In sci.physics.relativity, Tom Roberts

wrote
on Mon, 05 Sep 2005 03:50:32 GMT
:
The Ghost In The Machine wrote:
First, a clarification. c is of course always constant in SR.
This is a GR question, and is more of a measurement artifact
than anything else, since one cannot measure speed without
a nonzero distance.

OK.


In SR, one can take a rod and timer arrangement, assume space
isotropy, and simply measure lightspeed from any source

One can of course do this and analyze it using GR.


Now assume not SR, but *GR*, and distort local space by
placing the rod vertically in a gravitational field such
as Earth's. [...]

How much of an error is induced by the differences in
tick lengths if one has, say, an AB distance of 100 m?
(Say, along the side of the Empire State building, or
even the Harvard tower.)

A few parts in 10^15 or so for the 60m Harvard tower, IIRC. In any case,
it's far below the accuracy of atomic clocks. Pound and Snider had to
use the Moessbauer effect to obtain a measurement resolution that good.

Well, after asking this question I did discover the formula

lambda/lambda_0 = sqrt(1 - 2GM/(c^2*r))

in Eric Weissstein's scienceworld:

http://scienceworld.wolfram.com/phys...lRedshift.html

when Googling "gravitational redshift". Spun out to ridiculous
precision using GP/Pari one gets

K0 = sqrt(1 - 2GM/(c^2*r)) = 0.9999999993041993006903441138
= 1 - 6.958006993096558861204132123*10^-10
K = sqrt(1 - 2GM/(c^2*(r+60))) = 0.9999999993042058462609365986
= 1 - 6.957941537390634013562467185*10^-10

and the slightly illegitimate operation K-K0 yields

6.545570592484764166493710502 * 10^-15

which is probably best rendered as 6.55 * 10^-15, though
I do have 28 significant digits of which about 13 are left
after the subtraction. :-)

So 10^14 to 10^15 sounds about right.



Bear in mind that AFAIK instantaneous lightspeed in GR is
still considered a constant c; the problem is similar to
the slope of a tangent along a smooth curve in differential
calculus, versus the slope of a secant.

Yes. The tangent lighspeed always has value c, but in a situation where
the curvature of spacetime is not negligible compared to the measurement
accuracy, the secant line of a measurement can have a different slope.
This cn be achieved with either large fields (e.g. in the analysis of
the binary pulsars), or with excellent measurement accuracy (e.g. Pound
and Snider).


Also, has anyone measured this error, and how would one easily
calculate it? I'm not all that well-versed in tensors. :-)

I know of no speed-of-light measurements like you describe. It's not a
very difficult computation, as GR computations go, but compared to most
SR computations it is quite complicated.


Tom Roberts


--
#191,
It's still legal to go .sigless.

"The Ghost In The Machine" wrote in
message ...
| In sci.physics.relativity, Tom Roberts
|
| wrote
| on Mon, 05 Sep 2005 03:50:32 GMT
| :
| The Ghost In The Machine wrote:
| First, a clarification. c is of course always constant in SR.
| This is a GR question, and is more of a measurement artifact
| than anything else, since one cannot measure speed without
| a nonzero distance.
|
| OK.
|
|
| In SR, one can take a rod and timer arrangement, assume space
| isotropy, and simply measure lightspeed from any source
|
| One can of course do this and analyze it using GR.
|
|
| Now assume not SR, but *GR*, and distort local space by
| placing the rod vertically in a gravitational field such
| as Earth's. [...]
|
| How much of an error is induced by the differences in
| tick lengths if one has, say, an AB distance of 100 m?
| (Say, along the side of the Empire State building, or
| even the Harvard tower.)
|
| A few parts in 10^15 or so for the 60m Harvard tower, IIRC. In any
case,
| it's far below the accuracy of atomic clocks. Pound and Snider had
to
| use the Moessbauer effect to obtain a measurement resolution that
good.
|
| Well, after asking this question I did discover the formula
|
| lambda/lambda_0 = sqrt(1 - 2GM/(c^2*r))
|
| in Eric Weissstein's scienceworld:
|
| http://scienceworld.wolfram.com/phys...lRedshift.html
|
| when Googling "gravitational redshift". Spun out to ridiculous
| precision using GP/Pari one gets
|
| K0 = sqrt(1 - 2GM/(c^2*r)) = 0.9999999993041993006903441138
| = 1 - 6.958006993096558861204132123*10^-10
| K = sqrt(1 - 2GM/(c^2*(r+60))) = 0.9999999993042058462609365986
| = 1 - 6.957941537390634013562467185*10^-10
|
| and the slightly illegitimate operation K-K0 yields
|
| 6.545570592484764166493710502 * 10^-15
|
| which is probably best rendered as 6.55 * 10^-15, though
| I do have 28 significant digits of which about 13 are left
| after the subtraction. :-)
|
| So 10^14 to 10^15 sounds about right.

