Re: Anyone good with Tensors?

guskz@xxxxxxxxxxx wrote:
Igor wrote:
guskz@xxxxxxxxxxx wrote:
Igor wrote:
guskz@xxxxxxxxxxx wrote:
I think long ago I read (anyone have the link and Einstein's words on
it) that Einstein believed there was an Aether (is there any
relationship of the Aether with his cosmological constant mistake)?

*****When**** Einstein wrote his GR theory, did he still believe in an
Aether?

If so then it seems his warped space, rubber *** model and Einstein's
math for tensors could have based on an Aether (or space as a fabric),
if no then why not?

It's not warped space, it's curved spacetime. The rubber *** model
is a poor analogy used in popular treatments and can lead to tremendous
misunderstandings. Tensors already existed as mathematical objects
prior to Einstein, and they are just generalizations of vectors. And
no, Einstein never believed in an aether after his first papers on
relativity were published.

Check my other post, in 1920 Einstein said he based his GR on the
Ether.

No he did not. I think you must have your wires crossed and are taking
him out of context.



Tom Roberts wrote:
Igor wrote:
guskz@xxxxxxxxxxx wrote:
Check my other post, in 1920 Einstein said he based his GR on the
Ether.

No he did not. I think you must have your wires crossed and are taking
him out of context.

This is indeed out of context. In 1920 Einstein attended a conference on
the aether, and made remarks that essentially say that the "aether" of
GR is utterly unlike any other aether, in that it has no physical
properties (density, temperature, pressure, etc.), and no state of rest
can be ascribed to it.

To consider GR as an "aether theory" requires an incredible PUN on the
word that robs it of all meaning. Einstein knew this. But he spoke in
the style of his time, not ours. <shrug>


Einstein's own words in 1920 from the link I gave: "GR without an ETHER
IS UNTHINKABLE"

His further claims that the Ether is not a tangeable substance (perhaps
the same way photon has no mass or not a particle,etc...) is to cover
his behind on this claim.


Roberts is wrong on that. Einstein spoke, as ever, in term acceptable
to Einstein. Einstein's views on ether may not be liked by the modern
view, but that may mean that the modern view is wrong. But to give a
glib rejection of Einstein on his views on ether is to restart an
arguement that cannot succeed on this NG. In the end, I argue that
Einstein is entitled to HIS viewpoint, no matter how
out-of-the-mainstream it seems today! In any case, both sides on this
NG make too much out of Einstein's notion of ether in 1920. By neither
the relativistic nor Mechanistic viewpoint is his view on ether as
espoused in his 1920 essay a big deal.

The physics community today is no better than the lay community in
reading Einstein's physics essays to learn precisely what Einstein felt
about ether and many other things of a philosophical nature relating to
his interests in physics. Read Ideas and Opinions to find out what
Einstein really thought about these things. I can't understand how
anyone interested in relativity would not read it. Read it many times.
Get your highlighter out and use it!

On the other hand, Einstein was not "covering his ass," either. He
simply adopted a different definition of "ether" than you have. To
Einstein, it seems, an ether is any hypothetical space-filling thing
that is used in some physical theory. I sometimes leave out the word
"hypothetical" when defining "ether." I really shouldn't because
physics is not metaphysics and the truth of such a hypothetical thing
is irrelevant in physics. Under this definition, a space-filling field
is an ether, though Einstein might have thought of a narrower
definition of ether to accomodate the metric field alone. I see no need
to tailor the definition so restrictively.

I posted the following article recently but it seems to have gotten
lost in the shuffle. It explains exactly how Einstein regarded ether in
the post 1905 world of physics.


Ether, Mechanics, the Laws of Physics, and Relativity

Question: Did Einstein discover general relativity?

Well, invented is more like it. Einstein set about the intensional task
of explaining gravity from a field-theoretic viewpoint by

1) making the field equations for gravity and the equations of motion
generally covariant and

2) by intensionally generalizing the concept of the "laws of physics"
as behavioral constraints which do not give any intrinsic preference to
description from within inertial frames of reference. In other words,
Einstein set about the task of demoting the inertial frame of reference
relative to the concept of "law of physics" to just another frame;
accelerated frames of reference, in this viewpoint, are just as valid
for the discovery of the "laws of physics" as are the inertial frames.
And this generalization necessitated the generalization of what was
meant by a "law of physics" in SR.


