## General Lorentz Ether Theory (GLET)

### Why reviving ether theory?

Simply because it allows to solve problems of modern physics. GLET solves some important problems of classical GR.

These are problems in several domains: quantization problems (problem of time, topological foam and so on), the violation of Bell's inequality, the big bang singularity and the related cosmological horizon problem, the black hole singularity (information loss problem).

An additional term allows to describe some part of dark matter.

### What is General Lorentz Ether Theory?

General Lorentz Ether Theory (GLET) is a continuous ether theory of gravity. It is a generalization of Lorentz ether theory to gravity. The basic equations are the conservation laws for the ether.

An important point is that GLET is only a general scheme, a meta-theory. It defines only the most general properties of the ether, not the "material properties" of the ether. A complete ether theory would be the "theory of everything", but GLET is only a theory of gravity. A proposal for a complete ether model is the cellular lattice model.

### What are the postulates of GLET?

We postulate the following properties of the ether:

• We have a classical Newtonian absolute space and and absolute time. The space is filled with some matter named ether. This ether may be described by its (positive) density, velocity, (positive definite) stress tensor and some additional internal variables (material properties). Density, velocity and stress tensor define the gravitational field, the material properties define all other particles and fields. There is nothing except the ether, so that it is also a "theory of everything".
• The ether follows classical conservation laws of condensed matter theory.
• We have the continuity equation - the conservation law for the mass of the ether itself. It is the conservation law which follows, via the Noether theorem, from translational invariance in time direction.
• We have the Euler equations - the conservation law for the momentum of the ether. It is the conservation law which follows, via the Noether theorem, from translational invariance in the three spatial directions.
• For the whole theory exists a Lagrange formalism (that means there exists a miminum principle). All the equations are the Euler-Langrange equations following from this Lagrangian.
• We have a natural relation between conservation laws and the Euler-Lagrange equations for the preferred coordinates in the Lagrange formalism. This relation is a variant of Noether's theorem.

### What are the properties of the ether

Starting with these assumptions, we obtain in GLET equations for the ether which are very close to the Einstein equations of general relativity (GR).

There are two additional terms. They depend on two additional constants $$\Xi$$ and $$\Upsilon$$, which should be defined by observation. For zero values of two cosmological constants $$\Xi, \Upsilon \to 0$$ it becomes a hidden variable theory for general relativity, with the absolute Newtonian background space and absolute time as the "hidden variables".

There are also some interesting qualitative differences if $$\Upsilon > 0$$: Instead of the big bang in GR we obtain a big bounce with collapse before the expansion. We also have no black holes, but frozen stars - stable stars, slightly greater than their Schwarzschild radius, without horizon, but with very high time dilation.

The Einstein Equivalence Principle not only holds exactly, it is even derived from first principles: It is a consequence of the "action equals reaction" symmetry which follows from the Lagrange formalism.

### Is GLET in agreement with experiment?

Yes. In the limit $$\Xi, \Upsilon \to 0$$ the equations are the same as for general relativity. As a consequence, the empirical predictions are also almost the same. For small values $$\Xi, \Upsilon \ll 1$$ the additional effects will be small too, moreover, they will be very difficult to observe: There would be four additional massless dark matter fields, thus, the particles would not be visible, and, moreover, they would fly away with the speed of light.

General relativity itself is in quite good agreement with observation - except for some cosmological problems (dark matter, horizon problem) which seem solvable. Therefore it is considered to be viable. So, once GLET gives the GR equations in some natural limit, it will be viable too. All what one has to check is if the additional hidden structure, the Newtonian absolute space and absolute time - is compatible with the universe which we observe too.

GLET requires that a homogeneous universe is flat, which is in agreement with observation. The additional cosmological constants allow to solve the horizon problem and may be useful to solve the dark matter problem.

### Can the preferred frame be observed?

Yes, at least in principle. GLET leads to some predictions which are different from GR. These differences are results of the influence of the preferred frame.

In fact, if we assume that the ether is, for large distances, approximately homogeneous, we can identify the preferred frame of the Newtonian background space and absolute time with the CMBR frame defined by the background radiation.

### Does the universe expand?

No, the homogeneous universe in GLET does not expand. All galaxies remain on the same place relative to the Newtonian absolute space. Instead, our rulers are shrinking. But for an observer it looks like an expanding universe.

Note that this is not a difference in the observable predictions about the expansion, only another metaphysical interpretation: in GLET it is meaningful to talk about the "true" position.

### Was there a big bang?

In GLET we have no big bang singularity. Instead, there was a big collapse before. This prediction is different from the GR prediction. The time of the big bounce depends on the cosmological constant $$\Upsilon > 0$$. If we make it small enough, the predictions differ only for times before an arbitrary short time after the "big bounce" in GLET, resp. the "big bang" in GR.

After this short time, the $$\Upsilon$$-term does no longer influence the observable predictions. But what changes is the metaphysical interpretation. There is no expansion, everything remains on it's place. Instead, our rulers shrink. That's why the universe looks like expanding.

But this is only a reinterpretation, another description, the observable effects are the same. In the past, our rulers — and that's all around us — have been much greater, so that the universe was full of matter. Thus, there was a very dense state of the universe. The explanation of the background radiation is also essentially the same as in GR. Only the metaphysical interpretation differs.

