Schmelzer

The translational symmetry is a symmetry of the laws of Nature, not of the actual configurations. The laws of GR have such translational symmetry. We use the same equations for all times. The matter configuration we see around us have some approximate translational symmetry in space only, and only on very large distances. Nobody knows why, these are simply the facts we observe. That's wrong. The FLRW ansatz has translational symmetry in spatial directions only. There is no translational symmetry in time. Observers at other times will observe differences. They will observe, in particular, higher matter densities, a larger temperature of CMBR, less inhomogeneity in space. And, of course, they will, using the same methods we use, measure a different time after the BB.

Which uncertainty to a reference position? The preferred coordinates fix a particular reference position. And, note, they do this even if the metric in quantum gravity becomes uncertain. The preferred frame remains certain. This is the very point of introducing a fixed absolute background of absolute space and time: You have objects which are not uncertain because of quantum effects, but you have a classical stage where you can define which variable objects exists inside.

No, the guiding wave is \(\psi(q)\) itself. I don't prefer dBB too, there are better realist and causal interpretations. For QFT, I prefer the field ontology, not particles. The usual dBB texts favor the particle ontology. So I don't value them very much. Relativistic papers are usually special-relativistic papers. If they claim relativistic invariance, then there is usually something non-invariant hidden somewhere. If you have a time foliation, you can use it for some realistic causal interpretation. GR does not define one, and has solutions which do not even allow global time-like coordinates (like Goedel's rotating universe). But you can always introduce harmonic coordinates with a time-like time locally. And for the FLRW ansatz we observe (spatial curvature zero) there are also nice global harmonic coordinates. So I prefer to name this a Lorentz ether interpretation of the Einstein equations in harmonic coordinates. This is wrong. Once you make claims about "causative exchange of information", I can assume that you presuppose some notion of causality which includes Reichenbach's common cause principle. But then the assumption that there is no "causative exchange of information" immediately leads to the requirement of a common cause explanations of all possible 100% correlations. And this gives all you need to prove Bell's inequality. You also seem to mingle the necessity of FTL causal explanation of the observable correlations with the impossibility to use them for signalling. The logic behind this confusion is quite simple. Bell's theorem excludes the common cause explanation. So, it leaves two causal explanations: \(A \to B\) and \(B \to A\). Once both explanations are possible and sufficient to explain the correlations, they cannot be used to send information: Sending information would contradict one of the two possible explanations.

Bohmian mechanics cannot violate GR because it has nothing to do with GR. GR is a classical theory incompatible with quantum theory in general, and even more seriously with realist and causal interpretations of GR. To combine them, you have to throw away key properties of GR, like the Strong Equivalence Principle, and use the generalization of the Lorentz ether. Please don't speculate about what I understand and what I don't understand, and try to formulate your questions in a more precise way that can be understood. Simply use standard terminology and refer, if necessary, to standard textbooks.

I'm obviously not getting what you want. I work more in the context of GR, used to work with general systems of coordinates, the special ones known as "inertial reference frames" play no role there. And, given that SR is only the particular case of \(g^{mn}(x) = \eta^{mn}\), I see no reason to care especially about those frames. The three spatial coordinates \(X^i\) define absolute space, and do this at any given moment of absolute time \(T=X^0\). This makes them coordinates. The meaning of "your reference by the above equation isn't a space" remains mystical to me. The equations have been given, every valid particular solution contains four functions \(X^a(x)\) which define the preferred coordinates. You simply have to explain what you want. If you think there is some particular property necessary for kinematics or whatever, name it. If necessary, give a reference to standard GR textbooks where the thing you miss is explained and described. That's wrong. Causation is superluminal in dBB theory. It cannot be used to transfer signals, and this property holds only in quantum equilibrium. But the Bohmian velocity explicitly depends on the global configuration, thus, also on parts of the configuration which are far away.

Ok, second time the harmonic condition: \[ \square X^\alpha = \partial_\mu (g^{\mu\alpha}\sqrt{-g}) = 0 \] The second sentence makes no sense to me.

