Phil wrote:
One of the problems I have never resolved is the difference between
curvature and accelerations in flat space-time.

They are completely different concepts, and their physical affects are
quite different as well.

Note, please, that "acceleration" when used by itself is ambiguous in
GR. There are 3 commonly used meanings:
a) proper acceleration. This is the acceleration of an object in
its instantaneously comoving inertial frame
b) 4-acceleration. This is a 4-vector defined by dV/d\tau, where
V is the object's 4-velocity and \tau is its proper time
c) coordinate acceleration. This is just dv/dt, where v is the object's
coordinate velocity in some system of cooridnates, and is the time
coordinate.

It is quite common for newbies to use (c) -- in GR that is essentially
useless, because any system of coordinates can be used. (a) and (b) are
intimately related, because when projected onto the object's
instantaneously comoving inertial frame the 4-acceleration of (b) is the
proper acceleration of (a).

Note that the lowest-order effect of curvature in GR is "tidal forces".
Except in unusual circumstances these are much smaller than the usual
"gravitational forces". [I used quotation marks, because those are their
names in Newtonian gravitation; in GR these are not forces at all, but
rather are manifestations of the geometry of spacetime.]


Given a lab frame resting on a non-rotating earth. Is this frame
equivalent, (equally relevent to make predictions and conduct experiments),
as a frame accelerating at 9.80 m/s^2 located in space far from any gravity
source. The answer I keep getting is _no_.

And that's correct. They are not "equivalent" in the sense of conducting
ANY experiment or making ANY measurement.

But if the regions used are small enough, and the measurement accuracy
is poor enough, then it can be impossible to distinguish the two
situations, and the frames are "equivalent" in the sense of the
equivalence principle (EP).

In general, for the EP to apply one must restrict interest to a local
region of spacetime, and the size of this region depends on the details
of the manifold in that region and on one's measurement accuracy (better
accuracy means only a smaller region can be used).


Let both frames have identical systems of inertially moving objects. In the
frame located on the non-rotating earth, the objects all accelerate by
varying quantity wrt to the lab and all accelerate with respect to each
other.

Only if your region is large enough for the differences to be greater
than your measurement accuracy.

For instance, in a typical elevator at rest on earth with size ~2
meters, and measuring apparatus with resolutions of mm and milliseconds,
you cannot measure the difference in acceleration between the top and
bottom, or the angular convergence from the different sides. With
nanometer and nanosecond resolutions you could.


But then, I have the sense
that "locality" isn't meaningful anyway. By this I mean that I don't think
the difference between the two accelerated frames disappear in an interval
of infinitesimal domain. Here is why. The geodesics are the integrations
of the contributions of each infinitesmal interval. If the geodesics
differ, there must be some difference in the infinitesimal contributions.

The question is not really whether or not the geodesics are different,
but rather whether or not they are OBSERVABLY different. In the above
elevator, with the ordinary equipment they are not, but with the
high-precision equipment they are.

BTW this is the major difference between physics and math: in physics we
must account for finite measurement resolutions; in math one assumes
prefect knowledge. That's why I mention errorbars so often around here,
because they are a quantitative way of expression measurement resolution.


Pete wrote:
Try reading this. http://xxx.lanl.gov/abs/physics/0204044
It is a paper I wrote a few years back. The intent of the paper is to
directly answer your question.

A very quick perusal indicates it is trying to determine what "gravity"
and/or "gravitational field" mean. That is merely a linguistic issue.
Worrying about whether or not Einstein associated the word "curvature"
with "gravity" or "gravitational field" is irrelevant except to
historians and linguists.

Einstein essentially stopped working on GR in the 1920s, as did most
physicists. There were occasional papers on GR, but no major effort
until the 1960s (after Einstein's death), when the field experienced a
renaissance. "Modern" GR is no different at base from Einstein's
original papers, but there has been A LOT of understanding and
application to new and different situations.


Taking just this quotation of Einstein from that paper:
"It will be seen from these reflections that in pursuing the general
theory of relativity we shall be led to a theory of gravitation,
since we are able to “produce” a gravitational field merely by
changing the system of coordinates."

