# Relative Motion and Time Dependance on Velocity of Light

#### russ_watters

Mentor
I am referring to Lorentz contraction without the STR part in it, Remember - without the result from MM that implies that light has a constant relative velocity to the observer regardless of the motion of the observers's inertial system we have NO STR
As was already pointed out, there is a mountain of experimental verification of STR. You're really barking up the wrong tree here. Note also: it isn't clear if Einstein knew about the MMX and regardless, it isn't needed for the formulation of the theory (but does provide good evidence to support it).

And also, please note that our guidelines expressedly forbid free-form idle speculation and unverified personal theories. This is a place to learn physics, not a place to indulge your own personal speculations.

#### JesseM

This is actually not really relevant - unless we are trying to catch the 'exact same wavefront'?
What do you mean by "catch"? The idea is that if the peaks of the wave were lined up when the beams were departing (because they were created from a single beam using a beam splitter), they still need to be lined up when they merge again in order for there to be no interference observed. If you assume light moves at c in the rest frame of the apparatus, this would mean that if there were any difference in the length of the arms, it would have to be some integer multiple of the wavelength of the light in order to avoid interference. Since MM designed the arms to have the same length, obviously they were thinking that if the device were at rest relative to the ether, you would have exactly the same peaks lined up at the end as were lined up at the beginning. And in relativity, it's true that the same peaks that were lined up at the beginning will reunite at the end if the arms are equal length in the device's own frame, regardless of what inertial frame the device happens to be at rest in (it's no longer required that it be at rest in some preferred ether frame for this to be true). See the animations on this page, where the peaks going along one arm are shown in green and the peaks going along the other are shown in red (the page is from a somewhat crackpot site that advocates a Lorentz ether theory where objects objectively contract when moving relative to the ether, but the animations are helpful anyway).

edit: it seems I was incorrect that MM were trying to make sure the arms had exactly the same length, I was misled by schematic diagrams which show the device this way; see the link in my next post, which makes clear they just adjusted the arms so that no interference was seen initially, then rotated the device to see if this would change the pattern.

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#### russ_watters

Mentor
It is just difficult for me to understand that the results from the MM machine could have been used to arrive at a theory like GTR and STR. The machine had to be stable and mechanically exact within 6 e-7 m. Anybody spoke to an engineer about this? Are physicists willing to come to far reaching conclusions like the one's implied by GTR and STR on the grounds of the results of a machine like this?
While I've never personally done it (I'm an engineer, not a physicist), the MMX has been duplicated thousands of times. It isn't like they did it once and everyone just assumes what they said was right. It has been repeated and refined. Precision was, indeed, an issue, but a quick look at the Wiki for it shows that they did take that into account: the apparatus did have the required precision to find what they were looking for, had it existed. Speculation of flaws in the experimental setup is a non-starter.

#### JesseM

It is just difficult for me to understand that the results from the MM machine could have been used to arrive at a theory like GTR and STR.
Uh, in what way do you imagine the MM was used to arrive at GTR? You understand there has been a whole lot of subsequent evidence for the STR, and that completely different types of evidence are needed to verify the predictions of the GTR, right?

As for the original MM experiment, subsequent engineers and physicists have not questioned that it was sufficiently precise to get meaningful results, although of course much more precise versions of the experiment have been performed since. Here is a page which gives details of the setup if you're interested. It appears that they did not actually try to ensure that the arms were of equal length, just that the lengths were such that no interference pattern was observed at one orientation, and then they changed the orientation of the apparatus to see if this would change the interference pattern as would be expected if the device were in motion relative to the ether.

#### DewaldS

What do you mean by "catch"? The idea is that if the peaks of the wave were lined up when the beams were departing (because they were created from a single beam using a beam splitter), they still need to be lined up when they merge again in order for there to be no interference observed. If you assume light moves at c in the rest frame of the apparatus, this would mean that if there were any difference in the length of the arms, it would have to be some integer multiple of the wavelength of the light in order to avoid interference. Since MM designed the arms to have the same length, obviously they were thinking that if the device were at rest relative to the ether, you would have exactly the same peaks lined up at the end as were lined up at the beginning. And in relativity, it's true that the same peaks that were lined up at the beginning will reunite at the end if the arms are equal length in the device's own frame, regardless of what inertial frame the device happens to be at rest in (it's no longer required that it be at rest in some preferred ether frame for this to be true). See the animations on this page, where the peaks going along one arm are shown in green and the peaks going along the other are shown in red (the page is from a somewhat crackpot site that advocates a Lorentz ether theory where objects objectively contract when moving relative to the ether, but the animations are helpful anyway).
My calculations show that same length arms does not necessarily mean that the same wave front arrives at the same time. I set up formulaes to calculate the time it takes to meet the 'moving target' in the direction of the motion , then come back and also formulaes to calculate the time it takes to meet the 'moving target' on the right hand arm and then come back. Am I making an error?

