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Guest

Hi,

I commented that "if Einstein came back to Earth he would not
recognize his theory and he would be told to study MTW if he wanted to
learn General Relativity." As a response I was told that I did not
know GR so I should not posit such thing. I thought that was fair. So
what do experts here think? The assumption is that Einstein comes in
disguise, not as a celebrity, in that case, no one would care to tell
him to study GR.

Thanks, and hope this is not off-topic here.

Jonathan Thornburg [remov · Guest

azeynel1@gmail.com wrote:
[quote]I commented that "if Einstein came back to Earth he would not
recognize his theory and he would be told to study MTW if he wanted to
learn General Relativity." As a response I was told that I did not
know GR so I should not posit such thing. I thought that was fair. So
what do experts here think? The assumption is that Einstein comes in
disguise, not as a celebrity, in that case, no one would care to tell
him to study GR.
[/quote]
The basic concepts of differential geometry & coordinate invariance,
special relativity, the equivalence principle, and the Einstein field
equations, are all essentially as Einstein described them. This
suggests that yes, the "reincarnated Einstein" would indeed recognize
GR today as the theory he published in 1915.

But there are of course many many many new developments which Einstein
didn>t know in 1915, or even in 1955 when he died. For example, the
concept of a black hole wasn>t properly understood until about 1970,
with the work of Kruskal & Szekeres. (Wheeler coined the phrase
"black hole" around 1969-70.) MTW (among many other texts) would be
a fine place for the "reincarnated Einstein" to start learning this
new-to-him material.

Another (related) notable example would be the realisation (due to
Penrose & Hawking in the late 1960s - early 1970s) of the ubiquitous
nature of singularities in gravitational collapse. MTW gives some
discussion of this, and I>m sure a theoretical physicist of Einstein>s
brilliance could follow the more mathematical treatments of Wald or
Hawking & Ellis without difficulty.

References:
@book{Misner73,
key = {Misner73},
author = {Charles W. Misner and Kip S. Thorne and John A. Wheeler},
title = {Gravitation},
publisher = {W. H. Freeman},
address = {San Francisco},
year = 1973,
}

@Book{Wald84,
key = {Wald84},
author = {Robert M. Wald},
title = {General relativity},
publisher = {The University of Chicago Press},
year = 1984,
isbn = "0-226-87032-4 (hardcover), 0-226-87033-2
(paperback)",
address = {Chicago},
}

@Book{Hawking73a,
author = {Stephen W. Hawking and George F. R. Ellis},
title = {The large scale structure of spacetime},
publisher = {Cambridge University Press},
year = 1973,
address = {Cambridge, England},
isbn = {0-521-09906-4},
}

--
From: "Jonathan Thornburg [remove -animal to reply]"
<jthorn@astro.indiana-zebra.edu> Dept of Astronomy, Indiana University,
Bloomington, Indiana, USA "Washing one>s hands of the conflict between
the powerful and the powerless means to side with the powerful, not to
be neutral."

Rock Brentwood · Guest

azeyn...@gmail.com wrote:
[quote]I commented that "if Einstein came back to Earth he would not
recognize his theory and he would be told to study MTW if he wanted to
learn General Relativity."

The assumption is that Einstein comes in disguise, not as a celebrity,
in that case, no one would care to tell him to study GR.
[/quote]
You have to understand something that is almost completely unknown
about the history of Einstein -- something I, myself, didn>t learn up
until a month ago. 1905 didn>t just happen by itself. It was not
"silence, 1905, 5 landmark papers, boom." That>s all myth and
nonsense.

What it actually was is this (and there>s a moral lesson in this): it
was "a few essays on aether theory c. 1900, a few papers in Annalen
der Physik 1900-1905, then ... TWENTY ONE REVIEWS of others people>s
works in 1905, littered with a few papers of his own."

Then, like, 2 more reviews after 1905, then it was all "nobody but me"
afterwards. If you have to ask why it tapered off, after he crested
with SR and the magnum opus, GR, well there>s your answer.

And let that lesson be taken to heart by any who may be taking
themselves out of the loop, so to say, to spend 5 or 10 years writing
their "magnum opus" or get self-involved in their own school of
thought or creations or advocacies.

