Schmelzer

The most common sense compatible interpretation is IMHO Caticha's entropic dynamics Caticha, A. (2011). Entropic Dynamics, Time and Quantum Theory, J. Phys. A44:225303, arxiv:1005.2357 There is a configuration space trajectory \(q(t)\in Q\) and there are some other, unspecified variables y. I prefer to use as these variables simply the same configuration space, but of the external world. Then, we have incomplete information about it if we know only how the state was prepared, thus, we know some probability distribution \(\rho(q,y)\). Then we define for each \(q\in Q\) the resulting probability \(\rho(q) = \int \rho(q,y)dy\) and the entropy \(S(q) = -\int \ln \rho(q,y) \rho(q,y)dy\). Then we have for \(\rho(q)\) a diffusion (Brownian motion) with parameter \(\hbar\) combined with a movement toward higher entropy, and a generalization of the Hamilton-Jacobi equation for the entropy. This pair of equations gives, if one combines \(\rho(q)\) and \(S(q)\) into some artificial complex function with the phase \(\ln \rho - S\) (modulo signs and so on) this gives the Schrödinger equation for that complex function. This nice accident allows us to use the full power of the mathematics of quantum theory, but is otherwise of no fundamental importance. Just a happy accident.

The Schrödinger equation allows violations of the Bell inequalities. Classical theories (EM, GR) don't allow them, indepedent of any CPT or whatever symmetry. QFT allows violations of the BI. The formulations used for QFT, CPT symmetry and so on, are irrelevant for this question.

The Lorentz-Poincare interpretation of special relativity is not my pet theory, but was the only interpretation of SR from 1905-1909, until Minkowski proposed his spacetime interpretation in 1909. Before being banned forever for mentioning this triviality again, I would suggest the adminstration of the forum how to handle the original interpretation of SR, as proposed by Lorentz and Poincare, which is usually named "Lorentz ether", and those who follow the recommendations given by Bell in Bell, J.S. (1976). How to teach special relativity. Progress in Scientific Culture 1(2), reprinted in Speakable and Unspeakable in Quantum Mechanics where he suggests to teach also this traditional approach to relativity because it gives the people better intuitions. Some forums decide to ban discussions of the Lorentz ether as anathema. In this forum, it was suggested that it is possible to discuss it, but in reality I was banned for doing it. I think banning people for doing things not explicitly forbidden is much worse than explicitly forbidding whatever theories of physics the admins don't like. That's fine with me, I have, of course, my own opinion about the scientific value of such rules, but I accept the right of the administration of the forum to forbid whatever they don't like. But not to forbid it in the rules, but then banning people in reality, naming the Lorentz-Poincare interpretation a personal pet theory, ... Just to clarify how I see the actual situation: There are threads for discussing my "pet theories", namely my generalization of the Lorentz ether to gravity and my ether model of the SM. And there is the Lorentz ether, as the classical interpretation of SR, which is not my pet theory. Therefore I think that I'm allowed to discuss it in every thread about relativity, if it gives some other perspective which may be interesting for some readers. I do this following the recommendations made Bell, thus, I follow here an established mainstream scientist too, and I do not see any violation of the actually existing rules of the forum. So, please clarify the rules of this forum, regarding the discussion of the original interpretation of SR. Is it anathema or legitimate part of established science? Oh, I see the date is Friday. the 13th. So, the result of this posting is predictable - a ban forever. So, good buy.

It is simply wrong. The phrase "completely wrong" would be simply a quite meaningless amplification, the "not completely wrong" makes even less sense. Only observation - interpreted based on logic as well as the principles of scientific methodology. This is how empirical science proceeds. Logic and scientific methodology are not empirical science. And I disagree with them. No, I prefer to support them with arguments. To support something with references to authorities I leave to religious people. I use references to refer to particular papers if I use a result of this paper, or to refer to some standard textsbooks if the issue is not that interesting for me. For the important things, I rely on own arguments.

