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If you want to write, "Bohmian mechanics is incompatible with special relativity", then I will agree with you. If you want to write, "therefore special relativ

If you want to write, "Bohmian mechanics is incompatible with special relativity", then I will agree with you. If you want to write, "therefore special relativity is wrong", then do so, and we'll have a lot less to talk about given how well-supported special relativity is by direct in-solar-system evidence. In a previous edit up-thread you added that [de Broglie]-Bohmian mechanics has not been turned into a field theory. Incorrect. It is easy to do turn it into a field theory, but that field theory will not be relativistic. One can add extra structure on the spacetime of special relativity and get a quasi-relativistic field theory. As you note in your second paragraph 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 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.

naasking 4y ago
I'm genuinely confused about what we're disagreeing on. Yes, Bohmian mechanics has been extended into a field theory. In fact, it's been extended to many field theories all of which have flaws such that no single contender has emerged as it has with orthodox QM. I think this is a perfectly reasonable interpretation of my original claim that Bohmian mechanics doesn't have a field theory. I'm aware of the paper you linked. As with all other attempts, it hasn't really gone anywhere. There's nothing else from your comment I seriously disagree with, and it's not clear what, exactly, is your issue with how I've framed the problem. It's clear that orthodox QM posits a formal model that lets you make certain derivations that are compatible with relativity, and those derivations contain steps that are not compatible with Bohmian mechanics because of the latter's ontology. I'm positing: 1. that those steps merely kick the can down the road, leaving certain irreconcilable differences between relativity and QM that we're still dealing with. 2. that Bohmian mechanics puts this problem front and centre, and if it can be overcome, it will provide unique insight into how to solve those issues in other interpretations. It's kind of like how classical logic permits the excluded middle in a proof, where intuitionistic logic does not. Using the law of the excluded middle is a useful shortcut to truth, but it does not yield a path to a construction of the object in question. Explicit constructions are considerably richer in properties and so provide considerably more insight. Orthodox QM excludes many details of what's going on, sort of like a proof depending on the law of the excluded middle, where Bohmian mechanics makes everything explicit and manifest, sort of like a construction in an intuitionistic proof. It seems very plausible that the richer construction will be more difficult to reconcile with a different formal model, but it also will yield considerably more insight if it can be done.
- raattgift 4y ago
  tl;dr: > I'm genuinely confused about what we're disagreeing on. That our universe is locally Lorentz-invariant everywhere. > I think this is a perfectly reasonable interpretation of my original claim that Bohmian mechanics doesn't have a field theory. I don't, however charitably I am willing to read this as "Bohmian mechanics doesn't have a relativistic field theory" given the new material in your latest comment. "Relativistic" means that there is a Lorentzian manifold involved, either directly or as emergent property of the configuration space. > front and center No, what puts Lorentz-invariance front and centre in this context is the Standard Model Extension <https://en.wikipedia.org/wiki/Standard-Model_Extension https://en.wikipedia.org/wiki/Standard-Model_Extension> which can carry the parameters for a de Broglie-Bohm pseudo-relativistic field theory which has additional Lorentz-invariance-violating (LIV) structure. Tests of such parameterized theories have all failed unless the controlling coefficients are designed to vanish beneath the floor of current-technology testability (in which case is the more complicated theory useful?). There is no evidence at all for LIV physics in direct tests in multiple locations in our solar system, in observational tests within our solar system, or beyond it. Lorentz-invariance is probably the strongest-tested aspect of modern physics, as it forms part of any test of the standard model of particle physics, quantum electrodynamics, or general relativity. <https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_vi...> > irreconcilable differences between relativity and QM There are no such differences between special relativity and relativistic QM, nor can there be because of the design of the latter type of theory. So you must be arguing that quantum mechanics is not special-relativistic. OK, more on that below. The only thing that general relativity brings to the table is that global Lorentz-invariance becomes local Lorentz-invariance ("local" can be an arbitrarily large finite region, however) becomes ultralocal Lorentz-invariance in strong curvature, as in the radius of curvature is much less than the characteristic lengths in quantum chromodynamics (e.g., the available free-fall trajectories lead to spaghettification which ought to produce hadronization of the tidally-disrupted QGP or colour string, where the resulting hadrons are then themselves subject to tidal disruption; for a slowly-spinning black hole we're interested in the axial stress as the Weyl tensor deforms sphere->lengthening American football, one end pointing in, one pointing out->lengthening thin tube with slightly fatter middle than ends->...). Since in GR strong curvature is hidden within various types of horizons there is no need to worry about proving ultralocal Lorentz-invariance, rather than proving e.g. the existence and behaviour of horizons (which are more readily testable features of GR). Maybe someday we'll watch a black hole fully under our control evaporate completely; or be able to induce extreme angular momentum and/or electric charge on a black hole we control. Until then, all we can do is speculate that either Lorentz-invariance holds up even in black holes and during the hot big bang, or the LIV in those regions washes out of our present-day observability through some unknown process. > if it can be overcome Well, right, you seem to be claiming that the universe is not locally Lorentz-invariant at every point. That is, that the universe is not relativistic. Fine, that's a claim which has been made before, and it is almost always a physically testable claim. Now try to prove it, like the other claimants. It may take considerable effort to do so in some "ontologically pure" way, but that's on you and anyone you convince to collaborate with you in this programme of research. I promise that any serious effort would be taken seriously by at least some relativists. If nothing else, they would show you how to cast your attempted proof into a more standard test theory, and in particular how the test theory's coefficients relate to your proposal, and how they can be compared to experiment and observation. (Clever people like Clifford Will do this in gravitation with some regularity <https://en.wikipedia.org/wiki/Alternatives_to_general_relativity#Parametric_post-Newtonian_parameters_for_a_range_of_theories https://en.wikipedia.org/wiki/Alternatives_to_general_relati...>. There are numerous parametrized test theories of a range of aspects of the Standard Model and BSM particle physics, too.)

