Nova documentary on Einstein
John Montgomery
watching.
It was intereesting that Einstein had difficulties with the mathematics
associated with the general theory of relativity. In comparison the
other giant Newton developed new branches of mathematics to develop his
ideas.
The only other person I can think of who fundamentally changed how we
view nature was Darwin. Quantum mechanics also changed how we view the
world and is essential part of the computer revolution but no single
person seems to have struct the publics attention.
Newton's laws are the foundation of much of the engineering done in the
modern era. Einsten in the most part is accepted as being correct but
impose needless complications. The only major exceptions I can think of
are nuclear industry and the global positioning system.
Lawrence Foard
Although Einsteins theories are included implicitly in other theories.
For example Maxwell's equations are far simpler in a relativistic definition.
In there conventional form they have to essentially include relativity as
parts of themselves.
--
Be a counter terrorist perpetrate random senseless acts of kindness
Rave: Immanentization of the Eschaton in a Temporary Autonomous Zone.
"Anyone who trades liberty for security deserves neither liberty nor security"
-Benjamin Franklin
Robert Kolker
John Montgomery wrote:
> Newton's laws are the foundation of much of the engineering done in the
> modern era.
Not electrical engineering.
> Einsten in the most part is accepted as being correct but
> impose needless complications. The only major exceptions I can think of
> are nuclear industry and the global positioning system.
Try lasers. A.E. did fundemental work on lasers. He did fundemental work
on thermodynamics and statistical mechanics too.
As too his "needless complications" he came up with a correct theory of
gravitation with these needless complications. Newton's theory of
gravitational force acting instantly at a distance is wrong. It leads to
conclusions disproved by experiment.
Bob Kolker
Hayek
Robert Kolker wrote:
You should read this.
http://metaresearch.org/cosmology/speed_of_gravity.asp
The Speed of Gravity - What the Experiments Say
Tom Van Flandern
It starts with :
"
The most amazing thing I was taught as a graduate
student of celestial mechanics at Yale in the 1960s was
that all gravitational interactions between bodies in
all dynamical systems had to be taken as instantaneous.
"
Hayek.
--
The small particles wave at
the big stars and get noticed.
:-)
Dirk Van de moortel
"Hayek" <hay...@nospam.xs4all.nl> wrote in message news:3EA19E94...@nospam.xs4all.nl...
Also on metaresearch by Tom Van Flandern:
"PROOF THAT THE CYDONIA FACE ON MARS IS ARTIFICIAL"
http://metaresearch.org/solar%20system/cydonia/proof_files/proof.asp
So much for metaresearch.
So much for Tom Van Flandern.
Dirk Vdm
Tom Roberts
> You should read this.
> http://metaresearch.org/cosmology/speed_of_gravity.asp
> The Speed of Gravity - What the Experiments Say
> Tom Van Flandern
>
> It starts with :
> "The most amazing thing I was taught as a graduate student of celestial
> mechanics at Yale in the 1960s was that all gravitational interactions
> between bodies in all dynamical systems had to be taken as instantaneous.
> "
Aparently you don't realize that the Newtonian APPROXIMATION to GR has
this property, but is not GR. Neither does Van Flandern.
This property applies to celestial mechanics, because the Newtonian
APPROXIMATION to GR is valid in the solar system (except for certain
high-precision measurements like the precession of various perihelia).
This property does not hold in general, in GR. <shrug>
In order for this property to apply, there must be a "background"
Minkowski coordinate system in the region of interest in which all
objects are confined to a compact spatial region (which essentially
requires that the sun be at rest in it); "instantaneous" must be
referenced to THAT SPECIFIC COORDINATE SYSTEM. This clearly violates the
underlying concepts of GR, and is DIRECTLY related to the APPROXIMATION
involved.
An approximation to a theory is not the theory itself.