I have equations for it. A solution of these equations contains also the hidden quantity. Don't forget, the hidden preferred coordinates are also simply coordinates, so the solution in the hidden preferred coordinates can be used as any system of coordinates in GR too. What do you miss about using it? There are additional things which you cannot do in general coordinates. Like computing Bohmian trajectories.

Is there some textbook for this strange science I have never heard of?

The mathematical definition has been given by the harmonic condition. There is no such requirement for offering a mathematical advantage. Nonetheless, of course, harmonic coordinates essentially simplify the Einstein equations. This is well-known since they have been invented. You can find a lot about the mathematical advantages of harmonic coordinates in Fock, V.A. (1964). The Theory of Space Time and Gravitation, Pergamon Press, Oxford This simplification has also some qualitative aspects, namely the Einstein equations obtain the form G^{mn} = g^{ab}\partial_a\partial_b g^{mn} + terms in first order derivatives, the highest order derivatives no longer mix. This was essential for Bruhat to prove local existence and uniqueness theorems for the Einstein equations - in harmonic coordinates. This is mentioned, for example, in http://www.math.sci.hokudai.ac.jp/sympo/180702/slide/Sekiguchi_MSJ-SI_pdf.pdf

I don't understand these questions. What makes the harmonic coordinates preferred is the interpretation which gives these coordinates a preferred status. This has no relation at all to transformation rules or creation and annihilation operators. Preferred coordinates are coordinates, not fields. What means "macro field"?

I don't understand this point. The rules how to handle vectors, other tensor fields and spinors in spacetime are valid for all coordinates, and can be applied to the preferred coordinates too. What makes them preferred is that one has to fix one to define, for example, Bohmian trajectories.

\[\square X^a = \partial_m g^{ma}\sqrt{-g} = 0. \] Why do you think that a hidden preferred frame has to be Lorentz invariant? It certainly does not have to be Lorentz invariant. You can apply a preferred frame like a usual frame. The frame is, according to the equations, preferred if the preferred coordinates are harmonic. Thus, I have to prove that the preferred coordinates are harmonic.

I define a hidden preferred frame by equations for the preferred coordinates. I use harmonic coordinates for this. Given that the generalization of the Lorentz ether to gravity is my own contribution, I cannot refer here to other people than myself. But this should not be a problem, it is published in a good peer-reviewed journal: Schmelzer, I. (2012). A generalization of the Lorentz ether to gravity with general-relativistic limit, Advances in Applied Clifford Algebras 22, 1 (2012), p. 203-242, arXiv:gr-qc/0205035 Once there is a preferred absolute time coordinate, I can use it for quantum theory as usual. In particular, I can use it for the de Broglie-Bohm interpretation, or Nelsonian stochastics, or other realistic and causal interpretations of quantum theory. Once I actually prefer Caticha's entropic dynamics, here the reference to it: Caticha, A. (2011). Entropic Dynamics, Time and Quantum Theory, J. Phys. A 44 , 225303, arxiv:1005.2357 Once I can reuse all what is available in non-relativistic quantum theory, there is no problem with entangled particles in the relativistic domain too.

If you think so, you have not understood the very point of Bell's theorem. If there is no influence from particle A to B, then the 100% correlation if the measurement at B is in the same direction has to be explained by a common cause. Thus, at the time of the measurement, it has to be already well-defined by this common cause. This holds for all directions. But then you can prove the Bell inequalities. Which have been falsified. So, either you give up the common cause principle (and make tobacco industry happy) or you have to explain the correlation by a direct causal influence.

The absolute number is, indeed, the consequence of the universe changing. So, what you named "2. concept" is nonsense. This is already a metaphysical question. If you follow the spacetime interpretation, there exists no absolute time, and all the universe (including we ourselves in 20 years) exists. (Once in such a world there is no "now", one cannot say "exists now", but there would be no difference between what exists "now" and what exists "in 20 years", it is all the same whole history of the whole universe. But you can also assume that there exists an objective absolute time, which would be, roughly, the time after the BB as measured by an observer in rest relative to the CMB radiation. (But this would be only an approximation. The interpretation which would provide such an absolute time would have to provide an exact equation for absolute time too. In this case, the alien which exists now may look at us, but will see only our past.)

