# Speed of Light in a Gravitational Field

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### Ken H. Seto

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Sep 29, 1999, 3:00:00 AM9/29/99
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We know that a clock will run faster as it moves up a gravitational
field. In other words, a clock second high up in a gravitational
field will elapse faster then a clock second on earth. This is
confirmed by the GPS clocks compared to the ground clocks.
SR posits that the speed of light is a constant c in both locations,
My question is: since a clock second in both locations have different
duration, How can they both measure the speed of light to be a
constant c?

Ken seto

### Charles Francis

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Sep 30, 1999, 3:00:00 AM9/30/99
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In article <37f29c56...@news.erinet.com>, Ken H. Seto
<ken...@erinet.com> writes
Because they both measure distance in light seconds on their own clocks.
The speed of light is a definitional constant of their reference frames.

Since the high clock runs faster, distances measured in light seconds
are greater and we cannot have the circumference of a circle round the
planet equal to 2pi*r

>

--
Charles Francis
cha...@clef.demon.co.uk

http://xxx.lanl.gov/abs/physics/9905058
A Theory of Quantum Space-time
http://xxx.lanl.gov/abs/physics/9909047
A Model of Classical and Quantum Measurement
http://xxx.lanl.gov/abs/physics/9909048
Conceptual Foundations of Special and General Relativity
http://xxx.lanl.gov/abs/physics/9909051
A Pre-Geometric Model Exhibiting Physical Law
http://xxx.lanl.gov/abs/physics/9909055
An Alternative Model of Quark Confinement

### Tom Roberts

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Sep 30, 1999, 3:00:00 AM9/30/99
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"Ken H. Seto" wrote:
> We know that a clock will run faster as it moves up a gravitational
> field. [...] since a clock second in both locations have different

> duration, How can they both measure the speed of light to be a
> constant c?

Because the laws of physics are _locally_ Lorentz invariant, but
are not _globally_ so invariant.

Tom Roberts tjro...@lucent.com

### z@z

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Sep 30, 1999, 3:00:00 AM9/30/99
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Hello Ken H. Seto!

| We know that a clock will run faster as it moves up a gravitational

| field. In other words, a clock second high up in a gravitational
| field will elapse faster then a clock second on earth. This is
| confirmed by the GPS clocks compared to the ground clocks.
| SR posits that the speed of light is a constant c in both locations,

| My question is: since a clock second in both locations have different

| duration, How can they both measure the speed of light to be a
| constant c?

As far as I understand the principles of GR, gravitational
length contraction parallels gravitational time dilation. That
is a consequence of the postulated constancy of the speed of
light. The shrinking of rulers leads to black holes. The rulers
and wavelengths shrink to zero when they reach the Schwarzschild
radius.

The consequence that the wavelengths of e.m. radiation decrease
by the effect of a lower gravitational potential is exactly the
opposite we expect when analyzing the problem in a classical
way. A classical analysis leads to the conclusion that the
wavelengths are increased by gravity. It is the same effect as
the increase in distance between cars accelerating after a
bend. The only apparent problem of the assumption of length
increase instead of contraction is the fact that c depends on
the absolute gravational potential (the lower the potential,
the higher c).

Cheers, Wolfgang

A theory where c depends in such a way on gravitational
potential as if e.m. radiation were accelerated by gravity
like normal moving objects (in German):
http://members.lol.li/twostone/relationality.html

### Tom Roberts

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Oct 1, 1999, 3:00:00 AM10/1/99
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"z@z" wrote:
> As far as I understand the principles of GR, gravitational
> length contraction parallels gravitational time dilation.

That is not true. Neither in general, nor in any specific situation
I can think of.

Yes, timed pulses emitted from low in a gravitational well and observed
higher up will be received with a larger time difference than they
were emitted. And yes, at each location a local measurement of the
speed of light will yield c. This is a consequence of the curvature
of spacetime induced by the mass which generated the gravitational
well, and not due to "gravitational length contraction".

> The shrinking of rulers leads to black holes.

No. Black holes are the consequences of the fact that in GR any
pressure which is resisting gravitational collapse also contributes
to the energy-momentum tensor; for an object smaller than its
Schwarzschild radius any increase in pressure resisting collapse
contributes _more_ to an increase in gravity, and the collapse
"runs away".

> The rulers
> and wavelengths shrink to zero when they reach the Schwarzschild
> radius.

That is blatantly false. To an observer hovering just outside the
event horizon of a black hole, rulers appear normal, and light
has a local velocity of c (I'm assuming a black hole large enough
so the observer and his equipment (including a rocket to permit
him to hover) are "small").

In a _VERY_ loose sense this could be argued to be true for
radial rulers near the event horizon. But not at all for non-radial
rulers.

Tom Roberts tjro...@lucent.com

### Charles Francis

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Oct 2, 1999, 3:00:00 AM10/2/99
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In article <37F57B42...@lucent.com>, Tom Roberts
<tjro...@lucent.com> writes

>"z@z" wrote:
>> As far as I understand the principles of GR, gravitational
>> length contraction parallels gravitational time dilation.
>
>That is not true. Neither in general, nor in any specific situation
>I can think of.

It is fundamentally true, in that there is a "natural" system of
reference frames for space-time in which the speed of light is always 1.
However Riemann's non-Euclidean geometry makes no preference for one
system of co-ordinates over another. The removal of this degree of
generality can considerably simplify the treatment.

http://xxx.lanl.gov/abs/physics/9909048
Conceptual Foundations of Special and General Relativity

>

>Yes, timed pulses emitted from low in a gravitational well and observed
>higher up will be received with a larger time difference than they
>were emitted. And yes, at each location a local measurement of the
>speed of light will yield c. This is a consequence of the curvature
>of spacetime induced by the mass which generated the gravitational
>well, and not due to "gravitational length contraction".
>
>

Unless I misunderstand what you are saying, it is the same thing,
related by the field equation.

--
Charles Francis
cha...@clef.demon.co.uk

### Joe Fischer

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Oct 2, 1999, 3:00:00 AM10/2/99
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Charles Francis (cha...@clef.demon.co.uk) wrote:
: It is fundamentally true, in that there is a "natural" system of

: reference frames for space-time in which the speed of light is always 1.
: However Riemann's non-Euclidean geometry makes no preference for one
: system of co-ordinates over another. The removal of this degree of
: generality can considerably simplify the treatment.
:
: http://xxx.lanl.gov/abs/physics/9909048
: Conceptual Foundations of Special and General Relativity

Frankly, I resent your using lanl as your personal
homepage, if every nut like me did that it would not be
possible for anyone to stay within the bounds of rationality.

Joe Fischer

### Ken H. Seto

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Oct 2, 1999, 3:00:00 AM10/2/99
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On Thu, 30 Sep 1999 06:25:27 +0100, Charles Francis
<cha...@clef.demon.co.uk> wrote:

>In article <37f29c56...@news.erinet.com>, Ken H. Seto
><ken...@erinet.com> writes
>>

>>We know that a clock will run faster as it moves up a gravitational
>>field. In other words, a clock second high up in a gravitational
>>field will elapse faster then a clock second on earth. This is
>>confirmed by the GPS clocks compared to the ground clocks.
>>SR posits that the speed of light is a constant c in both locations,
>>My question is: since a clock second in both locations have different
>>duration, How can they both measure the speed of light to be a
>>constant c?
>>
>>

>Because they both measure distance in light seconds on their own clocks.
>The speed of light is a definitional constant of their reference frames.
>
>Since the high clock runs faster, distances measured in light seconds
>are greater and we cannot have the circumference of a circle round the
>planet equal to 2pi*r

So you are saying that even though that we know that the earth second
and the GPS second have different duration, we just simply define this
difference away by using a clock second for length measurement? Isn't
this kind of circular? What you are saying is that the speed of light
may be variable but we make it constant by using varying amount of
duration in different frames to measure light speed.

