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tech / sci.physics.relativity / 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’š

SubjectAuthor
* 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’šAether Regained
+- Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’šAether Regained
`* Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’šAether Regained
 +* Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’šTom Roberts
 |`- Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’šAether Regained
 `* Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’šRichard Hachel
  `- Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’šAether Regained

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1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’š

<upgnmm$267g1$1@dont-email.me>

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From: AetherRe...@invalid.com (Aether Regained)
Newsgroups: sci.physics.relativity
Subject: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”
π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•
π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’
𝒕𝒂𝒍 π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•
π’š
Date: Thu, 01 Feb 2024 18:25:00 +0000
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 by: Aether Regained - Thu, 1 Feb 2024 18:25 UTC

First some background:

π‘¬π’Šπ’π’”π’•π’†π’Šπ’ 1905: 𝑢𝒏 𝒕𝒉𝒆 π‘¬π’π’†π’„π’•π’“π’π’…π’šπ’π’‚π’Žπ’Šπ’„π’” 𝒐𝒇
π‘΄π’π’—π’Šπ’π’ˆ π‘©π’π’…π’Šπ’†π’”
https://en.wikisource.org/wiki/On_the_Electrodynamics_of_Moving_Bodies_(1920_edition)

𝑻𝒉𝒆 π’Šπ’π’•π’“π’π’…π’–π’„π’•π’Šπ’π’ 𝒐𝒇 𝒂 "π‘³π’Šπ’ˆπ’‰π’•π’‚Μˆπ’•π’‰π’†π’“" π’˜π’Šπ’π’
𝒃𝒆 𝒑𝒓𝒐𝒗𝒆𝒅 𝒕𝒐 𝒃𝒆 𝒔𝒖𝒑𝒆𝒓𝒇𝒍𝒖𝒐𝒖𝒔, 𝒇𝒐𝒓
π’‚π’„π’„π’π’“π’…π’Šπ’π’ˆ 𝒕𝒐 𝒕𝒉𝒆 π’„π’π’π’„π’†π’‘π’•π’Šπ’π’π’” π’˜π’‰π’Šπ’„π’‰
π’˜π’Šπ’π’ 𝒃𝒆 𝒅𝒆𝒗𝒆𝒍𝒐𝒑𝒆𝒅, π’˜π’† 𝒔𝒉𝒂𝒍𝒍 π’Šπ’π’•π’“π’π’…π’–π’„π’†
π’π’†π’Šπ’•π’‰π’†π’“ 𝒂 𝒔𝒑𝒂𝒄𝒆 π’‚π’ƒπ’”π’π’π’–π’•π’†π’π’š 𝒂𝒕 𝒓𝒆𝒔𝒕, 𝒂𝒏𝒅
π’†π’π’…π’π’˜π’†π’… π’˜π’Šπ’•π’‰ π’”π’‘π’†π’„π’Šπ’‚π’ π’‘π’“π’π’‘π’†π’“π’•π’Šπ’†π’”, 𝒏𝒐𝒓
𝒔𝒉𝒂𝒍𝒍 π’˜π’† π’‚π’”π’”π’π’„π’Šπ’‚π’•π’† 𝒂 π’—π’†π’π’π’„π’Šπ’•π’š-𝒗𝒆𝒄𝒕𝒐𝒓
π’˜π’Šπ’•π’‰ 𝒂 π’‘π’π’Šπ’π’• π’Šπ’ π’˜π’‰π’Šπ’„π’‰ π’†π’π’†π’„π’•π’“π’π’Žπ’‚π’ˆπ’π’†π’•π’Šπ’„
𝒑𝒓𝒐𝒄𝒆𝒔𝒔𝒆𝒔 π’•π’‚π’Œπ’† 𝒑𝒍𝒂𝒄𝒆.

