Something has been bothering me and I hope that someone can clear it up.

After reading about the Michelson-Morley experiment, I learned that relativity states that time dilation and length contraction in Special Relativity results in the speed of light remaining constant in all frames of reference.

However, if the light is travelling in a gravitational field, a second time dilation, this time from General Relativity, is affecting the light as well. If the principle of invariance of light is preserved with Special Relativity, won't this extra time dilation imposed by General Relativity violate this principle?

Tom,

<i>[R]elativity states that time dilation and length contraction in Special Relativity results in the speed of light remaining constant in all frames of reference.</i>

Wrong way round. The constancy of the speed of light leads to time dilation and length contraction.

<i>However, if the light is travelling in a gravitational field, a second time dilation, this time from General Relativity, is affecting the light as well.</i>

Light is not affected by time dilation at all. A photon effectively experiences no time in its own frame of reference.*

<i>If the principle of invariance of light is preserved with Special Relativity, won't this extra time dilation imposed by General Relativity violate this principle?</i>

There is no "extra" time dilation. The cause of time dilation in general relativity is a change of reference frame - the same as in special relativity.

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* Technically, the situation is a little more complex than this, but this will do for the present purposes.

James,

There is no "extra" time dilation. The cause of time dilation in general relativity is a change of reference frame - the same as in special relativity.

So time doesn't slow down in a strong gravitational field?

<i>So time doesn't slow down in a strong gravitational field?</i>

Yes, it does.

James R,
Light doesn't experience time in its own reference frame, true, but it does in ours. It changes frequency and wavelength when in a gravitational field (red shift) similar to but not the same as the way it changes frequency when the source or target is travelling at a high velocity. I propose that the speed of light does change but that we experience it as a shift in wavelength, not as a change of speed, because we aren't in the gravitational field that it is in (and for these effects to be measureable, the gravity needs to be too intense to survive). It might not be true, nor even likely, but can anyone say for certain that I am wrong?

James said it very succinctly. It is a change in reference frames. What this means is, if we were in that strong gravitational field, we would measure the velocity of that light at the same speed, c.

What it also means is that if the light is white, we would see it as white light inside that reference frame.

Outside that reference frame, we will measure the velocity of that same light at c, in a different phase shift, or color.

Time is frozen in the photon. Its speed is c in all reference frames. The phase shift is different in different reference frames. Time dilation affects the way we percieve the color of light, but not the way we measure its velocity. Time dilation cannot affect the photon, because the photon is frozen in time.

Fluidity,

Time dilation affects the way we percieve the color of light, but not the way we measure its velocity.

Doesn't time dilation affect the measurements of the velocity of light in the Michelson-Morley experiment? Why wouldn't time dilation caused by strong gravitational fields do the same?

James,

Maybe my questions were too vague. I've made an illustration that explains the problem that is bothering me.

In the illustration (see attachment) there is an observer and four mirrors that are stationairy in the observer's frame of reference. Mirrors 1 and 2 are in outer space (away from any gravitational fields) and mirrors 3 and 4 are in a strong gravitational field. There is light being bounced off mirrors 1 and 2, and off of mirrors 3 and 4, continuously. Every time the light hits mirror 1 or 3, the mirrors send a short pulse of light to the observer.

Question: Will the observer witness more pulses of light, per second, coming from mirror 1 than from mirror 3, or will the number of pulses of light per second from mirror 1 be identical to the number of pulses of light per second from mirror 3??

Quote: "The null results obtained by Michelson and subsequent experimenters showed that the ether hypothesis was flawed. The speed of light did not depend on the motion of the source, as had been widely assumed. The special theory of relativity, with its counterintuitive hypothesis that the speed of light is the same in all inertial frames, stepped into reconcile the results of the Michelson-Morley experiment with the rest of physics."

http://www.drphysics.com/syllabus/M_M/M_M.html
<HR>
Tom, do you really understand the results of the Michelson-Morely experiment? They did not measure time-dilation. They measured the velocity of light, and they found it to be the same regardless of the distance, position, and approach of the source. Special relativity stepped in to explain their results.

Where is the controversy you speak of?

The number of pulses per second will be different, the phase of light will be different, but the VELOCITY of the light will be the same. Frequencies are transverse, while velocity is linear.

So, I guess we could then suggest time is a transverse component to motion?

Fluidity,

They did not measure time-dilation. They measured the velocity of light, and they found it to be the same regardless of the distance, position, and approach of the source. Special relativity stepped in to explain their results.

Where is the controversy you speak of?

Relativity claims that it's time dilation and length contraction that keep the velocity of light constant. If it wasn't for time dilation, then the light in the Michelson-Morley experiment would appear to be travelling slower than c. So the time dilation is influencing the observer's measurement of the velocity of light.

The number of pulses per second will be different, the phase of light will be different, but the VELOCITY of the light will be the same.

Here's the problem: If the number of pulses per second are different, then the observer will see the two beams of light (between mirrors 1 and 2, and mirrors 3 and 4) reach mirror 1 and 3 at different times. If the observer assumes that the light in mirror 1 and 2 is travelling at c, then the observer cannot assume that the light travelling between mirrors 3 and 4 is travelling at c as well. This appears to break the rule than an observer will see all light, in his frame of reference, travelling at the speed of c.