I will not overstress the problems associated with making and measuring anything mechanical that is so exact - but it could be enlightening for anyone to visit a precision engineering workshop and ask them to show you how a micron is machined and or measured.

#### DewaldS

As was already pointed out, there is a mountain of experimental verification of STR. You're really barking up the wrong tree here. Note also: it isn't clear if Einstein knew about the MMX and regardless, it isn't needed for the formulation of the theory (but does provide good evidence to support it).

And also, please note that our guidelines expressedly forbid free-form idle speculation and unverified personal theories. This is a place to learn physics, not a place to indulge your own personal speculations.
The basis of the theory has to be verified otherwise it is useless. It is like division with zero - all that follows after that is worth nothing. I will look into the other experimental verifications.

I apologize for my own 'unverified' speculations.

#### JesseM

My calculations show that same length arms does not necessarily mean that the same wave front arrives at the same time.
It does if they are the same length in the device's rest frame, and likewise it does if you assume that in a frame where they are moving, the arm which is parallel to the direction of motion shrinks by a factor of $$\sqrt{1 - v^2/c^2}$$ (and in both cases you assume light moves at c in whatever frame you're calculating the time for the wave fronts to travel to the end of the arm and back).
DewaldS said:
I set up formulaes to calculate the time it takes to meet the 'moving target' in the direction of the motion , then come back and also formulaes to calculate the time it takes to meet the 'moving target' on the right hand arm and then come back. Am I making an error?
If your formulas disagree with what I say above, then you are making an error. Try applying these formulas to the specific numerical example I provided in post #51 of this thread.
DewaldS said:
I will not overstress the problems associated with making and measuring anything mechanical that is so exact - but it could be enlightening for anyone to visit a precision engineering workshop and ask them to show you how a micron is machined and or measured.
All I can tell you is that you will find no mainstream physicists or engineers who doubt that the equipment that MM were using had sufficient precision for their results to be meaningful. I have no idea if the techniques used then to get micron-level precision would be the same as the techniques used today.

#### DewaldS

Question: The 'ether' for which the MM device was actually designed. I would suppose the ether was up to some point in history used by some scientist to explain how light could 'move' through space? Why would the relative movement of the light through the ether be met by any restriction? I would suppose this is an energy consideration, but I would like to know, please.

#### atyy

It is just difficult for me to understand that the results from the MM machine could have been used to arrive at a theory like GTR and STR. The machine had to be stable and mechanically exact within 6 e-7 m.
Yes, the machine had to be stable to a high precision (ie. the measurements at different times had to be with the same machine, with all components at the same pressure,temperature etc). However, the key to the Michelson-Morley experiment is that it is measuring the difference in the speed of light due to the movement of the earth in space - which is about 30 km/s. Michelson and Morley's conclusion was "the measured velocity was approximately one-sixth of the expected velocity of the Earth’s motion in orbit and “certainly less than one-fourth.” Michelson and Morley, as model experimentalists, were among the greatest skeptics of their own result, and sought repeatedly to prove themselves wrong.

The textbook caveat to the Michelson-Morley experiment is that it places a limit on the two-way speed of light, and not the one-way speed of light. Apparently, experiments since then have shown that even the one-way speed of light is independent of the earth's movement, but I only know that as a textbook statement and don't know enough to refer you to an exact experiment.

As an example of an experiment since the MM experiment that gives us high confidence that the speed of light is constant is the experimental measurement of electron magnetic moment to greater than 1 part in 1000,000,000, AND the fact that this measurement matches the theoretical prediction incorporating the constancy of the speed of light as an assumption.

The experiment:
http://hussle.harvard.edu/~gabrielse/gabrielse/papers/2006/NewElectronMagneticMoment.pdf

The theoretical prediction using the constancy of the speed of light:
http://hussle.harvard.edu/~gabrielse/gabrielse/papers/2006/NewFineStructureConstant.pdf

You can see that the best physicists are actually the greatest skeptics. Before Gabrielse made these latest measurements, it was already known that experimental and theoretical the electron moments matched. He obviously wanted to see if there would be a mismatch with greater experimental accuracy. His more precise measurement forced a new theoretical calculation (using the same theory, but extracting consequences from it with higher precision). A discovery that the any of our present theories do not match experiment and need to be improved would actually be very exciting!