Tom Roberts tjro...@lucent.com
Bill Hobba
Try Feynman. In my opinion the second best of the 20th century. He did
fundamental work while at Los Alamos on computing and his popular books had
a strong impact on scientifically minded people. His contributions to QFT
also, IMHO, changed fundamentally how we view nature. You may counter that
what he did was done in conjunction with others (eg Dyson) but that seems
the way of modern science, it is much more cooperative.
Still he never did (except a little bit in his later years) catch the
imagination of the public - such a pity because he was much more interesting
than old Einstein who came across as a bit conservative.
Thanks
Bill
Robert Kolker
Bill Hobba wrote:
> Still he never did (except a little bit in his later years) catch the
> imagination of the public - such a pity because he was much more interesting
> than old Einstein who came across as a bit conservative.
That is because the Einstein that Americans best know is the older
Einstein who came to Princeton to live. Avuncular, slightly eccentric, a
great hair do, but basically square Einstein. Somehow I don't think they
had wild lound parties at 112 Mercer St., Princeton NJ.
As a young man he was a fulminating rebel (intellectually speaking) and
a lady killer. Actually the young Einstein and the practical joking
Feynman were probably alike in many ways.
Bob Kolker
John Anderson
John Montgomery wrote:
Sir,
With all due respect, you are a semi-literate ignoramus.
John Anderson
Bill Hobba
> Bill Hobba wrote:
> > Still he never did (except a little bit in his later years) catch the
> > imagination of the public - such a pity because he was much more
interesting
> > than old Einstein who came across as a bit conservative.
>
Robert Kolker replied:
> That is because the Einstein that Americans best know is the older
> Einstein who came to Princeton to live. Avuncular, slightly eccentric, a
> great hair do, but basically square Einstein. Somehow I don't think they
> had wild lound parties at 112 Mercer St., Princeton NJ.
>
> As a young man he was a fulminating rebel (intellectually speaking) and
> a lady killer. Actually the young Einstein and the practical joking
> Feynman were probably alike in many ways.
>
True Bob, too true. Possibly the reason I like Feynman was he was an
absolute natural. Even in his later years he was nothing like Einstein.
By now everyone knows Einstein was a lady killer in his younger days, among
other things. But they had to wait for the biographies to reveal it, not so
with Feynman.
Not that I am trying to say he had the same kind of impact that Einstein did
scientifically. QFT, while being just as fundamental, IMHO never quite took
off with the public like GR. Really the original poster was correct, no one
really had the fundamental impact that Einstein did, not even my hero
Feynman.
Thanks
Bill
Bill Hobba
> > You should read this.
> > http://metaresearch.org/cosmology/speed_of_gravity.asp
> > The Speed of Gravity - What the Experiments Say
> > Tom Van Flandern
> >
> > It starts with :
> > "The most amazing thing I was taught as a graduate student of celestial
> > mechanics at Yale in the 1960s was that all gravitational interactions
> > between bodies in all dynamical systems had to be taken as
instantaneous.
> > "
>
Tom Roberts replied:
> Aparently you don't realize that the Newtonian APPROXIMATION to GR has
> this property, but is not GR. Neither does Van Flandern.
>
> This property applies to celestial mechanics, because the Newtonian
> APPROXIMATION to GR is valid in the solar system (except for certain
> high-precision measurements like the precession of various perihelia).
> This property does not hold in general, in GR. <shrug>
>
> In order for this property to apply, there must be a "background"
> Minkowski coordinate system in the region of interest in which all
> objects are confined to a compact spatial region (which essentially
> requires that the sun be at rest in it); "instantaneous" must be
> referenced to THAT SPECIFIC COORDINATE SYSTEM. This clearly violates the
> underlying concepts of GR, and is DIRECTLY related to the APPROXIMATION
> involved.
>
> An approximation to a theory is not the theory itself.
>
Even SR implies that interactions (at least information carrying ones - QM
type state collapses act instantaneously but can't be used to carry
information so they are ok) cant happen instantaneously. If you think about
it this is one reason we have fields.
Thanks
Bill
Lawrence Foard
Hayek <hay...@nospam.xs4all.nl> wrote:
>
>You should read this.