"An educated fool is more foolish than an ignorant one." -- Molière
Androcles



|
|
| Bear in mind that AFAIK instantaneous lightspeed in GR is
| still considered a constant c; the problem is similar to
| the slope of a tangent along a smooth curve in differential
| calculus, versus the slope of a secant.
|
| Yes. The tangent lighspeed always has value c, but in a situation
where
| the curvature of spacetime is not negligible compared to the
measurement
| accuracy, the secant line of a measurement can have a different
slope.
| This cn be achieved with either large fields (e.g. in the analysis
of
| the binary pulsars), or with excellent measurement accuracy (e.g.
Pound
| and Snider).
|
|
| Also, has anyone measured this error, and how would one easily
| calculate it? I'm not all that well-versed in tensors. :-)
|
| I know of no speed-of-light measurements like you describe. It's not
a
| very difficult computation, as GR computations go, but compared to
most
| SR computations it is quite complicated.
|
|
| Tom Roberts
|
|
| --
| #191,
| It's still legal to go .sigless.

In sci.physics.relativity, Androcles

wrote
on Mon, 05 Sep 2005 13:44:33 GMT
:

"The Ghost In The Machine" wrote in
message ...
| In sci.physics.relativity, Tom Roberts
|
| wrote
| on Mon, 05 Sep 2005 03:50:32 GMT
| :
| The Ghost In The Machine wrote:
| First, a clarification. c is of course always constant in SR.
| This is a GR question, and is more of a measurement artifact
| than anything else, since one cannot measure speed without
| a nonzero distance.
|
| OK.
|
|
| In SR, one can take a rod and timer arrangement, assume space
| isotropy, and simply measure lightspeed from any source
|
| One can of course do this and analyze it using GR.
|
|
| Now assume not SR, but *GR*, and distort local space by
| placing the rod vertically in a gravitational field such
| as Earth's. [...]
|
| How much of an error is induced by the differences in
| tick lengths if one has, say, an AB distance of 100 m?
| (Say, along the side of the Empire State building, or
| even the Harvard tower.)
|
| A few parts in 10^15 or so for the 60m Harvard tower, IIRC. In any
case,
| it's far below the accuracy of atomic clocks. Pound and Snider had
to
| use the Moessbauer effect to obtain a measurement resolution that
good.
|
| Well, after asking this question I did discover the formula
|
| lambda/lambda_0 = sqrt(1 - 2GM/(c^2*r))
|
| in Eric Weissstein's scienceworld:
|
| http://scienceworld.wolfram.com/phys...lRedshift.html
|
| when Googling "gravitational redshift". Spun out to ridiculous
| precision using GP/Pari one gets
|
| K0 = sqrt(1 - 2GM/(c^2*r)) = 0.9999999993041993006903441138
| = 1 - 6.958006993096558861204132123*10^-10
| K = sqrt(1 - 2GM/(c^2*(r+60))) = 0.9999999993042058462609365986
| = 1 - 6.957941537390634013562467185*10^-10
|
| and the slightly illegitimate operation K-K0 yields
|
| 6.545570592484764166493710502 * 10^-15
|
| which is probably best rendered as 6.55 * 10^-15, though
| I do have 28 significant digits of which about 13 are left
| after the subtraction. :-)
|
| So 10^14 to 10^15 sounds about right.