This clearly indicates that Einstein identified "gravitational field"
with the connection. That is the geometric object that is the closest
analogy in GR of Newtonian gravitational force. But one must be careful,
because the connection can have all sorts of different interpretations,
precisely because it is not a tensor and is manifestly coordinate
dependent. For instance, polar and spherical coordinates on Euclidean
space have nonzero connections, but bear no resemblance at all to
"gravitational force".


Koobee Wublee wrote:
[...]

You have as little understanding of the actual history as you have of
the physics or the mathematics. shrug


Tom Roberts

Tom Roberts wrote:
Phil wrote:

One of the problems I have never resolved is the difference between
curvature and accelerations in flat space-time.

They are completely different concepts, and their physical affects are
quite different as well.

So much for the Equivalence Principle or equating acceleration with
gravitation locally, of.course. shrug

Note, please, that "acceleration" when used by itself is ambiguous in
GR. There are 3 commonly used meanings:
a) proper acceleration. This is the acceleration of an object in
its instantaneously comoving inertial frame

In GR, the only proper "something" is the proper time which is
nothing more than the absolute value of the spacetime divided the speed
of light in vacuum. A good hypothesis is to allow the acceleration to
be observed the same using one's coordinate system and with proper
unit translation, of course. The reason for this is not to manufacture
BS like (b) and (c) below.

b) 4-acceleration. This is a 4-vector defined by dV/d\tau, where
V is the object's 4-velocity and \tau is its proper time

c) coordinate acceleration. This is just dv/dt, where v is the object's
coordinate velocity in some system of cooridnates, and is the time
coordinate.

I smell BS here.

It is quite common for newbies to use (c) -- in GR that is essentially
useless, because any system of coordinates can be used. (a) and (b) are
intimately related, because when projected onto the object's
instantaneously comoving inertial frame the 4-acceleration of (b) is the
proper acceleration of (a).

Note that the lowest-order effect of curvature in GR is "tidal forces".
Except in unusual circumstances these are much smaller than the usual
"gravitational forces". [I used quotation marks, because those are their
names in Newtonian gravitation; in GR these are not forces at all, but
rather are manifestations of the geometry of spacetime.]

Typical of Dr. Robert's explanation, word salad without any
mathematics to back it up.

Given a lab frame resting on a non-rotating earth. Is this frame
equivalent, (equally relevent to make predictions and conduct experiments),
as a frame accelerating at 9.80 m/s^2 located in space far from any gravity
source. The answer I keep getting is _no_.

And that's correct. They are not "equivalent" in the sense of conducting
ANY experiment or making ANY measurement.

Thus, Einstein's Equivalence Principle is wrong. This is no big deal
because it serves no useful purpose in the development of GR. Only
dead ends.

But if the regions used are small enough, and the measurement accuracy
is poor enough, then it can be impossible to distinguish the two
situations, and the frames are "equivalent" in the sense of the
equivalence principle (EP).

Only in fairy tale. shrug

In general, for the EP to apply one must restrict interest to a local
region of spacetime, and the size of this region depends on the details
of the manifold in that region and on one's measurement accuracy (better
accuracy means only a smaller region can be used).

In another word for EEP to apply, one must go to the Never Never land
to witness such things, and I don't mean Michael Jackson's home.

Let both frames have identical systems of inertially moving objects. In the
frame located on the non-rotating earth, the objects all accelerate by
varying quantity wrt to the lab and all accelerate with respect to each
other.

Only if your region is large enough for the differences to be greater
than your measurement accuracy.

For instance, in a typical elevator at rest on earth with size ~2
meters, and measuring apparatus with resolutions of mm and milliseconds,
you cannot measure the difference in acceleration between the top and
bottom, or the angular convergence from the different sides. With
nanometer and nanosecond resolutions you could.

Or the possibility of faulty EEP.

But then, I have the sense
that "locality" isn't meaningful anyway. By this I mean that I don't think
the difference between the two accelerated frames disappear in an interval
of infinitesimal domain. Here is why. The geodesics are the integrations
of the contributions of each infinitesmal interval. If the geodesics
differ, there must be some difference in the infinitesimal contributions.

The question is not really whether or not the geodesics are different,
but rather whether or not they are OBSERVABLY different. In the above
elevator, with the ordinary equipment they are not, but with the
high-precision equipment they are.

BTW this is the major difference between physics and math: in physics we
must account for finite measurement resolutions; in math one assumes
prefect knowledge. That's why I mention errorbars so often around here,
because they are a quantitative way of expression measurement resolution.

