Schmelzer

These experiments certainly do not prove any retrocausality or backward in time influence or similar esoterics. This is a simple proven result, given that there exists a causal interpretation of quantum theory which does not have any retrocausality, namely de Broglie-Bohm (dBB) theory. And those experiments can be described in dBB theory as well. That there may be other interpretations which use retrocausality is irrelevant - you know that from everyday life, there are also sometimes situation where some retrocausality seems quite plausible (at least as a nice joke). Nobody takes such explanations seriously in everyday life. But in quantum theory they are, for whatever reasons, somehow taken seriously by some physicists. In reality, they deserve the same laughing as similar every day life explanations.

In science, it is often very useful to be pendantic. Maybe one day. But this would require knowledge of some theory beyond quantum theory. Of course, if there is real contemporaneity, there is only one candidate in reality for it, defined by the CMBR frame. But without a more fundamental theory, this is not more than a guess.

I did not say that some entries will be zero, I said the tensor is symmetric. That means, [math]g_{\mu\nu}(x)=g_{\nu\mu}(x)[/math]. This symmetry remains, a symmetric tensor will remain symmetric in other systems of coordinates. If I want to take a look at the Einstein equations, Wiki gives me quite immediately the formula [math]G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8 \pi G}{c^4} T_{\mu\nu}[/math] for copypasting. The term there is the cosmological constant [math]\Lambda[/math] multiplied by the metric tensor. SR is always global. If the masses and energies in the system are too big, SR is no longer a valid approximation, and GR has to be used. This does not change the fact that SR is global. It is always difficult to decide how much information has to be given. Those really interested in formulas will have to follow anyway a particular textbook, or whatever replaces it like Wiki. If one cares about c factors, then the formula I have given for proper time is assumed to have the unit of a distance, thus, you have to divide it by c to get the unit of seconds.

Hm. First of all, the metric tensor has from the start only ten coefficients, and what reduces it from 16 to 10 is simply the requirement that the tensor has to be symmetric. There is no other way in GR, Then, [math]\Lambda[/math] is simply a single real constant, which appears in the Einstein equations. There is no such thing as a [math]\Lambda[/math] tensor. Then, in SR the Minkowski metric is a global object. (It is "local" only if one talks about applying it in GR locally as an approximation.) The Minkowski spacetime is Lorentzian, not Euclidean. If I say nothing about it, I use c=1

The claim holds for both. The proper time formula in GR is [math]\tau = \int \sqrt{g_{\mu\nu} (x) \frac{dx^\mu}{dt}\frac{dx^\nu}{dt}} dt [/math], and the formula for proper time in SR is simply the particular case of the Minkowski metric [math]g_{\mu\nu}(x)=\eta_{\mu\nu}[/math]. And "proper time" is the time as measured by a clock following a particular trajectory. If you know proper time for all trajectories, you can define [math]g_{\mu\nu}(x)[/math] uniquely. So, the gravitational field in GR is simply the field defined by what the clocks measure. Unfortunately, length measurements are also distorted, and there is also no undistorted way to identify contemporaneity. All these distortions taken together make your proposal impossible.

Hm, if there are others who feel different, have they some arguments why, say, a simple lattice regularization on a large cube, which reduces the number of degrees of freedom to a finite number, nonetheless leads to big problems if the theory is not renormalizable? Or is there nothing but a feeling? The issue is not the renormalization procedure itself, Wilson has shown that it is useful for understanding condensed matter theory, even if it is a regular theory without divergences given that its atomic structure defines a sort of lattice regularization of the continuous theory.

There are other workable theories, all one needs for a workable theory is that the equations have the Einstein equations as a limit, in the same way as NT is the limit of GR. But to discuss now such alternatives would be off-topic. Given that "well-tested" has not been questioned here, I have seen no necessity to write this. But if what the clocks measure is worth to be named "time" is a matter of interpretation. The only thing which one can imagine as a proof that it is not time has been done, and shows that it is not time - namely that the same clocks show for the same pair of events different results, while the time difference should be the same. So, if one names what the clocks show "time", one invents a new notion of time, different from the classical one, and this is certainly a question of interpretation. If I have another interpretation of the GR equations, why do you think this would lead to differences in the empirical predictions? A prerequisite for gathering experimental evidence would be that it is not an interpretation, but a different theory. The theory says, in its empirical predictions, what the clocks and rulers show. It does not say if this is some strange curved four-dimensional spacetime or simply a distortion of clocks and rulers by the gravitational field.