"An educated fool is more foolish than an ignorant one." -- Molière
Androcles

Well, the classical variant is

C0=1 - GM/(c^2*r)

which gives

C0 = 0.9999999993041993009324134204
K0 = 0.9999999993041993006903441138
C = 0.9999999993042058465030013508
K = 0.9999999993042058462609365986

C-C0 = 6.545570587930372993109283667 * 10^-15
K-K0 = 6.545570592484764166493710502 * 10^-15

(C-C0)-(K-K0) = -4.55 * 10^-24

(anything more would be beyond my 28-digit significance level -- not
that this is close to right anyway since two of my constants,
M and r, I only keyed in at 3 figures anyway -- 5.976*10^24 kg
and 6.378 * 10^6 m).

I don't see an experiment distinguishing between these two using
a 60m tower -- not without a very carefully constructed
interferometer somehow. (The iron block is an interesting
wildcard; I don't know its response curve.)

Therefore classical gravitation has to be right and c' = c+v
and everyone lives happily ever after.

:-P

[rest snipped]

--
#191,
It's still legal to go .sigless.

"The Ghost In The Machine" wrote in
message ...
| In sci.physics.relativity, Androcles
|
| wrote
| on Mon, 05 Sep 2005 13:44:33 GMT
| :
|
| "The Ghost In The Machine" wrote in
| message ...
| | In sci.physics.relativity, Tom Roberts
| |
| | wrote
| | on Mon, 05 Sep 2005 03:50:32 GMT
| | :
| | The Ghost In The Machine wrote:
| | First, a clarification. c is of course always constant in SR.
| | This is a GR question, and is more of a measurement artifact
| | than anything else, since one cannot measure speed without
| | a nonzero distance.
| |
| | OK.
| |
| |
| | In SR, one can take a rod and timer arrangement, assume space
| | isotropy, and simply measure lightspeed from any source
| |
| | One can of course do this and analyze it using GR.
| |
| |
| | Now assume not SR, but *GR*, and distort local space by
| | placing the rod vertically in a gravitational field such
| | as Earth's. [...]
| |
| | How much of an error is induced by the differences in
| | tick lengths if one has, say, an AB distance of 100 m?
| | (Say, along the side of the Empire State building, or
| | even the Harvard tower.)
| |
| | A few parts in 10^15 or so for the 60m Harvard tower, IIRC. In
any
| case,
| | it's far below the accuracy of atomic clocks. Pound and Snider
had
| to
| | use the Moessbauer effect to obtain a measurement resolution
that
| good.
| |
| | Well, after asking this question I did discover the formula
| |
| | lambda/lambda_0 = sqrt(1 - 2GM/(c^2*r))
| |
| | in Eric Weissstein's scienceworld:
| |
| | http://scienceworld.wolfram.com/phys...lRedshift.html
| |
| | when Googling "gravitational redshift". Spun out to ridiculous
| | precision using GP/Pari one gets
| |
| | K0 = sqrt(1 - 2GM/(c^2*r)) = 0.9999999993041993006903441138
| | = 1 - 6.958006993096558861204132123*10^-10
| | K = sqrt(1 - 2GM/(c^2*(r+60))) = 0.9999999993042058462609365986
| | = 1 - 6.957941537390634013562467185*10^-10
| |
| | and the slightly illegitimate operation K-K0 yields
| |
| | 6.545570592484764166493710502 * 10^-15
| |
| | which is probably best rendered as 6.55 * 10^-15, though
| | I do have 28 significant digits of which about 13 are left
| | after the subtraction. :-)
| |
| | So 10^14 to 10^15 sounds about right.
|
| "An educated fool is more foolish than an ignorant one." -- Molière
| Androcles
|
| Well, the classical variant is