But we are talking about physics which is ruled by certain laws.
Statistics is another matter. I don't care how good of experimental
physicist you are, but you don't compare with the statistical data of
any actuary and their error bars.

Pete wrote:
Try reading this. http://xxx.lanl.gov/abs/physics/0204044
It is a paper I wrote a few years back. The intent of the paper is to
directly answer your question.

A very quick perusal indicates it is trying to determine what "gravity"
and/or "gravitational field" mean. That is merely a linguistic issue.
Worrying about whether or not Einstein associated the word "curvature"
with "gravity" or "gravitational field" is irrelevant except to
historians and linguists.

You can also extend your analogy to "Aether" versus "spacetime"
and "absolute time" versus "proper time". You should not hold
double standards

Einstein essentially stopped working on GR in the 1920s, as did most
physicists. There were occasional papers on GR, but no major effort
until the 1960s (after Einstein's death), when the field experienced a
renaissance. "Modern" GR is no different at base from Einstein's
original papers, but there has been A LOT of understanding and
application to new and different situations.

This is because the problems associated with GR were abundant. Folks
tried very hard to find anther solution still under the concept of
spacetime but got nowhere. Only the newer generations who have
forgotten exactly how silly the postulates that built up GR were began
in earnest to expand its ludicrous nature. Oh, and its Voodoo
mathematics. shrug

Taking just this quotation of Einstein from that paper:
"It will be seen from these reflections that in pursuing the general
theory of relativity we shall be led to a theory of gravitation,
since we are able to "produce" a gravitational field merely by
changing the system of coordinates."

This clearly indicates that Einstein identified "gravitational field"
with the connection. That is the geometric object that is the closest
analogy in GR of Newtonian gravitational force. But one must be careful,
because the connection can have all sorts of different interpretations,
precisely because it is not a tensor and is manifestly coordinate
dependent. For instance, polar and spherical coordinates on Euclidean
space have nonzero connections, but bear no resemblance at all to
"gravitational force".

All that BS is exactly designed to confuse the younger generations of
students. With peer pressure which works wonders as conceived and
proven by Tavistock for Human Relations, just tell everyone the emperor
has clothes on. shrug

Koobee Wublee wrote:
[...]

You have as little understanding of the actual history as you have of
the physics or the mathematics. shrug

For something who has claimed history is best left for historians to
sort out, his criticism on my actual historic account is questionable.
Also for someone who has tried to avoid mathematics with a ten-foot
pole, his criticism of my mathematical implications is very
questionable as well. shrug

Please go back to indulge yourself in your error-bars.

"Koobee Wublee" wrote in message ups.com...
Tom Roberts wrote:
Phil wrote:

One of the problems I have never resolved is the difference between
curvature and accelerations in flat space-time.

They are completely different concepts, and their physical affects are
quite different as well.

So much for the Equivalence Principle or equating acceleration with
gravitation locally, of.course. shrug

Note, please, that "acceleration" when used by itself is ambiguous in
GR. There are 3 commonly used meanings:
a) proper acceleration. This is the acceleration of an object in
its instantaneously comoving inertial frame

In GR, the only proper "something" is the proper time which is
nothing more than the absolute value of the spacetime divided the speed
of light in vacuum. A good hypothesis is to allow the acceleration to
be observed the same using one's coordinate system and with proper
unit translation, of course. The reason for this is not to manufacture
BS like (b) and (c) below.

b) 4-acceleration. This is a 4-vector defined by dV/d\tau, where
V is the object's 4-velocity and \tau is its proper time

c) coordinate acceleration. This is just dv/dt, where v is the object's
coordinate velocity in some system of cooridnates, and is the time
coordinate.

I smell BS here.

"I smell the absolute value of the spacetime here":
http://users.telenet.be/vdmoortel/di...SmellHere.html
Retired Aerospace Engineered Spacetime at its best.

Dirk Vdm

"Koobee Wublee" wrote in message ups.com...

Pete wrote:

Try reading this. http://xxx.lanl.gov/abs/physics/0204044
It is a paper I wrote a few years back. The intent of the paper is to
directly answer your question.

Your historical account on the development of GR is very incomplete and
misleading.

