The image of somebody who proposes an ether theory is not a very nice one. One imagines an old man, unable to understand relativistic physics, who tries to save the old, Kantian notions of absolute space and time, for philosophical reasons. It doesn't fit very well. What I have learned at the university is mathematics, especially differential geometry, thus, the basis of general relativity. Thus, I never had a problem understanding relativistic physics. The reason why I have started to develop an ether theory have been quite different, and I want to explain them here.
The strong relativistic program
Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. Hermann Minkowski
These programmatic words of Hermann Minkowski have been one of the starting points of modern, post-Newtonian, relativistic physics. The success of this program was overwhelming: All known physical fields are described today by relativistic theories. And the predictions of these theories – the standard model of particle physics and general relativity – agree with observation with astonishing accuracy.
Moreover, this relativistic program has changed, in a very strong way, our conception of the world. Concepts which have been considered, before relativity, as fundamental principles of physics, have been rejected. The most prominent of these concepts is absolute time, absolute contemporaneity. But this is not the only prominent principle: With general relativity, we have rejected, for example, the idea of local energy and momentum densities for the gravitational field. As a consequence, we have to reject conservation of energy and momentum.
But, given the success of the relativistic program, there seems to be no place for a revival of these old concepts in modern physics. And, moreover, there seems to be no necessity. Physicists have learned to live without them. And, after this, a revival of these concepts seems forbidden by Ockham's razor: "Don't multiply entities without necessity." Thus, even if it would be possible to revive them, for example as hidden entities, physicists would not care. They would reject them, together with other unobservable entities, like Gods or invisible flying spaghetti monsters.
My program
The first idea for my own research program was a quite technical one, about quantization of gravity. The idea was, that a variant of Einstein's famous hole argument for quantum gravity requires the revival of a fixed spacetime background. This background would be important – and, in principle, observable – in the domain of quantum gravity, but unobservable in the limit of classical general relativity. At this time, this was one of many ideas I have played with. Most ideas in science fail, most of my ideas too. But this idea survived. It started its own life. The current version of this first argument can be found in my article "A quantum variant of Einstein's hole argument".
In this hole argument, absolute time plays no role at all. What is proposed to revive is a flat, affine spacetime background. But then I recognized that reviving only this particular this particular concept is, in some sense, inconsequent. There are only two possibilities for quantum gravity: Or we have full, exact relativistic symmetry on the fundamental level, or not. If not, if relativistic symmetry is only emergent, only an approximation for large distances. But that means that the strong relativistic program is unjustified from the start: Relativistic symmetry is, then, not a symmetry of fundamental reality, and, therefore, even the first rejections of fundamental physical principles have to be reevaluated.
Why I don't like the field-theoretic approach
There is, of course, also a third way – and it is even the most popular one today, the one used in string theory. It is the field-theoretic approach to the quantization of general relativity. There, the gravitational field gμν(x) is obtained as a combination of the Minkowski metric ημν, and a spin-2 field hμν(x):
gμν(x) (-g)1/2 = (ημν + hμν(x)) (-η)1/2
As a consequence, general-relativistic symmetry is, together with the field gμν(x), only derived, emergent, not fundamental. Instead, the fundamental object – the Minkowski metric ημν – is as unobservable as the preferred frame. That means, the Minkowski metric, which was introduced into physics to get rid of unobservables, becomes, in this approach, itself an unobservable object.
This seems to me a philosophical absurdity. Or we follow the positivistic program to get rid of unobservables – in this case, we should not decompose gμν(x) into parts which are, taken alone, unobservable. Or we reject positivism and accept that not everything is observable, that unobservables have their place in realistic theories. But in this case, the rejection of a preferred frame is no longer justified, and we have no reason to prefer the Minkowski metric in comparison with the classical Newtonian framework of absolute space and time.