Ken Seto

### Ken H. Seto

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Oct 2, 1999, 3:00:00 AM10/2/99
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On Thu, 30 Sep 1999 11:30:30 -0500, Tom Roberts <tjro...@lucent.com>
wrote:

>"Ken H. Seto" wrote:
>> We know that a clock will run faster as it moves up a gravitational

>> field. [...] since a clock second in both locations have different

>> duration, How can they both measure the speed of light to be a
>> constant c?
>

>Because the laws of physics are _locally_ Lorentz invariant, but
>are not _globally_ so invariant.

Sorry but this does not answer my question: why we have two different
seconds that have different durations that measure the speed of light
to be c.

Ken Seto

### Charles Francis

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Oct 2, 1999, 3:00:00 AM10/2/99
to
In article <37f617d0\$0\$10...@news.voyager.net>, Ken H. Seto
<ken...@erinet.com> writes
>

>So you are saying that even though that we know that the earth second
>and the GPS second have different duration, we just simply define this
>difference away by using a clock second for length measurement? Isn't
>this kind of circular? What you are saying is that the speed of light
>may be variable but we make it constant by using varying amount of
>duration in different frames to measure light speed.
>
The argument is not actually circular, but it is based on definitional
truism. There is in practice no other strictly empirical notion of
space-time co-ordinate. This can be established without considering the
internal structure of a ruler, but if you do consider the internal
structure of a ruler you will find that it is based on electromagnetism,
which qed shows as the exchange of photons.

The speed of light cannot be variable because (except for trivial
changes in the unit of measurement) space-time coordinates depend for
their empirical definition on light.

--
Charles Francis
cha...@clef.demon.co.uk

http://xxx.lanl.gov/abs/physics/9905058
A Theory of Quantum Space-time
http://xxx.lanl.gov/abs/physics/9909047
A Model of Classical and Quantum Measurement

http://xxx.lanl.gov/abs/physics/9909048
Conceptual Foundations of Special and General Relativity

### Charles Francis

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Oct 2, 1999, 3:00:00 AM10/2/99
to
In article <37f6...@news.iglou.com>, Joe Fischer <joe...@iglou.com>
writes

>Charles Francis (cha...@clef.demon.co.uk) wrote:
>: It is fundamentally true, in that there is a "natural" system of
>: reference frames for space-time in which the speed of light is always 1.
>: However Riemann's non-Euclidean geometry makes no preference for one
>: system of co-ordinates over another. The removal of this degree of
>: generality can considerably simplify the treatment.
>:
>: http://xxx.lanl.gov/abs/physics/9909048
>: Conceptual Foundations of Special and General Relativity
>
> Frankly, I resent your using lanl as your personal
>homepage, if every nut like me did that it would not be
>possible for anyone to stay within the bounds of rationality.
>
I seriously do not believe I am doing that. It is not as though these
papers do not fit seemlessly with the standard model, or that I am not
well enough qualified to know that this is the case. Of course if you
can find a mistake in the mathematics, or show that it leads to results
which are incompatible with the standard model that would be different.
So far I have received no such criticism. Some people have criticised
what I have not said, but even that is helpful if it enables me to
clarify or improve the text.

### Joe Fischer

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Oct 2, 1999, 3:00:00 AM10/2/99
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Charles Francis (cha...@clef.demon.co.uk) wrote:
: Joe Fischer writes
: > Frankly, I resent your using lanl as your personal

: >homepage, if every nut like me did that it would not be
: >possible for anyone to stay within the bounds of rationality.
:
: I seriously do not believe I am doing that.

I guess you don't, else you wouldn't be doing it.
Look at it this way, if everybody that writes a paper were
to send it to the preprint server and list URLs in newsgroups,
that server would be tied up constantly.

: It is not as though these papers do not fit seemlessly with
: the standard model,

Do you mean "seamlessly"? It dosn't matter,
I couldn't care less about the standard model, unless
it correctly addresses gravitation.

: or that I am not well enough qualified to know that this
: is the case.

I will not remark on your qualifications, I only
object to posting lanl URLs as part of your signature.
And if you are discussing "a" paper, why post
a number of URLs in the same post.

: Of course if you can find a mistake in the mathematics,

I find mistakes in textbooks all the time, but
the issue here is discussing the matter described in
a subject line. I would think you would chose not
to publicize your own work.

: or show that it leads to results which are incompatible

: with the standard model that would be different.

Do you mean on Usenet? :-)

: So far I have received no such criticism. Some people have criticised

: what I have not said, but even that is helpful if it enables me to
: clarify or improve the text.

Actually, if you will forgive me, I haven't read
you theories or your papers. And I probably won't,
I am interested in gravity, and I don't see it listed. :-)

: --

: Charles Francis
: cha...@clef.demon.co.uk
:
: http://xxx.lanl.gov/abs/physics/9905058
: A Theory of Quantum Space-time
: http://xxx.lanl.gov/abs/physics/9909047
: A Model of Classical and Quantum Measurement
: http://xxx.lanl.gov/abs/physics/9909048
: Conceptual Foundations of Special and General Relativity
: http://xxx.lanl.gov/abs/physics/9909051
: A Pre-Geometric Model Exhibiting Physical Law
: http://xxx.lanl.gov/abs/physics/9909055
: An Alternative Model of Quark Confinement

This is what I am talking about, the conventional
thing to do is _have_ a homepage, list the URL for it,
and the list your papers there.

I apologize for saying this in a public forum,
it must be because you mentioned "particles" and space-time
in the same sentence. :-)
If you have made any prsentation on the Principle
of Equivalence, I would like to read that (I am hoping
you have not taken any classes with Synge (only because
of what he said about the Poe).

But frankly, there seems little hope of any
advance in the study of gravitation. Little things
like your title

: Conceptual Foundations of Special and General Relativity

seems to me to give the impression that the same
foundations apply to both SR and GR.
While the same fundamental processes no doubt
result in both, SR started out completely different.

So even a small homepage, with some introductory
information might get more people to actually read your
papers.
Also mentioning where those papers are/will be
published would help too, as I don't enjoy reading papers
on line, especially with a browser.

Regards,

Joe Fischer

### Joe Fischer

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Oct 2, 1999, 3:00:00 AM10/2/99
to
Charles Francis (cha...@clef.demon.co.uk) wrote:
: >My question is: since a clock second in both locations have different

: >duration, How can they both measure the speed of light to be a
: >constant c?
:
: Because they both measure distance in light seconds on their own clocks.

: The speed of light is a definitional constant of their reference frames.
:
: Since the high clock runs faster,

There is no way I ever thought I would be in this
reciprical discussion, but I think you are being led into
a maze of confusion here.
If the physics everywhere must be the same, then
it seems incorrect to say one clock runs faster than another.
If you say a detector receives signals at a different
rate, that says nothing about the rate of the emitter.

: distances measured in light seconds are greater and we cannot

: have the circumference of a circle round the planet equal to 2pi*r

We could, if the planet was a massless singularity.
Sorry I butted in, I just wanted to see what it feels like
to talk about gravity in terms of misinterpretations of SR. :-)

Joe Fischer

### Tom Roberts

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Oct 2, 1999, 3:00:00 AM10/2/99
to
Charles Francis wrote:
> Since the high clock runs faster, distances measured in light seconds

> are greater and we cannot have the circumference of a circle round the
> planet equal to 2pi*r

Hmmm. This depends upon what you mean by "runs faster".