So, as you can see: "would he recognize what>s present today?" is
clearly the wrong question -- were the same process to be repeated.
The only relevant question would be: "is there a venue to grab a bunch
of papers and books, facilities to study, critically review and
analyse them, and distribute commentary, rewrites and analyses of
them?"

Penrose, himself, made the point at the end of his 2006 "Road to
Reality" book, that the times called for someone to fill this role
once again -- the Integrator.

Let>s make the question more interesting: suppose he actually DID come
back -- in reincarnated form. Where would he be, and would he
recognize the published literature today?

He>d probably take up residence in the US, picking a spot that had a
history of a socialist government (surprisingly: one that was a well-
run, award-winning municipal government, with a legacy of open spaces,
large spanning parks and beach-fronts clearly show for it), a
university with a strong Jewish heritage, and a city whose very
conception (and city hall) are a replica of Munich (and the
Ratskellar). Of course, we>re talking about Milwaukee, UW-Milwaukee
(whose Library, the Golda Meir Library was named in honor of one of
its former residents).

Indeed, had UWM been around before its year of consolidation in 1956,
I>m convinced he would have taken up residence in Milwaukee, when
moving to the US; not the least because it feels most like being in
Munich. It was, at the time, socialist, clean, well-run and on a major
upswing in terms of population and prestige.

But anyway... in his new life, he>d take up violin in early childhood
[1], probably forego a drivers' license [2], visit southern Germany
and Hungary (where his former wife came from) [3], be conversant in
German, English, French and Hungarian [4], and be a strong advocate of
world federalism [5].

(And he>d have dark hair and a moustache [6], which is easily prone to
get bushy; and a somewhat dark complexion).

And he>d slowly and gradually get back into everything by critically
reviewing everything that>s out there [7]. All the literature from all
points of view, being nothing more than the analogue of the history of
Japanese automaking in the 1950>s -> 1990>s (Big 3 "copycats and
cloners" in the 1950>s, evolving into major market authorities by the
1980>s and on).

When it comes to the actual mathematical formalism: it was Einstein
who was the first or one of the first to use the van der Waerden 2-
component spinor notation to formulate the general wave equation. He
worked within the "new" geometry that proceeded from Cartan and others
that has, in the intervening years, led to a kind of Tower of Babel
split in the language between physicists and mathematicians.

He started dealing with the prospect of reformulating gravitational
theory as a purely algebraic theory at the end of his life. He was
familiar with the probabilistic interpretation of Quantum Theory
because he was, in fact, one of the first to raise the idea -- back
before 1910. The Dark Matter problem was essentially one of the topics
of the one of the appendix sections in the last edition of the Meaning
of Relativity.

I like to think that when he wrote the last appendix of the last
edition of the Meaning of Relativity, he keeled over and (dissatisfied
with the loose ends) ended up coming back. So, with that having been
said...

Notes (Halloween special: "The spooky parallels"):
[1] All the cool instruments were on Saturdays during grade school,
when my flag football league games at the YMCA were scheduled. All
that was available was violin lessons on Wednesday.
[2] Wisconsin didn>t allow people to get licenses who did not declare
their heritage or ancestry. I walk everywhere I go.
[3] Budapest in 1985. Munich last Spring.
[4] German immersion at 7. Formal study in Hungarian, French, German,
Portuguese (informal in Spanish and Russian)
[5] http://federation.g3z.com/FedSeries/index.htm#Progeny
[6] I shaved off my moustache and hair in the early 1990>s because it
was getting just a LITTLE BIT too close for comfort ... especially
when the moustache started greying.
[7] About 100 items under http://federation.g3z.com/Physics/index.htm

Guest

On Oct 28, 7:31 pm, Rock Brentwood <markw...@yahoo.com> wrote:
[quote]
You have to understand something that is almost completely unknown
about the history of Einstein -- something I, myself, didn>t learn up
until a month ago. 1905 didn>t just happen by itself. It was not
"silence, 1905, 5 landmark papers, boom." That>s all myth and
nonsense.
[/quote]
Thanks, both interesting answers. I wonder if we suppose that he does
not reveal himself as Einstein, he will no longer have the authority
to publish on GR independently. He has to take the academic route like
everybody else and get a degree. What you wrote it seems that the
authority has shifted to MTW and probably he will have to conform to
that. But what about something like PPN formalism? Would he have
approved of that? I was reading that his original derivation was no
longer used for Mercury and light bending tests, instead PPN
parameters are fit to data.