naasking 4y ago

I'm genuinely confused about what we're disagreeing on. Yes, Bohmian mechanics has been extended into a field theory. In fact, it's been extended to many field theories all of which have flaws such that no single contender has emerged as it has with orthodox QM. I think this is a perfectly reasonable interpretation of my original claim that Bohmian mechanics doesn't have a field theory. I'm aware of the paper you linked. As with all other attempts, it hasn't really gone anywhere. There's nothing else from your comment I seriously disagree with, and it's not clear what, exactly, is your issue with how I've framed the problem. It's clear that orthodox QM posits a formal model that lets you make certain derivations that are compatible with relativity, and those derivations contain steps that are not compatible with Bohmian mechanics because of the latter's ontology. I'm positing: 1. that those steps merely kick the can down the road, leaving certain irreconcilable differences between relativity and QM that we're still dealing with. 2. that Bohmian mechanics puts this problem front and centre, and if it can be overcome, it will provide unique insight into how to solve those issues in other interpretations. It's kind of like how classical logic permits the excluded middle in a proof, where intuitionistic logic does not. Using the law of the excluded middle is a useful shortcut to truth, but it does not yield a path to a construction of the object in question. Explicit constructions are considerably richer in properties and so provide considerably more insight. Orthodox QM excludes many details of what's going on, sort of like a proof depending on the law of the excluded middle, where Bohmian mechanics makes everything explicit and manifest, sort of like a construction in an intuitionistic proof. It seems very plausible that the richer construction will be more difficult to reconcile with a different formal model, but it also will yield considerably more insight if it can be done.

raattgift 4y ago
tl;dr: > I'm genuinely confused about what we're disagreeing on. That our universe is locally Lorentz-invariant everywhere. > I think this is a perfectly reasonable interpretation of my original claim that Bohmian mechanics doesn't have a field theory. I don't, however charitably I am willing to read this as "Bohmian mechanics doesn't have a relativistic field theory" given the new material in your latest comment. "Relativistic" means that there is a Lorentzian manifold involved, either directly or as emergent property of the configuration space. > front and center No, what puts Lorentz-invariance front and centre in this context is the Standard Model Extension <https://en.wikipedia.org/wiki/Standard-Model_Extension https://en.wikipedia.org/wiki/Standard-Model_Extension> which can carry the parameters for a de Broglie-Bohm pseudo-relativistic field theory which has additional Lorentz-invariance-violating (LIV) structure. Tests of such parameterized theories have all failed unless the controlling coefficients are designed to vanish beneath the floor of current-technology testability (in which case is the more complicated theory useful?). There is no evidence at all for LIV physics in direct tests in multiple locations in our solar system, in observational tests within our solar system, or beyond it. Lorentz-invariance is probably the strongest-tested aspect of modern physics, as it forms part of any test of the standard model of particle physics, quantum electrodynamics, or general relativity. <https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_vi...> > irreconcilable differences between relativity and QM There are no such differences between special relativity and relativistic QM, nor can there be because of the design of the latter type of theory. So you must be arguing that quantum mechanics is not special-relativistic. OK, more on that below. The only thing that general relativity brings to the table is that global Lorentz-invariance becomes local Lorentz-invariance ("local" can be an arbitrarily large finite region, however) becomes ultralocal Lorentz-invariance in strong curvature, as in the radius of curvature is much less than the characteristic lengths in quantum chromodynamics (e.g., the available free-fall trajectories lead to spaghettification which ought to produce hadronization of the tidally-disrupted QGP or colour string, where the resulting hadrons are then themselves subject to tidal disruption; for a slowly-spinning black hole we're interested in the axial stress as the Weyl tensor deforms sphere->lengthening American football, one end pointing in, one pointing out->lengthening thin tube with slightly fatter middle than ends->...). Since in GR strong curvature is hidden within various types of horizons there is no need to worry about proving ultralocal Lorentz-invariance, rather than proving e.g. the existence and behaviour of horizons (which are more readily testable features of GR). Maybe someday we'll watch a black hole fully under our control evaporate completely; or be able to induce extreme angular momentum and/or electric charge on a black hole we control. Until then, all we can do is speculate that either Lorentz-invariance holds up even in black holes and during the hot big bang, or the LIV in those regions washes out of our present-day observability through some unknown process. > if it can be overcome Well, right, you seem to be claiming that the universe is not locally Lorentz-invariant at every point. That is, that the universe is not relativistic. Fine, that's a claim which has been made before, and it is almost always a physically testable claim. Now try to prove it, like the other claimants. It may take considerable effort to do so in some "ontologically pure" way, but that's on you and anyone you convince to collaborate with you in this programme of research. I promise that any serious effort would be taken seriously by at least some relativists. If nothing else, they would show you how to cast your attempted proof into a more standard test theory, and in particular how the test theory's coefficients relate to your proposal, and how they can be compared to experiment and observation. (Clever people like Clifford Will do this in gravitation with some regularity <https://en.wikipedia.org/wiki/Alternatives_to_general_relativity#Parametric_post-Newtonian_parameters_for_a_range_of_theories https://en.wikipedia.org/wiki/Alternatives_to_general_relati...>. There are numerous parametrized test theories of a range of aspects of the Standard Model and BSM particle physics, too.)