Edit: The erratum at the end of the second paper is very interesting to read, if you're interested in details.

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#### DewaldS

It does if they are the same length in the device's rest frame, and likewise it does if you assume that in a frame where they are moving, the arm which is parallel to the direction of motion shrinks by a factor of $$\sqrt{1 - v^2/c^2}$$ (and in both cases you assume light moves at c in whatever frame you're calculating the time for the wave fronts to travel to the end of the arm and back).

If your formulas disagree with what I say above, then you are making an error. Try applying these formulas to the specific numerical example I provided in post #51 of this thread.

All I can tell you is that you will find no mainstream physicists or engineers who doubt that the equipment that MM were using had sufficient precision for their results to be meaningful. I have no idea if the techniques used then to get micron-level precision would be the same as the techniques used today.
Yes, the formulae do agree with what you are saying. I am a slow mover - I will only use any STR derived formulaes once I am convinced that the theory is sound.

#### JesseM

Question: The 'ether' for which the MM device was actually designed. I would suppose the ether was up to some point in history used by some scientist to explain how light could 'move' through space? Why would the relative movement of the light through the ether be met by any restriction? I would suppose this is an energy consideration, but I would like to know, please.
What do you mean "restriction"? Light waves were assumed to be vibrations in the ether just like sound waves are vibrations in air. In the rest frame of the air, all sound waves move at the same speed regardless of the speed of the emitter, so it was assumed light waves worked the same way (the speed of vibrations in any medium depends on physical properties of the medium like density and rigidity). And if you're moving at some speed v relative to the rest frame of the air, then in your frame sound waves will move at s + v in one direction and s - v in the opposite direction, and similarly it was assumed that if you were moving at v relative to the ether, you'd measure light waves to move at c + v in one direction and c - v in the other. Since Maxwell's laws predict that light waves always move at c, it was assumed Maxwell's laws would only work exactly in the rest frame of the ether, in other frames they'd have to be modified by a Galilei transformation.

#### DewaldS

What do you mean "restriction"? Light waves were assumed to be vibrations in the ether just like sound waves are vibrations in air. In the rest frame of the air, all sound waves move at the same speed regardless of the speed of the emitter, so it was assumed light waves worked the same way (the speed of vibrations in any medium depends on physical properties of the medium like density and rigidity). And if you're moving at some speed v relative to the rest frame of the air, then in your frame sound waves will move at s + v in one direction and s - v in the opposite direction, and similarly it was assumed that if you were moving at v relative to the ether, you'd measure light waves to move at c + v in one direction and c - v in the other. Since Maxwell's laws predict that light waves always move at c, it was assumed Maxwell's laws would only work exactly in the rest frame of the ether, in other frames they'd have to be modified by a Galilei transformation.
OK that is clear.

#### atyy

Yes, the formulae do agree with what you are saying. I am a slow mover - I will only use any STR derived formulaes once I am convinced that the theory is sound.
I think you should use the STR formulas even before you are convinced they are experimentally right. The reason is that to prove STR wrong, we need to know what it predicts, and we must therefore use the theory (but we need not accept the theory if its predictions conflict with experiments).

#### DewaldS

As an example of an experiment since the MM experiment that gives us high confidence that the speed of light is constant is the experimental measurement of electron magnetic moment to greater than 1 part in 1000,000,000, AND the fact that this measurement matches the theoretical prediction incorporating the constancy of the speed of light as an assumption.

The experiment:
http://hussle.harvard.edu/~gabrielse/gabrielse/papers/2006/NewElectronMagneticMoment.pdf

The theoretical prediction using the constancy of the speed of light:
http://hussle.harvard.edu/~gabrielse/gabrielse/papers/2006/NewFineStructureConstant.pdf
I am not well versed enough at physics (at this stage) to understand the papers.

We are making a distinction her between two concepts

i) The speed of light through a vacuum is constant.
ii) The speed of light is constant relative to an observer regardless of the motion of the observer's inertial frame?

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#### atyy

We are making a distinction her between two concepts

i) The speed of light through a vacuum is constant.
ii) The speed of light is constant relative to an observer regardless of the motion of the observer's inertial frame?
Those are the same, though I am somewhat unsure of what you mean by the second statement.

The correct statement is:
Consider two observers moving at constant velocity relative to each other. If both observers measure the speed of light in vacuum to be the same, then both observers have inertial reference frames. Any other observers moving at constant velocity relative to these two observers will also have inertial reference frames, and also measure the same speed of light in vacuum.

Edit: I made a slight change to the above statement from "speed of light" to "speed of light in vacuum".

