Did Einstein get this wrong?
Jim Akerlund
No, I'm not saying Special Relativity or General Relativity are wrong,
I am referring to a different situation. This different situation was
written by Einstein for his book "Relativity: The Special And The
General Theory", in the chapter called; "Behavior Of Clocks And
Measuring-Rods On A Rotating Body Of Reference". I now quote the
suspect text.
"We start of again from quite special cases, which we have
frequently used before. Let us consider a space-time domain in which
no gravitational field exists relative to a reference-body K whose
state of motion has been suitably chosen. K is then a Galileian
reference-body as regards the domain considered, and the results of
the special theory of relativity hold relative to K. Let us suppose
the same domain referred to a second body of reference K', which is
rotating uniformly with respect to K. In order to fix our ideas, we
shall imagine K' to be in the form of a plane circular disc, which
rotates uniformly in its own plane about its centre. An observer who
is sitting eccentrically on the disc K' is sensible of a force which
acts outwards in a radial direction, and which would be interpreted as
an effect of inertia (centrifugal force) by an observer who was at
rest with respect to the original reference-body K. But the observer
on the disc may regard his disc as a reference-body which is "at
rest"; on the basis of the general principle of relativity he is
justified in doing this. The force acting on himself, and in fact on
all other bodies which are at rest relative to the disc, he regards at
the effect of a gravitational field. Nevertheless, the space-
distribution of this gravitational field is of a kind that would not
be possible on Newton's theory of gravitation. But since the observer
believes in the general theory of relativity, this does not disturb
him; he is quite in the right when he believes that a general law of
gravitation can be formulated--a law which not only explains the
motion of the stars correctly, but also the field force experienced by
himself.
The observer performs experiments on his circular disc with clocks
and measuring-rods. In doing so, it is his intention to arrive at
exact definitions for the signification of time- and space-data with
reference to the circular disc K', these definitions being based on
his observations. What will be his experience in this enterprise?
To start with, he places one of two identically constructed clocks
at the centre of the circular disc, and the other on the edge of the
disc, so that they are at rest relative to it. We now ask ourselves
whether both clocks go at the same rate from the standpoint of the non-
rotating Galileian reference-body K. As judged from this body, the
clock at the centre of the disc has no velocity, whereas the clock at
the edge of the disc is in motion relative to K in consequence of the
rotation. According to a result obtained in Section 12, it follows
that the later clock goes at a rate permanently slower than that of
the clock at the centre of the circular disc, i.e. as observed from
K. It is obvious that the same effect would be noted by an observer
whom we will imagine sitting alongside his clock at the centre of the
circular disc. Thus on our circular disc, or, to make the case more
general, in every gravitational field, a clock will go more quickly or
less quickly, according to the position in which the clock is situated
(at rest). For this reason it is not possible to obtain a reasonable
definition of time with the aid of clocks which are arranged at rest
with respect to the body of reference. A similar difficulty presents
itself when we attempt to apply our earlier definition of simultaneity
in such a case, but I do not wish to go any further into this
question.
Moreover, at this stage the definition of the space coordinates
also presents insurmountable difficulties. If the observer applies
his standard measuring-rod (a rod which is short compared with the
radius of the disc) tangentially to the edge of the disc, then as
judged from the Galileian system, the length of this rod will be less
than 1, since according to Section 12, moving bodies suffer a
shortening in the direction of the motion. On the other hand, the
measuring-rod will not experience a shortening in length, as judged
from K, if it is applied to the disc in the direction of the radius.
If, then, the observer first measures the circumference of the disc
with his measuring-rod and then the diameter of the disc, on dividing
the one by the other, he will not obtain as quotient the familiar
number π = 3.14..., but a larger number, whereas of course, for a disc
which is at rest with respect to K, this operation would yield π
exactly. This proves that the propositions of Euclidean geometry
cannot hold exactly on a rotating disc, nor in general in a
gravitational field, at least if we attribute the length 1 to the rod
in all positions and in every orientation."
Here is where I am having problems with the above excerpt. The
propositions of Euclidean geometry are idealized and can't be applied
to physical reality in non-rotating disc much less rotating discs.
And I know of a bunch of situations where you can get the correct
value of π in the above rotating disc frame of reference, one even
using clocks and rods. The above model that Einstein creates throws
in an unsuspecting element that everyone misses, that element is the
calculation of π itself using math. The same math he uses to
calculate π using clocks and rods can also calculate π without using
clocks and rods and will get the same result in both K and K'. That
would be the algebraic calculation of π. Now for the correct
calculation of π using clocks and rods as exactly described above.