>http://metaresearch.org/cosmology/speed_of_gravity.asp
>The Speed of Gravity - What the Experiments Say
>Tom Van Flandern
>
>It starts with :
>"
>The most amazing thing I was taught as a graduate
>student of celestial mechanics at Yale in the 1960s was
>that all gravitational interactions between bodies in
>all dynamical systems had to be taken as instantaneous.
>"
This does seem to imply the ability to transmit information
back in time with a great deal of work. Something that would
cause lots of problems. But there is another more mundane answer:
First of all as they do finally admit, its obvious that linear
velocity of a source can be anticipated by its field. This is
an obvious consequence of SR.
However there is an important difference between gravity and E&M.
E&M only effects charges, gravity effects absolutely everything,
no exceptions allowed. If you have two pulsars #1 and #2. The field
of #1 will not only effect the motion of #2, but it will effect the
motion of the field of #2 as well, and vice versa. Therefore it seems
that gravity should anticipate gravitational accelerations. If anything
it should over anticipate them because the field of #1 will effect the
field of #2 more strongly (its closer) than it will effect #2 itself.
John Anderson
John Montgomery wrote:
Relativity does not introduce needless complications if you are trying
todescribe things moving close to the speed of light wrt yourself.
Engineering may deal with constructing apparati to observe such things
but not with constructing them.
John Anderson
Tom Van Flandern
"Tom Roberts" <tjro...@lucent.com> writes:
>> [tvf, quoted]: "The most amazing thing I was taught as a graduate
student of celestial mechanics at Yale in the 1960s was that all
gravitational interactions between bodies in all dynamical systems had
to be taken as instantaneous."
> [tr]: Apparently you don't realize that the Newtonian APPROXIMATION to
GR has
this property, but is not GR. Neither does Van Flandern. This property
applies to celestial mechanics, because the Newtonian APPROXIMATION to
GR is valid in the solar system (except for certain high-precision
measurements like the precession of various perihelia). This property
does not hold in general, in GR.
First, my quoted statement was about GR, not Newtonian
mechanics. Secondly, whether you are aware of it or not, GR equations of
motion (as on p. 1095 of MTW) use instantaneous interactions. Moreover,
if they did not, GR could not reduce to Newtonian gravity in the
weak-field, low-velocity limit (which covers to most of the solar
system) because the speed of gravity is infinite in Newtonian gravity
(of necessity, not by approximation). Moreover, the so-called
"approximations" introduced into the GR equations of motion introduce
errors roughly six orders of magnitude smaller than the effect of
letting gravitational forces propagate at lightspeed. Any computer
experiment immediately shows that the latter assumption, even in a full
GR context, is disastrous.
In GR, propagation delays are inserted only into the
behavior of the gravitational potential field. But when the gradient of
that field is taken to get a force or acceleration, an instantaneous
gradient is used in GR. Moreover, when two or more bodies have potential
fields, they are superimposed instantly in GR, not with delays.
Or do you think Einstein, Infeld, Hoffman, Robertson,
Noonan, Misner, Thorne, and Wheeler all got this wrong in their papers
on the GR equations of motion?
> [tr]: In order for this property to apply, there must be a
"background" Minkowski coordinate system in the region of interest in
which all objects are confined to a compact spatial region (which
essentially requires that the sun be at rest in it); "instantaneous"
must be referenced to THAT SPECIFIC COORDINATE SYSTEM. This clearly
violates the underlying concepts of GR, and is DIRECTLY related to the
APPROXIMATION involved. An approximation to a theory is not the theory
itself.
Equations of motion are developed in a Euclidean coordinate
system at rest with respect to the center of mass of the dynamical
system, using coordinate time (as would be shown on a non-moving clock
at infinity).