Name it causal influence faster than light, whatever. You are, of course, free to hold your belief, but to save the Minkowski interpretation against the Lorentz ether you have to give up a lot: Realism (in the very weak form of the EPR criterion of reality), causality (in any form which contains Reichenbach's common cause principle) and, following my argumentation in Schmelzer, I. (2017). EPR-Bell realism as a part of logic, arxiv:1712.04334 even logic (the "logic of plausible reasoning" or the objective Bayesian interpretation of probability). Of course, this is only special pleading in defense of holy metaphysical principles about the fundamental character of relativistic symmetry. Nobody would reject all these principles in any part of science except the violations of the Bell inequalities. Else, you could as well stop doing science, and first of all the tobacco industry would be happy, given that all that with lung cancer and so on are simply statistical correlation between measurement outcomes; there is no causative “action” involved.

Khrennikov is not really a good source for this. Khrennikov has his own ideas about developing QT, and I don't think they are reasonable. The majority thinks that it is GR which creates the problem, and here I follow the mainstream. No need for this. In fact, it is well-known that the Bell inequality is violated in QFT too. There is some truth in his claim that non-relativistic QM and QFT live separate from each other, with all the foundational discussions localized in non-relativistic QM. But this is not really an issue, because both have the same abstract QT as the base. This abstract QT is essentially non-relativistic. QFT solves this by emphasizing only those parts where the non-relativistic character is less visible. So there is simply silence about the other parts. Those other parts are discussed in non-relativistic QM. A reason is that many, in fact all realist interpretations also need the Schrödinger equation with Relativistic field theories have a similar structure, but those who care about the foundational questions sometimes don't even know this, while others don't want to consider the infinities of field theories so they prefer to restrict themselves to the non-relativistic case. Another problem with the infinities is that there are simple regularizations, like lattice regularizations - but those regularizations destroy relativistic symmetry. This is quite trivial, even in Euclidean space a lattice regularization destroys rotational symmetry. But for those who consider relativistic symmetry as something fundamental, such a breaking of relativistic symmetry is unacceptable. That's why they cannot accept that the theories we have work only for large distances and below some critical length there will be some other theory without relativistic symmetry.

This is a problem of inadequate choices of informal descriptions. The best way to "understand" this is to consider all these Feynman diagrams simply as formal denotations for particular terms in the particular approximation without any deeper meaning. The language was developed for scattering processes, where free particles fly around, hit each other, and then fly away again. Other things, like static field configurations, were irrelevant. If we consider particles flying away independently, when we have to care for the EM field only about light - transversal EM waves. But there are also other EM fields, which do not consist of light freely flying around, namely static EM fields between static sources. When all the particles hit each other, these forces clearly will be important too, even if they don't consist of photons which can fly away freely. So, the approximation formulas will contain the corresponding terms too. And these things have been named "virtual particles". A denotation which confuses many people, but if one accepts that it is only a bad name given to a particular term in a particular approximation, it is not really a problem. Don't forget that photons are essentially quantum effects of the EM field, in a way completely similar to the phonons in condensed matter theory. These are simply discrete energy levels. Don't invest too much in taking them seriously as real particles. (In semiclassical gravity it becomes quite obvious that the fields are more fundamental than the particles - the notion of particles, as well as the vacuum, changes there together with the gravitational field, while the field degrees of freedom don't change.) If you consider things different from scattering theory, this approximation becomes quite irrelevant, and all the methods developed to handle them may appear useless.

QED is, of course, a fine working theory. Gauge theories were favored some time because they are renormalizable and it was thought that non-renormalizable theories make no sense, are unable to make nontrivial physical predictions. But after Wilson we know that such theories make sense as effective field theories. Compatibility of the field equations with SR is also not a problem at all.

