Einstein on faster than light
Anthony F. Badalamenti
In 1907 Einstein wrote the following in "On The Influence Of
Gravitation On The Propagation Of Light":
"If we call the velocity of light at the origin of
co-ordinates c0, then the velocity of light c at
a place with the gravitation potential phi will
be given by the relation c = c0(1 + phi/c^2).
(my note: c^2 = c squared)
"The principle of the constancy of the velocity of
light hold good according to this theory in a
different form from that which usualy underlies
the ordinary theory of relativity."
In Einstein's narrative phi is negative. This implies that c0 > c. That
is, Einstein is saying that gravity alters not only the direction of
light (as in solar deflection) but also the speed of light. In fact,
his next line begins:
"From the proposition which has just been proved, that
the velocity of light in the gravitational field is a
function of the place..."
Einstein is referring to the speed of light at this point, not its
direction.
Comments? -- Tony
Lawrence Sparks
I have often wondered if this is because time changes with gravity? (or
should I say acceleration on earth that is 9.8 m/s)
but then what do I know.
does time control the speed of light or does the speed of light control
time?
---------------
LMSparks
to reply remove the SPAM or use lmsp...@directinter.net
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Anthony F. Badalamenti <af...@ix.netcom.com> wrote in article
<5rj0eg$i...@agate.berkeley.edu>...
> In Einstein's narrative phi is negative. This implies that c0 > c. That
> is, Einstein is saying that gravity alters not only the direction of
> light (as in solar deflection) but also the speed of light.
[Moderator's note: Quoted material mercilessly excised left and right.
Please, folks, do this yourselves so we don't have to! -TB]
Wayne Hayes
In article <5rj0eg$i...@agate.berkeley.edu>,
Anthony F. Badalamenti <af...@ix.netcom.com> wrote:
>In 1907 Einstein wrote the following in "On The Influence Of
>Gravitation On The Propagation Of Light":
>
> "If we call the velocity of light at the origin of
> co-ordinates c0, then the velocity of light c at
> a place with the gravitation potential phi will
> be given by the relation c = c0(1 + phi/c^2).
> (my note: c^2 = c squared)
>
> "The principle of the constancy of the velocity of
> light hold good according to this theory in a
> different form from that which usualy underlies
> the ordinary theory of relativity."
>
Yes, but c0 is the "constant", ie, the fastest possible speed of light.
c is the variable, and c < c0 in a gravitational well, or in a material
other than a vacuum, etc. There's no "faster than light" here, because
c0 is speed of light in the above equation, not c.
> "From the proposition which has just been proved, that
> the velocity of light in the gravitational field is a
> function of the place..."
Since this is 1907, it's before Einstein had worked out the details
of General Relativity. He was probably thinking that the speed of
light in flat space depends upon the gravitational potential. The
stronger the potential, the slower the speed. Thus, a beam of light
sent past a star would have it's inside half move slower than it's
outside half, thus bending it towards the star.
Although this is not unreasonable at first glance, he presumably found a
flaw in the deteals of this line of reasoning, forming another step in the
long sequence of steps leading him to GR.
--
"Life is raw material. We are artisans. || Wayne Hayes, wa...@cs.utoronto.ca
We can sculpt our existence into something || Astrophysics & Computer Science
beautiful, or debase it into ugliness. || http://www.cs.utoronto.ca/~wayne
It's in our hands." -- Cathy Better ||
Doug Natelson
af...@ix.netcom.com (Anthony F. Badalamenti) writes:
[snipped quotes from '07 Einstein work with c as scalar
field influenced by gravitational potential]
>
>Comments? -- Tony
>
If you found this interesting, I recommend that you read
"Subtle is the Lord", Abraham Pais' technical biography of
Einstein. It's very enlightening, and you get to see the
ways that a great mind works on physics problems, including all
the various blind alleys.
Einstein tried lots of things between 1905 (publ. of spec. rel.)
and November, 1915 (publ. of gen. rel. in final form). One thing
he tried was having c, the speed of light, be a special scalar
field which depended locally on the Newtonian gravitational
potential. This doesn't work (I can't recall the details, but
I believe the problem is with Lorentz invariance; the way the
speed-of-light field looks to different inertial frames is
inconsistent w/ special relativity). Of course, the way
out of this mess is to actually have intervals between
events in spacetime be determined using a metric tensor (which
transforms in particular ways and is dependent on mass distributions
via the Einstein field equations), i.e. classical general relativity.