Just to clarify some things: The BB is a solution of GR. GR it itself is not a theory which allows to describe the creation of the universe out of nothing, even in principle. The GR BB solution is singular, that means, it makes some physical variables (like the density) infinite at the singularity, and arbitrary large near the singularity. This is obviously nonsense, so that we certainly know that GR has to be replaced by some better, yet unknown theory which does not have such a nonsensical singularity. We don't know up to which density the solution makes sense as an approximation. But we can make reasonable guesses about this. Say, we have studied in particle accelerators sufficiently well matter with a density of atomic nuclei. We have also observations and theory about neutron stars, which have the same density. So, it makes sense to assume that our theories are fine for such densities. Optimists may think our theories are much more reliable, and become problematic only where quantum gravity effects become important. Whatever, if we look at this and compare it with the GR solution, we can identify a moment of time after the singularity in the GR solution when the GR solution possibly starts to become a reasonable approximation of reality. This leads to expressions like "[math]10^{-43}[/math] seconds after the BB". Such expressions implicitly suggest that there is something meaningful we can say about the world before those "[math]10^{-43}[/math] seconds after the BB", namely that this period lasts only [math]10^{-43}[/math] seconds and starts with some moment of creation of the universe as we know it. In reality, we know exactly nothing about the time before. The Big Bang may be as well a Big Bounce with an infinite history of time in the past. The other thing which requires clarification is that GR is only a theory about what clocks and rulers measure. If the clocks really measure time or are, instead, distorted by the gravitational field (or the ether) so that it is not time what they measure, remains a question of interpretation. In fact, once two similar clocks following different trajectories between two events where they are together and can be compared immediately show different numbers, it is quite clear for common sense that what the clocks have measured is not time in the common sense meaning of time. Thus, the naive common sense interpretation would be that GR proper time is simply what clocks measure, and has no relation to time. Common sense time would have to be something like a time coordinate: Between two events there can be only one time difference, defined by the difference of the time coordinates of the two events. GR simply does not make any claims which of the many imaginable time coordinates is what is our naive common sense time. It is unobservable, in the sense that we have no reliable clocks to measure it.

My question is not if gauge symmetry is useful. Symmetries are technically always useful, even if they are only approximate symmetries. The issue is if there are today, in the light of the Wilsonian approach (means, of understanding non-renormalizable theories as effective field theories, not Wilsonian lattice gauge theory) any problems with massive gauge theories. Why this interests me is because of my own theories, which have problems similar to lattice gauge theories: The vector gauge fields do not create problems, here Wilsonian lattice gauge theory gives a nice lattice gauge theory with exact gauge symmetry on the lattice. This does not work for chiral gauge theories. All what has been proposed to solve this looks completely artificial to me, but there is a quite simple solution: The lattice theory for the chiral gauge fields simply does not have an exact gauge symmetry on the lattice. What would be the straightforward consequence? The large distance approximation of chiral gauge fields would not be gauge invariant, in particular it could contain mass terms. But this is also what we observe: chiral gauge fields are massive. So we have a nice correspondence between observation (vector gauge fields massless, chiral gauge fields massive) and simple lattice theories (vector gauge fields allow exact lattice gauge symmetry following Wilson, chiral gauge theories not). But the mainstream does not like this. Instead, they consider this to be a big problem that there is no exact lattice gauge symmetry for chiral gauge fields, only to use later the Higgs mechanism to create a massive gauge field out of these gauge fields with exact lattice gauge symmetry. Something I can understand, given that massive gauge theory is non-renormalizable and many physicists have not recognized that this is no longer a problem. But beyond this, I cannot see any justification to look for exact gauge symmetry for chiral gauge fields.