Thus, each time the principle of relativity is generalized the notion
of "law of physics" is generalized. Einstein revealed this clearly in
the following quote:

H. A. Lorentz even discovered the "Lorentz transformation," later
called after him, though without recognizing its group character.
To him Maxwell's equations in empty space held only for a particular
coordinate system distinguished from all other coordinate systems by
its state of rest. This was a truly paradoxical situation because
the theory seemed to restrict the inertial system more strongly than
did classical mechanics. This circumstance, which from the empirical
point of view appeared completely unmotivated, was bound to lead
to the theory of special relativity.
---- Einstein, "H. A. Lorentz, Creator and Personality,"
Ideas and Opinions, p. 75.


To understand what Einstein meant by the "group character" of the
transformation, we can go back to Newton's mechanics. That formal
system had a set of "laws" that were covariant under Galilean
transformation of the equations between any two inertial frames. (The
compositon of these transformations form a mathematical group, which
may not be a familiar term to physics laymen.) Thus, in Newton's
mechanics, all inertial frames are equivalent for the discovery of the
laws of physics, because the simplest interpretation of the covariance
of the equations of that system, consistent with empirical data, demand
that "law of physics" be conceptualized as "in their covariant forms
they are true of all inertial frames." (Of course, definitions don't
give us physical content, but a good definition can be of heuristic
use.)

Now, Lorentz invented a theory of electrodynamics that showed that one
does not have to conceptualize the "laws of physics" as tied to all
inertial frames by a covariance group connecting all inertial frames.
Ironically, his attempt to generalize Newton's mechanics to include
electrodynamics with a mechanical explanation of E&M built into it, led
to the demotion of the concept of "laws of physics" to mere
"regularities true only in the rest frame of the ether." So, from this
formal point of view, Lorentz was not motivated to investigate the
"group nature" of Maxwell's equations. (Einstein referred to the
"synthesis" Lorentz obtained of Newton's mechanics and Maxwell's field
theory, Physics and Reality, Ideas and Opinions, p. 306.)

What Einstein meant by "restrict the inertial system more strongly than
did classical mechanics" is that Newton's mechanics had no concept of a
"special" inertial frame because in that theory the laws of physics are
the same in all inertial systems (frames) --the PoR. But in Lorentz's
theory, one claims that: there exists a special frame (system of
coordinates) in which in that frame alone the "laws of physics" hold.

What could have led Lorentz to adopt this bizarre viewpoint, which was
discordant with classical mechanics? I can think of only one hypothesis
to proffer: Besides the imperative implicit in the mechanical program,
Lorentz additionally took the view that the laws of physics are
SUPPOSED to tell us about what is really, truly happening in nature,
whereas to Einstein, the laws of physics were merely faithful
descriptions of the behavior of phenomena (though admittedly Einstein
equivocated from that simple doctrine with respect to his views on QM).
To Lorentz, the true behavior was only knowable in the rest frame of
the ether because in that frame alone stationary rods and clocks give
"true" values.

But to Einstein, once the operational definitions that connect the
measurements of variables to the theoretical variables have been made,
then the "laws of physics" are covariant manifestations of the
variable-relationship regularities true of the behavior of phenomena as
seen in any inertial system. (For example: F= ma is a
variable-relationship regularity, covariant under a Galilean
transformation of coordinates.) This is the same viewpoint as in
classical mechanics with only one important generalization (neglecting
gravity): whereas classical mechanics was about the (covariant) laws of
the description of the behavior of uncharged particles, SR is about the
(covariant) laws of the local description of the behavior of particles,
uncharged or charged. And in the latter case, that brings in
electrodynamics for the 1905 version of SR. Now, however, SR is about
the local laws for all phenomena, not just electrodynamics.

There are two profound differences between classical mechanics and
relativistic mechanics: The former does not allow field to be treated
as an irreducible of the theory and the latter does not allow for
action-at-a-distance, or effects traveling 'through space' faster than
the speed of light (in flat spacetime, of course).

Finally, Einstein said, "This circumstance, which from the empirical
point of view appeared completely unmotivated, was bound to lead to the
theory of special relativity." What did he mean? He told us in his 1905
SR paper. He said that the description of the behavior of
electrodynamics is dependent only on the relative velocities among the
interacting parts, and not on their absolute velocities in any way, and
also that all experiments designed and implemented to detect the
earth's absolute velocity through "space" (if there really is such a
thing) had failed. I.e., no empirical justification!