As now already usual, I have got another warning for "bringing my pet theory" into a discussion where nothing in my post has any relation to my pet theories. These pet theories are, first, an ether theory of gravity, arxiv:gr-qc/0205035, and, second, an ether model for the SM arXiv:0908.0591. The thing I have introduced was, instead, the Lorentz ether interpretation, which is the classical, original interpretation of special relativity before Minkowski proposed his spacetime interpretation 1908, as explained in the posting itself. It looks like in this sense even https://www.physicsforums.com/ is more moderate - they at least openly declare that the Lorentz ether is forbidden, here there is no such rule forbidding the Lorentz ether but it looks I will receive warnings until I get banned simply for discussing the original interpretation of SR.

No, classical logic has a different status. That it is incomplete does not make it wrong. (That it is incomplete was obvious to me even as a child, it was, last but not least, clear that for most of what one needs in everyday life classical logic is not directly applicable because we do not have enough certain presuppositions to derive something nontrivial. The logic of plausible reasoning - the objective Bayesian interpretation of probability - has solved this problem for me.) Physical theories, if not "completely wrong" (which happens, often enough, too, essentially all the GUTs, strings, and supersymmetric theories are certain candidates for being completely wrong) usually survive only as approximations. So, in a strong sense they are completely wrong: Even an acceptable approximation is wrong. Strangely, many people like to weaken the meaning of wrong and claim that once something is, under some circumstances, acceptable as an approximation, it is fine, not wrong. I'm unable to understand why one would do such things. You seem to be one of them. So, I think "not completely wrong" means "sometimes useful as an approximation". I have explained that this is not the case. It cannot be observation that shows you are wrong, but observation in combination with interpretation. This interpretation always uses logic as well as scientific methodology. You simply ignore this explanation and repeat a primitive simplification. And you completely ignore the argument that all that is imaginable as a conflict between observation and the principle that observable correlations require causal explanations is that for some observed correlation no causal explanation is known - and that this would be simply an open scientific problem, no justification for a rejection of the principle. So, how an empirical falsification of the principle that observable correlations require causal explanation You think so? This principle is straightforward common sense. Searching for a reference where such elementary things are explained? Sorry, I'm too lazy for this. Feel free to conclude that, given that I do not present a reference, the principle is my personal invention, and that the arguments I have provided to support its importance can be, without reference, ignored. If you really would like to read something about it, I would recommend to search for literature about Reichenbach's principle of common cause.

What if observations show the invented principles of classical logic to be wrong? This is simply not possible. Observations by themselves show nothing. Something has happened, I have seen a nice picture. Fine. Observations can show something only if evaluated appropriately, following the rules of logic as well as the rules of scientific methodology. How can observations show that these principles are wrong? For the principle that observable correlations require causal explanations it is impossible even in principle, because all what is imaginable is that you have correlations but no causal explanation. But this is simply an open scientific problem. And an open scientific problem is certainly not a sufficient reason to reject scientific methodology.