As for this "approximation" distraction, GR is validated by
observations and experiments only to the degree that the "approximation"
is correct. But even calling it an approximation is just a diversion
because it is a simple series expansion, retaining as many terms of the
infinite series as needed in any given application. So the fact that it
is technically an "approximation", as is any truncated series expansion,
is irrelevant to the matters under discussion.
and ent...@farviolet.com (Lawrence Foard) writes:
> [lf]: This does seem to imply the ability to transmit information back
in time with a great deal of work. Something that would cause lots of
problems.
It is now a published and unrefuted conclusion that
propagation speeds *in forward time* are not limited to the speed of
light. See, e.g., the discussion of Lorentzian relativity (LR) in
["Experimental Repeal of the Speed Limit for Gravitational,
Electrodynamic, and Quantum Field Interactions", T. Van Flandern and
J.P. Vigier, Found.Phys. 32(#7), 1031-1068 (2002)]. Yes, this means
gravity can be used for ftl signaling, and this causes no causality
violations because it takes place in forward time. LR allows this, even
if SR does not.
> [lf]: First of all as they do finally admit, its obvious that linear
velocity of a source can be anticipated by its field. This is an obvious
consequence of SR.
Of course. But such cases are trivial. A problem with the
interpretation first arises when target bodies have a motion relative to
the source mass and its field. Further problems of interpretation arise
when the source mass accelerates. The experimental results for these
cases are discussed in ["The speed of gravity - What the experiments
say", Phys.Lett.A 250, 1-11 (1998)], and both set lower limits to the
speed of gravitational force that is strongly ftl.
> [lf]: However there is an important difference between gravity and
E&M. E&M only effects charges, gravity effects absolutely everything, no
exceptions allowed. If you have two pulsars #1 and #2. The field of #1
will not only effect the motion of #2, but it will effect the motion of
the field of #2 as well, and vice versa.
You have a problem with causality there. If what you just
said were true, then the effect of field #1 on field #2 would be
different in different places depending on distance and direction of the
field point *relative to pulsar #1*, so the field of #2 would become
quite distorted. The distortion would be greatest near pulsar #1.
In reality, observations show what happens is that the field
of #1 acts on pulsar #2, and pulsar #2 then regenerates its own field to
be consistent with its new location and motion. The field remains
symmetric about pulsar #2.
> [lf]: Therefore it seems that gravity should anticipate gravitational
accelerations. If anything it should over anticipate them because the
field of #1 will effect the field of #2 more strongly (its closer) than
it will effect #2 itself.
The field of pulsar #2 always acts as if it arises from
pulsar #2's true, instantaneous location and direction, even when both
pulsars accelerate significantly during the light-time between them.
(See the reference I cited.) How can any change to the field by pulsar
#1, which knows only about its own location, possibly modify the field
of pulsar #2 toward #2's instantaneous location, a direction that
presumably won't be known at pulsar #1 until one light-time into the
future? -|Tom|-
Tom Van Flandern - Washington, DC - see our web site on replacement
astronomy research at http://metaresearch.org
Tom Roberts
> "Tom Roberts" <tjro...@lucent.com> writes:
>>>[tvf, quoted]: "The most amazing thing I was taught as a graduate
> student of celestial mechanics at Yale in the 1960s was that all
> gravitational interactions between bodies in all dynamical systems had
> to be taken as instantaneous."
>>[tr]: Apparently you don't realize that the Newtonian APPROXIMATION to
>> GR has this property, but is not GR. Neither does Van Flandern.
> mechanics.
But GR quite clearly does not have that property. This has been known
since a few years after its inception, and has been reitereated many
times. You fool yourself, and prove my point in your very next sentence:
> Secondly, whether you are aware of it or not, GR equations of
> motion (as on p. 1095 of MTW) use instantaneous interactions.
You just proved my point that you do not distinguish between GR and an
APPROXIMATION to GR. Please note the title of that exercise is
"Many-Body system in Post-Newtonian Limit of General Relativity" [MTW
p1091]. Their usage of the word "limit" is synonomous to my usage of
"approximation".
> Moreover,
> if they did not, GR could not reduce to Newtonian gravity in the
> weak-field, low-velocity limit (which covers to most of the solar
> system) because the speed of gravity is infinite in Newtonian gravity
> (of necessity, not by approximation).