For historical accounts by Koobee Wublee (aka Australopithecus
Afarensis aka Scholarly Fungi aka ...), you need stuff like this:

http://groups.google.co.uk/groups?&threadm=V1r09.661180$352.138570@sccrnsc02
| "Scholarly Fungi" wrote in message
| ...
| It is also unfortunate that most of the folks blindly embracing this
| holohaux come from the white supremacists. I don't see what this would gain
| for them other than trying to antagonize the Jews. However, this is
| history. When I was in my early high school years, I independently came up
| with what Butz was saying without knowing his existence. Hey, I am very
| proud of my humble analytical skills.

http://groups.google.co.uk/groups?&t... g.google.com
| "Scholarly Fungi" wrote in message
| . ..
| All history is written upon congruency among the historians but except one.
| The Holocaust was born in the court rooms of Nueremberg. It is a complete
| hoax.
|
| I did not know of Arthur Butz, but I independently came up with that
| hypothesis noticing the tremendous amount of inconsistencies while studying
| holohoax in high school.

http://groups.google.co.uk/groups?&threadm=XvKJa.100908$hd6.25327@fed1read05
| "Australopithecus Afarensis" wrote in message
| news:fytJa.78487$%42.6441@fed1read06...
| Thanks for posting all that and your own comments at the end. There are so
| many lies after lies conjured up against the Nazis. I guess I'd better read
| "Mein Kampf" to get it from the horse's mouth. It will be on my
| things-to-do list for the near future.

http://groups.google.co.uk/groups?&t...07ev @4ax.com
| On Tue, 3 Jun 2003 21:42:04 -0700, "Australopithecus Afarensis"
| wrote:
|
| Thanks for answering these questions fair and square.
|
| Although I don't speak for all other Australopithecine, I certainly want to
| be as less nationalistic as possible. I am an individual just trying to
| learn as much as I can before my short life expires on this earth.
|
| OK, now the media and "media"-controlled educational history have painted
| the Nazis as the most fiendish group of people ever lived through out the
| entire history of mankind. When I was growing up, I was constantly reminded
| that the Nazis were so genocidal, they will kill any non-Germans in a heart
| beat. After getting constantly bombarded with Nazi atrocities, I was very
| much like the rest. Well, until one clip of film showing mountains of hair
| inside a giant oven, the purpose was to show how many people murdered and
| cremated. As a young scientist-to-be, it just hit me that the whole sh*t
| was a lie. As far as I knew, the human hair would burn first. After
| meticulous research and reasoning, I have concluded the WWII Nazis were no
| more atrocious than any other governments in the 20th century or beyond.
| Many of these information mostly came out after the explosion of the
| internet where all skeletons in the closets finally have a chance to tell
| their side of the story. Now, what is your plan to the public to shed these
| negative sentiments accused against your political group?
|

Koobee Wublee at his best.

Dirk Vdm

Koobee Wublee wrote:
Pete wrote:

Try reading this. http://xxx.lanl.gov/abs/physics/0204044
It is a paper I wrote a few years back. The intent of the paper is to
directly answer your question.

Your historical account on the development of GR is very incomplete and
misleading.

We all know how Newton devised the law of gravity by watching a falling
apple under gravitational influence. Einstein's breakthrough tried
to outdo Newton by fantasizing himself as that apple falling under the
influence of gravity. Hey, as doctor Roberts ingeniously pointed out.
The outcome of that would eventually intercept the ground in a tragic
end. So, Einstein co-operated with Grossmann trying to devise a theory
of gravity based on his version of Equivalence Principle. It turned
out to be a failure. Disgusted with Grossmann, he started looking for
help in Goettingen.

At Goettingen, Klein, Hilbert, and Schwarzschild were very good friends
with Minkowski who had since passed away but not before suggesting the
postulate on the existence of spacetime after abandoning the Aether by
the scientific communities. Thus, Hilbert was interested in
Einstein's work. However, instead of co-operation, Einstein and
Hilbert became rivals with each one trying to beat the other one in
coming up with the field equations.

A spark came to Hilbert after Einstein bragged about derivation of
Mercury's orbital anomaly. This derivation without using GR and thus
without the necessary Schwarzschild metric was an entire plagiarism of
Gerber's work. Of course, Hilbert did not know Einstein's work was
total BS. Thinking he had lost the race, he basically pulled out a
Hail-Mary throw. He pulled out this Hilbert Langrangian out of his
*ss, and the field equations were born. Thus, GR was actually
Hilbert's work.