In fact, in the Schwarzschild spacetime, the circumference of a circle
at r=R is indeed 2pi*R. And the speed of light around this circle is
c, AS MEASURED BY AN OBSERVER STATIONARY WRT THE SCHW. COORDS. AT r=R.
But, of course, that r=R is not "radius" in the conventional sense, and
is essentially defined by the circumference of the circle; after all,
there _IS_ curvature present in the manifold.

Yes, a light ray sent from lower to higher will experience a redshift.
Does that mean the higher clock "runs faster", or the light ray is
affected by gravitation, or....? The answer depends only upon how
you choose to use words; the mathematical relationships are clear
and unambiguous.

Tom Roberts tjro...@lucent.com

### Joe Fischer

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Oct 2, 1999, 3:00:00 AM10/2/99
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Ken H. Seto (ken...@erinet.com) wrote:

: Tom Roberts <tjro...@lucent.com> wrote:
: >"Ken H. Seto" wrote:
: >> We know that a clock will run faster as it moves up a gravitational
: >> field. [...] since a clock second in both locations have different

: >> duration, How can they both measure the speed of light to be a
: >> constant c?
: >
: >Because the laws of physics are _locally_ Lorentz invariant, but
: >are not _globally_ so invariant.
:
: Sorry but this does not answer my question: why we have two different
: seconds that have different durations that measure the speed of light
: to be c.

You seem kind of hung up on clocks and the length
of their seconds.
Even in flat space-time, or even in Euclidean
space with constant time, observers see the length
of seconds as different if they are moving relative
to each other, even in inertial motion, _BECAUSE_
of the motion and the constancy of the speed of light.

Joe Fischer

### Charles Francis

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Oct 3, 1999, 3:00:00 AM10/3/99
to
In article <37f6...@news.iglou.com>, Joe Fischer <joe...@iglou.com>
writes
>Charles Francis (cha...@clef.demon.co.uk) wrote:
>: >My question is: since a clock second in both locations have different

>: >duration, How can they both measure the speed of light to be a
>: >constant c?
>:
>: Because they both measure distance in light seconds on their own clocks.
>: The speed of light is a definitional constant of their reference frames.
>:
>: Since the high clock runs faster,
>
> There is no way I ever thought I would be in this
>reciprical discussion, but I think you are being led into
>a maze of confusion here.
> If the physics everywhere must be the same, then
>it seems incorrect to say one clock runs faster than another.

It does doesn't it? But if that were so then the special theory would
refute the general theory. We must be careful about the meaning of the
principle of homogeneity. The laws of physics as determined with the one
clock, local to that clock, are the same as the laws of physics as
determined by the other clock, local to the second clock.

> If you say a detector receives signals at a different
>rate, that says nothing about the rate of the emitter.

If the two clocks have an identical mechanism, then the principle of
homogeneity says that the measure the same unit of time (even if, as a
result of the geometry of space-time, one is faster than the other).
>
>: distances measured in light seconds are greater and we cannot

>: have the circumference of a circle round the planet equal to 2pi*r
>

> We could, if the planet was a massless singularity.

No, it is the definition of a singularity that the circumference of a
small circle around it does not tend to 2pi*r as r goes to zero.

>Sorry I butted in, I just wanted to see what it feels like
>to talk about gravity in terms of misinterpretations of SR. :-)
>

Not at all. I think these questions confuse a lot of people - they
certainly confused me when I was learning the subject, so I hope the
answers are also useful.

--
Charles Francis
cha...@clef.demon.co.uk

### Charles Francis

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Oct 3, 1999, 3:00:00 AM10/3/99
to
I take your point, I should remove the URLs from my signature, where I
put them for convenience, and start planning myself a homepage where I
can introduce the papers. Thanks for the advice.

>
> Actually, if you will forgive me, I haven't read
>you theories or your papers. And I probably won't,
>I am interested in gravity, and I don't see it listed. :-)
>

While two of my papers directly concern the theory of gravity
>:

>: http://xxx.lanl.gov/abs/physics/9909048
>: Conceptual Foundations of Special and General Relativity
>: http://xxx.lanl.gov/abs/physics/9909051
>: A Pre-Geometric Model Exhibiting Physical Law
>
>

Only 'Conceptual Foundations of Special and General Relativity' actually
deals with it. However this paper gives a non-rigorous description of
particle interactions. A pre-Geometric model gives a rigorous
description, and shows where the space-time metric fits into particle
wave functions.

As far as the POE is concerned, I do not give an explicit discussion of
it. However I prove Newton's First Law (no great shakes, just a result
of wave mechanics)

http://xxx.lanl.gov/abs/physics/9905058
A Theory of Quantum Space-time

and demonstrate in Conceptual Foundations of Special and General
Relativity that the classical (relativistic) energy equation for a body
in a gravitating field (equivalent to geodesic motion) is the effect of
non-Euclidean geometry on the wave function. I think you would be able
to add any remarks about the Poe yourself.

>: Conceptual Foundations of Special and General Relativity
>
> seems to me to give the impression that the same
>foundations apply to both SR and GR.
> While the same fundamental processes no doubt
>result in both, SR started out completely different.

By foundations I am referring to the fundamental processes, not the
historical development. GR can be seen as the consequences of a small
relaxation of a rule of SR which looks right, but is actually too
strong. (See my response to your other post).

>
> Also mentioning where those papers are/will be
>published would help too, as I don't enjoy reading papers
>on line, especially with a browser.
>

Do they not print correctly? They have been submitted for publication.
--
Charles Francis
cha...@clef.demon.co.uk

### Charles Francis

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Oct 3, 1999, 3:00:00 AM10/3/99
to
In article <37F67DD7...@lucent.com>, Tom Roberts
<tjro...@lucent.com> writes
>Charles Francis wrote:
>> Since the high clock runs faster, distances measured in light seconds

>> are greater and we cannot have the circumference of a circle round the
>> planet equal to 2pi*r
>
>Hmmm. This depends upon what you mean by "runs faster".
>
>In fact, in the Schwarzschild spacetime, the circumference of a circle
>at r=R is indeed 2pi*R. And the speed of light around this circle is
>c, AS MEASURED BY AN OBSERVER STATIONARY WRT THE SCHW. COORDS. AT r=R.
>But, of course, that r=R is not "radius" in the conventional sense, and
>is essentially defined by the circumference of the circle; after all,
>there _IS_ curvature present in the manifold.
>
>Yes, a light ray sent from lower to higher will experience a redshift.
>Does that mean the higher clock "runs faster", or the light ray is
>affected by gravitation, or....? The answer depends only upon how
>you choose to use words; the mathematical relationships are clear
>and unambiguous.
>
>
Yes, it is easy to be inexact in these postings. As a general rule I
make all my statements in the context of natural metric in which the
speed of light is (locally) always 1. I try to be more precise in my
papers.

Conceptual Foundations of Special and General Relativity
http://xxx.lanl.gov/abs/physics/9909051

--
Charles Francis
cha...@clef.demon.co.uk

### z@z

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Oct 3, 1999, 3:00:00 AM10/3/99
to
Tom Roberts wrote:
| Wolfgang G. wrote:

| > As far as I understand the principles of GR, gravitational
| > length contraction parallels gravitational time dilation.
|
| That is not true. Neither in general, nor in any specific situation
| I can think of.

Imagine a given position in a galaxy at rest relativ to the galaxy
center and suppose that there is only empty space in the neighbourhood
of this location. Because there is no gravitation-induced curvature
worth mentioning, we can introduce an Euclidean coordinate system
with its origin at this position.