It's as if Einstein were saying: "In our efforts to generalize Newton's
mechanics to include electrodynamics, do we really have to drag along
this dead horse of the mechanical ether with its unique, but
unobservable, rest frame, given that 1) there is no empirical mandate
to do so, and 2) the formal equations of electrodynamics, being Lorentz
covariant (the "group nature"), makes this unique frame undetectible
even if it exists? So, even if it does exist, it's superfluous to a
minimalist mind frame.

To Einstein, the answer was an obvoiusly no. To Einstein, Lorentz's
theory wasn't so much "being wrong" as "being unsimple and
disharmonious." It was unsimple formally because it postulated the
existence of a special frame which SR shows to be superfluous (which is
a violation of parsimony). It was disharmonious because it purported to
be a generalization of Newton's physics, yet it contradicted the
classical mechanical notion of a "law of physics," which is implicit in
the classical theory. Ironically, instead of the notion of "law of
physics" generalizing going from Newton to Lorentz, the notion actual
became narrower!

Einstein wrote much about what led him to SR. The quote above says a
lot about that in a succinct but cryptic way. Let's add to that from
what he and Infeld wrote in "The Evolution of Physics":

There seems to be only one way out of all these
difficulties. In the attempt to understand the phenomena
of nature from the mechanical point of view,
throughout the whole development of science up to the
twentieth century, it was necessary to introduce artificial
substances like electric and magnetic fluids, light corpuscles,
or ether. The result was merely the concentration of all
the difficulties in a few essential points, such as ether
in the case of optical phenomena. Here all the fruitless
attempts to construct an ether in some simple way,
as well as the other objections, seem to indicate that the
fault lies in the fundamental assumption that it is possible to
explain all events in nature from a mechanical
point of view. Science did not succeed in carrying
out the mechanical program convincingly,
and today no physicist believes in the possibility of its
fulfillment.
--- Evolution of Physics, p. 120-121.


Both SR and early QM contributed to the demise of the philosophical
viewpoint held up to the end of the nineteenth century that all
phenomena HAVE to be explained in terms of particles in motion
influenced by forces acting at-a-distance (i.e., in terms of classical
mechanics). And thus physics evolved not only by adding new empirical
information to its corpus, but also by adding new modes (i.e.,
non-mechanical modes) of physical explanation.

If you missed the subtle point relative to Lorentz's theory and 1905
SR, I'll explain. In Lorentz's theory you have the irreducible concepts
of mass (material) particles and forces acting-at-a distance. The EM
field was "explained" as emergent properties of states in the
mechanical ether. In SR you have mass/energy particles and forces
derived from fields, which are held to be irreducible; that is, they
are not treated as "explainable" in terms of a mechanical states of
some material ether.

Einstein said:

Since the special theory of relativity revealed the physical
equivalence of all inertial systems, it proved the untenability
of the hypothesis of an ether at rest. It was therefore necessary
to renounce the idea that the electromagnetic field is to be
regarded as a state of a material carrier. The field thus
becomes an irreducible element of physical description,
irreducible in the same sense as the concept of matter in the
theory of Newton.
--- Relativity and the Problem of Space, Ideas and Opinions,
p. 371.

So, when the mechanical program fell, the field program was initiated.

In other place Einstein said:

For several decades most physicists clung to the conviction
that a mechanical substructure would be found for Maxwell's
theory. But the unsatisfactory results of their efforts led to the
gradual acceptance of the new field concepts as irreducible
fundamentals---in other words, physicists resigned themselves
to giving up the idea of a mechanical foundation.
---- The Fundaments of Theoretical Physics, Ideas and
Opinions, p. 328.

Einstein went on to say that the beginnings of a new program of field
research was instituted. In other words, physics had evolved to a new
paradigm for theoretical research.

Another quote in which Einstein argued clearly, solely on the principle
of parsimony (no unnecessary hypotheses!) and irrespective of his or
his generation's intuitions of deep reality, to a theoretic ontology
without an underlying ether to explain Maxwell's field equations:

Now a question arose: Since the field exists even in a
vacuum, should one conceive of the field as a state of a
"carrier," or should it rather be endowed with an independent
existence not reducible to anything else? In other words,
is there an "ether" which carries the field; the ether being
considered in the undulatory state, for example, when it
carries light waves.
The question has a natural answer: Because one cannot
dispense with the field concept, it is preferable not to introduce
in addition a carrier with hypothetical properties. However, the
pathfinders who first recognized the indispensibility of the field
concept were still too strongly imbued with the mechanistic
tradition of thought to accept unhesitatingly this simple point of
view. But in the course of the following decades this view
imperceptibly took hold.
--- On the Generalized Theory of Gravitation, Ideas and Opinions,
p. 344.

