Can Bohmian mechanics be made relativistic?

above, one can do this by picking out a universally true time axis and demoting the infinity of others to pseudo-time. However, in "Can Bohmian mechanics be made relativistic?" <https://arxiv.org/abs/1307.1714v2> the authors take seriously the idea that the distribution of matter (and its dynamics) picks out a particular foliation. As a relativist this doesn't bother me: the distribution of matter at cosmological scales (i.e., ignoring "local stuff" it's effectively homogeneous and isotropic from all vantage points) and its dynamics picks out the cosmological frame, after all, and we use that to talk about things happening billions of years ago. However, it's hard to grind this kind of matter-picks-out-a-frame thinking down to the scale of a terrestrial particle-collider experiment or to natural astrophysical "experiments" like magnetars. (The second-last paragraph of the Discussion section of the paper is provocative, however.) Also, I am cautious about predicting whether one can successfully "comma-goes-to-semicolon" a possibly-relativistic frame into a properly covariant theory. Often attempting to do so shows that one has what one might roughly call a surplus of long-distance forces that vanish only in the possibly-relativistic frame (or some family of related frames) but can be made incredibly strong in some other frame (or set of families of frames). The authors above are similarly cautious, and cannot answer their own question. Finally, > general relativity if you are incompatible with special relativity at every point then you are also automatically incompatible with general relativity, because that guarantees SO(3,1)+ at every point and in its ultra-local neighbourhood even if you abolish it as a global symmetry. So your qualification of "relativity" as "general relativity" is unhelpful; SR, after all, just a special case of general relativity which is much closer to everywhere in the solar system than anything with strong enough curvature to make a difference in a beta- decay or relativistically smashing together two lead nuclei.

from the wave function itself [1], which means a preferred reference frame is actually a part of every interpretation of QM. This is the kind of result that probably would have never been found without research into Bohmian mechanics. > Also, if it were the leading view, I don't think discussions of a simulated universe would be as popular. I don't see why. Simulated reality is a purely logical argument [2]. [1] https://arxiv.org/abs/1307.1714 [2] http://www.simulation-argument.com/

What does that mean? Well, there is some stuff with positions and those positions change in time. And that's what BM gives. It explains, immediately, why a wave function is on a configuration space of particles. Having this leads to a variety of important notions. For example, having a position leads to clarity on identical particles, namely, use a space without labels on the particles and the wave functions just work out[1] (disclaimer: I am an author on that one and did part of my PhD thesis on that [4]; my thesis also derives spin as well as the Dirac equation from a Bohmian perspective). Another example is QFT and divergences. From a Bohmian perspective, QFT is best thought of as about wave functions over a configuration space consisting of different disjoint sectors involving different number of particles. To do this, there is a random jump process created (not deterministic!). Thinking about wave functions that work with that, one is led to wave functions where the probability moves from one sector to another appropriately based on this jumping. And that solves, at least in some simple cases, the UV divergence of QFT.[2] The randomness of BM is actually quite interesting. It is all about the Quantum Equilibrium Hypothesis, something which is justified in similar ways to thermodynamics kinds of arguments. In fact, it makes it clear that what is interesting is not why we can't know some things, but why we can know stuff at all. [3] Also, in case you have not seen it, you might want to take a look at a version of MW by some of the Bohmians behind the papers.[4] As with most things, there is a lot of clarity in their perspective. Finally, as for why BM is not more popular, well, let's just say it is rather hard to stay in academia as a Bohmian. I barely tried, largely because academia is unpleasant for a variety of other reasons, but it simply is very hard to get hired when working on unfashionable material. Grants and all that. This is on top of the problem of getting people to change some fundamentally long held beliefs. This goes hand in hand with the fact that standard QM is the thermodynamics version of BM and so QM agrees with BM empirically to the extent that QM makes predictions. That is to say, BM provides the rigorous foundation for the collapse rules. [0]: Can Bohmian Mechanics be Made Relativistic? http://arxiv.org/pdf/1307.1714 [1]: Fermionic Wavefunctions on Unordered Configuration Space. http://arxiv.org/pdf/1403.3705 [2]: Bohmian Trajectories for Hamiltonians with Interior–Boundary Conditions. https://arxiv.org/pdf/1809.10235.pdf [3]: Quantum Equilibrium and the Origin of Absolute Uncertainty. http://arxiv.org/pdf/quant-ph/0308039 [4]: Many Worlds and Schrodinger's First Quantum Theory. http://arxiv.org/pdf/0903.22111 [5]: Connections with Bohmian Mechanics. http://jostylr.com/thesis.pdf