Further suppose that some time later an orbiting black hole with
the mass of our sun is located at the origin of the coordinate
system. Now we have huge deviations from flat geometry (and even
the implication that inside the black hole the r-coordinate
represents time while the t-coordinate represents space).

The Schwarzschild radius of the black hole is around 3 km. I
suppose that the 3 km refer to the local coordinate system which
was valid before the arrival of the black hole.

But if rulers do not change when the black hole arrives, there
cannot be a deviation from the flat geometry, can it? So the
rulers must change. There are only two possibilties: either
their length decreases or increases (relative to the flat
space) when approximating the event horizon of the black hole.

| > The rulers
| > and wavelengths shrink to zero when they reach the Schwarzschild
| > radius.
|
| That is blatantly false. To an observer hovering just outside the
| event horizon of a black hole, rulers appear normal, and light
| has a local velocity of c (I'm assuming a black hole large enough
| so the observer and his equipment (including a rocket to permit
| him to hover) are "small").

There is no contradiction between what you write and what I have
written. Because the observers shrink in the same way as the rulers,
the latter necessarily appear normal to former.

Cheers, Wolfgang

A simple black hole paradox:
http://members.lol.li/twostone/E/paradoxGR.html

### Tom Roberts

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Oct 4, 1999, 3:00:00 AM10/4/99
to
"Ken H. Seto" wrote:
> On Thu, 30 Sep 1999 11:30:30 -0500, Tom Roberts <tjro...@lucent.com>
> wrote:
> >Because the laws of physics are _locally_ Lorentz invariant, but
> >are not _globally_ so invariant.
> Sorry but this does not answer my question: why we have two different
> seconds that have different durations that measure the speed of light
> to be c.

Yes, it does answer your question. Your claim that "we have two
different seconds that have different durations that measure the
speed of light to be c" is merely words; you have no way to specify
what you mean by "different durations" of "different seconds". If
you would restrict your claims to _physically-observable_measurements_
you would not have these difficulties. You assume the existence of
some "absolute time"; in GR the absence of that negates your entire
approach.

Tom Roberts tjro...@lucent.com

### Tom Roberts

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Oct 4, 1999, 3:00:00 AM10/4/99
to
"z@z" wrote:
> The Schwarzschild radius of the black hole is around 3 km. I
> suppose that the 3 km refer to the local coordinate system which
> was valid before the arrival of the black hole.

No. The 3 km refers to the radius of an imaginary sphere IN FLAT
SPACETIME which has the same area as the event horizon of the black
hole IN NON-FLAT SPACETIME. But the curvature of the Schwarzschild
spacetime does not affect the area of a spherical surface centered
on the origin; note the Schwarzschild r coordinate is not a "radius"
in the usual sense (e.g. it is impossible to lay rulers along it to
measure it, nor could one use radar to measure it).

Your "example" of starting with a Euclidean spacetime and then later
bringing in a black hole is completely bogus -- in GR the geometry
is of the 4-dimensional spacetime manifold, and what you say simply
does not make sense. Yes, you could imagine an observer located
at a point far from any masses who starts out using Euclidean
coordinates, and later a black hole approaches the observer and
prevents the use of Euclidean coordinates, but that cannot be
described as you attempt -- there is no identification of spatial
points independent of time, the manifold consists of events (i.e.
points labeled by all 4 coordinates), not a separate space and time
as your description assumes.

> But if rulers do not change when the black hole arrives, there
> cannot be a deviation from the flat geometry, can it? So the
> rulers must change.

You need to define what you mean by "change". In particular, no
given ruler ever changes its own proper length, because one can
always place a standard ruler right next to it (at rest wrt it)
and measure the ruler's length -- whatever "change" occured to the
ruler will equally affect the standard.

I don't think you can give a self-consistent definition of "change"
in the sense you apparently intend....

Note also that in GR this is a spaceTIME manifold, and the curvature
in question is primarily in a space-time plane. If one considers a
given 3-space projection onto constant time coordinate t=T, there is
curvature in the 3-space USING SCHWARZSCHILD COORDINATES. But in any
locally-inertial coordinate system, the projection onto its time
coordinate has ZERO 3-curvature, and this can be extended over as
large a region of the spacetime as the locally-inertial coordinates
themselves are valid.

A change in coordinates cannot change the curvature of a
manifold. But when one projects onto a coordinate axis,
the curvature of the sub-manifold depends _explicitly_
upon the coordinates used. That's what happens here. By
"curvature" I always mean _intrinsic_ curvature.

It is this construction which implies that rulers do not "change".
Ditto for clocks.

> There are only two possibilties: either
> their length decreases or increases (relative to the flat
> space) when approximating the event horizon of the black hole.

You are merely playing fast and loose with words. You cannot give
self-consistent definitions of the words you use ("decreases" or
"increases" with respect to what? -- THERE IS NO "FLAT SPACE";
that black hole is _there_ when the rulers approach its horizon,
so spacetime is not flat there).

Tom Roberts tjro...@lucent.com

### Ken H. Seto

unread,
Oct 4, 1999, 3:00:00 AM10/4/99
to
On Sat, 2 Oct 1999 17:22:23 +0100, Charles Francis
<cha...@clef.demon.co.uk> wrote:

>In article <37f617d0\$0\$10...@news.voyager.net>, Ken H. Seto
><ken...@erinet.com> writes
>>
>>So you are saying that even though that we know that the earth second
>>and the GPS second have different duration, we just simply define this
>>difference away by using a clock second for length measurement? Isn't
>>this kind of circular? What you are saying is that the speed of light
>>may be variable but we make it constant by using varying amount of
>>duration in different frames to measure light speed.
>>
>The argument is not actually circular, but it is based on definitional
>truism.

It is a definition but it is not a truism. The definition tells us
that if you ignore the existence absolute time then the speed of light
is constant in all frames by using a different amount of absolute time
to measure light speed. Still seems pretty circular to me.
I can understand it if we acknowledge that there exist two kinds of
time: clock time and background. Using a clcok second to measure light
speed will get c in all frame. using a background time second to
measure light speed will get different light speed in different
frames.

Ken Seto

### Ken H. Seto

unread,
Oct 4, 1999, 3:00:00 AM10/4/99
to
On 2 Oct 1999 18:55:43 -0500, joe...@iglou.com (Joe Fischer) wrote:

>Ken H. Seto (ken...@erinet.com) wrote:
>: Tom Roberts <tjro...@lucent.com> wrote:
>: >"Ken H. Seto" wrote:
>: >> We know that a clock will run faster as it moves up a gravitational

>: >> field. [...] since a clock second in both locations have different
>: >> duration, How can they both measure the speed of light to be a
>: >> constant c?
>: >
>: >Because the laws of physics are _locally_ Lorentz invariant, but

>: >are not _globally_ so invariant.
>:
>: Sorry but this does not answer my question: why we have two different
>: seconds that have different durations that measure the speed of light
>: to be c.
>

> You seem kind of hung up on clocks and the length
>of their seconds.

Not any more than you are 'hung up' on divergent matter.

> Even in flat space-time, or even in Euclidean
>space with constant time,

Here you demonstrated that you don't understand the nature of time.
There is no constant clcok time in flat or curved space.

>observers see the length
>of seconds as different if they are moving relative
>to each other, even in inertial motion, _BECAUSE_

>of the motion and the constancy of the speed of light.

Again this demonstrates your poor understanding of time. The speed of
light is km/second. Therefore the constancy of the speed of light is
still dependent on the length of absolute duration of the second in
different frames.