http://einstein.stanford.edu/SPACETIME/spacetime3.html

Rock Brentwood · Guest

On Oct 29, 1:22Â pm, azeyn...@gmail.com wrote:
[quote]Thanks, both interesting answers. I wonder if we suppose that he does
not reveal himself as Einstein, he will no longer have the authority
to publish on GR independently.
[/quote]
You can publish independently (that is: unaffiliated). I don>t think
even arXiv has restrictions on that, per se (other than that you have
a tie-in by someone else who>s in arXiv). You only need Word or TeX
and a place to upload ... and you need to be cogent. IOP charges
nothing for submissions (unless you want color in your journal
article), so you don>t even need money, per se. (Technically: you
don>t need money for an ISP either, since there>s still one free ISP
left).

[quote]But what about something like PPN formalism? Would he have approved of that?
[/quote]
Do you mean Penrose-Newman by PPN? Given his history with metric-
affine geometry and with the spinor 2-index notation, that would be
nothing less than vintage Einstein, if he were still around.

But the explanation and account of the notation would be markedly
different (and in many ways more classical and transparent). No sigma
matrix or indexing. Instead, a simple representation of orthonormal
bases by tensor products of left- and right- spin spaces,
schematically denoted: 4 = 2_R x 2_L = 2_L x 2_R.

Everything would be rendered in more algebraic language. (I strongly
suspect that Einstein got the algebra bug from von Neumann and
probably even conversed with him in Hungarian).

Instead of the well-known result equating anti-symmetric 2-tensors to
symmetric spin-1 spinors, you>d simply have the Clebsch-Gordon
decomposition,
4 x 4 = (2_R x 2_L) x (2_R x 2_L)
= (2_R x 2_R) x (2_L x 2_L)
= (3_R + 1_R) x (3_L + 1_L)
which distributes into the sum:
3_R x 3_L -- symmetric trace-less tensors
1_R x 1_L -- the "trace" part
3_R x 1_L + 1_R x 3_L -- the anti-symmetric part.

Seen in this light, it>s easy to understand how it generalizes to
decompositions for 3-forms, 4-forms, for symmetric products (2-form) x
(2-form) (important for decomposing the Weyl and Riemann tensors).

Second, instead of applying the spinor notation to Riemannian
geometry, it>d be applied to Riemann-Cartan geometry, given the prior
collaboration with Cartan. Then one actually has TWO sets of
coefficients in place of the spin coefficients:
the spin coefficients ... Gamma^c_{ab} = e^c . (Del_a e_b)
the structure coefficients ... f^c_{ab} = e^c . [e_a,e_b]
where ().() denotes contraction, (e_a) an orthonormal basis, and (e^a)
its dual.

The Penrose-Neuman equations are just an application of the Cartan
structure equations. So, it>s nothing more than an outgrowth of stuff
available by the 1920>s and heavily used by Einstein, himself (given
his history with the 2-component notation).

In fact, the Penrose coefficients are somewhat ad hoc and miss a lot
of regularities, and seem to come out of nowhere. The formalism is
seriously defective.

It can be cleaned up and made to work (a) to any fixed-metric basis
(not just a null basis), (b) to metric-affine geometry and (c) Newton-
Cartan geometry and Galilean physics. Carrying out the latter exercise
helps you to establish a better defined correspondence limit between
GR and Newton (among other things, allowing you to see that
"gravitomagnetism and frame-dragging are NOT exclusively relativistic
phenomena). This leads to a better formulation of the post-Newtonian
approximation (since there>s actually no expansion per se, but simply
a 1-parameter family of theories with exact equations). It generalizes
to Riemann-Cartan spacetimes ... which also helps you bring in
spinors.