This is nonsense. GR does indeed reduce to Newtonian gravitation in the
appropriate limit, and yet in GR gravitational interactions propagate at
c, not with "infinite speed" as in Newtonian gravitation.
In Newtonian coordinates the equations of GR can be interpreted as a
converging sequence in which the gravitational interaction here and now
due to an object a distance L away depends upon its position, its
velocity, its acceleration, ... all measured L/c ago. The first three
terms essentially provide a second-order extrapolation to its position
now, and the approximation involved includes ignoring higher terms in
the series.
Note this applies ONLY in those specific coordinates. And
ONLY in cases where all the requirements of the approximation
hold. As I keep saying, this is NOT GR, it is an approximation
to GR.
Note Van Flandern could make the same claims about E&M.
He seems unable to grasp that the retarded Lienard-Wichert
potentials yield Coulomb's law in lowest order. This occurs
essentially via the same mechanism, but one less order.
> Moreover, the so-called
> "approximations" introduced into the GR equations of motion introduce
> errors roughly six orders of magnitude smaller than the effect of
> letting gravitational forces propagate at lightspeed.
Only if one does that last incorrectly.
> Any computer
> experiment immediately shows that the latter assumption, even in a full
> GR context, is disastrous.
I agree that simply evaluating the position of a distant object L/c ago
will be disasterous. But you are supposed to be applying an
approximation to GENERAL RELATIVITY, and not merely something you made up.
> Or do you think Einstein, Infeld, Hoffman, Robertson,
> Noonan, Misner, Thorne, and Wheeler all got this wrong in their papers
> on the GR equations of motion?
I think they got it right. And unlike you, I think they also realized
they were working with an APPROXIMATION to the actual equations of GR.
> As for this "approximation" distraction, GR is validated by
> observations and experiments only to the degree that the "approximation"
> is correct.
All experiments are approximations to some degree or other. So what?
An approximation to a theory is not the theory itself. This is so basic
it boggles the mind that you make such long-winded arguments to avoid
such a basic fact.
> But even calling it an approximation is just a diversion
Not a "diversion", but rather an important distinction.
> [... more of the same...]
Tom Roberts tjro...@lucent.com
lukas
wrote:
> Note Van Flandern could make the same claims about E&M.
> He seems unable to grasp that the retarded Lienard-Wichert
> potentials yield Coulomb's law in lowest order. This occurs
> essentially via the same mechanism, but one less order.
>
Thanks for your post. I'm trying to understand these subtleties.
Clarification: is this lowest order in v/c?
Some other posts have suggested that ignoring magnetic field,
Lienard-Wichert electric potential is EXACTLY Coulomb's law for
instantaneous position of source. Is this true?
Tom Van Flandern
>>>> [tvf, quoted]: "The most amazing thing I was taught as a graduate
student of celestial mechanics at Yale in the 1960s was that all
gravitational interactions between bodies in all dynamical systems had
to be taken as instantaneous."
> [tr]: But GR quite clearly does not have that property. This has been
known since a few years after its inception, and has been reiterated
many times.
I am sorry you are unfamiliar with equations of motion and
celestial mechanics, because without both of these sub-fields, GR could
not be tested against astrophysical observations. You have no hope of
achieving a better understanding of the physics behind the math of GR
without gaining a familiarity with these equations.
>> [tvf]: Secondly, whether you are aware of it or not, GR equations of
motion (as on p. 1095 of MTW) use instantaneous interactions.
> [tr]: You just proved my point that you do not distinguish between GR
and an APPROXIMATION to GR. Please note the title of that exercise is
"Many-Body system in Post-Newtonian Limit of General Relativity" [MTW
p1091]. Their usage of the word "limit" is synonymous to my usage of
"approximation".
All expansions of functions into infinite series technically
are "approximations". But because one is free to use as many terms in
the series as desired, the approximation may be made as exact as one
pleases. So the fact that equations of motion are an "approximation" is
irrelevant because the error has been made negligible.