The first pulse of light will arrive simultaneously with the other. The pulses are lengthened. The end of each pulse of light will arrive later. Its energy has been stretched over time. Its velocity is the same.
If two trains going the same speed have the same number of cars, but one has longer cars than the other, their velocities are still the same, even if it takes one longer to pass than ther other. The train with longer cars will APPEAR to be moving slower, but it is not. In this case, each train car is being stretched out over time. The pulses of light are lenghened by time-dilation, but the velocity is exactly the same. The space between pulses will actually be shorter on the return. The pulses could run together if time dilation is severe enough, and the time between pulses is short enough.

Originally posted by Prosoothus



Relativity claims that it's time dilation and length contraction that keep the velocity of light constant. If it wasn't for time dilation, then the light in the Michelson-Morley experiment would appear to be travelling slower than c. So the time dilation is influencing the observer's measurement of the velocity of light.


No, it does not. What you are giving is the Pre-Relativity attempt to explain the M-M experiment. One that still relied on the idea of an "absolute" reference frame or "Aether".

The idea was that movement through the aether caused clocks to slow down and objects to contract along the axis of movement according to the Lorentz transformations

Relativity does away with the concept of a fixed, absolute reference frame. Under Relativity, objects moving wrt the observer are measured as undergoing time dilation and length contraction. It is never the Observer who's being influenced. (After all, it is motion relative to the observer that causes time dilation, and the Observer's motion wrt himself is always zero.)

Fluidity,

The first pulse of light will arrive simultaneously with the other. The pulses are lengthened. The end of each pulse of light will arrive later. Its energy has been stretched over time. Its velocity is the same.

If I was the observer, how would I calculate the speed of light between the mirrors? First, I would measure the time between pulses of light from mirror 1:

t1= t(second pulse from mirror 1) - t(first pulse from mirror 1)

Then I would multiply the distance between mirrors 1 and 2 by 2, and divide that by t1 to get the speed of light, between mirrors 1 and 2, relative to me:

c1=2d/t1

In the case of mirrors 3 and 4, I would measure the time between the pulses of light from mirror 3:

t2= t(second pulse from mirror 3) - t(first pulse from mirror 3)

Then I would multiply the distance between mirrors 3 and 4 by 2, and divide that by t2 to get the speed of light, between mirrors 3 and 4, relative to me:

c2=2d/t2

As you can see, if there is a smaller time difference between the pulses from mirror 1, than from the pulses between mirror 2, then c1 cannot equal c2. If c1=c then c2 can't equal c. I would be witnessing two beam of light, one of which must be travelling slower than c in my frame of reference. This fact appears to be violating the principle of invariance of light.

Janus58,

Relativity does away with the concept of a fixed, absolute reference frame. Under Relativity, objects moving wrt the observer are measured as undergoing time dilation and length contraction. It is never the Observer who's being influenced.

Example 1: I'm moving at .50c relative to the Earth. I look at my Michelson-Morley inferometer, that I'm carring with me, and I notice that that the speed of light is equal to c in my frame of reference.

Example 2: I increase my speed to .90c relative to the Earth. I look again at my Michelson-Morley inferometer, and I notice that the speed of light is still equal to c.

What is responsible for keeping the speed of light constant for me in the two examples I provided? Is it length contraction and time dilation? If it wasn't for length contraction and time dilation would the speed of light remain constant to me? Doesn't that mean that length contraction and time dilation are influencing my measurements of the speed of light in my frame of reference?

Originally posted by Prosoothus
What is responsible for keeping the speed of light constant for me in the two examples I provided?

This sounds like one of those questions physics can safely ignore. The speed of light just is constant for you. A question along the same lines would be, What is responsible for the speed of light being 299,792 km/s?

If it wasn't for length contraction and time dilation would the speed of light remain constant to me? Doesn't that mean that length contraction and time dilation are influencing my measurements of the speed of light in my frame of reference?

If yes, does it buy you anything? It’s like asking, If it wasn’t for the Earth being the just-right distance from the Sun, would I be alive? Doesn’t that mean that the Earth’s distance from the Sun is influencing my life? The speed of light being constant in your frame of reference may best be something to accept, and then see to where it leads your understanding. It led Einstein to realize what Janus58 said.

Tom:

In your example with the two sets of mirrors, who measures the distance between the mirrors? The precise setup is important, because the distance will vary depending on the spacetime curvature.

James,

In your example with the two sets of mirrors, who measures the distance between the mirrors? The precise setup is important, because the distance will vary depending on the spacetime curvature.

Are you claiming that the speed of light is constant in a strong gravitational field, but that it doesn't appear that way to an outside observer because the space in the gravitational field is curved?

The speed of light is constant for all observers.

James,

The speed of light is constant for all observers.

If you take the curvature of space into consideration, right??

Yes.

Tom,

This is a simple model of how I would measure time-dilation with light pulses as you mention. It should also explain the problem you mentioned in your reply to me earlier in the thread.

Guys, be sure and point out any problems you see in this model.
(I know the actual times listed are incorrect.)

Thanks,

Clay

Fluidity,

This is a simple model of how I would measure time-dilation with light pulses as you mention. It should also explain the problem you mentioned in your reply to me earlier in the thread.

Never mind. James pointed out the error that I made.

It turns out that space is curved between the two mirrors in the gravitational field. Light still travels at c between the two mirrors but because it doesn't travel in a straight line (it follows the curvature of space), it gives the impression that it's travelling slower than c.

Tom