So, there>s nothing really new in the "modern" formulations of GR that
would elude him, since nothing really new is present that wasn>t
already there in the 1920>s. On the contrary: the freshness of
perspective and of having skipped the 1950>s and 1960>s would lead to
a better formulation to replace Penrose-Newman.

Last, but not least, the summation convention itself would probably
have been generalized to a form to allow one to bridge the Tower
of l spit between the mathematician>s and physicist>s language.
Here>s how it would work.

ANY linear functional of tangent vectors and one forms would be
written in indexed notation. The indices would be nothing more than
the function arguments. Upper indices being 1-forms, lower indices
tangent vectors.

The summation convention would be used to denote contraction and would
be restricted to products. Specifically, one upper index in one factor
(or distributed among terms in one factor) would be contracted with a
matching lower index in the same or different factor (likewise
distributed).

"Tensoriality" would be an attribute applied on an index-by-index
basis. Hence, a quantity T^w_v is tensorial in the 1-form index w, if
T^{fw}_v = f T^w_v, and tensorial in tangent vector index v, if
T^w_{fv} = f T^w_v.

A tensor is then a linear functional tensorial in all arguments.

This simplifies everything considerably, conceptually. For one,
instead of a multiplicity of notations for the connection, you have
just one:
Gamma^w_{uv} = w . (Del_u v) = (Del_u v)^w = w_{Del_u v}.
The linear functional is tensorial in w and u, but not in v.

The structure coeffcient functional would just be
f^w_{uv} = w . [u,v] = [u,v]^w = w_{[u,v]}.

The Dirac delta functional would be the kernel of the contraction
operator,
delta^w_u = w.u = w_u = u^w.

The differential operator (using @ to denote the curly d in ASCII
notation) would be
@_u = u = u^{mu} @/@x^{mu}.
Mathematicians' convention is to just use the vector u, itself. But
for reasons of clarity (and backwards' compatibility) one may continue
to use @_u.

The transformation property of Gamma in the v index would be,
Gamma^w_{u (fv)} = f Gamma^w_{uv} + delta^w_u @_v f

The index notation could be generalized to operators -- hence leading
both to the concepts of operator-valued linear functionals and
operator-valued tensors.

Hence, @_u @_v is tensorial in u, but not in v, while
D_{uv} = @_u @_v - Del_u v
is tensorial in both u and v and is, thus, an operator-valued tensor.

The torsion is then just the anti-symmetric part of this,
T_{uv} = Del_u v - Del_v u - [u,v] = D_{vu} - D_{uv}.

And you can go a lot further with all this. It obsoletes the idea of
"abstract index" and yet grandfathers in the older indexing and
Einstein summation convention. And it>s a modernization that fits in
with the algebraization programme that originated with Cartan to
reformulate differential geometry in invariant form. So, you might
think of it as Einstein II.

So, with all that, you can begin to see -- if the same person came
back, with the same frame of mind and the same proclivity toward
reinventing everything in more transparent form, the operative
question would NOT be "would HE be able to understand and keep up with
the literature?", but rather, "would OTHERS be able to understand and
keep up with HIS literature?"

A person>s not made by the times given to them, but by what they do
with the time they are given. (Sounds like a familiar quote).

Guest

On Oct 31, 2:18 pm, Rock Brentwood <markw...@yahoo.com> wrote:
[quote]On Oct 29, 1:22 pm, azeyn...@gmail.com wrote:

if the same person came
back, with the same frame of mind and the same proclivity toward
reinventing everything in more transparent form, the operative
question would NOT be "would HE be able to understand and keep up with
the literature?", but rather, "would OTHERS be able to understand and
keep up with HIS literature?"
[/quote]
Thanks, this makes sense. One last point, I guess that, today, he
would be adding incrementally to the literature, instead of creating
the revolutionary framework. But we cannot be sure of that either.
Also, I meant, not Penrose-Newman but Parametrized Post-Newtonian
formalism.

Gerry Quinn · Guest

In article <ge17e7$l36$1@fb07-hees.theo.physik.uni-giessen.de>,
jthorn@astro.indiana-zebra.edu says...