I certainly do not propose that foolish idea. I simply oppose the even more foolish idea to limit research to things that are in contradiction to common sense. This is essentially what has been done. See Freire, O. (2005) Science and exile: David Bohm, the hot times of the Cold War, and his struggle for a new interpretation of quantum mechanics. Historical Studies on the Physical and Biological Sciences 36(1), 1-34, arXiv:physics/0508184 for how the most common sense compatible interpretation of quantum theory has been handled. Here the situation has improved somewhat, dBB is now an interpretation one is allowed to consider, if one does not care that much about the mainstream and does not depend on getting grants or so. The situation with the Lorentz ether is much worse, here you risk being banned from forums for publishing references to peer-reviewed journals like Foundations of Physics. I disagree. If something is reasonable or unreasonable depends on the arguments proposed. If the arguments are valid or not depends, in part, on quite objective things like agreement with the rules of logic. Moreover, one can certainly argue about this, by presenting counterarguments. The phrase "purely subjective" refers to something where this is not possible, for example if one likes a particular meal or so. Of course, every reasonable argumentation is a statement made by some subject, and in this trivial sense subjective. But this would not make something "purely subjective" because it would require the exclusion of non-subjective things like arguments playing a role. Funding decisions will always depend on subjective judgments of the science bureaucrats, there is no way to avoid this. And the choice of a research direction will also be a subjective choice, either of the scientist himself (which would be what is required by freedom of science) or by the scientific bureaucracy (by the prescription what has to be done in a grant) or by the latest mainstream fad (what has to be expected in a "publish or perish" environment). All one could hope for would be that the subjective element remains small, and that reasonable arguments would play a large role.

So I do not argue that particular interpretations are right vs. wrong, but about reasonable vs. unreasonable. This holds for interpretations understood as research programs (where the mainstream-supported interpretations have not given anything more fundamental beyond QM and GR despite the open problem of finding a consistent theory of QG, thus, have completely failed.) as well as their pedagogical value (where you can see the failure to understand essential parts of QM as well as GR in forum discussions like here). I do not propose to rule out lines of investigation. I argue in favor of adding some competition in form of other lines of investigation, namely the line of investigation to find interpretations as close to classical common sense as possible and then to try to find a theory of QG starting with those interpretations as the research program.

No. I have given arguments which you obviously decide to ignore. The questions of choice between research programs is, IYO, not part of science? And the question how to teach students too?

I disagree. The different interpretations are not at all on equal foot. Choices between interpretations are essential for an important part of fundamental science, namely the development of more fundamental theories. Interpretations are simply starting points for research programs. The principles which are preserved in a given interpretation are also those to be preserved in those more fundamental theories. If you start with an interpretation which rejects causality, your research program gives up causality. Your choice. If you think that research programs for more fundamental theories are not relevant, then the next important point is which interpretation is easier to understand, and gives the best intuitions for those who learn it. Here, different interpretations are also in no way on equal foot. Those in better agreement with common sense are clearly easier to understand and, given that one can use the intuitions related with the principles which have not been given up, gives better intuitions too. If you want to prevent pupils from using their intuitions related with classical causality, and think this will help them, your choice. The choice of a research program is a personal guess of the researchers, which have to pay for a wrong choice with a personal complete failure of their whole scientific research. But this harms only the researcher himself. So, given this penalty, here it is reasonable to leave complete freedom. This is not the case if we consider the pedagogical differences. Here the wrong choice by the teacher confuses the students, thus, harms other people.

I'm arguing not about about a particular theory, but about causality. Once all leading theories have interpretations compatible with classical causality, there is no evidence in favor of its rejection. Accepting retrocausality would require the rejection of classical causality. There should be quite serious justifications for this, but there are none.

If you want to take retrocausality seriously, your choice. Extraordinary claims need extraordinary evidence. Causal influences into the past is certainly extraordinary. And there is zero evidence for this, given that already good old dBB theory explains all this nicely without any retrocausality.