Somehow, you have just blacked out this part of the history, is it
because you don't understand the field equations?

In case some innocent soul has read it: all of the above is baloney.

--
Jan Bielawski

JanPB wrote:
Koobee Wublee wrote:

We all know how Newton devised the law of gravity by watching a falling
apple under gravitational influence. Einstein's breakthrough tried
to outdo Newton by fantasizing himself as that apple falling under the
influence of gravity. Hey, as doctor Roberts ingeniously pointed out.
The outcome of that would eventually intercept the ground in a tragic
end. So, Einstein co-operated with Grossmann trying to devise a theory
of gravity based on his version of Equivalence Principle. It turned
out to be a failure. Disgusted with Grossmann, he started looking for
help in Goettingen.

At Goettingen, Klein, Hilbert, and Schwarzschild were very good friends
with Minkowski who had since passed away but not before suggesting the
postulate on the existence of spacetime after abandoning the Aether by
the scientific communities. Thus, Hilbert was interested in
Einstein's work. However, instead of co-operation, Einstein and
Hilbert became rivals with each one trying to beat the other one in
coming up with the field equations.

A spark came to Hilbert after Einstein bragged about derivation of
Mercury's orbital anomaly. This derivation without using GR and thus
without the necessary Schwarzschild metric was an entire plagiarism of
Gerber's work. Of course, Hilbert did not know Einstein's work was
total BS. Thinking he had lost the race, he basically pulled out a
Hail-Mary throw. He pulled out this Hilbert Langrangian out of his
*ss, and the field equations were born. Thus, GR was actually
Hilbert's work.

Somehow, you have just blacked out this part of the history, is it
because you don't understand the field equations?

In case some innocent soul has read it: all of the above is baloney.

To someone who lives in that fat castle in the air such as yourself,
Mr. Bielawski, it appears to be baloney because you don't know any
better and refuse to check out historic facts for yourself. You live
in the fantasy land where everything should turn out to be as perfect
as these second rated films you endorse. shrug

Koobee Wublee wrote:
Tom Roberts wrote:

Einstein essentially stopped working on GR in the 1920s, as did most
physicists. There were occasional papers on GR, but no major effort
until the 1960s (after Einstein's death), when the field experienced a
renaissance. "Modern" GR is no different at base from Einstein's
original papers, but there has been A LOT of understanding and
application to new and different situations.

This is because the problems associated with GR were abundant. Folks
tried very hard to find anther solution still under the concept of
spacetime but got nowhere. Only the newer generations who have
forgotten exactly how silly the postulates that built up GR were began
in earnest to expand its ludicrous nature. Oh, and its Voodoo
mathematics. shrug

How dare you question a theory that E-N-T-I-R-E-L-Y rests on such a
solid and established pillar as Mach's principle???

Chris

"Mach was wrong. Albert was naive, and drank too much German beer."
-- Chris

"JanPB" wrote in message
oups.com...
Koobee Wublee wrote:
Pete wrote:

Try reading this. http://xxx.lanl.gov/abs/physics/0204044
It is a paper I wrote a few years back. The intent of the paper is to
directly answer your question.

Your historical account on the development of GR is very incomplete and
misleading.

We all know how Newton devised the law of gravity by watching a falling
apple under gravitational influence. Einstein's breakthrough tried
to outdo Newton by fantasizing himself as that apple falling under the
influence of gravity. Hey, as doctor Roberts ingeniously pointed out.
The outcome of that would eventually intercept the ground in a tragic
end. So, Einstein co-operated with Grossmann trying to devise a theory
of gravity based on his version of Equivalence Principle. It turned
out to be a failure. Disgusted with Grossmann, he started looking for
help in Goettingen.

At Goettingen, Klein, Hilbert, and Schwarzschild were very good friends
with Minkowski who had since passed away but not before suggesting the
postulate on the existence of spacetime after abandoning the Aether by
the scientific communities. Thus, Hilbert was interested in
Einstein's work. However, instead of co-operation, Einstein and
Hilbert became rivals with each one trying to beat the other one in
coming up with the field equations.