Ken Seto

### Ken H. Seto

unread,
Oct 4, 1999, 3:00:00 AM10/4/99
to
On Mon, 04 Oct 1999 10:03:10 -0500, Tom Roberts <tjro...@lucent.com>
wrote:

>"Ken H. Seto" wrote:
>> On Thu, 30 Sep 1999 11:30:30 -0500, Tom Roberts <tjro...@lucent.com>
>> wrote:

>> >Because the laws of physics are _locally_ Lorentz invariant, but
>> >are not _globally_ so invariant.
>> Sorry but this does not answer my question: why we have two different
>> seconds that have different durations that measure the speed of light
>> to be c.
>

>Yes, it does answer your question. Your claim that "we have two

>different seconds that have different durations that measure the

>speed of light to be c" is merely words; you have no way to specify
>what you mean by "different durations" of "different seconds".

Yes I have a way. A new GPS clock second is set to have less ticks
than an earth second. In other words, an earth clock second will have
9,192,631,770 ticks of Cs atom and a new GPS clock second will have
less than 9,192,631,770 ticks of Cs atom Up at the GPS clock's
position, if you uses 9,192,631,770 ticks of Cs atom to measure light
speed then you will get c but if you use the new GPS second to measure
light speed you will not get c.

>if you would restrict your claims to _physically-observable_measurements_

>you would not have these difficulties.

In other words, when you compare clock rate you use the existence of
absolute time. That's the reason why you set the GPS clock second to
have different tick count. When you measure light speed you use the
tcik count definition because the tcik count definiton automatically
contain the exact amount of absolute time to make the measurement of
light speed constant in all frames.

>You assume the existence of
>some "absolute time"; in GR the absence of that negates your entire
>approach.

But you are acknowledging the existance of absolute time when you set
the GPS clock second to have a different number of ticks of the Cs
atom than the earth second.

Ken Seto

### Tom Roberts

unread,
Oct 5, 1999, 3:00:00 AM10/5/99
to
"Ken H. Seto" wrote:
> On Mon, 04 Oct 1999 10:03:10 -0500, Tom Roberts <tjro...@lucent.com>
> wrote:
> >you have no way to specify
> >what you mean by "different durations" of "different seconds".
> Yes I have a way. A new GPS clock second is set to have less ticks
> than an earth second. In other words, an earth clock second will have
> 9,192,631,770 ticks of Cs atom and a new GPS clock second will have
> less than 9,192,631,770 ticks of Cs atom Up at the GPS clock's
> position, if you uses 9,192,631,770 ticks of Cs atom to measure light
> speed then you will get c but if you use the new GPS second to measure
> light speed you will not get c.

1) You are discussing mere words, and not any physically-observable
difference _IN_TIME_ITSELF_ or the duration of "seconds". Yes, GPS
satellite clocks count a different number of Cs "ticks" than does a
standard clock, because the GPS clocks are designed to read
_COORDINATE_TIME_ and not true seconds where they are located.
2) You got it wrong -- a GPS satellite clock counts _more_ ticks than
does a standard clock on earth to reach "1 second". Note that
earthbound GPS clocks count the usual number of ticks per second.
Note that this difference is in the physical construction of the
clock, and is observable between a GPS satellite clock and a
standard clock when they sit next to each other on a bench in a lab.
3) If you use the GPS satellite clocks in the way they were designed,
you will indeed measure c for the speed of light -- that is
essentially the inverse of their usage to locate positions, and if
the speed of light were measured other than c the GPS would not work.
But you have to measure the speed of light in the ECI frame, not
via a local measurement; you can use _any_ pair of GPS clocks for
such a measurement (it is to gain this flexibility and universality
that GPS clocks tick _COORDINATE_TIME_ and not true seconds).
4) Your claim that a GPS clock won't measure the correct value c for
the speed of light is true for a local measurement -- that is
essentially claiming that one can detect that the clock is broken
by the incorrect values it gives! That's no surprise, and is not
related the question in any way at all. GPS satellite clocks were
deliberately "broken" so that they would read _COORDINATE_TIME_
rather than true seconds where they are located (in orbit).
Remember, please, that SR and GR require the speed of light to be
locally c _WHEN_MEASURED_WITH_STANDARD_CLOCKS_AND_RULERS_, but
GPS clocks are not standard -- they read _COORDINATE_TIME_.

Yes, for GPS satellite clocks in orbit coordinate time does not
correspond to the time of a standard clock. So what? This does not
begin to address your claim of "different durations" of "different
seconds". Thie difference between GPS satellite clocks and standard
clocks is akin to the difference between inches and centimeters --
they are different BY DEFINITION, and there is a clear and obvious
conversion between them.

OK, in a purely linguistic sense it does address "different
seconds", because the GPS coordinate system denotes time in
seconds. This is equivalent to calling centimeters "inches"
and then discussing the "different inches".

> In other words, when you compare clock rate you use the existence of
> absolute time.

Not true at all. To compare two clock rates (for clocks which are
separated) requires a physical situation which permits their rates to
be compared. Inevitably that includes some method of transfering the
ticks of one to the location of the other. One must then analyze the
physical situation used.... No assumption about "absolute time" is
required for this; all one does is compare the arrival of the tick
signals from the distant clock to the ticks of the local clock.

> That's the reason why you set the GPS clock second to
> have different tick count.

Again, GPS satellite clocks use a different number of ticks because the
"seconds" they mark are NOT standard seconds, but are _COORDINATE_TIME_.

> But you are acknowledging the existance of absolute time when you set
> the GPS clock second to have a different number of ticks of the Cs
> atom than the earth second.

No "acknowledgement" of "absolute time" is implied at all. This is
merely correcting for the difference between standard time and
_COORDINATE_TIME_.

Tom Roberts tjro...@lucent.com

### Ken H. Seto

unread,
Oct 6, 1999, 3:00:00 AM10/6/99
to
On Tue, 05 Oct 1999 13:28:02 -0500, Tom Roberts <tjro...@lucent.com>
wrote:

>

>> That's the reason why you set the GPS clock second to
>> have different tick count.
>
>Again, GPS satellite clocks use a different number of ticks because the
>"seconds" they mark are NOT standard seconds, but are _COORDINATE_TIME_.
>
>
>> But you are acknowledging the existance of absolute time when you set
>> the GPS clock second to have a different number of ticks of the Cs
>> atom than the earth second.
>
>No "acknowledgement" of "absolute time" is implied at all. This is
>merely correcting for the difference between standard time and
>_COORDINATE_TIME_.

Let me see if I got this right:

1. A standard clock second will have 9.192,631,770 ticks of Cs atom in
all coordinates (frames). A standard clock second will measure the
speed of light ot be c in all frames..Now if we choose the earth lab
as a reference for absolute time then a clock second and an absolute
second will have 9.192,631,770 ticks of Cs atom in the earth lab.

2. A GPS coordinate second up at the GPS location will have more than
9.192,631,770 ticks of Cs atom. But this higher tick count will
correspond to exactly 9.192,631,770 ticks of Cs atom on earth. A GPS
coordinate second will not measure the speed of light to be c.

3. An absolute second at the GPS coordinate will have more than
9.192,631,770 ticks of Cs atom. But this higher tick count of an
absolute second up at the GPS location will correspond to exactly
9.192,631,770 ticks of Cs atom on earth. An absolute second at the GPS
location will not measure the speed of light to be c.

Seems to me a coordinate second at the GPS location is exactly the
same as an absolute second at the GPS location. So are you saying that
because your naming it a "coordinate second" is voiding the existence
of an absolute second?

Ken Seto

### Tom Roberts

unread,
Oct 6, 1999, 3:00:00 AM10/6/99
to
"Ken H. Seto" wrote:
> Let me see if I got this right:

You seem to be getting closer, but are not yet correct.... Part of
your problem is that you never seem to specify things precisely enough,
and the looseness and ambituigy in your words are important.