exist as there are particles with trajectories that go somewhere. I suspect that if the predictions were proven right, someone would look at standard QM and deduce that that should have been considered the right answer all along. --- As for quantum field theory and its divergences, while the work has only been done on some of the simpler models, there is a process called "Interior Boundary Conditions" which removes the need for ultraviolet cutoffs: https://arxiv.org/abs/1703.04476 The basic idea is that the free Hamiltonian's natural domain is not appropriate when adding in the particle creation/annihilation operators and thus a boundary condition representing those interactions needs to be chosen. More or less, the appropriate set of wave functions are those whose probabilities adjust themselves appropriately for the particle creation and annihilation. This approach was inspired by a Bohmian perspective, but it is a mathematical methodology that does not require accepting that perspective. Thus, there is some hope that the divergences are solvable already with what we know. --- As far as I know, the most fundamental issue of relativity and quantum mechanics is that of time. Namely, there is a strong notion of "now" seemingly from QM and there is a strong notion of "not now" from relativity. Neither statements are absolute, but the tendencies are there. Bell's work suggests that nature is either nonlocal (nowish) or there is something not quite defined about experiments from what we think there is (many universes, experimental results not finalized until actually compared, somehow). In Bohmian mechanics, the issue of "now" is quite acute as the trajectories of each particle depends not only on the wave function, but on the position of all the other particles "now". This is problematic as there is no definite "now" in relativity. One solution is to define a "now", namely, define slices of space-time which define the instants of now. This can be done in a Lorentz covariant way in flat space-time in such a manner that we cannot detect the foliation, by defining the foliation from the dynamic structures already present: https://arxiv.org/abs/1307.1714 The authors are not necessarily advocating for this as it seems philosophically wrong, but, again, Bell's work strongly suggests something of this kind needs to be true, no matter how distasteful it is. This would necessarily imply that space-time can have a foliation, something which is not always true. Perhaps the dynamics defining the space-time metric in the quantum framework ensures that this does indeed stay the case.

other issues [1]. Which is more parsimonious between many-worlds and pilot waves is hotly debated among philosophers of science. > Also: aren't we to the point where measurement makes perfect sense (besides the values of the probabilities, as given by the Born rule), via entanglement between experiment+lab frames, and decoherence of unrelated Degrees of Freedom? "Measurement now makes perfect sense" is an interpretation-specific claim. Measurement still doesn't make sense in Copenhagen, measurement mostly makes sense in Many-Worlds, modulo some of the difficulties I mentioned earlier [1]. > Also, pilot wave fails badly in relativistic extensions, for the obvious reason that a universe-wide pilot wave function is hard to make covariant. It's actually pretty trivial if you're willing accept a preferred foliation of space-time, as long as the preferred frame is unobservable. This seems aesthetically unappealing, hence why people perpetuate this myth of "difficulty", but it's not a priori wrong. Fortunately, a preferred foliation can actually be derived from the wave function itself, which means this foliation exists in every interpretation of QM [2]. This is the kind of surprising result that probably no one would have even bothered looking for, and I think it proves John Bell's position that non-locality is the unresolved problem of QM [3]. Other interpretations just let you paper over it, to our detriment IMO. [1] https://plato.stanford.edu/entries/qm-manyworlds/#6 [2] https://arxiv.org/abs/1307.1714 [3] John Bell, who was a big fan of pilot waves by the way.

foliation though there are possibilities to use within the existing structures: https://arxiv.org/abs/1307.1714 I also think NSA has a naming problem. By its very name, how can it ever be standard? I think the issue is also that the limit fits in with numerical analysis in that it talks about errors. NSA sounds like it skips the error analysis and is only concerned with stuff at the limit which is certainly useful in many instances, but not always.