A spark came to Hilbert after Einstein bragged about derivation of
Mercury's orbital anomaly. This derivation without using GR and thus
without the necessary Schwarzschild metric was an entire plagiarism of
Gerber's work. Of course, Hilbert did not know Einstein's work was
total BS. Thinking he had lost the race, he basically pulled out a
Hail-Mary throw. He pulled out this Hilbert Langrangian out of his
*ss, and the field equations were born. Thus, GR was actually
Hilbert's work.

Somehow, you have just blacked out this part of the history, is it
because you don't understand the field equations?

In case some innocent soul has read it: all of the above is baloney.

Okay. Its all irrelevant to my response anyway. Unless you are saying that
my response is baloney too?

Best wishes

Pete

"JanPB" wrote in message
oups.com...
Koobee Wublee wrote:
Pete wrote:

Try reading this. http://xxx.lanl.gov/abs/physics/0204044
It is a paper I wrote a few years back. The intent of the paper is to
directly answer your question.

Your historical account on the development of GR is very incomplete and
misleading.

Hi Jan

As you can see from this comment from Koobee about the paper I referenced is
way out of wack. If one had read the paper one would first read the title of
the paper "Einstein's gravitational field". Take note of the term "Einstein"
in the title. The paper had a single purpose - Provide the definition of
"gravitional field as viewed by Einstein." It had nothing to do with the
development of GR. It is a statement of a definition with hisorical account
of the term "gravitational field" as Einstein used the term, from 1907 to
1916. If one had read the abstract of the paper then one can readily see
that there was zero intention of giving an historical account of the
development of GR. That never even crossed my mind when I wrote that paper.
The abstract states

"There exists some confusion, as evidenced in the literature, regarding the
nature of the gravitational field in Einstein's General Theory of
Relativity. It is argued here the this confusion is a result of a change in
interpretation of the gravitational field. Einstein identified the existence
of gravity with the inertial motion of accelerating bodies (i.e. bodies in
free-fall) whereas contemporary physicists identify the existence of gravity
with space-time curvature (i.e. tidal forces). The interpretation of gravity
as a curvature in space-time is an interpretation Einstein did not agree
with."

It therefore appears doubtfull to me that Koobee wasn't reading the paper
for what it was, only for what he thought it was. The tone in his writing is
rather demeaning which demonstrates to me a rather arrrogant person. Do you
find this to be true as well?

Pete

However, a define as a definate, a differential geometry would clarify that
matter a definitely, when the equation of Einstein, has had already explain
that a matter curves space-time, and its curvature would be a proportional
to an energy density.

Therefore, a curvature has to satisfy a set of an identities, which are a
just a mathematical necessity along that matter, whether, they do have
nothing to do with the theory of Einstein, along the general relativity.

However, they are absolutely a valid matter along any space-time as along
its curvature, but, when the curvature would be a proportional matter to an
energy density according to the equation of Einstein, however, how the
identities has to apply to the equation of Einstein, and that the question.

Therefore, along that matter, it would be a just a matter of an energy
conservation, when the curvature is a proportional matter to an energy
density, then all that, would a simply means, that along that matter, the
curvature would be an equal matter to an energy density, which it has to be
a just multiplied by a specific number, along a proportional constant,
something, which it would be hidden along the speed of light along which
would be a proportional constant as would a definitely be a constant, and
this is what would be all about, a definitely as a matter a fact.

--
Ahmed Ouahi, Architect
Best Regards!


wrote in message
s.com...
Koobee Wublee wrote:
Tom Roberts wrote:

Einstein essentially stopped working on GR in the 1920s, as did most
physicists. There were occasional papers on GR, but no major effort
until the 1960s (after Einstein's death), when the field experienced a
renaissance. "Modern" GR is no different at base from Einstein's
original papers, but there has been A LOT of understanding and
application to new and different situations.

This is because the problems associated with GR were abundant. Folks
tried very hard to find anther solution still under the concept of
spacetime but got nowhere. Only the newer generations who have
forgotten exactly how silly the postulates that built up GR were began
in earnest to expand its ludicrous nature. Oh, and its Voodoo
mathematics. shrug

How dare you question a theory that E-N-T-I-R-E-L-Y rests on such a
solid and established pillar as Mach's principle???

Chris

"Mach was wrong. Albert was naive, and drank too much German beer."
-- Chris