> 1. A standard clock second will have 9.192,631,770 ticks of Cs atom in
> all coordinates (frames). A standard clock second will measure the
> speed of light ot be c in all frames.

Only for a _local_ measurement in which the distance is measured using
standard rulers at rest wrt the clock.

> Now if we choose the earth lab
> as a reference for absolute time then a clock second and an absolute
> second will have 9.192,631,770 ticks of Cs atom in the earth lab.

Yes, for a lab located on earth's geoid. [I do not know the precise
number, and assume you copied it correctly from some standard
reference.]

> 2. A GPS coordinate second up at the GPS location will have more than
> 9.192,631,770 ticks of Cs atom. But this higher tick count will
> correspond to exactly 9.192,631,770 ticks of Cs atom on earth.

Yes, assuming "GPS location" == GPS satellite orbits (there are other
clocks and locations used in the GPS), and assuming your "will
correspond" means a comparison of clock synchronization via light
signals between a GPS satellite clock and a clock on the earth's geoid
-- after accounting for the light travel time IN THE ECI FRAME these
clocks will remain in synch.

> A GPS
> coordinate second will not measure the speed of light to be c.

As I said before, if you measure the distance traveled IN THE ECI FRAME,
and use GPS coordinate clocks, you will obtain c for the speed of light.
If you make a _local_ measurement up in orbit using standard rulers at
rest wrt the satellite clock then you won't.

> Seems to me a coordinate second at the GPS location is exactly the
> same as an absolute second at the GPS location.

But there is no "absolute second".... And this depends strongly on what
you mean by "the same" -- you cannot use the usual meaning of that
phrase and still make your claim (as best I can interpret it).

The usual meaning of clocks running at "the same" rate is
that if one places them adjacent to each other (i.e. at
rest wrt each other) then they will tick at the same rate.

If you want to claim that two _separated_ clocks run at "the same"
rate, then you need to specify how this is to be determined (i.e.
how they are compared).

> So are you saying that
> because your naming it a "coordinate second" is voiding the existence
> of an absolute second?

No, I'm saying that there is no way to consistently define any sort
of "absolute second". And the way the GPS uses coordinate time does
not in any way imply that there is. All one can do is define
coordinates which cover the region of spacetime of interest, and then
use them to measure/predict/compute quantities of interest. The
GPS does this for the region of spacetime surrounding the earth
(out to GPS orbits, or so). While different choices of coordiantes
will yield different coordinate values, when physically-observable
quantities are computed from raw coordiante measurements, all
choices of coordiantes will yield the same results.

Tom Roberts tjro...@lucent.com

### Ken H. Seto

unread,
Oct 7, 1999, 3:00:00 AM10/7/99
to
On Wed, 06 Oct 1999 10:27:19 -0500, Tom Roberts <tjro...@lucent.com>
wrote:

>"Ken H. Seto" wrote:

>> Let me see if I got this right:
>
>You seem to be getting closer, but are not yet correct.... Part of
>your problem is that you never seem to specify things precisely enough,
>and the looseness and ambituigy in your words are important.
>
>
>> 1. A standard clock second will have 9.192,631,770 ticks of Cs atom in
>> all coordinates (frames). A standard clock second will measure the
>> speed of light ot be c in all frames.
>
>Only for a _local_ measurement in which the distance is measured using
>standard rulers at rest wrt the clock.

Since we measure distance with clock second in the frame of the clock
so this is an automatic assumption.

>
>
>> Now if we choose the earth lab
>> as a reference for absolute time then a clock second and an absolute
>> second will have 9.192,631,770 ticks of Cs atom in the earth lab.
>
>Yes, for a lab located on earth's geoid. [I do not know the precise
>number, and assume you copied it correctly from some standard
>reference.]

So here you are agreeing that absolute time can exist and that it is
possible to use the earth clock second as reference for absolute time
(or coordinate time).

>
>
>> 2. A GPS coordinate second up at the GPS location will have more than
>> 9.192,631,770 ticks of Cs atom. But this higher tick count will
>> correspond to exactly 9.192,631,770 ticks of Cs atom on earth.
>
>Yes, assuming "GPS location" == GPS satellite orbits (there are other
>clocks and locations used in the GPS), and assuming your "will
>correspond" means a comparison of clock synchronization via light
>signals between a GPS satellite clock and a clock on the earth's geoid
>-- after accounting for the light travel time IN THE ECI FRAME these
>clocks will remain in synch.
>
>
>> A GPS
>> coordinate second will not measure the speed of light to be c.
>
>As I said before, if you measure the distance traveled IN THE ECI FRAME,
>and use GPS coordinate clocks, you will obtain c for the speed of light.

We are talking about using a coordinate second up at the GPS position.

>If you make a _local_ measurement up in orbit using standard rulers at
>rest wrt the satellite clock then you won't.

OK we are in agreement.

>
>> Seems to me a coordinate second at the GPS location is exactly the
>> same as an absolute second at the GPS location.
>
>But there is no "absolute second"....

Why not? I have shown that a coordinate second is in fact an absolute
second.

>And this depends strongly on what
>you mean by "the same" -- you cannot use the usual meaning of that
>phrase and still make your claim (as best I can interpret it).

Your description of a coordinate second can be adopted as a
description for an absolute second. So what is your description for a
coordinate second?

>
> The usual meaning of clocks running at "the same" rate is
> that if one places them adjacent to each other (i.e. at
> rest wrt each other) then they will tick at the same rate.

I am saying that a coordinate second can be interpreted as an absolute
second. It is just two names describing the same process.

>
>If you want to claim that two _separated_ clocks run at "the same"
>rate, then you need to specify how this is to be determined (i.e.
>how they are compared).

No not two clocks just one GPS clock.
A coordinate second on the GPS clock = An absolute second on the
GPS clock

>> So are you saying that
>> because your naming it a "coordinate second" is voiding the existence
>> of an absolute second?
>
>No, I'm saying that there is no way to consistently define any sort
>of "absolute second". And the way the GPS uses coordinate time does
>not in any way imply that there is.

Perhaps your definition for an absolute seocnd is different than mine.
My says that a coordinate seocnd and an absolute second have the same
absolute duration. The absolute duration for an absolute second on
earth is 9,192,631,770 ticks of Cs atom. Up at the GPS position a
coordinate second and an absolute second both have the same number of
ticks of Cs atom and this number is more than 9,192,631,770 ticks of
Cs atom. However, In terms of absolute duration, the 9,192,631,770
ticks of Cs atom on earth is equal to the higher tick count up at the
GPS location.

>All one can do is define
>coordinates which cover the region of spacetime of interest, and then
>use them to measure/predict/compute quantities of interest.

But your defined coordinate second is also a definition for an
absolute seocond.

>The GPS does this for the region of spacetime surrounding the earth
>(out to GPS orbits, or so). While different choices of coordiantes
>will yield different coordinate values, when physically-observable
>quantities are computed from raw coordiante measurements, all
>choices of coordiantes will yield the same results.

Although you keep on saying that there is no absolute second, but you
failed to give me a reason why a coordinate second is not an absolute
second.

Ken Seto

### Tom Roberts

unread,
Oct 7, 1999, 3:00:00 AM10/7/99
to
"Ken H. Seto" wrote:
> [... much deleted...]

> Although you keep on saying that there is no absolute second, but you
> failed to give me a reason why a coordinate second is not an absolute
> second.

You seem to want to merely pick some clock and _define_ "absolute second"
to be what that clock reads, extended throughout the universe in some
unspecified manner (perhaps via light rays, but you never say precisely
how). This has no relationship whatsoever to the usual meanings of the
word "absolute". As a mere label it can be done, but you inevitably
confuse anybody who reads what you write because of the implicit and
explicit meanings of the word "absolute".