[quote]The basic concepts of differential geometry & coordinate invariance,
special relativity, the equivalence principle, and the Einstein field
equations, are all essentially as Einstein described them. This
suggests that yes, the "reincarnated Einstein" would indeed recognize
GR today as the theory he published in 1915.

But there are of course many many many new developments which Einstein
didn>t know in 1915, or even in 1955 when he died. For example, the
concept of a black hole wasn>t properly understood until about 1970,
with the work of Kruskal & Szekeres. (Wheeler coined the phrase
"black hole" around 1969-70.) MTW (among many other texts) would be
a fine place for the "reincarnated Einstein" to start learning this
new-to-him material.
[/quote]
When we say "properly understood", shouldn>t we also ponder whether
Stephen Hawking>s current picture of a black hole is closer to the
"better understood" black hole with its non-trivial topology, or to the
earlier concept of a "frozen star"? It doesn>t seem obvious that these
advances in the general relativity theory of black holes were also
advances in physical understanding of the world as it is.

[quote]Another (related) notable example would be the realisation (due to
Penrose & Hawking in the late 1960s - early 1970s) of the ubiquitous
nature of singularities in gravitational collapse. MTW gives some
discussion of this, and I>m sure a theoretical physicist of Einstein>s
brilliance could follow the more mathematical treatments of Wald or
Hawking & Ellis without difficulty.
[/quote]
I don>t dispute the results about ubiquitous singularities. Again,
though, isn>t the obvious interpretation of a theory that sprouts
singularities "this theory is fundamentally wrong in some way"?

A singularity is a place where theory breaks down. A correct theory of
nature has no singularities.

- Gerry Quinn

Igor Khavkine · Guest

On Nov 18, 4:06 am, Gerry Quinn <ger...@indigo.ie> wrote:
[quote]In article <ge17e7$l3...@fb07-hees.theo.physik.uni-giessen.de>,
jth...@astro.indiana-zebra.edu says...

But there are of course many many many new developments which Einstein
didn>t know in 1915, or even in 1955 when he died. For example, the
concept of a black hole wasn>t properly understood until about 1970,
with the work of Kruskal & Szekeres. (Wheeler coined the phrase
"black hole" around 1969-70.) MTW (among many other texts) would be
a fine place for the "reincarnated Einstein" to start learning this
new-to-him material.

When we say "properly understood", shouldn>t we also ponder whether
Stephen Hawking>s current picture of a black hole is closer to the
"better understood" black hole with its non-trivial topology, or to the
earlier concept of a "frozen star"? It doesn>t seem obvious that these
advances in the general relativity theory of black holes were also
advances in physical understanding of the world as it is.
[/quote]
Hawking>s recent work on the resolution of the black hole information
paradox says nothing about black holes being like frozen stars. His
main claim is that an evaporating black hole is sufficiently described
by a Euclidean path integral over topologies that include
topologically trivial space-times as well as eternal black holes (non-
evaporating and already formed) only. His conclusion being that this
path integral remains unitary, thus preserving information. Roughly
speaking Hawking claims that an evaporating black hole is a quantum
superposition of space-times without a singularity or a horizon and of
space-times with eternal singularities and horizons.

Finally, while Hawking>s claims may hold in the Euclidean path
integral approach to quantum gravity, the final word on what the right
approach to quantum gravity is has not yet been said. Hence these
results are provisional only and not nearly as certain as most of the
classical developments described in MTW.

[quote]Another (related) notable example would be the realisation (due to
Penrose & Hawking in the late 1960s - early 1970s) of the ubiquitous
nature of singularities in gravitational collapse. MTW gives some
discussion of this, and I>m sure a theoretical physicist of Einstein>s
brilliance could follow the more mathematical treatments of Wald or
Hawking & Ellis without difficulty.

I don>t dispute the results about ubiquitous singularities. Again,
though, isn>t the obvious interpretation of a theory that sprouts
singularities "this theory is fundamentally wrong in some way"?

A singularity is a place where theory breaks down. A correct theory of
nature has no singularities.
[/quote]
Newtonian gravity of point particles predicts singularities as well.
Yes, this theory is ultimately flawed (the flaw being the point-
particle idealization). However, this flaw does not prevent a highly
successful description of the solar system. Just saying...

Igor


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