π‘¬π’Šπ’π’”π’•π’†π’Šπ’ 1920: ᴁ𝒕𝒉𝒆𝒓 𝒂𝒏𝒅 𝒕𝒉𝒆 π‘»π’‰π’†π’π’“π’š 𝒐𝒇
π‘Ήπ’†π’π’‚π’•π’Šπ’—π’Šπ’•π’š
https://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity

π‘Ήπ’†π’„π’‚π’‘π’Šπ’•π’–π’π’‚π’•π’Šπ’π’ˆ, π’˜π’† π’Žπ’‚π’š π’”π’‚π’š 𝒕𝒉𝒂𝒕
π’‚π’„π’„π’π’“π’…π’Šπ’π’ˆ 𝒕𝒐 𝒕𝒉𝒆 π’ˆπ’†π’π’†π’“π’‚π’ π’•π’‰π’†π’π’“π’š 𝒐𝒇
π’“π’†π’π’‚π’•π’Šπ’—π’Šπ’•π’š 𝒔𝒑𝒂𝒄𝒆 π’Šπ’” π’†π’π’…π’π’˜π’†π’… π’˜π’Šπ’•π’‰
π’‘π’‰π’šπ’”π’Šπ’„π’‚π’ π’’π’–π’‚π’π’Šπ’•π’Šπ’†π’”; π’Šπ’ π’•π’‰π’Šπ’” 𝒔𝒆𝒏𝒔𝒆,
𝒕𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆𝒓𝒆 π’†π’™π’Šπ’”π’•π’” 𝒂𝒏 𝒂𝒆𝒕𝒉𝒆𝒓.
π‘¨π’„π’„π’π’“π’…π’Šπ’π’ˆ 𝒕𝒐 𝒕𝒉𝒆 π’ˆπ’†π’π’†π’“π’‚π’ π’•π’‰π’†π’π’“π’š 𝒐𝒇
π’“π’†π’π’‚π’•π’Šπ’—π’Šπ’•π’š 𝒔𝒑𝒂𝒄𝒆 π’˜π’Šπ’•π’‰π’π’–π’• 𝒂𝒆𝒕𝒉𝒆𝒓 π’Šπ’”
π’–π’π’•π’‰π’Šπ’π’Œπ’‚π’ƒπ’π’†; 𝒇𝒐𝒓 π’Šπ’ 𝒔𝒖𝒄𝒉 𝒔𝒑𝒂𝒄𝒆 𝒕𝒉𝒆𝒓𝒆
𝒏𝒐𝒕 π’π’π’π’š π’˜π’π’–π’π’… 𝒃𝒆 𝒏𝒐 π’‘π’“π’π’‘π’‚π’ˆπ’‚π’•π’Šπ’π’ 𝒐𝒇
π’π’Šπ’ˆπ’‰π’•, 𝒃𝒖𝒕 𝒂𝒍𝒔𝒐 𝒏𝒐 π’‘π’π’”π’”π’Šπ’ƒπ’Šπ’π’Šπ’•π’š 𝒐𝒇
π’†π’™π’Šπ’”π’•π’†π’π’„π’† 𝒇𝒐𝒓 𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅𝒔 𝒐𝒇 𝒔𝒑𝒂𝒄𝒆 𝒂𝒏𝒅
π’•π’Šπ’Žπ’† (π’Žπ’†π’‚π’”π’–π’“π’Šπ’π’ˆ-𝒓𝒐𝒅𝒔 𝒂𝒏𝒅 π’„π’π’π’„π’Œπ’”), 𝒏𝒐𝒓
𝒕𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆 π’‚π’π’š 𝒔𝒑𝒂𝒄𝒆-π’•π’Šπ’Žπ’† π’Šπ’π’•π’†π’“π’—π’‚π’π’” π’Šπ’
𝒕𝒉𝒆 π’‘π’‰π’šπ’”π’Šπ’„π’‚π’ 𝒔𝒆𝒏𝒔𝒆. 𝑩𝒖𝒕 π’•π’‰π’Šπ’” 𝒂𝒆𝒕𝒉𝒆𝒓 π’Žπ’‚π’š
𝒏𝒐𝒕 𝒃𝒆 π’•π’‰π’π’–π’ˆπ’‰π’• 𝒐𝒇 𝒂𝒔 π’†π’π’…π’π’˜π’†π’… π’˜π’Šπ’•π’‰ 𝒕𝒉𝒆
π’’π’–π’‚π’π’Šπ’•π’š π’„π’‰π’‚π’“π’‚π’„π’•π’†π’“π’Šπ’”π’•π’Šπ’„ 𝒐𝒇 𝒑𝒐𝒏𝒅𝒆𝒓𝒂𝒃𝒍𝒆
π’Žπ’†π’…π’Šπ’‚, 𝒂𝒔 π’„π’π’π’”π’Šπ’”π’•π’Šπ’π’ˆ 𝒐𝒇 𝒑𝒂𝒓𝒕𝒔 π’˜π’‰π’Šπ’„π’‰ π’Žπ’‚π’š
𝒃𝒆 π’•π’“π’‚π’„π’Œπ’†π’… π’•π’‰π’“π’π’–π’ˆπ’‰ π’•π’Šπ’Žπ’†. 𝑻𝒉𝒆 π’Šπ’…π’†π’‚ 𝒐𝒇
π’Žπ’π’•π’Šπ’π’ π’Žπ’‚π’š 𝒏𝒐𝒕 𝒃𝒆 π’‚π’‘π’‘π’π’Šπ’†π’… 𝒕𝒐 π’Šπ’•.

