Re: The most ridiculous science mistake in history.

gharnagel:> aether wrote:

>
Without an aether, the state of physics is little different than "angels
pulling/pushing around objects in accordance with the force laws".

>
"But neither Maxwell nor his followers succeeded in elaborating a
mechanical
model for the ether which might furnish a satisfactory mechanical
interpretation
of Maxwell's laws of the electro-magnetic field. The laws were clear and
simple,
the mechanical interpretations clumsy and contradictory....
>
>
"the whole change in the conception of the ether which the special
theory of
relativity brought about, consisted in taking away from the ether its last
mechanical quality, namely, its immobility...."
>
"More careful reflection teaches us however, that the special theory of
relativity
does not compel us to deny ether. We may assume the existence of an
ether; only we
must give up ascribing a definite state of motion to it, i.e. we must by
abstraction
take from it the last mechanical characteristic which Lorentz had still
left it."
>
"What is fundamentally new in the ether of the general theory of
relativity as
opposed to the ether of Lorentz consists in this, that the state of the
former
is at every place determined by connections with the matter and the
state of the
ether in neighbouring places, which are amenable to law in the form of
differential
equations; whereas the state of the Lorentzian ether in the absence of
electromagnetic
fields is conditioned by nothing outside itself, and is everywhere the
same...."
>
"Recapitulating, we may say that according to the general theory of
relativity space is endowed with physical qualities; in this sense,
therefore, there exists an ether. According to the general theory of
relativity space without ether is unthinkable; for in such space there
not only would be no propagation of light, but also no possibility of
existence for standards of space and time (measuring-rods and clocks),
nor therefore any space-time intervals in the physical sense. But this
ether may not be thought of as endowed with the quality characteristic
of ponderable media, as consisting of parts which may be tracked through
time. The idea of motion may not be applied to it."
>
https://mathshistory.st-andrews.ac.uk/Extras/Einstein_ether/

Gary (@gharnagel), you have overlooked an important part of my post,
namely Dirac's 1951 note: Is there an Aether?

You can read the note here:

https://doi.org/10.1038/168906a0

and, the original paper which the note refers to here:

Dirac, P. A. M. (1951). A New Classical Theory of Electrons. Proceedings
of the Royal Society A: Mathematical, Physical and Engineering Sciences,
209(1098), 291–296.

https://doi.org/10.1098/rspa.1951.0204

The important point is that Dirac observes that even Einstein's notion
that an aether compatible with relativity theory "may not be thought of
as endowed with the quality characteristic of ponderable media, as
consisting of parts which may be tracked through time. The idea of
motion may not be applied to it" is obsolete.

In Dirac's words (since the note is short, I reproduce it in full below):

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In the last century, the idea of a universal and all-pervading aether
was popular as a foundation on which to build the theory of
electromagnetic phenomena. The situation was profoundly influenced in
1905 by Einstein's discovery of the principle of relativity, leading to
the requirement of a four-dimensional formulation of all natural laws.
It was soon found that the existence of an aether could not be fitted in
with relativity, and since relativity was well established, the aether
was abandoned.

Physical knowledge has advanced very much since 1905, notably by the
arrival of quantum mechanics, and the situation has again changed. If
one re-examines the question in the light of present-day knowledge, one
finds that the aether is no longer ruled out by relativity, and good
reasons can now be advanced for postulating an aether.

Let us consider in its simplest form the old argument for showing that
the existence of an aether is incompatible with relativity. Take a
region of space-time which is a perfect vacuum, that is, there is no
matter in it and also no fields. According to the principle of
relativity, this region must be isotropic in the Lorentz sense—all
directions within the light-cone must be equivalent to one another.
According to the ather hypothesis, at each point in the region there
must be an aether, moving with some velocity, presumably less than the
velocity of light. This velocity provides a preferred direction within
the light-cone in space-time, which direction should show itself up in
suitable experiments. Thus we get a contradiction with the relativistic
requirement that all directions within the light-cone are equivalent.