????? Of course, the development of new theories is based on what has been reached by old theories. But they necessarily contain essentially new elements. One cannot derive them based on old theories, they contradict them in some essential points. I disagree. If you present a new theory, you have to start with some axioms. These axioms cannot be derived from old theories, at least some of them are in conflict with the old theories, contradict them. What you use as axioms, is a free choice. But the axioms of a theory may be, at best, plausible from the point of view of the old theories. It is quite common in classical physics to define new theories by postulating a Lagrangian. For a test particle on a fixed background of a metric theory of gravity, proper time can be used as the Lagrangian. Once one has defined that theory in this way, everything else can be derived from this. So, the , and geodetic equations will be derived as Euler-Lagrange equations. And a derivation is certainly also an explanation. What's the point of this remark? I was also able to develop new theories and to publish them. They have big enough advantages compared with existing competitors, their only problem is that they are completely ignored by the mainstream. Ignorance is not an argument, so I have no reason at all for shame even in comparison with Einstein. It is not, because, following Newton's definition, time measured with clocks is not absolute time, but apparent time. He writes in Principia Mathematica (1687) Nobody cares about where things come from. Kepler's laws came from astrological considerations, this does not diminish their scientific value. Mathematical methods can be used freely, without any copyright. So, if you want to compute Doppler-shifted sound waves, you are free to use the Lorentz transformations with the speed of sound instead of c. Moreover, if we look at the history, we find that the Lorentz transformations go back to Lorentz 1895, thus, was developed before Einstein's 1905 paper, and therefore independently of SR. My description differs from SR in its Minkowski time interpretation in quite obvious ways, it does not presuppose the existence of any spacetime, but is compatible with classical absolute space and absolute time, following Newton's definition of them. The Lorentz transformation simply transforms one particular solution of some wave equations into other, Doppler-shifted ones. This is a useful operation without any theory of relativity behind it. There is no ether in the Minkowski spacetime interpretation of special relativity. The key source for the Minkowski interpretation is "space and time", a talk held 21. Sept. 1908 and published 1909. The original interpretation goes back to Lorentz and Poincare and is named today "Lorentz ether". That it is possible is an obvious consequence of the history: One of the key parts of the SM, the EM field, has been constructed by Maxwell completely without relativity, based on an ether theory. Nothing would have changed if, for whatever reason, Minkowski would not have invented his spacetime interpretation, and the Lorentz ether would have remained the standard interpretation of SR.

I don't try. I simply explain the situation. If the admins decide to ban me, such is life. Indeed. But this is only half of the problem. The other half is what the moderators think about it. In another thread, where the Newtonian definition of time was discussed, and I have given an answer to your question ("You didn't answer my question. Is my coordinate time the same as yours?"), I have received the following reaction: I care a lot about the members who actually want to learn mainstream physics. I follow in these question the recommendations given by Bell in this paper Bell, J.S. (1976). How to teach special relativity. Progress in Scientific Culture 1(2), reprinted in Speakable and Unspeakable in Quantum Mechanics: And I fully agree with Bell - it is better to teach students those interpretations which are more compatible with classical common sense. Like the realistic and causal interpretations of QT as well as the Lorentz ether interpretation of special relativity. Which is, BTW, the original interpretation, the spacetime interpretation was proposed only later by Minkowski. Whatever, my evil "pet theory" had not even been mentioned. I was not bringing up it, I simply answered a question of another moderator, who insisted on an answer. It did not help. This is, again, not about evil moderators handling me in an unjust way. It is simply an illustration of an obvious problem: Forum rules are far from certain because they cannot be certain, they always require interpretation. I have moderated forums too, so that I know such problems from the other side too. And I also know about the role of agreement about the content. It is important that moderators feel morally obliged to follow only the rules and to be fair to opponents. But it is really hard to follow these rules in reality. If one participates in forums where one is in conflict with the administration about the content, the burden of following the rules becomes automatically heavier. This is simply a fact of life, no reason to whine about. So that people have to think that I simply ignore their reasonable questions, maybe because I'm unable to answer them? This is already close to the main problem: People write all the time things which are plainly wrong. Once the wrong claim is written in a given thread, discussing that wrong claim is on-topic. So I think it is necessary to correct such wrong claims. And in this case one is obliged to give some evidence that the claim is wrong. The evidence has not yet been discussed in that thread, else the wrong claim would not have been made, so the evidence may be classified as off-topic. What to do? Leave the wrong claims unquestioned? Claim that they are wrong, without presenting any evidence? (BTW, what to do if, which often happens, claims are made about the nonexistence of theories if my evil pet theory is a straightforward counterexample?) So my choice in such a situation is to correct the wrong claims, and, if it seems problematic to present the evidence, then to tell about this. But this requires to say something about it. I have already accepted that it will take at least decades. Last but not least, the first decade of complete ignorance is already over - the paper was published 2009: Schmelzer, I.: A Condensed Matter Interpretation of SM Fermions and Gauge Fields, Foundations of Physics, vol. 39, 1, p. 73 – 107 (2009), arXiv:0908.0591; During the first years, I was surprised by the complete ignorance by the scientific community, and that the publication has changed nothing in the negative reactions in forums, despite the results reached in the paper. But I have essentially already accepted that it will be completely ignored forever. Everything else would be an unexpected surprise. Such is life. Given the actual general developments in science, I think one can be happy if science simply survives the next decades and preserves what has been reached.