Took Einstein 8 more years to get there.
In short: this "c > c_0" stuff is part of a scalar (rather than
tensor) theory of gravity that Einstein tried out and rejected
before arriving at general relativity.
Best,
Doug Natelson
nate...@embezzle.stanford.edu
Anil Trivedi
>
>Comments? -- Tony
>
What is loosely called "speed of light" should be called
"speed of light in the vacuum" or even better "the maximum
possible speed of light or anything else"!
Actual speed of light varies not only in gravitational
field but also in air, water, glass, etc. Not only that,
it varies differently for different frequencies.
It is possible to accelerate physical particles such as
electrons so much that they travel faster than light in the
accelerator tunnel! (I don't mean it as a mere theoretical
possibility, but rather as something which actually happens
in experiments.) This is because there is air in the tunnel;
of course, make it vacuum and the light would win.
-Anil Trivedi
Steve Carlip
Anthony F. Badalamenti (af...@ix.netcom.com) wrote:
: In 1907 Einstein wrote the following in "On The Influence Of
: Gravitation On The Propagation Of Light":
: "From the proposition which has just been proved, that
: the velocity of light in the gravitational field is a
: function of the place..."
: Einstein is referring to the speed of light at this point, not its
: direction.
The problem here comes from the fact that "speed" is a
coordinate-dependent quantity, and is therefore somewhat
ambiguous. To determine speed---distance/time---you must
first choose some standards of distance and time, and
different choices can give different answers. This is
already true in special relativity: if you measure the
speed of light in an accelerating reference frame, the
answer will, in general, differ from c.
In special relativity, the speed of light is constant when
measured in any *inertial* frame. In general relativity,
the appropriate generalization is that the speed of light
is constant in any freely falling reference frame (in a
region small enough that tidal effects can be neglected).
In this passage, Einstein is not talking about a freely
falling frame, but rather about a frame at rest relative
to a source of gravity. In such a frame, the speed of
light can differ from c, basically because of the effect
of gravity (spacetime curvature) on clocks and rulers.
Steve Carlip
car...@dirac.ucdavis.edu
Anthony F. Badalamenti
In <5rtcoj$a...@agate.berkeley.edu> sjca...@ucdavis.edu (Steve Carlip)
writes:
>Anthony F. Badalamenti (af...@ix.netcom.com) wrote:
>: In 1907 Einstein wrote the following in "On The Influence Of
>: Gravitation On The Propagation Of Light":
>
>: "From the proposition which has just been proved, that
>: the velocity of light in the gravitational field is a
>: function of the place..."
[Unnecessary quoted text deleted. - jb]
>In special relativity, the speed of light is constant when
>measured in any *inertial* frame. In general relativity,
>the appropriate generalization is that the speed of light
>is constant in any freely falling reference frame (in a
>region small enough that tidal effects can be neglected).
>In this passage, Einstein is not talking about a freely
>falling frame, but rather about a frame at rest relative
>to a source of gravity. In such a frame, the speed of
>light can differ from c, basically because of the effect
>of gravity (spacetime curvature) on clocks and rulers.
Yes, that was my point. The discussion suggests that light
(everywhere) has a natural upper limiting velocity while accepting that
the sun's mass accelerates light rays by changing their direction.
When I first read this it seemed odd to me that mass could accelerate
light only by altering its direction and not its speed. Then I came
upon this passage in Einstein and felt more satisfied. It is not that
nature could not be so constructed as to allow the oddity of a force
effect only on direction and not speed. It is rather that this does not
happen elsewhere in force/object interactions.
The question is, have experiments been done to demonstrate the effect?
--Tony Badalamenti
[Moderator's note: the first experimental confirmation of general
relativity, apart from its prediction of the already observed
anomalous precession of the perhelion of Mercury, was the observation
of the bending of starlight in the Sun's gravitational field by
Crommelin and Eddington in 1919. - jb]