A similar thing is true in many applications of math to
physics. The GR equations of motion make no approximation that is
significant here. What were you thinking?
>> [tvf]: Moreover, if they did not, GR could not reduce to Newtonian
gravity in the weak-field, low-velocity limit (which covers to most of
the solar system) because the speed of gravity is infinite in Newtonian
gravity (of necessity, not by approximation).
> [tr]: This is nonsense. GR does indeed reduce to Newtonian gravitation
in the appropriate limit, and yet in GR gravitational interactions
propagate at c, not with "infinite speed" as in Newtonian gravitation.
Where have you been for the last nine months of discussion
of this point? Gravitational interactions propagate at speed c only for
changes in the gravitational potential field. When the equations of
motion are formed from the potential (as described by solutions to the
GR field equations) by forming a Lagrangian, a Hamiltonian, or simply by
taking a gradient, the spatial partial derivatives used are
instantaneous derivatives, not retarded derivatives. This makes the
force or acceleration an instantaneous quantity, not a retarded one.
See the detailed discussion and demonstration of this in
["Experimental Repeal of the Speed Limit for Gravitational,
Electrodynamic, and Quantum Field Interactions", T. Van Flandern and
J.P. Vigier, Found.Phys. 32(#7), 1031-1068 (2002)].
Speaking of "nonsense", how can two theories reduce to
equivalency under certain conditions while one of them has propagation
of gravity at speed c and the other has infinite speed? Anyone who
thinks that is physically possible does not understand aberration.
Assuming a common source mass and linear propagation at different
speeds, the spatial directions of approach to a moving target body would
necessarily be different.
[tr]: In Newtonian coordinates the equations of GR can be interpreted as
a converging sequence in which the gravitational interaction here and
now due to an object a distance L away depends upon its position, its
velocity, its acceleration, ... all measured L/c ago. The first three
terms essentially provide a second-order extrapolation to its position
now, and the approximation involved includes ignoring higher terms in
the series.
I have three comments on this: (1) What are "Newtonian
coordinates"? Perhaps you mean "Euclidean"?
(2) Assuming so, there is a not-so-subtle point that you
overlooked. This "second-order extrapolation" is an approximation to the
*true, instantaneous* positions of the source masses, not an
approximation to their retarded positions. The position of an orbiting
body today can be expanded in terms of its position, velocity,
acceleration, and many higher-order terms at one million B.C., but that
doesn't change the fact that the relevant physical quantity is the
instantaneous position today, not the retarded one at one million B.C.
or any other epoch.
(3) More to the point, no such approximation is used in
deriving the equations of motion, which simply use truly instantaneous
spatial derivatives, not expansions in terms of quantities one
light-time ago. See, for example, [Einstein, Infeld, and Hoffmann, "The
gravitational equations and the problem of motion", Ann.Math., v. 39,
pp. 65-100 (1938)], where the equations of motion are derived.
> [tr]: Note Van Flandern could make the same claims about E&M. He seems
unable to grasp that the retarded Lienard-Wiechert potentials yield
Coulomb's law in lowest order. This occurs essentially via the same
mechanism, but one less order.
I addressed Lienard-Wiechert retarded potentials in ["Reply
to comments on 'The speed of gravity'", Phys.Lett.A, v. 262, pp. 261-263
(1999/11/01)]. And the "Foundations" reference above describes the
similarity between gravitation and electrodynamics, and shows how the
same properties apply there. In short, potential field changes (e.g.,
gravitational waves or light waves) propagate at speed c. Forces
propagate at near-instantaneous speeds.
>> [tvf]: Moreover, the so-called "approximations" introduced into the
GR equations of motion introduce errors roughly six orders of magnitude
smaller than the effect of letting gravitational forces propagate at
lightspeed.
> [tr]: Only if one does that last incorrectly.
This appears flatly wrong on its face. Would you care to
provide some justification for this claim?