There is no justification whatsoever for claiming (as you seem
to) that a clock on earth represents an "absolute second", if
one accepts the usual meanings of "absolute".

It is poor form to select words like this with a deliberate intent
to confuse the reader. Call this a "Paris second" or somesuch (for that
is the location of the clock you originally mentioned some time ago)....

Note that in GR, it is in general impossible to relate such a definition
to all regions of spacetime. It is not in general possible to cover the
manifold with a single coordinate patch.

Tom Roberts tjro...@lucent.com

### Joe Fischer

unread,
Oct 8, 1999, 3:00:00 AM10/8/99
to
Ken H. Seto (ken...@erinet.com) wrote:
: Although you keep on saying that there is no absolute second, but you

: failed to give me a reason why a coordinate second is not an absolute
: second.

Sorry to butt in, but I would like to try to
explain this (one try only).

There is no absolute second, they are all
coordinate seconds, and all are the same duration.

But when an observer in one coordinate system
views signals from another coordinate system, the
number of emitted signals does not equal the number
of received signals.

This is complicated by the fact that doppler
shift (due to velocity) is present, and another
shift due to gravity (actually this is a combination
of only velcity and ordinary acceleration).
(You do know about Doppler shift, maybe it
is like Doppler Gravity).

The clocks are all alike, but if we want to
read "the time" on a GPS clock, we are receiving
signals at a different rate, so the GPS clock is
made to run at a rate that sends signals so that
when we read them, they tell the time correctly
according to our clock, as if the GPS clock
was _NOT_ moving relative to us, and as if the
GPS clock was not way up high.

This is not correct, but I hope it helps
to realize that Doppler is involved, in both
velocity and gravity. :-)

Joe Fischer

### Ken H. Seto

unread,
Oct 8, 1999, 3:00:00 AM10/8/99
to
On Thu, 07 Oct 1999 23:55:29 -0500, Tom Roberts <tjro...@lucent.com>
wrote:

>"Ken H. Seto" wrote:
>> [... much deleted...]

>> Although you keep on saying that there is no absolute second, but you
>> failed to give me a reason why a coordinate second is not an absolute
>> second.
>

>You seem to want to merely pick some clock and _define_ "absolute second"
>to be what that clock reads, extended throughout the universe in some
>unspecified manner (perhaps via light rays, but you never say precisely
>how).

There is no problem to extend a "defined absolute second" throughout
the universe. The choosen observer's clock second as representing an
absolute clock second would just use the Doppler Transform equation to
inform each of the observers in the universe the value of his
absolute second. in terms of ticks of Cs atom.
In this way each observer in the universe would have two types of
second. One is the regular clock second which will measure the speed
of light to be c. A clock second would show time dilation between
frames. The other is an absolute second which will measure the speed
of light to be different in different frames. An absolute second will
have the same absolute duration in all the frames in the universe. In
a limited way that's what we are doing with the GPS system which
chooses the ECI clcok second as representing an absolute second. We
can extend the ECI clock second throughout the universe using SR/GR or
Doppler Relativity transform equations.

>This has no relationship whatsoever to the usual meanings of the
>word "absolute".

Yes it means that an absolute second will have the same absolute
duration in all frames of reference.

>As a mere label it can be done, but you inevitably
>confuse anybody who reads what you write because of the implicit and
>explicit meanings of the word "absolute".

If you don't like absolute then how about "Background Time Second" or
BTsecond

>
> There is no justification whatsoever for claiming (as you seem
> to) that a clock on earth represents an "absolute second", if
> one accepts the usual meanings of "absolute".

A clock second on earth or anyplace else represents a specific
absolute duration. Therefore if we can transform this specific
absolute duration to different frames using the Doppler Relativity
equation then we are justified to call it an absolute second or
BTsecond.

>
>It is poor form to select words like this with a deliberate intent
>to confuse the reader. Call this a "Paris second" or somesuch (for that
>is the location of the clock you originally mentioned some time ago)....

In my book I call it the BT second.

>
>Note that in GR, it is in general impossible to relate such a definition
>to all regions of spacetime. It is not in general possible to cover the
>manifold with a single coordinate patch.

But that's exactly what they are doing when they design the GPS
system. All you need to do is extend the GPS system to the rest of
the universe.

Ken Seto

### Tom Roberts

unread,
Oct 8, 1999, 3:00:00 AM10/8/99
to
"Ken H. Seto" wrote:
> There is no problem to extend a "defined absolute second" throughout
> the universe.

Nonsense. If there is non-zero curvature anywhere in the universe, then
a single coordinate patch cannot cover the entire universe (manifold) --
at least not one which retains the properties of the ECI coordinates.
One can do so _approximately_, but that is not good enough, and the
approximation is guaranteed to break down far enough away (see below).

> >Note that in GR, it is in general impossible to relate such a definition
> >to all regions of spacetime. It is not in general possible to cover the
> >manifold with a single coordinate patch.
> But that's exactly what they are doing when they design the GPS
> system.

Not at all! The GPS coordinate system is valid only in the spacetime
region near the earth. For instance, near the sun measurements using it
would be significantly wrong. But nobody would do that, because this is
well known.

The ECI coordinates of the GPS take into account the gravitation
of the earth, but not that of the sun (except to low order
sufficiently accurate near the earth, but woefully inadequate
near the sun).

> All you need to do is extend the GPS system to the rest of
> the universe.

That cannot be done.

The basic requirement of a coordinate system is that it be a one-to-one
correspondence between 4-tuples of coordinate values and points of the
manifold. Consider the inertial frame in which the sun is at rest (the
SCI), and extend it out many lightyears. In the SCI frame the earth is
accelerating, and the ECI coordinates of the GPS will be ambiguous for
distances far enough from the earth. That is, one will be able to assign
two (or more) different ECI coordinate 4-tuples to a single event of
spacetime (as labeled in the SCI coordinates). This occurs a distance of
~c^2/a from the sun, where a is the (Newtonian) centripetal acceleration
of the earth in the SCI coordinates. I don't have the numbers handy, but
IIRC this is ~1000 ly away.

Yes, this is GR, so how do those Newtonian terms come in?
Because in this case all fields are small and all velocities
are << c, so the Newtonian approximation is valid, and
Euclidean coordinates can be erected in the SCI.

Note that this is merely a counterexample to the claim that the ECI
coordinates of the GPS can be extended throughout the universe. There
are most definitely regions of the universe with significantly larger
curvatures than occur near the earth, and ECI coordinates would be
inextensible into such regions on far smaller scales. For example,
near the sun.

Note that this same argument applies to the SCI coordinates. And to....

Tom Roberts tjro...@lucent.com

### Charles Francis

unread,
Oct 9, 1999, 3:00:00 AM10/9/99
to
In article <37f907be\$0\$10...@news.voyager.net>, Ken H. Seto

<ken...@erinet.com> writes
>On Sat, 2 Oct 1999 17:22:23 +0100, Charles Francis
><cha...@clef.demon.co.uk> wrote:
>
>>In article <37f617d0\$0\$10...@news.voyager.net>, Ken H. Seto
>><ken...@erinet.com> writes
>>>
>>>So you are saying that even though that we know that the earth second
>>>and the GPS second have different duration, we just simply define this
>>>difference away by using a clock second for length measurement? Isn't
>>>this kind of circular? What you are saying is that the speed of light
>>>may be variable but we make it constant by using varying amount of
>>>duration in different frames to measure light speed.
>>>
>>The argument is not actually circular, but it is based on definitional
>>truism.
>
>It is a definition but it is not a truism. The definition tells us
>that if you ignore the existence absolute time then the speed of light
>is constant in all frames by using a different amount of absolute time
>to measure light speed. Still seems pretty circular to me.