No. There are many people who think so, but it is far from being consensus. Fundamental relativity is the assumption that relativistic symmetry is not simply an approximation, but really fundamental. The LQG people, in particular Rovelli, emphasize the central role of background independence in their approach. Background independence is the established attempt to formalize diff invariance as having a physical meaning, despite Kretschmann's objection. String theory I do not take seriously, whatever they think. Beyond these two there is essentially nothing. If it would be accepted that relativistic symmetry is only an approximation, it would be fine. I have yet to find people ready to accept this together with the consequences. Namely, it follows almost automatically that the classical objections against the Lorentz ether are worth nothing - some approximate symmetry may be useful in some computations, but has no fundamental significance at all. No. Kretschmann's objection was essentially accepted by Einstein. GR remained nonetheless unchanged and unquestioned. The question has more metaphysical character. I have never claimed that Einstein causality is a law of logic. My claim is about realism, and not realism in general (philosophers have invented hundreds of variants of it) but of the particular formula used in Bell's proof which is usually interpreted as following from realism. I have shown that it follows from the Bayesian interpretation of probability, which is an interpretation of the rules of probability as rules of consistent thinking in a situation of uncertainty. (The logic of plausible reasoning.) In other words, for a consistent model one can simply construct that space \(\Lambda\) which is usually interpreted as some set of hidden variables. The construction for the case of quantum theory is there too. It has been found earlier by Kochen and Specker and is not really complicate. Of course, there may be useful physical theories without realism and causality. They may be, indeed, useful. But they are incomplete. (But to name a theory which is not realistic a valid description of physical reality becomes funny. The rejection of realism means that theory refuses to describe reality.)

If this is all, one can easily prove Bell's inequality. If both measure the same direction, they get 100% correlation. If the preparation is the common cause, and no interaction happens later, it follows that the results have been predefined. This holds for all directions. But for predefined results, Bell's inequality holds.

The theories have been published in proper peer-reviewed journals. This does not help at all, they have been (and predictably will be) simply ignored. The funny thing is that the standard argument against cranks is "publish your theory in a peer-reviewed journal, then ...". But in reality nothing changes. My ether theories have been published, but nothing has changed. (In fact, in the old days of sci.physics.research I had more and qualitatively better communications with mainstream physicists.)

Which is what I have done. Once the principle is a methodological principle (correlations require causal explanations), the stance is not anti-scientific. And I don't ignore any observational evidence. I work until I find an explanation of the observations which is compatible with the principles of scientific methodology. No. Quantum theory allows you to compute the numbers without giving any explanation for them. Note also that what is required is causal explanation. Of course, correlation does not imply causation. This is what makes the search for causal explanations a serious scientific problem. And Reichenbach's common cause principle defines precisely what counts as a causal explanation and what does not count.