>> [tvf]: Any computer experiment immediately shows that the latter
assumption, even in a full GR context, is disastrous.
> [tr]: I agree that simply evaluating the position of a distant object
L/c ago will be disastrous. But you are supposed to be applying an
approximation to GENERAL RELATIVITY, and not merely something you made
up.
My statement referred to a numerical integration of the GR
equations of motion at any desired level of completeness. If you use
retarded positions, then elliptical orbits change into spirals. Use
instantaneous positions and they become ellipses again.
That is what my statement meant. What did yours mean?
>> [tvf]: Or do you think Einstein, Infeld, Hoffman, Robertson, Noonan,
Misner, Thorne, and Wheeler all got this wrong in their papers on the GR
equations of motion?
> [tr]: I think they got it right. And unlike you, I think they also
realized they were working with an APPROXIMATION to the actual equations
of GR.
This "approximation" would have to be good enough to show
all post-Newtonian effects, such as perihelion advance. But in reality,
there is no such approximation as you described, using extrapolated,
retarded positions. Instead, the superposition principle is invoked, by
virtue of which any two potential fields may be added with their
instantaneous values everywhere, ignoring retardation. Look it up in the
references. Here's another one you can check: [Robertson and Noonan,
"Relativity and Cosmology", W.B. Saunders Co., Philadelphia, p. 45
(1938)].
My statement quoted above was made in support of the
following statement from my previous message: "In GR, propagation delays
are inserted only into the behavior of the gravitational potential
field. But when the gradient of that field is taken to get a force or
acceleration, an instantaneous gradient is used in GR. Moreover, when
two or more bodies have potential fields, they are superimposed
instantly in GR, not with delays." What exactly are you claiming is
wrong with any of these statements?
>> [tvf]: As for this "approximation" distraction, GR is validated by
observations and experiments only to the degree that the "approximation"
is correct.
> [tr]: All experiments are approximations to some degree or other. So
what?
My point exactly. Why did you make an issue of
"approximation" when both theory and observations are easily good enough
to distinguish GR from Newton and instantaneous propagation of forces
from light-speed propagation?
> [tr]: An approximation to a theory is not the theory itself. This is
so basic it boggles the mind that you make such long-winded arguments to
avoid such a basic fact.
You invoke this truism as if it had some relevance to this
discussion. Please show where the "approximation" has *any* relevance to
this discussion. Show where it fails to be exact to the accuracy needed
to draw conclusions about propagation speed of forces.
>> [tvf]: But even calling it an approximation is just a diversion
> [tr]: Not a "diversion", but rather an important distinction.
Please explain its importance, especially
quantitatively. -|Tom|-
Jan
> "Tom Roberts" <tjro...@lucent.com> writes:
> >> [tvf]: Secondly, whether you are aware of it or not, GR equations of
> motion (as on p. 1095 of MTW) use instantaneous interactions.
>
> > [tr]: You just proved my point that you do not distinguish between GR
> and an APPROXIMATION to GR. Please note the title of that exercise is
> "Many-Body system in Post-Newtonian Limit of General Relativity" [MTW
> p1091]. Their usage of the word "limit" is synonymous to my usage of
> "approximation".
>
> All expansions of functions into infinite series technically
> are "approximations". But because one is free to use as many terms in
> the series as desired, the approximation may be made as exact as one
> pleases. So the fact that equations of motion are an "approximation" is
> irrelevant because the error has been made negligible.
Hahahahaha! This has got to be the stupidest thing I've read in a while.
Jan Bielawski
Dirk Van de moortel
"Jan" <dev_n...@yahoo.com> wrote in message news:5a3651e8.03042...@posting.google.com...
Quite indeed :-)
Title: "Infinite series are approximations"
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/TVFSeries.html
Dirk Vdm
Stephen Speicher
You should have kept reading. :)
--
Stephen
s...@speicher.com
Ignorance is just a placeholder for knowledge.
Printed using 100% recycled electrons.
-----------------------------------------------------------