Indeed, why should we reject absolute time? Because of the general-relativistic symmetry we observe? But this is, according to the field-theoretic approach, only an emergent, non-fundamental symmetry, it cannot justify a rejection of a fundamental notion. So, should we reject absolute time because of the Lorentz symmetry of the hidden Minkowski metric ημν – that means of a symmetry we cannot even observe? This idea seems absurd to me.
Reviving rejected concepts
Now, absolute time is only one example – a very prominent one – of a fundamental physical principle which has been rejected because of incompatibility with the relativistic program. And, once we consider general-relativistic symmetry to be emergent, derived, then no fundamental physical principle should be rejected because of incompatibility with relativistic symmetry.
All we have to do is to care about relativistic symmetry of the observable effects. But to reject a fundamental physical concept or principle, simply because of incompatibility with some approximate symmetry, is unjustified. And, that's why, every rejection of some fundamental principle, which was based on the strong relativistic program, should be reevaluated. The consequence is a research program for revival of rejected concepts, which can be summarized as following:
As long as it is possible to have relativistic symmetry, without giving up some other physical principles, use relativistic symmetry.
But, whenever some useful physical principle or some beautiful mathematical structure has been, because of incompatibility with the relativistic program, ignored or rejected by other scientists, try to revive it, whenever possible, even if only as some hidden entity.
Feel free to play around with concepts and ideas which other scientist would, because of their incompatibility with the strong relativistic program, immediately reject.
Doing all this, remain as close as possible to the established physical theories, that means, to general relativity and the standard model of particle physics.
Note that this program is in no way anti-relativistic. It is better characterized as a weak relativistic program: We revive only those concepts, which are compatible with relativistic symmetry, understood as an approximate symmetry – that means, concepts, which have been, if relativistic symmetry is only emergent, rejected for insufficient reason.
The results
There appears to be a surprisingly large list of very different physical principles, which have been rejected because of incompatibility with the strong relativistic program:
Beautiful concepts in general relativity
Of course, the concepts which we name here "beautiful" are not beautiful at all from point of view of the strong relativistic program. Indeed, they violate relativistic symmetry, thus, in the sense of the relativistic program, are dirty by definition.
Harmonic coordinates: A beautiful set of preferable coordinates in general relativity. In these coordinates, the Einstein equations obtain an especially simple form.
The ADM decomposition: A three-dimensional geometric interpretation for metric theories of gravity, including general relativity. In this interpretation, the gravitational field is described by a positive scalar density, a three-dimensional vector field, and a three-dimensional positive-definite symmetric tensor field (or a three-dimensional metric field). This decomposition depends on a particular choice of coordinates.
Local energy and momentum conservation laws: In general relativity, it is impossible to define local integrable conservation laws for energy and momentum, as well as local energy and momentum densities for the gravitational field. This becomes possible in harmonic gauge.
A condensed matter interpretation: In harmonic coordinates, the geometric fields of the ADM decomposition fulfill equations which are similar to well-known classical condensed matter equations, if we interpret the scalar density as density, the three-vector field as the momentum, and the three-metric as the stress tensor. The harmonic condition for the time coordinate becomes the continuity equation, and the harmonic conditions for the three spatial coordinates become the Euler equations of classical condensed matter theory.
Back-reaction of quantum matter: Some approximation to quantum gravity – semiclassical gravity – is compatible with relativistic symmetry. It allows to predict, for example, Hawking radiation. But if we leave this domain, to compute, for example, how Hawking radiation reduces the energy of the black hole, we need a notion of energy and momentum which already violates relativistic symmetry. Esepecially the evaporation of a black hole already cannot be predicted in agreement with relativistic symmetry principles.
No black hole and big bang singularities: If we enforce the harmonic condition with an additional term in the Lagrangian of general relativity, the big bang and black hole singularities disappear. Instead of black holes we obtain stable gravastars.