Any mathematician well versed in geometry will tell you that no matter
what kind of space you are in you will always get the correct value of
Ï€ physically if you measure a small enough space. In other words, the
smaller the space you are measuring the closer you are getting to
Euclidean space and geometry. So Einstein in the above situation
concludes that in the Global measurement of π you will not get a
correct value of π, but as I tell you now, as you shrink the above
situation in spacetime to a smaller and smaller disc you will get
closer and closer to a correct value of π and still be using clocks
and rods in the process. So I ask, did Einstein get this wrong? Here
is another situation where I question the results. It goes along the
lines of his global value of π he finds for the whole disc. Here we
set an observer sitting on the edge of the rotating disc and he, using
clocks and rods, calculates π for a small portion of the space he is
in (a space which is small compared to the radius of the disc). He
will arrive at a value of π which is larger then π but smaller then
the global value of π arrived at above. This leads to the question,
which value of π arrived at is the correct value for the disc?
To be fair, Einstein is using the above situation to justify his
reasoning to bring about the math and physics of curved spacetime
geometry as applied through the General Theory of Relativity (GR) in
the book. In his thinking he used a completely different route to
arrive at GR. My main point is that I am having a problem with his
concluding that you don't arrive at a correct value of π for a
rotating disc when I have several ways to arrive at a correct value of
Ï€ on the same rotating disc all within the same parameters he
described above.
Jim Akerlund
Oh No
The centrifugal force is not a gravitational field, and the observer on
the disc would be able to do experiments to determine the difference
>number ð = 3.14..., but a larger number, whereas of course, for a disc
>which is at rest with respect to K, this operation would yield ð
>exactly. This proves that the propositions of Euclidean geometry
>cannot hold exactly on a rotating disc, nor in general in a
>gravitational field, at least if we attribute the length 1 to the rod
>in all positions and in every orientation."
>
>Here is where I am having problems with the above excerpt. The
>propositions of Euclidean geometry are idealized and can't be applied
>to physical reality in non-rotating disc much less rotating discs.
>And I know of a bunch of situations where you can get the correct
>value of ð in the above rotating disc frame of reference, one even
>using clocks and rods. The above model that Einstein creates throws
>in an unsuspecting element that everyone misses, that element is the
>calculation of ð itself using math. The same math he uses to
>calculate ð using clocks and rods can also calculate ð without using
>clocks and rods and will get the same result in both K and K'. That
>would be the algebraic calculation of ð. Now for the correct
>calculation of ð using clocks and rods as exactly described above.
>Any mathematician well versed in geometry will tell you that no matter
>what kind of space you are in you will always get the correct value of
>ð physically if you measure a small enough space. In other words, the
>smaller the space you are measuring the closer you are getting to
>Euclidean space and geometry. So Einstein in the above situation
>concludes that in the Global measurement of ð you will not get a
>correct value of ð, but as I tell you now, as you shrink the above
>situation in spacetime to a smaller and smaller disc you will get
>closer and closer to a correct value of ð and still be using clocks
>and rods in the process. So I ask, did Einstein get this wrong?
General relativity says that the measured value will approach pi in a
small enough region. There is nothing wrong.
>
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)
harry
"Jim Akerlund" <picr...@yahoo.com> wrote in message
news:d1bf18bf-1791-4e69...@c58g2000hsc.googlegroups.com...
I have problems with this part: I know of no law that can explain anything;
moreover I know of no explanation for the circular motion of all the stars
at speeds higher than that of light around a stationary disc...
> The observer performs experiments on his circular disc with clocks
> and measuring-rods. In doing so, it is his intention to arrive at
> exact definitions for the signification of time- and space-data with
> reference to the circular disc K', these definitions being based on
> his observations. What will be his experience in this enterprise?
[...]
> Moreover, at this stage the definition of the space coordinates
> also presents insurmountable difficulties. If the observer applies
> his standard measuring-rod (a rod which is short compared with the
> radius of the disc) tangentially to the edge of the disc, then as
> judged from the Galileian system, the length of this rod will be less
> than 1, since according to Section 12, moving bodies suffer a
> shortening in the direction of the motion. On the other hand, the
> measuring-rod will not experience a shortening in length, as judged
> from K, if it is applied to the disc in the direction of the radius.
> If, then, the observer first measures the circumference of the disc
> with his measuring-rod and then the diameter of the disc, on dividing
> the one by the other, he will not obtain as quotient the familiar
> number ð = 3.14..., but a larger number, whereas of course, for a disc
> which is at rest with respect to K, this operation would yield ð
> exactly. This proves that the propositions of Euclidean geometry
> cannot hold exactly on a rotating disc, nor in general in a
> gravitational field, at least if we attribute the length 1 to the rod
> in all positions and in every orientation."
>
> Here is where I am having problems with the above excerpt. The
> propositions of Euclidean geometry are idealized and can't be applied
> to physical reality in non-rotating disc much less rotating discs.