π‘«π’Šπ’“π’‚π’„ 1951: 𝑰𝒔 𝒕𝒉𝒆𝒓𝒆 𝒂𝒏 Æ𝒕𝒉𝒆𝒓?
https://doi.org/10.1038/168906a0

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 senseβ€”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 symmetryβ€”any spectroscopic S-state is such a
state β€”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 stateβ€”the wave function representing it can be normalized. This
is not so for the state of Lorentz symmetry of the ether.

Let us assume the four components vo 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 :

vβ‚€Β²-v₁²-vβ‚‚Β²-v₃² = 1, vβ‚€ > 0 (1)

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 kindβ€”the wave function cannot be normalized because
from the uncertainty principle the particle would have to be distributed
over the whole universe β€” and such states are needed in collision problems.


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Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’š

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From: AetherRe...@invalid.com (Aether Regained)
Newsgroups: sci.physics.relativity
Subject: Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Š
π’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”
π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†
𝒏𝒕𝒂𝒍 π’‚π’ƒπ’”π’–π’“π’…π’Š
π’•π’š
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 by: Aether Regained - Thu, 1 Feb 2024 18:37 UTC

> k₁A_ΞΌ = v_ΞΌ (2)

Sorry, this must be:

k⁻¹A_μ = v_μ (2)

Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’š

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Subject: Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Š
π’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”
π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†
𝒏𝒕𝒂𝒍 π’‚π’ƒπ’”π’–π’“π’…π’Š
π’•π’š
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 by: Aether Regained - Sat, 3 Feb 2024 19:18 UTC

ASCII friendly version, just in case OP's UTF-8 version is not supported
by all readers:

1951: Dirac dismisses Einstein's MONUMENTAL ABSURDITY
=====================================================

-------------------------------------------------------------
Einstein 1905: On the Electrodynamics of Moving Bodies
https://en.wikisource.org/wiki/On_the_Electrodynamics_of_Moving_Bodies_(1920_edition)

The introduction of a "Lightaether" will be proved to be superfluous,
for according to the conceptions which will be developed, we shall
introduce NEITHER A SPACE ABSOLUTELY AT REST, AND ENDOWED WITH SPECIAL
PROPERTIES, NOR SHALL WE ASSOCIATE A VELOCITY-VECTOR WITH A POINT IN
WHICH ELECTRO-MAGNETIC PROCESSES TAKE PLACE.
-------------------------------------------------------------

