Speed of Gravitational Waves

  • #26
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sgralla: << 2) your "velocity" is a coordinate velocity dr/dt,>>

Me <<Yes, that is what it indeed is. Why do you consider that to be an error?>>

sgralla <<If you choose some other coordinates, and compute dr/dt for those, you'll get a different answer. Which one represents the "speed of light propagation" in this spacetime? If you want to calculate something about light, you need to ask a question that doesn't depend on the choice of coordinates.>>

You are acting as if the speed of something should not depend on the coordinate system, when in fact it should.

A different coordinate system can indeed have a different speed for the wave. The metric components g00 and g11 will of course be different too, and thus the square root of g11/g00 formula still applies.
 
  • #27
95
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Okay, well at least we are in agreement that you are computing the speed of a shape in a particular coordinate system. The reader can now decide for himself whether this computation has anything to do with the "speed of light".
 
  • #28
tom.stoer
Science Advisor
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"Gravity does NOT stop light. Even inside the event horizon light travels always with constant speed c - measured locally in a physical reference frame."

So how can it not come out from the black hole? We know gravity can bend light. But we couldnt notice the change if we measure locally neither.
Ok, let's say it doesnt stop light, just bends to itself. In other words, it has been stopped, or didnt?
If you travel into the black hole (e.g. free falling) you have the chance to make experiments and measure speed of light locally (in your free-fall reference frame). You will measure exactly the same speed of light as outside and even as in flat space.

That's what I am saying: "speed" loses its global meaning in curved spacetime; only local measurements (in a small region of space where curvature can be neglected) make sense.
 
  • #29
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<<Okay, well at least we are in agreement that you are computing the speed of a shape in a particular coordinate system. >>

Physical quantities often have different values in different coordinate systems. It is not as if only scalars are real physical quantities. It has meaning, for example, to say "I am driving my car at 75 miles per hour relative to the Earth".

Linear gravitational waves (just like light) have the same speeds in different INERTIAL coordinate systems, but not the same speeds more generally in different coordinate systems.

(BTW, I made quite a few high school algebra type errors earlier--it is not worth going thru them unless someone asks.)
 
  • #30
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<<That's what I am saying: "speed" loses its global meaning in curved spacetime>>

I don't see what you are getting at. "Electric field" has only a local meaning, too. Local quantities are perfectly legitimate.
 
  • #31
jtbell
Mentor
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Local quantities are perfectly legitimate.
Sure. But you have to measure them locally. That is, you have to be at the location in question. If you measure them "remotely", from some other location, you have to take into account the spacetime curvature between the two locations.
 
  • #32
tom.stoer
Science Advisor
5,766
161
I am saying the following: Two observers A and B in curved spacetime at rest w.r.t each other but located at different spacetime points PA and PB will not agree on the velocity of a test body C w.r.t. to e.g. observer A:

vC(w.r.t. A, measured by A = observed from PA) != vC(w.r.t. A, measured by B = observed from PB)

That means the velocity is no longer globally valid. It does not only depend on the velocity of the two reference frames for A and B (wich is well-known from SR), but also on the location of these reference frames (= tangent-spaces) in spacetime.
 

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