Not clear to me why you make that claim - I would think that it works fine
on a rotating space station deep in space.
> And I know of a bunch of situations where you can get the correct
> value of ð in the above rotating disc frame of reference, one even
> using clocks and rods.
He did NOT discuss calculating the value of pi...
[...]
> Now for the correct calculation of ð
> using clocks and rods as exactly described above.
No, he did NOT discuss calculating the value of pi!
[...]
> So I ask, did Einstein get this wrong?
I would say that you simply misread what he wrote. He discussed how
measurements are affected due to length contraction (in theory, for the
effect is probably too small to be measurable), and that the same is to be
expected due to gravitation.
> Here
> is another situation where I question the results. It goes along the
> lines of his global value of ð he finds for the whole disc.
No.
[...]
Regards,
Harald
Jim Akerlund
> "Jim Akerlund" <picros...@yahoo.com> wrote in message
It looks like the symbol my computer used for pi got translated into
some other Greek letter which I cannot identify (guessing Delta). So,
yes Einstein was discussing the calculation of pi.
Jim Akerlund
Ken S. Tucker
My goodness sir, I have the book, and I admire
your typing skills and patience!
("pi" is understood").
> number ð = 3.14..., but a larger number, whereas of course, for a disc
> which is at rest with respect to K, this operation would yield ð
> exactly. This proves that the propositions of Euclidean geometry
> cannot hold exactly on a rotating disc, nor in general in a
> gravitational field, at least if we attribute the length 1 to the rod
> in all positions and in every orientation."
>
> Here is where I am having problems with the above excerpt. The
> propositions of Euclidean geometry are idealized and can't be applied
> to physical reality in non-rotating disc much less rotating discs.
> And I know of a bunch of situations where you can get the correct
> value of ð in the above rotating disc frame of reference, one even
> using clocks and rods. The above model that Einstein creates throws
> in an unsuspecting element that everyone misses, that element is the
> calculation of ð itself using math. The same math he uses to
> calculate ð using clocks and rods can also calculate ð without using
> clocks and rods and will get the same result in both K and K'. That
> would be the algebraic calculation of ð. Now for the correct
> calculation of ð using clocks and rods as exactly described above.
> Any mathematician well versed in geometry will tell you that no matter
> what kind of space you are in you will always get the correct value of
> ð physically if you measure a small enough space. In other words, the
> smaller the space you are measuring the closer you are getting to
> Euclidean space and geometry. So Einstein in the above situation
> concludes that in the Global measurement of ð you will not get a
> correct value of ð, but as I tell you now, as you shrink the above
> situation in spacetime to a smaller and smaller disc you will get
> closer and closer to a correct value of ð and still be using clocks
> and rods in the process. So I ask, did Einstein get this wrong? Here
> is another situation where I question the results. It goes along the
> lines of his global value of ð he finds for the whole disc. Here we
> set an observer sitting on the edge of the rotating disc and he, using
> clocks and rods, calculates ð for a small portion of the space he is
> in (a space which is small compared to the radius of the disc). He
> will arrive at a value of ð which is larger then ð but smaller then
> the global value of ð arrived at above. This leads to the question,
> which value of ð arrived at is the correct value for the disc?
>
> To be fair, Einstein is using the above situation to justify his
> reasoning to bring about the math and physics of curved spacetime
> geometry as applied through the General Theory of Relativity (GR) in
> the book. In his thinking he used a completely different route to
> arrive at GR. My main point is that I am having a problem with his
> concluding that you don't arrive at a correct value of ð for a
> rotating disc when I have several ways to arrive at a correct value of
> ð on the same rotating disc all within the same parameters he
> described above.
AE is demonstrating, (using words) a nonorthogonal
geometry on the disc, such that two perpendicular
lines cannot exist on a rotating disc.
What you say is true, if the radius=>0 the effect
diminishes, but that's the same as saying let
the "rate of rotation"=>0 or the strength of the
"centrifugal acceleration" and likewise the antithesis
"gravitational effect" =>0.
But at a point nothing physically exists. It's a math-
matical idealism created by Newton using a Limit,
of /\x =>0 , x=>dx, that plagues thinkers to this day.
Spin angular momentum is an invariant, and cannot
be "transformed away".
Regards
Ken S. Tucker
PS: I should mention Jay Yablon is developing very
sophisticated theory's along those lines.
harry
> On May 9, 9:14 am, "harry" <harald.vanlintelButNotT...@epfl.ch> wrote:
>> "Jim Akerlund" <picros...@yahoo.com> wrote in message
>>
>> news:d1bf18bf-1791-4e69...@c58g2000hsc.googlegroups.com...
???
Again: He was NOT discussing the calculation of pi. Instead, he was
discussing how measurements are affected due to length contraction, and in
that discussion he mentions pi = 3.1415... as a fixed constant that everyone
knows - it is a given. Which sentence did you read as discussing the
calculation of pi?