Or from other metric theories of gravity. I have had enough negative experience showing me that relying on rules in forums gives nothing. Last but not least, rules are necessarily vague, and have to be interpreted, and if an admin interprets them differently than I do, I'm the loser. But, ok, in future I will write, instead of "forbidden here" something like "I'm afraid it may be forbidden here". In Newtonian physics time runs at a constant rate, in quantum theory there is not even a time measurement operator, and the time parameter is absolute, so based on Newtonian physics I cannot explain it. Relativity you have excluded explicitly. I don't know any more fundamental theory than GR which is not speculation, and even if you would accept string theory or LQG as such theories, I would certainly not use them, given my own opinion about their scientific value. The "speculation" which I would agree to use would be based on my own pet theory. So, your request remains problematic. But, ok, one thing I can try. I take the SM of particle physics. I ignore relativity, as required. The SM consists of field equations, they make sense without relativity too. Last but not least, the Maxwell equations have made sense long before 1905 too. Then, I know that if you have a wave equation, you can construct for each solution also a Doppler-shifted solution. This construction uses simply the Lorentz transformation with the speed of that particular wave equation. It works for sound waves too, if you use the speed of sound in the Lorentz transformation, it gives you the Doppler-shifted sound waves. So, I can use Lorentz transformations without invoking relativity simply because I have some wave equations. Now, take a solution of the SM which describes a material clock at rest which measures 1 second. All the SM equations are wave equations with the same c, so this trick can be applied to construct a Doppler-shifted solution. This gives a solution for a material clock of the same construction moving with some velocity and measuring the same 1 second. Looking now what is measured in terms of absolute time, one can easily see that it is a different amount of absolute time which is measured by the two clocks as 1 second. Really. In the Lorentz ether interpretation of special relativity time is absolute, only clock time is relative. It is the Minkowski spacetime interpretation where time itself becomes relative. The thing named proper time (badly translated "Eigenzeit") is relative in both interpretations, but this is only clock time, apparent time, not absolute time. "Time is what the clock shows" is already interpretation, not physics.

The remark was a general one, about scientific forums. Here an open letter I have written to https://www.physicsforums.com/ in protest against a violation of their own rules, which resulted in banning me. Here is what an admin wrote recently here: "Well, then, this will be put in speculations and you will limit your discussion of this subject to this thread, and this thread alone." So my "some move them into subforums for cranks" holds here too, and "this thread alone" is not much space. So, I have to care here all the time if answering honestly a particular question would violate such restrictions and get me banned here too. Which is quite difficult, because many questions of laymen have simple answers in the Lorentz ether interpretation. (This is not questioning this decision, I fully acknowledge the right of the administration to impose whatever rules they like, it is simply a description of the situation.)

(1) no, but he suggested something very close, namely "Would a better explanation for the novice be to say things fall because they are seeking out the place where time runs the slowest?". That's the wrong sign, but the idea is a quite reasonable one, so I tell him that this can, indeed, be done, the equations for the test particle can be derived from such a maximum principle. (2) \(g_{\mu\nu}\) is the gravitational field, and \(\dot{\gamma}\) is the velocity of the clock. (3) Incorrect question. Explanation always requires a base, some more fundamental things which do not require further explanation. Some more fundamental theory which explains GR would be speculation, thus, forbidden here. (BTW, relativity also does not explain why time runs at a different rate.)

In the context of GR, probably not, because GR does not fix a time coordinate as preferred. In a theory with preferred absolute time, if you choose absolute time as the time coordinate, yes, but in principle even in such a theory you are allowed to use other time coordinates. I prefer to give also the title, so that people know at least something about the paper. I'm doing science. That's why I don't give up principles of scientific methodology. That correlations require causal explanations is such a principle. If you think you can do science without any principles, your choice. Without some basics like logic, you will end nowhere.

No. There is absolute space and absolute time, as described by the preferred coordinates. Then there is an ether. Density, velocity and stress tensor of the ether are described by the gravitational field, all other properties of the ether described by matter fields. So, all the degrees of freedom of the ether interact with each other. The frame of absolute space and time is simply what is used to write down the equations of quantum theory. And these equations describe, in a very explicit way, FTL causation (not signalling). You know, from the Schroedinger equation follows a continuity equation for \(\rho(q)=|\psi(q)|^2\), and the velocity in this continuity equation, which defines how the probability distribution changes in time, depends on the whole actual configuration, in the whole universe. That the only formula we need from realism to prove Bell's inequality is part of the logic of plausible reasoning (the objective Bayesian interpretation of probability) I have shown in Schmelzer, I. (2017). EPR-Bell realism as a part of logic, arxiv:1712.04334. That without Reichenbach's principle of common cause we we have to give up key methodological principles which distinguish science from astrology I have already argued. Correlations require explanation, and no observation can force me to give up this principle because this is part of the scientific method.