This argument is unassailable from the 1905 point of view, but at the
present time it needs modification, because we have to apply quantum
mechanics to the aether. The velocity of the aether, like other physical
variables, is subject to uncertainty relations. For a particular
physical state the velocity of the aether at a certain point of
space-time will not usually be a well-defined quantity, but will be
distributed over various possible values according to a probability law
obtained by taking the square of the modulus of a wave function. We may
set up a wave function which makes all values for the velocity of the
aether equally probable. Such a wave function may well represent the
perfect vacuum state in accordance with the principle of relativity.

One gets an analogous problem by considering the hydrogen atom with
neglect of the spins of the electron and proton. From the classical
picture it would seem to be impossible for this atom to be in a state of
spherical symmetry. We know experimentally that the hydrogen atom can be
in a state of spherical symmetry—any spectroscopic S-state is such a
state —and the quantum theory provides an explanation by allowing
spherically symmetrical wave functions, each of which makes all
directions for the line joining electron to proton equally probable.

We thus see that the passage from the classical theory to the quantum
theory makes drastic alterations in our ideas of symmetry. A thing which
cannot be symmetrical in the classical model may very well be
symmetrical after quantization. This provides a means of reconciling the
disturbance of Lorentz symmetry in space-time produced by the existence
of an aether with the principle of relativity.

There is one respect in which the analogy of the hydrogen atom is
imperfect. A state of spherical symmetry of the hydrogen atom is quite a
proper state—the wave function representing it can be normalized. This
is not so for the state of Lorentz symmetry of the aether.

Let us assume the four components v_μ of the velocity of the aether at
any point of space-time commute with one another. Then we can set up a
representation with the wave functions involving the v's. The four v's
can be pictured as defining a point on a three-dimensional hyperboloid
in a four-dimensional space, with the equation :

    v₀²-v₁²-v₂²-v₃² =  1, v₀ > 0 (1) [LaTeX: v_0^2 - v_1^2 - v_2^2 -
v_3^2 = 1, v_0 > 0]

A wave-function which represents a state for which all aether velocities
are equally probable must be independent of the v's, so it is a constant
over the hyperboloid (1). If we form the square of the modulus of this
wave function and integrate over the three-dimensional surface (1) in a
Lorentz-invariant manner, which means attaching equal weights to
elements of the surface which can be transformed into one another by a
Lorentz transformation, the result will be infinite. Thus this wave
function cannot be normalized.

The states corresponding to wave functions that can be normalized are
the only states that can be attained in practice. A state corresponding
to a wave function which cannot be normalized should be looked upon as a
theoretical idealization, which can never be actually realized, although
one can approach indefinitely close to it. Such idealized states are
very useful in quantum theory, and we could not do without them. For
example, any state for which there is a particle with a specified
momentum is of this kind—the wave function cannot be normalized because
from the uncertainty principle the particle would have to be distributed
over the whole universe — and such states are needed in collision problems.

We can now see that we may very well have an aether, subject to quantum
mechanics and conforming to relativity, provided we are willing to
consider the perfect vacuum as an idealized state, not attainable in
practice. From the experimental point of view, there does not seem to be
any objection to this. We must make some profound alterations in our
theoretical ideas of the vacuum. It is no longer a trivial state, but
needs elaborate mathematics for its description.

I have recently (Proc. Roy. Soc., [A, 209, 291 (1951)]) put forward a
new theory of electrodynamics in which the potentials A_μ, are
restricted by :

    A_μA_μ= k², [LaTeX: A_{\mu} A_{\mu} = k^2]

where k is a universal constant. From the continuity of A₀ we see that
it must always have the same sign and we may take it positive. We can
then put

    k⁻¹A_μ = v_μ (2) [LaTeX: k^{-1} A_{\mu} = v_{\mu}]

and get v's satisfying (1). These v's define a velocity. Its physical
significance in the theory is that if there is any electric charge it
must flow with this velocity, and in regions where there is no charge it
is the velocity with which a small charge would have to flow if it were
introduced.

We have now the velocity (2) at all points of space-time, playing a
fundamental part in electrodynamics. It is natural to regard it as the
velocity of some real physical thing. THUS WITH THE NEW THEORY OF
ELECTRODYNAMICS WE ARE RATHER FORCED TO HAVE AN AETHER.

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