Finally, Einstein seems to suggest in the first quote that SR was
inevitable in the face of all this supporting evidence of the
superfluous nature of the mechanical ether. Yet, I sometimes wonder if
we'd still be without special relativity were it not for Einstein.

And to those who would jump to the name of Poincare or someone else, I
say: Even holding a comittment to the Einstein (SR) version of the PoR
does not forbid one to also hold a belief in the use of an underlying
mechanical ether. This is precisely what Einstein said in the last
quote! It's a free choice and part of one's elective formal point of
view.

And one last quote in which Einstein expounded this notion of the
formal point of view:

In order to construct a theory, it is not enough to have a
clear conception of the goal. One must also have a formal
point of view which will sufficiently restrict the unlimited
variety of possibilities.
--- The Fundaments of Theoretical Physics, Ideas and Opinions,
p. 328.

There seems to be a common incredulity of laymen in physics who cannot
grasp why today's physicist cannot just "see the necessity of having a
mechanical ether underlying phenomena." And modern physicists are not
very good at explaining their lack of attraction to this mechanical
model. I have given some of the reasons why physicists over the long
decades had left the old bandwagon of support for a mechanical ether,
but something more needs to be emphasized.

It's a question of freedom of choice! Prior to the general acceptance
of SR, physicists had only one choice for a foundation to physics:
Mechanics. Therefore in those dogmatic days it was a matter of course
that if you dealt in electrodynamics, you needed some mechanical
interpretation for Maxwell's fields that appeared in his field
equations. But today, it's wide open. One can invent any foundation one
wants, so long as it produces a theory that works. Therefore, the
physicist of today, who has been educated in such a liberal school of
foundations, is hardly automatically impressed by the claimed
"obviousness of the existence of an underlying mechanical ether to
explain electrodynamical phenomena."

The answer is that there is nothing obvious about what goes on beneath
the "visible to the naked eye." Physical concepts are free creations of
the human mind. Any time a modern physicist desires to reduce the EM
field to something "more primitive," he or she has the virtual infinite
freedom of choice by which to do so, and to do so by the mode of
classical mechanics is only one of those many choices by which it could
be done. On the other hand, the long history of the failed attempts of
physicists to invent an elegant mechanical explanation of
electrodynamics is why they are so skeptical of such a claim, and
deservedly so.

One last question to answer: What explains the huge gap between the
typical layman and the professional physicist in their philosophical
outlook on foundational issues in physics? The obvious answer is
education. But that is a mere truism at this point.

The next question is: Exactly what is it about their differences in
physics education accounts for this philosophical divergence? Okay,
let's start with what they probably have in common: university or
college physics. Aaah, university physics! That unabashed dogmatic
promotion of the efficacy of the Mechanical Progam to answer all
questions in physics -- or so it seems to the naive physics student!
Physics education at this level seems to create the same misconceptions
in physics students that had dominated the thinking of early modern
physicists, which put blinders on their eyes to the possibility of any
explanation in physics other than in term of classical mechanics. (I'm
speaking in generalities, of course. By the leadership of a few
individuals over the centuries since Newton, ending in Einstein, they
led physics away from that dogma.) Unwittingly, we're doing it all over
again. We're allowing the Mystery of Mechanics to deceive people who
take lower-division physics classes. And this is an explanation why so
many engineers come to this NG so resistant to the philosophy of modern
physics. Modern physics got to where it is by a long and hard process
of evolution away from classical mechanics.

Every introductory physics textbook should report as it develops the
material, not only where the theory of mechanics succeeds, but also
were it fails. We all tend to come out of such a class "strongly imbued
with the mechanistic" philosophy or outlook or prejudice, as Einstein
put it. However, the layman's formal education in physics is likely to
end there or with some other mechanical subject at the lower-division
level. But the professional physicist will of necessity take those
classes, such as special relativity and QM, in which it becomes obvious
that mechanics is not the foundation for all of physics! Hence the
philosophical divide and the layman can't fathom why the divide even
exists. Well, maybe now he or she can a little better.

.

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