Won't I Measure C As Being Slower

[Little Bang]

Moderation note: this post and replies to it were move from the strange claims forum thread Strange replies to “Why Doesn't The Speed Of Light Change?”, because they involve a strait-forward, non-strange question about the theory of General Relativity

Suppose I have a device that measures the speed of light. I measure C here on Earth and I get 3.0 X 10^6 Km/sec. Now I rocket my device out to a place of low gravity where my clock runs faster. Won't I measure C as being slower?

[Little Bang]

No one wants to answer my question?

Suppose I have a device that measures the speed of light. I measure C here on Earth and I get 3.0 X 10^6 Km/sec. Now I rocket my device out to a place of low gravity where my clock runs faster. Won't I measure C as being slower?

[Aethelwulf]

No one wants to answer my question?

Suppose I have a device that measures the speed of light. I measure C here on Earth and I get 3.0 X 10^6 Km/sec. Now I rocket my device out to a place of low gravity where my clock runs faster. Won't I measure C as being slower?

 

Not in your frame of reference, no.

[Little Bang]

If light propagates at the same rate in no gravity as it does in a gravity well then I don't understand your logic. If the clock I use to measure C in the gravity well speeds up in no gravity then I well measure C to be slower.

[CraigD]

If light propagates at the same rate in no gravity as it does in a gravity well then I don't understand your logic. If the clock I use to measure C in the gravity well speeds up in no gravity then I well measure C to be slower.

You’re missing a key aspect of Relativity’s equivalence principle, LB: all clocks, including light itself, experience time dilation (either gravitational or velocity).

 

A distant observer observes the clocks deeper in the gravity well to be slower, and the speed of light there to be slower by exactly the same factor. The observer in the gravity well observes his clock, and the speed of light, to be unchanged.

 

The constancy of the speed of light applies only locally. An observer observes the speed of light in a region with different gravitational potential to be slower or faster.

[Little Bang]

The constancy of the speed of light applies only locally. An observer observes the speed of light in a region with different gravitational potential to be slower or faster.

 

Isn't that exactly what I said Craig?

[Aethelwulf]

If light propagates at the same rate in no gravity as it does in a gravity well then I don't understand your logic. If the clock I use to measure C in the gravity well speeds up in no gravity then I well measure C to be slower.

 

Maybe it is just the way you are wording your question. If you send a rocket into a gravity well designed to send signals of light back to an observer sitting outside the well, the observer outside the well will notice a gravitational dilation.

[CraigD]

Suppose I have a device that measures the speed of light. I measure C here on Earth and I get 3.0 X 10^6 Km/sec. Now I rocket my device out to a place of low gravity where my clock runs faster. Won't I measure C as being slower?

To avoid confusion, let’s restate this question very explicitly, as a thought experiment.

 

Assume we have an apparatus that emits on command a brief laser light pulse that follows a 29979.2458 long path, in a near perfect vacuum, to arrive at a detector close to the emitter (the apparatus needs at least 1 mirror). At a typical near sea level location near the equator on Earth, at midnight, the elapsed time between the emission of the light pulse and its detection is measured with a precise clock of any kind, and found to be precisely 0.0001 s.

 

The apparatus is then put in a spacecraft and placed at the Earth-Sun L₂ point, which is about 53600000 m above sea level. The elapsed time between the emission and detection of its light pulse is again measured, and found to be precisely 0.0001 s.

 

We conclude, therefore, that the speed of light in vacuum is the same at near sea level on Earth as at 53600000 m above sea level. Of course, this agrees with the postulate of Relativity that the speed of light is invariant, which applies to both the Special and General theory.

 

Notice that it’s not necessary to calculate the time dilation of the clock at sea level and at the Earth-Sun L₂ point. Because it’s a postulate, Relativity requires that the speed of light be constant in any local uncelebrated laboratory.