That means, you talk only about signal causality. No. They are preferred by the interpretation of the theory. Formally, it is the same preference as for the Cartesian coordinates and absolute time in pre-relativistic physics. They identify absolute space and time. I have no problem at all with physicists following the "shut up and calculate" prescription. They have given a lot, in particular the SM. But this does not make more fundamental research meaningless. Those who do fundamental research have to make metaphysical choices, simply because the principles they choose are their guidelines toward a more fundamental theory. The difference between me and the relativist fundamentalists is quite obvious: I have no problem at all with other scientists, say, Rovelli, trying out other ways, namely assuming that relativistic symmetry, background freedom, are fundamental insights to be preserved in quantum gravity. Instead, their behavior is different, my proposals are handled like anathema. Some forums completely forbid to discuss the Lorentz ether, some move them into subforums for cranks, one permanently risks to be banned, arxiv rejects even some published papers, and so on. Reasonable, scientific arguments against my theories are almost absent. You use here, again, the very weak notion of signal causality. You cannot use the BI violations to send signals, and think that after this everything is fine with causality. But causality is about something different - it is about the necessity to find causal explanations for observed correlations. Without such necessity, we could continue to believe astrology. The problem of astrology (beyond the difficult to prove point that the claimed correlations do not exist too) is that they do not even look for causal explanations. But the notion of causality which requires to look for causal explanations of observed correlations is what you have to give up - it is Reichenbach's principle of common cause. There are laws or rules of thinking. We cannot rationally think without accepting and following them. The laws of logic. Can you accept that the laws of logic are something different from hypotheses of particular physical theories? Realism as well as causality have a similar character. Essentially, without realism even the laws of logic become unnecessary, in poetry one lives nicely violating them. And causality is what distinguishes astrology from science. Necessities of thought, presuppositions of the scientific method itself - these are things which are not open to empirical falsification because we have to presuppose them to start the evaluation of what we observe. Once both are in good agreement with the available data, this is not at all the question. They are on equal foot in this question. I have yet to see any problem created by a preferred frame. Regarding diff invariance, it is anyway quite dubious as a physical principle. Here, one can start with Kretschmann, E. (1917). Über den physikalischen Sinn der Relativitätspostulate, A. Einsteins neue und seine ursprüngliche Relativitätstheorie, Ann. Phys. 53, 575-614 where the point is made that every physical theory can be presented in a covariant form. Rovelli and Anderson IIRC have tried to replace this with the concept of background independence, but this formalization has been criticized too. Whatever, background independence may be a nice principle, but it is incompatible with quantum theory, which is a decisive argument against it. Sorry, I'm not a perpetuum mobile constructor, I accept simple theorems like Bell's theorem. You have yet to present any problems and complications.