Relativity isn't "classical".
"There are well-dressed foolish ideas, just as there are well-dressed
fools."--Nicolas Chamfort

|
| C0=1 - GM/(c^2*r)
|
| which gives
|
| C0 = 0.9999999993041993009324134204
| K0 = 0.9999999993041993006903441138
| C = 0.9999999993042058465030013508
| K = 0.9999999993042058462609365986
|
| C-C0 = 6.545570587930372993109283667 * 10^-15
| K-K0 = 6.545570592484764166493710502 * 10^-15
|
| (C-C0)-(K-K0) = -4.55 * 10^-24
|
| (anything more would be beyond my 28-digit significance level -- not
| that this is close to right anyway since two of my constants,
| M and r, I only keyed in at 3 figures anyway -- 5.976*10^24 kg
| and 6.378 * 10^6 m).
|
| I don't see an experiment distinguishing between these two using
| a 60m tower -- not without a very carefully constructed
| interferometer somehow. (The iron block is an interesting
| wildcard; I don't know its response curve.)
|
| Therefore classical gravitation has to be right and c' = c+v
| and everyone lives happily ever after.
|
| :-P
|
| [rest snipped]

Bean-counting solves all problems, huh?
Androcles.
"Honesty is praised and starves." --Juvenal

In sci.physics.relativity, Androcles

wrote
on Mon, 05 Sep 2005 15:26:53 GMT
:

"The Ghost In The Machine" wrote in
message ...
| In sci.physics.relativity, Androcles
|
| wrote
| on Mon, 05 Sep 2005 13:44:33 GMT
| :
|
| "The Ghost In The Machine" wrote in
| message ...
| | In sci.physics.relativity, Tom Roberts
| |
| | wrote
| | on Mon, 05 Sep 2005 03:50:32 GMT
| | :
| | The Ghost In The Machine wrote:
| | First, a clarification. c is of course always constant in SR.
| | This is a GR question, and is more of a measurement artifact
| | than anything else, since one cannot measure speed without
| | a nonzero distance.
| |
| | OK.
| |
| |
| | In SR, one can take a rod and timer arrangement, assume space
| | isotropy, and simply measure lightspeed from any source
| |
| | One can of course do this and analyze it using GR.
| |
| |
| | Now assume not SR, but *GR*, and distort local space by
| | placing the rod vertically in a gravitational field such
| | as Earth's. [...]
| |
| | How much of an error is induced by the differences in
| | tick lengths if one has, say, an AB distance of 100 m?
| | (Say, along the side of the Empire State building, or
| | even the Harvard tower.)
| |
| | A few parts in 10^15 or so for the 60m Harvard tower, IIRC. In
any
| case,
| | it's far below the accuracy of atomic clocks. Pound and Snider
had
| to
| | use the Moessbauer effect to obtain a measurement resolution
that
| good.
| |
| | Well, after asking this question I did discover the formula
| |
| | lambda/lambda_0 = sqrt(1 - 2GM/(c^2*r))
| |
| | in Eric Weissstein's scienceworld:
| |
| | http://scienceworld.wolfram.com/phys...lRedshift.html
| |
| | when Googling "gravitational redshift". Spun out to ridiculous
| | precision using GP/Pari one gets
| |
| | K0 = sqrt(1 - 2GM/(c^2*r)) = 0.9999999993041993006903441138
| | = 1 - 6.958006993096558861204132123*10^-10
| | K = sqrt(1 - 2GM/(c^2*(r+60))) = 0.9999999993042058462609365986
| | = 1 - 6.957941537390634013562467185*10^-10
| |
| | and the slightly illegitimate operation K-K0 yields
| |
| | 6.545570592484764166493710502 * 10^-15
| |
| | which is probably best rendered as 6.55 * 10^-15, though
| | I do have 28 significant digits of which about 13 are left
| | after the subtraction. :-)
| |
| | So 10^14 to 10^15 sounds about right.
|
| "An educated fool is more foolish than an ignorant one." -- Molière
| Androcles
|
| Well, the classical variant is

Relativity isn't "classical".