Hidden variable theories for quantum theory
The search for hidden variable interpretations of quantum theory has been given up by mainstream physics. If asked for the reasons, people refer to quantum strangeness. But this is wrong: The real reason is the relativistic program: Namely, hidden variable theories which violate relativistic symmetry exist. And they are in no way strange, difficult, or otherwise non-beautiful, in comparison with the strangeness of quantum theory. What is "dirty" and "wrong" with these theories is that they have, among their hidden variables, also the "hidden variable" forbidden by the relativistic program, namely, the preferred frame (absolute time):
There is the de Broglie-Bohm or pilot wave theory – a deterministic theory, which makes, in so-called "quantum equilibrium", the same predictions as ordinary quantum theory.
There is Nelsonian stochastics – a stochastic theory, which also makes the same predictions as ordinary quantum theory. It is non-deterministic, but the non-deterministic part of it is a classical Wiener process. That means, nothing remains here from the "quantum strangeness" – as in classical probability theory, we simply don't know the details of the process. From mathematical point of view, Nelsonian stochastics is more beautiful in comparison with Bohmian mechanics – it does not need the "quantum potential" of the Bohmian theory as well as a special "quantum equilibrium" condition.
Realism
It should be noted that the violation of relativistic symmetry by these hidden variable theories is not a special property of these two particular theories. It is a property of every realistic theory which gives the same predictions as quantum theory. This is the consequence of Bell's theorem.
The assumptions of Bell's theorem are extremely weak: We need only Einstein causality and realism. Because of the violation of Bell's inequality in quantum theory, one has to give up or Einstein causality, or realism.
Our choice is, clearly, the preservation of realism.
The alternative – to give up realism – is extremely problematic. It may be interpreted as giving up an essential part of the scientific method itself – the search for realistic explanations of the observable facts.
The basic principles of quantum mechanics
In some sense, the classical Schrödinger picture of quantum theory has to be mentioned too.
Formally, nobody has rejected it. Modern quantum field theory prefers, for the reason of more relativistic invariance, the Heisenberg picture. But, of course, above pictures remain equivalent as physical theories.
Nonetheless, the wave function of the Schrödinger picture, as well as the Schrödinger equation, is obviously and openly non-relativistic: The quantum state, as defined by the wave function, is defined on the whole space, in one moment of absolute time. And absolute time is what appears in the Schrödinger equation.
This becomes especially important for some interpretations of quantum theory. Especially the collapse of the wave function – a key element of the Copenhagen interpretation – clearly violates relativistic symmetry.
Geometric and condensed matter interpretations of standard model fields
There is a large number of occurrences of the number three in the standard model of particle physics: Three generations, three colors, three generators of the weak group. In the condensed matter interpretation I have found, all they become associated with directions in space. Such three-dimensional interpretations are, of course, incompatible with the relativistic program.
For more details about this part of my research see here.
A four-dimensional geometric version of the Dirac equation for fermions – the Dirac-Kähler equation for differential forms – gives four Dirac fermions. A three-dimensional version gives, instead, only two Dirac fermions. This allows a geometric interpretation of electroweak pairs.
Together with the geometric Dirac equation on the space of differential forms, there exists also a discrete version. Again, in the four-dimensional version, this lattice equation describes four Dirac fermions. In a three-dimensional variant, we have a lattice only in space, and time is left continuous. The resulting lattice equation describes, again, a pair of Dirac fermions, which can be interpreted as an electroweak pair.
There are twelf such electroweak pairs in the standard model. They appear in a 3 × (3+1) form: We have three generations, and in each generation we have three differently colored quark doublets and one lepton doublet. In our interpretation, this structure is associated with a three-dimensional affine transformation – a (3 × (3+1)) matrix. An affine transformation describes, in a natural way, the state of deformation of an elementary cell.
These observations, taken together, give a condensed matter interpretation of the standard model fermions as describing a three-dimensional lattice of elementary three-dimensional cells.
Gauge fields appear in this model in a natural way, and we can almost exactly compute the gauge group of the standard model and its action on the fermions.