What one uses as an effect and what as an explanation depends on the choices of axioms. It is quite usual to define theories postulating a Lagrangian. Proper time defines a nice Lagrangian for the movement of test particles on a fixed GR background. That means, if you define the maximum principle that \(\tau= \int \sqrt{g_{\mu\nu}(x,t)\dot{\gamma}^\mu\dot{\gamma}^\nu}dt\) has to be maximal, you can derive the geodetic equation for the test particle. The usual visualizations of curvature using curved surfaces in a higher dimensional flat space has, indeed, the disadvantage of suggesting the existence of such a higher dimensional space. Test particles seek the path where time runs the fastest way. So, in the twin experiment, the twin which simply follows his own geodesic trajectory - the one who remains at home - is the older one. Similarly, if you travel from point A to B which is opposite of the Sun, going the direct way would leave you most of the time in a region where time runs slower. So, it is better to stay away from these inner regions. But going too far away too fast is not a good idea too, because fast motion slows time too. So, it appears optimal to move around the Sun following a Keplerian orbit (almost). This approach is valid. Ther other question is how to visualize curvature without external dimensions. There are nice ways to do this. One can measure distances with usual metallic rulers, which expand with temperature. Then, if you have homogeneous temperature in flat Eucliean space, you will not see anything strange, Euclidean geometry works fine, no curvature. But if the temperature is inhomogeneous, the metric defined by the measurements with temperature-dependent rulers will give a metric with non-trivial curvature. Say, if the center of a circle is hotter, the radius measurement will be distorted distorted because the ruler expands. Measuring u and r will be influenced by this effect differently, and you will measure \(u>2\pi r\). Another nice analogy are crystal deformations. If the lattice is regular but deformed by external pressure, you can describe this by a tensor field with described the deformation. It is a symmetric tensor, in fact simply the difference between the original Euclidean metric and the deformed metric. As long as the original regular lattice remains valid, the curvature of this metric is zero. But there may be defects in the lattice. For a lattice with such defects, there is already no way to deform it into a stress-free state. And this can be computed by computing the curvature tensor of the deformed metric.

The first problem: Quantum theory is incompatible with fundamental relativistic symmetry. In quantum theory, you have a configuration q of the system you consider, and the main object is the wave function \(\psi(q)\). It changes in absolute time \(\psi(q,t)\). The configuration is something global. For N particles, it consists of the 3N coordinates of these particles. So, this gives a wave function \(\psi(x_1,y_1,z_1, ...,x_N, y_N, z_N, t)\) There is no natural way to define a Lorentz transformation. (For special-relativistic field theory, there have been found ways to circumvent this, but an essential part of this is the decision simply not to talk about everything which does not follow relativistic symmetry. All the conceptual problems, especially those related with the violation of the Bell inequalities, remain problematic in this theory too, but one simply does not argue about it, creating (surprisingly quite successful) that there are no problems with this. In GR, this becomes much worse. One cannot really write down a reasonable quantum theory without specifying some time coordinate. In the naive hope, one would like to be able to show that this can be done in a way that does not depend on the choice of the time coordinate. This fails, and the resulting problem is named "problem of time in QG". The second problem is that GR is not renormalizable. This was thought, initially, as being fatal, but today we know that it is not a big problem at all, if one accepts that it is an effective field theory, that means, a theory which is only a large distance approximation of some yet unknown different theory. Unfortunately, for those who like the spacetime interpretation, this is hard to accept. To replace GR below some critical distance (say, Planck length) by some different theory without any infinities (this is called regularization) leads to theories which violate relativistic symmetry. Of course, it would be quite natural to assume that a more fundamental theory has a different symmetry than its large distance approximation. But for most proponents of fundamental relativity this is simply unacceptable.

Given that the theory forbidden for discussion here has now been introduced by somebody else, I will answer here, and leave it to the admins (if they find it necessary) to split this part of the discussion and move it to some other place. Present the evidence. Have we already observed some wormholes or some causal loops? Have we any empirical evidence against the Einstein equations of GR, which the theory gives as an approximation? I do not "feel", but I have a theory which contains absolute time. This is in no conflict with GR time dilation because GR time dilation is simply clock time dilation. Clocks are influenced by the gravitational field, and my theory makes the same empirical predictions about that clock time dilation. Absolute time is, in that theory, defined by equations but not measurable with clocks. In fact, you are free to use other coordinates in Newtonian physics as well. It makes not much sense, that's all. My theory distinguishes clock time (time as measured with clocks) and absolute time. The formula for clock time \(\tau = \int \sqrt{g_{\mu\nu}(x,t) \frac{d \gamma^\mu}{dt}\frac{d \gamma^\nu}{dt}} dt\) is the same as in GR. And, don't forget, Newton has distinguished two notions of time, absolute time and apparent time, the same two notions of time I distinguish too, and, BTW, are distinguished even in GR (coordinate time vs. proper time). Once Newton already claims that apparent time does not have to I would have to reject basic principles of science, realism as well as causality, given the violation of the Bell inequalities. This alternative is unacceptable for me, given that there is a simple viable alternative which preserves realism as well as classical causality. The Einstein equivalence principle is a proven theorem in my theory. It follows from translational symmetry, the Noether theorem, and the action equals reaction principle.