Correct. That's why I said "classical". The C0 formula is
derived from Galilean/Newtonian precepts, according to Eric
Weisstein.

"There are well-dressed foolish ideas, just as there are well-dressed
fools."--Nicolas Chamfort

|
| C0=1 - GM/(c^2*r)
|
| which gives
|
| C0 = 0.9999999993041993009324134204
| K0 = 0.9999999993041993006903441138
| C = 0.9999999993042058465030013508
| K = 0.9999999993042058462609365986
|
| C-C0 = 6.545570587930372993109283667 * 10^-15
| K-K0 = 6.545570592484764166493710502 * 10^-15
|
| (C-C0)-(K-K0) = -4.55 * 10^-24
|
| (anything more would be beyond my 28-digit significance level -- not
| that this is close to right anyway since two of my constants,
| M and r, I only keyed in at 3 figures anyway -- 5.976*10^24 kg
| and 6.378 * 10^6 m).
|
| I don't see an experiment distinguishing between these two using
| a 60m tower -- not without a very carefully constructed
| interferometer somehow. (The iron block is an interesting
| wildcard; I don't know its response curve.)
|
| Therefore classical gravitation has to be right and c' = c+v
| and everyone lives happily ever after.
|
| :-P
|
| [rest snipped]

Bean-counting solves all problems, huh?

Only if you're into counting beans. I personally prefer physical
data, though I'm not equipped for extracting such.

Failing that, it depends on whom one trusts. Experiments thus far
confirm SR and GR to a high degree of accuracy, with the exception
of such anomalies as the ones you've already pointed out; there are
also issues regarding "dark energy" which I personally don't like.

And I'm still wondering why you haven't contacted CERN to fix their
parameters for the beam frequency. 11.2455 kHz is just too danged
slow for superluminal protons. :-)

Androcles.
"Honesty is praised and starves." --Juvenal



--
#191,
It's still legal to go .sigless.