Wikipedia attributes this to Joseph Larmor (1897) at least for electrons and Emil Cohn (1904) for clocks in general. One would have to research when Lorentz and Poincare became aware of this, but I'm not too much interested in such questions of priority.

But among that infinite number it is quite easy to make a choice. If one assumed that some theory beyond GR, say QG, will define an absolute space, one would have to specify equations which distinguish absolute space, thus, a condition which would distinguish the preferred coordinates. But there is essentially only one candidate for such a condition, namely harmonic coordinates. And there is also a single distinguished set of such particular harmonic coordinates, namely the comoving coordinates of the FLRW ansatz. For zero spatial curvature, which is what we observe, the FLRW ansatz would be [math]ds^2 = d\tau^2 - a^2(\tau)(dx^2+dy^2+dz^2)[/math], and the coordinates x,y,z are harmonic. Absolute time would have to be harmonic too, but this is also not difficult, the slightly modified ansatz [math]ds^2 = a^6(t)dt^2 - a^2(t)(dx^2+dy^2+dz^2)[/math] has already a harmonic time coordinate too, so that harmonic time and proper time are connected by the simple equation [math] d\tau = a^3(t)dt.[/math] This would be the only choice where the Copernican principle holds, with no center of the universe. So, to make a plausible choice among that infinite number is very easy, no trouble at all.

Thanks, the second article has answered one of the questions, namely why this coupling of the Higgs to fermions to get the mass terms: The standard mass term simply destroys the gauge invariance of the chiral gauge fields. Fine. Unfortunately it leaves unanswered the original question why we need a gauge invariant theory at all, given that we do not need renormalizability any more once we have learned how to handle non-renormalizable theories as effective field theories, but from the start assumes the gauge invariance as obligatory. It was my understanding that the primary reason for having gauge invariance is that gauge theories are renormalizable but massive gauge theories not. So, I have understood the Higgs only as a trick to gain gauge invariance, and not as a tool to do actual renormalization or so. The point with the neutrino masses I don't understand. Of course, initially there were none, they were later added. But as far as I understand, one uses now the same formalism (simply with another mass matrix) as for leptons, as for quarks. Not?

What is the advantage of the mass terms related with the Higgs field in comparison with the straightforward mass term? I do not plan to question the Higgs boson detection, but I want to understand what has been really detected, what was the advantage or necessity of proposing such a model. The necessity of obtaining a renormalizable theory is bogus, given effective field theory. What could replace it?

No, only Einstein-causal hidden variable theories. There are deterministic hidden variable interpretations of quantum theory, de Broglie-Bohm theory. They have to contain causal influences faster than light, but these cannot be used to send information.

There was at that time no need for specifying any frame of reference, because the reference was self-evident: Absolute space and absolute time. The theory did not have Galilean symmetry, so the issue of distinguishing absolute rest from inertial movement was a problem for Newtonian gravity, but not for EM theory. I see vol. 6 of Einstein collected papers for free, for example https://book4you.org/book/3343023/5642aa

If there is absolute time depends on the theory. In Newtonian gravity, there is absolute time. In quantum theory too. In relativity, in its spacetime interpretation, there is no absolute time. The two theories are incompatible, and part of this incompatibility are the different notions of time. This is also named "problem of time in quantum gravity". If you think there is no absolute time in Nature, ok, once you have received a revelation, so be it. But your revelations are not relevant for physics. Moreover, even in this case you would be wrong about quantum theory.

If you think it is incorrect, explain.

Not in this case. The time will be computed by [math]\tau = \int_{t_0}^{t_1} \sqrt{1-\frac{|v(t)|^2}{c^2}} dt,[/math] and if |v| is constant, then it does not matter how the trajectory itself is curved, you get [math]\tau = \sqrt{1-\frac{|v|^2}{c^2}} (t_1-t_0)[/math] without any necessity to care about frames and so on.

No, you can live in a quite comfortable way with a single frame, and apply, instead, Lorentz transformations to particular solutions. This gives you different, Doppler-shifted solutions. There was a simple explanation proposed by Lorentz. Namely, if what holds together condensed matter is the EM force, then condensed matter has to have the same symmetry properties as the EM equations. Thus, a Lorentz-transformed (Doppler-shifted) solution for some piece of condensed matter will be a solution too. But the Lorentz-transformed piece of matter is contracted. The actual explanation works in the same way, we have a lot more fields in the SM, but they all are wave equations with the same c, so that a Lorentz-transformed solution will be a solution too.