I still don't see the point of your question. The preferred coordinates are also coordinates, the formulas to be used for arbitrary coordinates remain valid for the preferred coordinates too. So, what's the problem to deal with vector or tensor components? In fact I have not heard much arguments. The usual way to handle such approaches in science forums is to ban them instead of discussing them. Criticizing GR using an ether approach is anathema, not handled in a rational way. Except that those who quantize gravity without a fixed preferred background have failed almost a century to combine these two rather simple theories. Instead, quantizing gravity in an ether approach is standard condensed matter theory. A main argument is the violation of Bell's inequality. In fact, it is a decisive one. Those who reject the simple and straightforward solution of a preferred frame, where causal influences faster than light are allowed without endangering causality and realism, and are ready to give up all the fundamental principles of science (realism, causality, logic of plausible reasoning) to save fundamental(ist) relativistic symmetry seem unreachable by any further scientific arguments. Yes, there are people who are ready to reject realism and causality to preserve their dogma, given that the only way to preserve realism and causality would be to give up the dogma. To hope that such people can be reached by scientific arguments seems naive. I have given up this hope. The important point of the realist and causal interpretations is that they explicitly prove the existence of interpretations which preserve realism and causality. Even if this requires a preferred frame. So, it shows that to blame quantum strangeness as a justification for giving up realism and causality is unjustified. The only justification for giving up realism and causality is the dogma of fundamental relativity.

In GR, the physical predictions do not depend on the choice of coordinates, thus, the physical predictions will be the same, even if you choose another coordinate time. We don't know this. We know that the Newtonian theory of gravity is wrong. We don't know that the Newtonian definitions for time are wrong. We talk here about GR, and interpretations of the GR equations which differ from the spacetime interpretation. If one talks about different interpretations, even thought experiments distinguishing them cannot be expected. Even less actual experiments. To discuss alternative theories of gravity, which could provide differences in actual experiments, would be forbidden here as speculation. I do not need excuses. Take a look at these threads. If you miss something, ask where it is not forbidden to answer.

Given that new physics would be speculation, I'm forbidden to present them here. Fortunately, nothing new is necessary here. I can take good old Newton's definitions. He already distinguished absolute time which flows independent of any human action and apparent time, the result of the attempts of humans to measure time. Technically, absolute time survives in GR as coordinate time - if there would be some absolute time, it would be defined by some time coordinate as the corresponding coordinate time. But GR has no equations for absolute time, and it does not appear in the spacetime interpretation. Standard twin experiment. Use two identical clocks moving from a common starting event to a common end event on different trajectories. The result will be that the clocks show different time. In an interpretation based on the Newtonian concept of time, this would not be possible for absolute time, only for apparent time, and would prove the existence of some distortion of the clocks. I think having different interpretations for the same equations is always useful. It helps very much to distinguish what follows from experiments and observation (these things would be the same in different interpretations) from metaphysical assumptions (which can be different in different interpretations). No problem. Except that I'm not allowed to deliver such things here. Except, I hope, for the simple formula \(\tau = \int \sqrt{g_{\mu\nu}(x,t) \frac{d\gamma^\mu}{dt}\frac{d\gamma^\nu}{dt}} dt\) which quite explicitly described that (and how) the gravitational field (described by \(g_{\mu\nu}(x,t)\)) distorts the time measurement for a clock moving along the trajectory \(\gamma^\mu(t)\).