It would not be true if there were an absolute time, but that was pretty
suspect in Newton's day and known to be false now.

>I can understand it if we acknowledge that there exist two kinds of
>time: clock time and background. Using a clcok second to measure light
>speed will get c in all frame. using a background time second to
>measure light speed will get different light speed in different
>frames.

But there is no way in practice to measure such a thing, so it can be
clearly stated on philosophical grounds that it does not exist.
--
Charles Francis
cha...@clef.demon.co.uk

### Ken H. Seto

unread,
Oct 10, 1999, 3:00:00 AM10/10/99
to
On Fri, 08 Oct 1999 23:49:30 -0500, Tom Roberts <tjro...@lucent.com>
wrote:

>"Ken H. Seto" wrote:
>> There is no problem to extend a "defined absolute second" throughout
>> the universe.
>
>Nonsense. If there is non-zero curvature anywhere in the universe, then
>a single coordinate patch cannot cover the entire universe (manifold) --
>at least not one which retains the properties of the ECI coordinates.
>One can do so _approximately_, but that is not good enough, and the
>approximation is guaranteed to break down far enough away (see below).

We are discussing two points:
1. Whether a coordinate second is a background time second (absolute
second). This would refute what you said that there is no absolute
second.
2. The difficulty of extending the ECI coordinate second to the far
reached regions of the universe.

I think that you cannot keep on saying that a coordinate second is not
an absolute second. The reason is that a coordinate second have the
exact description as an absolute second. Accepting the existence of
absolute time will give us an explanation why the speed of light is
constant in all frames. The reason is that a clock second will have
the exact amount of absolute absolute duration to give constant light
speed in all frames..

You are right about the difficulty of extending the ECI coordinate
second to the rest of the universe. The reason is that all the frames
in the universe are not in a constant state of absolute moiton. This
is evident that the GPS clocks must be adjusted daily(?). But
nevertheless, we are using absolute time to Synch the GPS clocks with
the ground clocks.

Ken Seto

### francis Rey

unread,
Oct 11, 1999, 3:00:00 AM10/11/99
to
Francis Rey

It appears clearly that you all relativists or not, have got a huge problem
of clocks. You
would ask Swiss people who have the fame to be very good clock builders.

That comes from your absolute will to avoid to see that in SR it never
existed a right
demonstration of time dilation, nor length contraction.
See the criticism of Einstein's texts.

Now I can point out to this person, and others who know this Einstein's
book, that the
chapter 12 is the chapter where Einstein said that the lengths and the times
are
contracted, or dilated, in accordance to the relative velocity V of a moving
referential in
respect to another one at rest .

In this chapter 12 there are calculations and not only words, and these
calculations are
intrinsically wrong.

They are wrong, and even more wrong in the frame of the SR itself.

Einstein assumes an 1 meter length rule is placed on the axis O'x' of K'.
Why not ?
The origin of the rule coincides with the origin O', then:
x' = 0
the end of the rule coincides with the point:
x' = 1
Why not? Then he says:

""In accordance to the first equation of the Lorentz transformation, the
values of these
two points, at time _t_, are:

x( origin of the rule) = 0*(squart (1 - V^2/C^2) )

x(end of the rule) = 1*( squart ( 1 - V^2/C^2) ) """

False !
a) For the origin of the rule:
at time "t" the first Lorentz equation, two pages before, gives if x'
= 0 :

0 = (x - Vt)/(...) , then x = Vt

To have x = 0 , as written by Einstein, it is necessary that

t = 0 , or that : V = 0

Since _t_ is assumed not to be zero we have necessarily:

V = 0

The moving system has the nice velocity ZERO. We must not fear any accident.

b) For the end of the rule:
the first Lorentz equation gives:

1 = ( x - Vt)( 1/ sqrt( 1 - V^2/C^2) )

The time is always "t" and the velocity always V = 0 , since it can only
exist one time t
for the rule.
Then:
x = 1

THE BEST LAW IN RELATIVITY:
A RULE MOVING WITH A VELOCITY _V_ EQUAL TO ZERO, DON'T VARY.

The relativity seems to be the theory of the "at rest movement".
It is not demonstrated that a length contraction is a function of the value
of the velocity
V of the moving frame.

I must say that there is another peremptory argument, that I keep for myself
at the
moment, which tells us that it is absolutely impossible that lengths and
times vary in
accordance with their velocity, when they have any velocity.

As did say Have Faith, don't burn any calories to tell me the content of
this chapter
was devoted to people who don't know Relativity - to whom one can tell any
story -,
because the good derivation of the variation of length and time is in the
article of 1905.
The 1905 article is worse on this point, that is explicitly detailed in my
book, "Three
memories about physics".

Mind you the well chosen name: Have Faith . Does not someone already tell us
about
the equation: Relativity = Religion ?

Now I let you the care to establish that there is no more time dilatation
than length
dilatation in this chapter 12. If somebody cant see that, he can ask me for
a
demonstration.
The clocks times

Let us consider a seconds clock which is at rest permanently at the origin
O' of k' , that is to say
with x' = 0 .
Be t' = 0 and t' = 1 two successive clicks of this clock.
The first an the fourth Lorentz equations give, for these two beatings

t = 0 and t = 1/ sqrt( 1 - V^2/C^2)
False !
x' = 0 t' = 0
means
x = Vt , if one takes t = 0 , that means x = 0 , but in no way that
means necessarily V = 0 .

But that means also that there is not yet any light ray in the problem, if
it was a light ray we would
have got x = C t .
These conditions are the initial conditions of the derivation of the Lorentz
formulae, then x' = 0, t'
= 0 , give x = 0, t = 0, V = 0, C = 0 .

If t' = 1 , since x' = C t' = 0 that means C = 0 No light in the
problem .

If V = 0 then t' = 1 = (1/(1 - v^2/C^2)*( t - vx/C^2) = t
t' = 1 = t
Very logical result.

If V is different from 0 , with C = 0, then

t' = (1/(1 - v^2/C^2) * ( t - vx /C^2) = gamma*( t - Infinite ) = 1

Impossibility.
It never has existed a time dilatation.

In fact C = 0 meaning that there is not any light in the problem, the use
of the Lorentz formulae is
quite forbidden.
It is a great fault to use them.
Fault done first by Lorentz, Einstein, Poincare, in their derivations about
the electron, massive
particle which has not the property to have got a constant velocity in all
inertial frames.

--
francis Rey

The fact much to learn don't teach intelligence
Heraclite of Ephesus.

Joe Fischer a écrit :

> Ken H. Seto (ken...@erinet.com) wrote:

> : Tom Roberts <tjro...@lucent.com> wrote:
> : >"Ken H. Seto" wrote:

> : >> We know that a clock will run faster as it moves up a gravitational
> : >> field. [...] since a clock second in both locations have different

> : >> duration, How can they both measure the speed of light to be a
> : >> constant c?
> : >
> : >Because the laws of physics are _locally_ Lorentz invariant, but

> : >are not _globally_ so invariant.
> :
> : Sorry but this does not answer my question: why we have two different

> : seconds that have different durations that measure the speed of light
> : to be c.
>

> You seem kind of hung up on clocks and the length
> of their seconds.

> Even in flat space-time, or even in Euclidean

> space with constant time, observers see the length

> of seconds as different if they are moving relative
> to each other, even in inertial motion, _BECAUSE_
> of the motion and the constancy of the speed of light.
>

> Joe Fischer

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