"The Ghost In The Machine" wrote in
message ...
| In sci.physics.relativity, Androcles
|
| wrote
| on Mon, 05 Sep 2005 15:26:53 GMT
| :
|
| "The Ghost In The Machine" wrote in
| message ...
| | In sci.physics.relativity, Androcles
| |
| | wrote
| | on Mon, 05 Sep 2005 13:44:33 GMT
| | :
| |
| | "The Ghost In The Machine" wrote
in
| | message ...
| | | In sci.physics.relativity, Tom Roberts
| | |
| | | wrote
| | | on Mon, 05 Sep 2005 03:50:32 GMT
| | | :
| | | The Ghost In The Machine wrote:
| | | First, a clarification. c is of course always constant in
SR.
| | | This is a GR question, and is more of a measurement
artifact
| | | than anything else, since one cannot measure speed without
| | | a nonzero distance.
| | |
| | | OK.
| | |
| | |
| | | In SR, one can take a rod and timer arrangement, assume
space
| | | isotropy, and simply measure lightspeed from any source
| | |
| | | One can of course do this and analyze it using GR.
| | |
| | |
| | | Now assume not SR, but *GR*, and distort local space by
| | | placing the rod vertically in a gravitational field such
| | | as Earth's. [...]
| | |
| | | How much of an error is induced by the differences in
| | | tick lengths if one has, say, an AB distance of 100 m?
| | | (Say, along the side of the Empire State building, or
| | | even the Harvard tower.)
| | |
| | | A few parts in 10^15 or so for the 60m Harvard tower, IIRC.
In
| any
| | case,
| | | it's far below the accuracy of atomic clocks. Pound and
Snider
| had
| | to
| | | use the Moessbauer effect to obtain a measurement resolution
| that
| | good.
| | |
| | | Well, after asking this question I did discover the formula
| | |
| | | lambda/lambda_0 = sqrt(1 - 2GM/(c^2*r))
| | |
| | | in Eric Weissstein's scienceworld:
| | |
| | |
http://scienceworld.wolfram.com/phys...lRedshift.html
| | |
| | | when Googling "gravitational redshift". Spun out to
ridiculous
| | | precision using GP/Pari one gets
| | |
| | | K0 = sqrt(1 - 2GM/(c^2*r)) =
0.9999999993041993006903441138
| | | = 1 - 6.958006993096558861204132123*10^-10
| | | K = sqrt(1 - 2GM/(c^2*(r+60))) =
0.9999999993042058462609365986
| | | = 1 - 6.957941537390634013562467185*10^-10
| | |
| | | and the slightly illegitimate operation K-K0 yields
| | |
| | | 6.545570592484764166493710502 * 10^-15
| | |
| | | which is probably best rendered as 6.55 * 10^-15, though
| | | I do have 28 significant digits of which about 13 are left
| | | after the subtraction. :-)
| | |
| | | So 10^14 to 10^15 sounds about right.
| |
| | "An educated fool is more foolish than an ignorant one." --
Molière
| | Androcles
| |
| | Well, the classical variant is
|
| Relativity isn't "classical".
|
| Correct. That's why I said "classical". The C0 formula is
| derived from Galilean/Newtonian precepts, according to Eric
| Weisstein.
|
| "There are well-dressed foolish ideas, just as there are
well-dressed
| fools."--Nicolas Chamfort
|
| |
| | C0=1 - GM/(c^2*r)
| |
| | which gives
| |
| | C0 = 0.9999999993041993009324134204
| | K0 = 0.9999999993041993006903441138
| | C = 0.9999999993042058465030013508
| | K = 0.9999999993042058462609365986
| |
| | C-C0 = 6.545570587930372993109283667 * 10^-15
| | K-K0 = 6.545570592484764166493710502 * 10^-15
| |
| | (C-C0)-(K-K0) = -4.55 * 10^-24
| |
| | (anything more would be beyond my 28-digit significance level --
not
| | that this is close to right anyway since two of my constants,
| | M and r, I only keyed in at 3 figures anyway -- 5.976*10^24 kg
| | and 6.378 * 10^6 m).
| |
| | I don't see an experiment distinguishing between these two using
| | a 60m tower -- not without a very carefully constructed
| | interferometer somehow. (The iron block is an interesting
| | wildcard; I don't know its response curve.)
| |
| | Therefore classical gravitation has to be right and c' = c+v
| | and everyone lives happily ever after.
| |
| | :-P
| |
| | [rest snipped]
|
| Bean-counting solves all problems, huh?
|
| Only if you're into counting beans. I personally prefer physical
| data, though I'm not equipped for extracting such.

Looks like you did a lot of bean counting to me.

| Failing that, it depends on whom one trusts. Experiments thus far
| confirm SR and GR to a high degree of accuracy, with the exception
| of such anomalies as the ones you've already pointed out; there are
| also issues regarding "dark energy" which I personally don't like.

You are not equipped for extracting data, so by criteria to you assert
"confirm" ?


| And I'm still wondering why you haven't contacted CERN to fix their
| parameters for the beam frequency. 11.2455 kHz is just too danged
| slow for superluminal protons. :-)


The book is in progress. I don't think they'll have too much trouble
changing a little thing like frequency, my radio tunes to lots of them.

|
| Androcles.
| "Honesty is praised and starves." --Juvenal
|
|
|
| --
| #191,
| It's still legal to go .sigless.

If time slows down so does everything else!

Physics is geared to how time passes.

Mitch -- Light Falls --

Androcles the self-descriptive quoter, stop cascading!