Quantum theory is a theory with absolute time. So, there is no time travel in quantum theory.

In the past, everything was quite clear - non-renormalizable theories are unable to make any predictions, given that they need an infinite number of parameters, thus, a reasonable theory has to be renormalizable. A massive gauge field would give a non-renormalizable theory, while gauge symmetry gives a renormalizable theory. So, massive gauge fields are not possible, except they have been constructed with some trick and are, fundamentally, something different, as with the Higgs mechanism. Then, if the gauge theory is anomalous, it is also non-renormalizable. So, the gauge theory has to be non-anomalous. That's fine and not problematic, given that we have with the SM a non-anomalous gauge group and can fake massive gauge fields with the Higgs mechanism. Then came Wilson and told us that non-renormalizable theories are not a problem at all, they are fine as effective field theories. An effective field theory has one important unknown parameter, the critical length, and below that critical length the theory has to be replaced by another one. All the infinity of the parameters defining the general Lagrangian of such a theory can be restricted by the condition that they all have to have a comparable order at the critical length. Once this is assumed, one can consider the large distance limit, and all those non-renormalizable terms go to zero very fast. The higher their order, the higher the suppression with increasing length. The highest order terms are the renormalizable ones. In comparison with them, all the non-renormalizable ones will become irrelevant in comparison with the renormalizable ones if the critical length is small enough. The only exception is gravity, because there is no renormalizable theory, thus, the lowest order non-renormalizable one is what remains - even if it has to be, for the same reasons, very weak. This approach de-facto solves not only the problem with quantization of gravity (as an effective field theory, it works fine), replacing it with the problem to find a theory for distances below the critical length. It also by the way explains why gravity is so weak in comparison with the other forces. Wilson has got a Nobel for this, justified. But it follows that there is no longer a need to have renormalizable theories. We could as well have non-renormalizable ones. Say, a simple massive gauge theory would be non-renormalizable, but the essentially not that different theory using the Higgs mechanism is renormalizable. What is the difference? The reasonable guess is that it is some non-renormalizable component of the massive gauge theory which becomes irrelevant at large distances. That means, we could use massive gauge fields as they are, in the effective field theory approach the non-renormalizable components will become irrelevant. The same for anomalous gauge fields. They are non-renormalizable? Fine, that means, they will disappear themselves, without any further need to suppress them. But, once they disappear automatically, this would be a natural way to extend the SM. If one uses only anomalous gauge fields to extend the gauge group at the critical length, one does not even have to invent anything to suppress them. The serious problem of all other extensions of the standard model - how to suppress the additional fields to make them invisible at large distances - simply disappears into thin air as long as the extensions are anomalous. There is a particular example of such an extension - [math]U(3)_C\times U(2)_L \times U(1)_R[/math], with two U(1) fields added. The color group acts, then, only on the color degrees of freedom, and the other two only on the electroweak degrees of freedom without any dependence on color and baryon/lepton charge. So, this simplifies the SM giving the charges a much simpler structure. But this thread is not about this particular speculative proposal, but about the justification for using the Higgs mechanism (instead of simply using massive gauge fields) and restricting oneself to non-anomalous gauge fields, given that in a Wilsonian effective field theory all this is unproblematic.

I want to present here a model which gives all the fermions and gauge fields of the Standard Model of particle physics (SM). Given that it is my own theory, one could argue it should be published in "Speculations". But it has been published in a peer-reviewed journal, which makes it different from usual speculations: I. Schmelzer, A Condensed Matter Interpretation of SM Fermions and Gauge Fields, Foundations of Physics, vol. 39, nr. 1, p. 73 (2009), resp. arxiv:0908.0591. Popular representation of the model is given in my home page LINK REMOVED As the three generations of fermions, as the three colors are interpreted in the model in a geometric way, related with three-dimensional space. The electroweak pair also get a geometric interpretation, in terms of three-dimensional differential forms.