-------------------------------------------------------------

Einstein 1920: Aether and the Theory of Relativity
https://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity

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.
-------------------------------------------------------------

-------------------------------------------------------------
Dirac 1951: Is there an Aether?
https://doi.org/10.1038/168906a0

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 senseβ€”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 symmetryβ€”any spectroscopic S-state is such a
state β€”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 stateβ€”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_ΞΌ 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 :

vβ‚€Β²-v₁²-vβ‚‚Β²-v₃² = 1, vβ‚€ > 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 kindβ€”the wave function cannot be normalized because
from the uncertainty principle the particle would have to be distributed
over the whole universe β€” 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_ΞΌ, are
restricted by :

A_ΞΌA_ΞΌ= kΒ², [LaTeX: A_{\mu} A_{\mu} = k^2]

where k is a universal constant. From the continuity of Aβ‚€ 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.

Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’š

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 by: Tom Roberts - Sat, 3 Feb 2024 21:22 UTC

On 2/3/24 1:18 PM, Aether Regained wrote:
> [...]

How are you coming with explaining quantum phenomena using an aether?
Without that you have no hope of convincing anybody that your fantasies
are valid.

Tom Roberts

Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’š

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𝒄 π’…π’Šπ’”π’Ž
π’Šπ’”π’”π’†π’”
π‘¬π’Šπ’π’”π’•
π’†π’Šπ’'𝒔
π’Žπ’π’π’–π’Ž
𝒆𝒏𝒕𝒂𝒍
𝒂𝒃𝒔𝒖𝒓
π’…π’Šπ’•π’š
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From: pourquoi...@tiscali.fr (Richard Hachel)
 by: Richard Hachel - Wed, 7 Feb 2024 10:00 UTC

Le 03/02/2024 Γ  20:18, Aether Regained a Γ©crit :

> THUS WITH THE NEW THEORY OF
> ELECTRODYNAMICS WE ARE RATHER FORCED TO HAVE AN AETHER.

? ? ?

R.H.

Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’š

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From: AetherRe...@invalid.com (Aether Regained)
Newsgroups: sci.physics.relativity
Subject: Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Š
π’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”
π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†
𝒏𝒕𝒂𝒍 π’‚π’ƒπ’”π’–π’“π’…π’Š
π’•π’š
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 by: Aether Regained - Thu, 8 Feb 2024 18:23 UTC

Tom Roberts:
> On 2/3/24 1:18 PM, Aether Regained wrote:
>> [...]
>
> How are you coming with explaining quantum phenomena using an aether?
> Without that you have no hope of convincing anybody that your fantasies
> are valid.
>
> Tom Roberts

That is a work in progress, moving slowly.

Meanwhile, here is Dirac's paper on an aether based electrodynamics:

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

and here is SchrΓΆdinger's commentary on Dirac's aether electrodynamics:

https://www.nature.com/articles/169538a0.pdf

Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Šπ’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†π’π’•π’‚π’ π’‚π’ƒπ’”π’–π’“π’…π’Šπ’•π’š

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Subject: Re: 1951: π‘«π’Šπ’“π’‚π’„ π’…π’Š
π’”π’Žπ’Šπ’”π’”π’†π’” π‘¬π’Šπ’π’”
π’•π’†π’Šπ’'𝒔 π’Žπ’π’π’–π’Žπ’†
𝒏𝒕𝒂𝒍 π’‚π’ƒπ’”π’–π’“π’…π’Š
π’•π’š
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 by: Aether Regained - Thu, 8 Feb 2024 18:24 UTC

Richard Hachel:
> Le 03/02/2024 Γ  20:18, Aether Regained a Γ©crit :
>
>> THUS WITH THE NEW THEORY OF
>> ELECTRODYNAMICS WE ARE RATHER FORCED TO HAVE AN AETHER.
>
> ? ? ?
>
> R.H.
>

Dirac is referring to his own paper that was published the same year
(1951).

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

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.

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