Timeline for Can the pilot wave theory explain why the circumference of an orbit has to be an integer multiple of the wavelength of the electron orbiting it?
Current License: CC BY-SA 4.0
8 events
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| Nov 27, 2022 at 7:29 | comment | added | Valter Moretti | Many thanks for this quick review! So there are problems with a full relativistic construction. I know one of the authors: Nino Zanghi. | |
| Nov 27, 2022 at 2:10 | comment | added | J. Murray | Finally, there are proposals that the privileged foliation could be extracted from the wavefunction(al) itself, rather than being an extra structure which we impose on spacetime by hand. This would alleviate some of the tension with relativity, but would still conflict with our relativistic intuition that no such privileged foliations should need to exist. This reference reviews some such possibilities. | |
| Nov 27, 2022 at 2:10 | comment | added | J. Murray | See this reference for more on deBroglie-Bohm and bosonic fields - I am not aware of the current status of extending this to fermionic fields, and as far as I know it remains an open problem. | |
| Nov 27, 2022 at 2:10 | comment | added | J. Murray | Next, de Broglie-Bohm can be extended to (at least bosonic) field theories, where the fundamental "beables" of the theory are not lists of particle positions, but rather field configurations. In essence, the "pilot wave" becomes a functional which guides the evolution of the field configurations, rather than a function which guides the evolution of the particle positions. By imposing relativistic wave equation and choosing a privileged foliation of spacetime, such theories may also be made pseudo-relativistic. | |
| Nov 27, 2022 at 2:09 | comment | added | J. Murray | This fixes the most egregious problem with making deBroglie-Bohm relativistic - namely that the velocity of a particle depends on the simultaneous positions of the other particles - but does so in the bluntest possible way (by introducing a privileged notion of simultaneity). In this sense, the theory is not really relativistic in a fundamental way. See this reference for more on such models. | |
| Nov 27, 2022 at 2:09 | comment | added | J. Murray | @ValterMoretti Greetings Valter, I am unfortunately not much of an expert, but I can tell you what I know. First, one can define a pseudo-relativistic deBroglie-Bohm theory for $N$ relativistic point particles by choosing a relativistic wave equation (e.g. the Dirac eqn) and imposing a privileged foliation of spacetime into spacelike leaves $\Sigma$. The idea is that the velocity $\dot x_k$ of the $k^{th}$ particle on a given leaf $\Sigma$ depends on the positions of the other particles where their worldlines intersect $\Sigma$. | |
| Nov 26, 2022 at 17:17 | comment | added | Valter Moretti | It seems that you are an expert on these issues. As far as you know, what is the actual status of the relativistic generalisation of the deBroglie-Bohm theory? | |
| Jul 17, 2022 at 2:49 | history | answered | J. Murray | CC BY-SA 4.0 |