Timeline for What is the proper time of a particle in a superposition?
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 3, 2021 at 6:52 | vote | accept | Mauricio | ||
| Jul 3, 2021 at 5:50 | answer | added | Prof. Legolasov | timeline score: 0 | |
| Jul 2, 2021 at 18:29 | comment | added | Mauricio | @Prof.Legolasov sure! But how do you write such a thing? | |
| Jul 2, 2021 at 17:43 | comment | added | Prof. Legolasov | @Mauricio any function on the classical phase space becomes an operator after quantization, so proper time between coordinate time slices $t_1$ and $t_2$ can be rewritten as a function of coordinates and momenta (actually, momenta only) of the particle and hence becomes an operator after quantization. Does this answer your question? | |
| Jul 1, 2021 at 13:02 | comment | added | Mauricio | @AlfredCentauri I agree with your comment "How then does one connect this with a definite proper time? Also, is proper time an observable in QM? " That is basically my question. | |
| Jul 1, 2021 at 13:00 | comment | added | Mauricio | @DvijD.C. Let me see if this makes sense. Suppose that the particle has two complementary eigenvalues $a$ and $V$ (speed/momentum), so that we make a superposition $|a,V=0\rangle + |a,V=v\rangle$ so that $v\lesssim c$ (speed of light). Suppose also that $a$ evolves into $b$ after a time $t$ since the experiment started for speed $v=0$. Would then I find that exactly after time $t$ that the particle is in state $|b,0\rangle + |a,v\rangle$ since the state to the right experiences a different proper time and not enough time has passed to change from $a$ to $b$? | |
| Jul 1, 2021 at 6:50 | comment | added | Mauricio | @JEB thanks! I would just like to say that the link you provided is about GR and QM, not SR, but it is still interesting. | |
| Jun 30, 2021 at 23:35 | comment | added | Alfred Centauri | I don't follow the 3rd paragraph. As I understand QM, the fact that one finds the particle in a definite state of momentum just after the momentum is measured doesn't imply that the particle had that momentum (or a definite momentum at all) before the measurement. How then does one connect this with a definite proper time? Also, is proper time an observable in QM? | |
| Jun 30, 2021 at 21:57 | review | Close votes | |||
| Jul 5, 2021 at 3:33 | |||||
| Jun 30, 2021 at 21:35 | comment | added | user87745 | What do you mean by "mismatch"? A superposition is a superposition, it's not a mismatch. A particle can simply be in a superposition. As for the observable effects, of course, there would be. For example, if one prepares the system in the same initial state and does the experiment repeatedly, one would find the particle in different momentum eigenstates each time they measure its momentum, etc. I don't exactly see what's the question. | |
| Jun 30, 2021 at 21:00 | history | tweeted | twitter.com/StackPhysics/status/1410342399667224583 | ||
| Jun 30, 2021 at 19:33 | comment | added | JEB | arxiv.org/pdf/1710.06504.pdf | |
| Jun 30, 2021 at 16:44 | comment | added | Mauricio | @Prof.Legolasov sure, that's what I said in the text above. | |
| Jun 30, 2021 at 16:43 | comment | added | Mauricio | @JEB if you prefer you can think not of an elementary particle but more like a complex composite quantum system with some internal clock or change $t$ for a half-life time. I sure get that that relativistic QM leads to QFT, which can be much harder, but is proper time never ever treated in quantum mechanics? | |
| Jun 30, 2021 at 16:25 | comment | added | Prof. Legolasov | "What is the proper time of a particle in a superposition?" a superposition of the two proper times? | |
| Jun 30, 2021 at 14:40 | comment | added | JEB | Why does proper time matter? Particles don't age, and you can't decay in fixed time, rather it's a fixed probability per unit time. Particles and QM are inherently non-relativistic, so once you bring in relativity you need fields are then all you know are approximate free-particle initial and final states, along with a transition amplitude. | |
| Jun 30, 2021 at 12:24 | history | edited | Mauricio | CC BY-SA 4.0 |
added 362 characters in body
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| Jun 30, 2021 at 12:19 | history | asked | Mauricio | CC BY-SA 4.0 |