
| Jul 5, 2018 at 7:52 | history | edited | jak | CC BY-SA 4.0 |
added 2 characters in body
|
| Jul 5, 2018 at 7:22 | history | answered | jak | CC BY-SA 4.0 |