Mach's Ether Principle

Mach tried to avoid assigning reality to a non-observable thing. Instead of an acceleration with reference to absolute space, he used all of the masses in the universe as reference.

But inertial resistance opposed to relative acceleration of distant masses presupposes action at a distance.

Anyone who follows Mach will still end up with the ether as medium for the effects of inertia. But Mach’s ether is different from the ether of Newton, Fresnel, and Lorentz.

Mach’s ether not only conditions the behaviour of inert masses, but is also conditioned in its state by them.

Mach’s idea finds its full development in the ether of General Relativity which says that the metrical qualities of space-time:

• differ in the different points of space-time
• are partly conditioned by the matter existing outside of the territory

Space is not physically empty.

This is because:

• space and time have reciprocal relations
• “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by 10 functions (the gravitation potentials gμν)

This makes the ether useful. But this ether is very different from that of the ether of the mechanical wave-theory of light.

The ether of General Relativity is a medium which is itself devoid of all mechanical and kinematical qualities. But it helps to determine mechanical (and electromagnetic) events.

Difference Between GR Ether and Lorentz Ether

The state of General Relativity (GR) Ether is at every place determined by connections with:

• the matter and
• the state of the ether in neighbouring places.

These are amenable to law through differential equations.

The Lorentzian ether in the absence of electromagnetic fields is:

• conditioned by nothing outside itself
• everywhere the same

The GR ether is transmuted conceptually into the Lorentz ether if we substitute constants for the functions of space which describe the GR ether, disregarding the causes which condition its state.

Thus, the GR ether is the outcome of the Lorentzian ether, through relativation.

I do not know what part my ether is to play in the physics of the future.

My ether determines the metrical relations in the space-time continuum, e.g. the configurative possibilities of solid bodies as well as the gravitational fields.

But we do not know whether:

• it has an essential share in the structure of the electrical quantum particles constituting matter, or
• it is only in the proximity of ponderable masses that its structure differs essentially from that of the Lorentz ether, or
• the geometry of spaces of cosmic extent is approximately Euclidean.

But we can assert by reason of the relativistic equations of gravitation that there must be a departure from Euclidean relations, with spaces of cosmic order of magnitude, if there exists a positive mean density, no matter how small, of the matter in the universe.

If we consider the gravitational field and the electromagnetic field from the standpoint of the ether hypothesis, we find a remarkable difference between the two.

There can be no space nor any part of space without gravitational potentials. This is because gravitational potentials give space its metrical qualities, without which it cannot be imagined at all.

The existence of the gravitational field is inseparably bound up with the existence of space.

On the other hand, it is possible for a part of space to have no electromagnetic field.

Thus in contrast with the gravitational field, the electromagnetic field is only secondarily linked to the ether. The formal nature of the electromagnetic field is in no way determined by that of gravitational ether.

The electromagnetic field, as opposed to the gravitational field, rests on an entirely new formal motif, as though nature might just as well have endowed the gravitational ether with fields of quite another type. For example, it could have fields of a scalar potential, instead of fields of the electromagnetic type.

The quantum particles of matter are merely condensations of the electromagnetic field.

This leads to two views of the universe:

1. Gravitational ether (space)
2. Electromagnetic field (matter)

These 2 realities are completely separated from each other conceptually, although connected causally.

It would be a great advance if we could comprehend the gravitational field and the electromagnetic field together as one unified conformation.

This would conclude the the epoch of theoretical physics founded by Faraday and Maxwell. It would remove the contrast between ether and matter.

Through General Relativity*, the whole of physics would become a complete system of thought, like geometry, kinematics, and the theory of gravitation.

The mathematician H. Weyl is trying to do this. But I do not think that his theory will hold in reality.

We should not unconditionally reject the possibility that the facts comprised in the quantum theory may set bounds to the field theory beyond which it cannot pass.

According to GR, space has physical qualities represented by the ether.

But this ether is not a ponderable media which has parts which may be tracked through time. The idea of motion may not be applied to it.