### Can the universe be curved as in GR?

In principle, this would be formally possible. But a curved global universe would not be homogeneous, it would have a center. The homogeneous universe should be flat.

### Are there black holes in GLET?

No, the gravitational collapse of a star stops immediately before horizon formation. There will be a "bounce back" from the Schwarzschild radius, and there will be stable "frozen stars" — stars with a radius close to their Schwarzschild size, with high time dilation inside. Thus, they are not black, only highly red-shifted. The red-shift depends on $$\Upsilon>0$$. For small enough $$\Upsilon>0$$ we have an extremely large red-shift, so that the surface will be de-facto invisible (much less radiation than the background radiation).

### Does the universe expand forever?

If the sign of Einstein's cosmological constant $$\Lambda$$ has been defined correctly by the latest observation, the universe expands as long as GLET may be used for prediction. But this cannot be "forever". In GLET, we have a constant ether density, shrinking matter rulers, and matter consisting of something like defects in a crystal. This cannot continue forever. In some, may be far away, future rulers become small enough to measure effects of the atomic structure of the ether. What happens after this, GLET cannot predict. A microscopic, atomic ether theory should be used.

If the sign of Einstein's cosmological constant $$\Lambda$$ is the reverse, we obtain an oscillating universe.

### Does the ether consist of ether atoms?

There is strong evidence that GLET cannot be true for arbitrary small distances. Especially, this leads to divergent integrals in quantum field theory (ultraviolet problems), but already in classical theory we obtain solutions with infinities in finite time.

We assume that GLET fails for very small distances and should be replaced by some microscopic, possibly atomic ether theory. This solves these conceptual problems at least in principle. Moreover, it is in agreement with the "ether hypothesis" in general - that ether is similar to usual condensed matter. A proposal for an atomic ether model is the cellular lattice model.

### What about quantization of GLET?

GLET is a classical field theory. Quantization of GLET is as simple as the quantization of classical condensed matter theory.

Of course, GLET is only a large distance, continous approximation of a yet unknown microscopic ether theory. Having only an approximation, we can compute quantum effects also only in a certain approximation. For higher order effects we need details of microscopic ether theory.

### Is there relativistic symmetry in GLET?

Yes and no. The most important part of relativistic symmetry — the Einstein equivalence principle — is fulfilled. (That means we have a metric theory of gravity.) By observation of usual matter in a small region so that the gravitational field is approximately constant we cannot detect effects of the preferred frame.

On the other hand, we do not have full general-relativistic symmetry. There are additional non-covariant terms in the Einstein equations. But they are observable only in a very hard way - as "dark matter". That means, the preferred frame influences usual matter only in an indirect way — via gravity. Only the gravitational field is influenced directly.

Moreover, if the additional cosmological constants are small enough, these additional terms become unimportant. In this limit, we obtain the classical Einstein equations.

The additional terms become important for cosmological questions, in the very early universe, and near the black hole horizon. In the solar system these terms are not important. Thus, for all experiments in the solar system we have exact relativistic symmetry.

### Does GLET explain relativistic symmetry?

Yes. The equations of GLET themself have a very good explanation starting with postulates about the ether. Therefore, the symmetry properties of the GLET equations are explained by GLET.

Once GLET is a metric theory of gravity, the Einstein equivalence principle is exactly fulfilled and therefore explained. Full relativistic symmetry occurs only in a limit of zero cosmological constants, GLET requires that these constants have at least in principle non-zero values. Thus, full relativistic symmetry (active diffeomorphism invariance) occurs only in some limit.

The explanation of the Einstein equivalence principle is essentially simple. There are four universal equations - the conservation laws. It is well-known (Noether's theorem) that they are related with translational invariance, that means, with the preferred coordinates. They are universal and therefore do not depend on the material properties or inner degrees of freedom of the ether. Now, action equals reaction. Therefore, the equations for these material properties should not depend on the preferred coordinates too.

### Is the GLET ether similar to usual matter?

That's unknown yet. GLET considers only a few general properties of the ether. Some of these properties are also properties of usual matter. For another property (existence of a Lagrange formalism of the type used in GLET) I don't know if it is fulfilled for usual condensed matter.

Note that GLET describes only a general scheme. Very different ether theories may be described in this scheme. Therefore it is meaningless to talk about the properties of "the ether" as long as we have only GLET without a matter Lagrangian. This matter Lagrangian describes most properties of the ether.

### What are elementary particles?

All elementary particles are purely quantum effects, similar to "phonons" — the quantum "particles" of sound. This is in full agreement with the standard quantum field theory (QFT) picture of the world. For every sort of elementary particles there is a single field — the EM field for photons, an "electron field" for electrons, and so on. These fields describe some properties of the ether. GLET does not tell which property of the ether is described by a given field — it does not even tell how many ether properties exist. A proposal for a complete ether model, which explains which properties of the ether are descibed by which field, is the cellular lattice model.

### What about the Michelson-Morley experiment?

That's trivial. The no-gravity limit of GLET is a well-known ether theory — classical Lorentz-Poincare ether theory, which is simply another metaphysical interpretation of special relativity, which contains an unobservable preferred frame. The predictions of this theory are identical with special relativity. (The only exception I know of is Bell's theorem.)