Regards,
Harald
Ken S. Tucker
Hi Harald.
In GR 1916 Chp. 3, AE takes pains to explain why "pi"
does NOT apply in rotating CS's to invalidate the
universal applicablity of Euclidean geometry.
That's online, anyway that's the way I understand his
argument.
Regards
Ken
Pmb
"harry" <harald.vanlin...@epfl.ch> wrote in message
news:1210340...@sicinfo3.epfl.ch...
> moreover I know of no explanation for the circular motion of all the stars
> at speeds higher than that of light around a stationary disc...
I assume that you are saying this because laws of physics describe nature
rather than explain it, right? If so then you'd probably disagree in
principle with a great number of physicisits since they tend to use the term
"explain" rather than "describe". This really means that its not the laws of
GR that you are objecting to or the physics therein but the use of the term
"explain". Is that correct?
By the way, the speed of light is not an invariant in general relativity.
The stars actually don't move faster than light in GR. They simply move
faster than 3x10^8 m/s.
>> If, then, the observer first measures the circumference of the disc
>> with his measuring-rod and then the diameter of the disc, on dividing
>> the one by the other, he will not obtain as quotient the familiar
>> number Å¡ = 3.14..., but a larger number, whereas of course, for a disc
>> which is at rest with respect to K, this operation would yield Å¡
>> exactly. This proves that the propositions of Euclidean geometry
>> cannot hold exactly on a rotating disc, nor in general in a
>> gravitational field, at least if we attribute the length 1 to the rod
>> in all positions and in every orientation."
I myself have a problem with this. I haven't figured out a resolution yet
(on my back burner). More later this year when I study this more.
>> Here is where I am having problems with the above excerpt. The
>> propositions of Euclidean geometry are idealized and can't be applied
>> to physical reality in non-rotating disc much less rotating discs.
>
> Not clear to me why you make that claim - I would think that it works fine
> on a rotating space station deep in space.
Since the spacetime here is globally flat I don't see how space can be
anything other than Euclidean.
Pete
Pmb
"Pmb" <som...@someplace.com> wrote in message
news:m-KdnQVYAo5HIBXV...@comcast.com...
> By the way, the speed of light is not an invariant in general relativity.
> The stars actually don't move faster than light in GR. They simply move
> faster than 3x10^8 m/s.
Correction. That should have read that the speed of light is dependant on
the observers coordinate system.
Pete
harry
Quite*. If we use the word "explain" to mean "describe", Keppler's regret
that his laws didn't explain the motion of planets becomes meaningless. And
related discussions concerning the foundations of physics become messed up.
> By the way, the speed of light is not an invariant in general relativity.
> The stars actually don't move faster than light in GR. They simply move
> faster than 3x10^8 m/s.
I meant that I know of no law law of nature that predicts such a fast
rotation of stars around the earth - there isn't even a black hole here! ;-)
>>> If, then, the observer first measures the circumference of the disc
>>> with his measuring-rod and then the diameter of the disc, on dividing
>>> the one by the other, he will not obtain as quotient the familiar
>>> number Å¡ = 3.14..., but a larger number, whereas of course, for a disc
>>> which is at rest with respect to K, this operation would yield Å¡
>>> exactly. This proves that the propositions of Euclidean geometry
>>> cannot hold exactly on a rotating disc, nor in general in a
>>> gravitational field, at least if we attribute the length 1 to the rod
>>> in all positions and in every orientation."
>
> I myself have a problem with this. I haven't figured out a resolution yet
> (on my back burner). More later this year when I study this more.
Strangely enough, I don't see the problem. However, I would not formulate it
that way. Here's another one: let's say that you buy a barrel of oil for 125
dollar in the USA, and you take it with you to in Switzerland where you
sell it for 126 francs. However, you made a small loss. This "proves" that
the laws of accountacy "cannot hold exactly" when moving from the USA to
Switzerland. ;-)
>>> Here is where I am having problems with the above excerpt. The
>>> propositions of Euclidean geometry are idealized and can't be applied
>>> to physical reality in non-rotating disc much less rotating discs.
>>
>> Not clear to me why you make that claim - I would think that it works
>> fine on a rotating space station deep in space.
>
> Since the spacetime here is globally flat I don't see how space can be
> anything other than Euclidean.
Measurement space (as distinguished from physical space) is certainly not
flat in a rotating measurement frame because of length contraction
anisotropy of the rulers. Moreover, optical measurements also mess up as
light doesn't even propagate in a straight line relative to such a frame.
* Note that I don't buy the general principle of relativity as it was
originally meant; this was discussed in an earlier thread in this group
under the title "Einstein 1918 - The clock paradox and other objections
against 1916 GRT".
Harald