#### atyy

It is just difficult for me to understand that the results from the MM machine could have been used to arrive at a theory like GTR and STR. The machine had to be stable and mechanically exact within 6 e-7 m.
Michelson and Morley's conclusion was "the measured velocity was approximately one-sixth of the expected velocity of the Earth’s motion in orbit and “certainly less than one-fourth.”
I got the Michelson-Morley conclusion from Wikipedia, so I'm not sure it's right. But let's work with it.

Expected velocity = 30 km/s
Measured velocity = 30/4 = 8 km/s
Fractional difference =(30-8)/30 = 0.75 = 3/4

Thus either Michelson and Morley made a 3/4 (not 1/1000,000) error in their apparatus, or the measured velocity is really different from the expected velocity by at least 22 km/s.

Edit: Obviously, that is not enough to prove STR right, nor does it prove that the aether theory cannot be modified to account for the difference, but it certainly puts STR in contention as an alternative to aether theory. If STR is in contention, one needs to use the theory to make predictions, and then check if those predictions agree with experiment (to date, there is complete agreement between STR and experiments).

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#### Constructe

I think he has a correct point here. Space time curves in the face of mass. Thus space time becomes more cureved the more massive a planet gets. This implies that time actually slows in the face of massive object offsetting the stretching of space. If you were walking on the sun and we were watching you from space you would wonder why are we walking so slow. How we got onto this topic from the first I don't quite recall.

I agree that light moves the same speed everywhere in a vacuum with the consideration of the bending of space time from the effects of gravity. I suppose this is what the poster is wondering about. So far no one has witnessed a directional effect of either if it exists but also, no one has actually witnessed a gravity wave or graviton particle either. All we can do is look at the effects and postulate if the effects match a certain explaination.

Can something move faster than light, in theory it is possible. I suppose it would be hard to recognize since it would be percieved going backwards in time and cause and effect won't match to our perception of how we are used to seeing things. Can they go faster than light but move forward in time? Well you'd have to make a exclusion to the know physical properties of the universe as we understand them (like a wormhole where our vision of space time is warped).

#### DewaldS

I got the Michelson-Morley conclusion from Wikipedia, so I'm not sure it's right. But let's work with it.

Expected velocity = 30 km/s
Measured velocity = 30/4 = 8 km/s
Fractional difference =(30-8)/30 = 0.75 = 3/4

Thus either Michelson and Morley made a 3/4 (not 1/1000,000) error in their apparatus, or the measured velocity is really different from the expected velocity by at least 22 km/s.

Edit: Obviously, that is not enough to prove STR right, nor does it prove that the aether theory cannot be modified to account for the difference, but it certainly puts STR in contention as an alternative to aether theory. If STR is in contention, one needs to use the theory to make predictions, and then check if those predictions agree with experiment (to date, there is complete agreement between STR and experiments).
The way I understand it the 8km/h would be 'calculated' back form the infringement pattern. For me that could also mean that one of the mirrors have moved 670nm*8/30.

#### DewaldS

The way I understand it the 8km/h would be 'calculated' back form the infringement pattern. For me that could also mean that one of the mirrors have moved 670nm*8/30.
This calculation of mine is probably nonsense. I will redo it. The point is (and I ask you to check this out) - a substantial 'aether speed' would be needed to cause an asynchronous beam detection, but a REALLY SMALL mechanical deviation will do the same.

#### JesseM

This calculation of mine is probably nonsense. I will redo it. The point is (and I ask you to check this out) - a substantial 'aether speed' would be needed to cause an asynchronous beam detection, but a REALLY SMALL mechanical deviation will do the same.
And again, generations of physicists and engineers have looked at the MM experiment and agreed it was sufficiently well-constructed so we don't have to worry about this sort of mechanical deviation being the explanation, not to mention that the experiment has been repeated over and over and over again by subsequent experimenters with the same result.

#### DewaldS

You are probably right. I will however also look at it until I am satisfied. I think I should rather do it in my own space and time, and once I am equipped to learn more from or contribute to the discussion I will return.

Thanks for all the input, everyone.

#### atyy

Thus either Michelson and Morley made a 3/4 (not 1/1000,000) error in their apparatus
The point is (and I ask you to check this out) - a substantial 'aether speed' would be needed to cause an asynchronous beam detection, but a REALLY SMALL mechanical deviation will do the same.
I think I should rather do it in my own space and time, and once I am equipped to learn more from or contribute to the discussion I will return.

Thanks for all the input, everyone.
Yes, I am not sure I'm drawing the right inference from my calculation. Anyway, this is obviously at the limit of my knowledge of the MMX. I wish you much fun on your studies of it!

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