Here I present an exchange between Mr. Mathis and myself regarding the Micelson Morley Interferometer. His analysis of the experiment is incorrect ([url2=
http://milesmathis.com/mich.html]Mathis MM Interferometer[/url2]) because he assigns the two men on the plane (2 light pulses) equal velocities relative to the plane (apparatus) instead of equal velocities relative to the eye (aether). I have not been able to help him see his error and I believe he has lost patience, although he has generally been respectful and patient. I hope that viewers of this forum will be able to see his mistake upon reading his article and our exchange, and may help convince him of it. This would keep this mistake from detracting from Mr. Mathis' higher quality work, giving less excuses for people to dismiss him. He makes some statements which indicate he does not quite understand the aether hypothesis of the time, and we should help him with that.
Note, in these exchanges when I use the word "aether" unqualified it is meant to refer to a passive, stationary medium vis a vis Michelson et. al.
My words are in blue.
Miles' words are in navy.
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Dear Mr. Mathis,
I have visualized, calculated, and otherwise evaluated your analysis of the MM setup. I do think you are mistaken on this particular and have made an error in your analysis.
Light speed is 1. Let us say the lab is moving to the right at .5. Let us say that the distance from the silvered mirror to either of the reflective mirrors is 2 unit distances. According to the aether the horizontal pulse will have to traverse 4 unit distances to get to its reflective mirror. However the vertical pulse will only have to traverse 2.309 {that's 2/sqrt(.75)}, again according to the aether. On the way back the horizontal pulse only has to traverse 1.5 unit distances to get to the silvered mirror, whereas the vertical pulse must again traverse 2.309.
5.5 != 4.619
You have to keep in mind that the pulse always travels the same speed wrt the underlying "grid" (aether). However the distance it must go on this grid varies because of how the interferometer moves.
I've done this over and over every which way. I've even draw it out on grid paper, redrawing the cross translated over .5 grid box lengths and the pulses moved 1 full grid box length over and over and watching the pulses travel. Each "unit time" each pulse must move exactly one box length on the grid. This means when it bounces off the mirror it only moves .866 box lengths toward the reflective mirror, although it still moves a full box length away from its previous location in the aether. The horizontal one moves a full box length relative to its previous location, but only .5 box lengths toward its respective reflective mirror.
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[Alton, Yes, your analysis of the diagram you are using is correct. But the diagram is not correct itself. The diagram you are drawing, in your head or on your paper, is not a correct representation of the situation.
You are using your own visualization instead of mine, so how can you say I am wrong? It is your visualization that is wrong, as I show in the paper. In the paper, I show why your diagram is wrong. Instead of plowing through the standard visualization over and over, look again at my correct visualization. Concentrate on my diagram of the two men in the airplane walking at right angles. That is a correct visualization. I have shown why the standard diagrams are wrong. Tell me why my new diagram is wrong.
You may also want to read my paper on the light clock, and my section on the Lorentz diagram in my long paper on SR. I hit the problem two more times, in slightly different language in those places, and that may jog something in your head where this M/M paper failed. It's tricky, I admit, but I stand by my correction.
Also, remember that I am not critiquing M/M in order to jettison SR. I believe in transforms, I just think the M/M experiment was improperly prepared and improperly diagrammed. The experiment could only find a null answer.
Miles
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Your error is that the velocity of each man in the plane relative to the observer must be the same. This was by hypothesis, the aether stationary frame was "special" because light always propagated in it at the same speed, just like sound in a medium.
It is true that, according to Galileo and Newton, a uniformly translating frame may consider itself not to be moving. The aether physicists of the time, however, were positing that this classical law was broken. They were positing that a uniformly translating frame CAN consider itself to be moving with respect to the aether.
You are analyzing the problem without an aether, without a LCM. You are analyzing the situation as if light were bullets being fired from two perpendicular identical guns.
You are analyzing the same experiment with different coordinates. Of course the results of an experiment are independent of the coordinates used to analyze it. You have to perform (at least 2) *different* experiments. According to Michelson and Morley (and almost everyone else at the time), the difference between the lab moving through the aether at v and the motionless wrt the aether was not just a difference of coordinates. They were 2 physically distinct scenarios.
If there were, indeed, a passive and motionless underlying aether, then the experiment would have yielded a "fringe effect" and motion would no longer be considered "purely relative" as Galileo and Newton had proposed. These physicists were willing to overturn Newton on this because it was the only way they could conceive of light to propagate. This was the point of the experiment!
You are analyzing the experiment from the POV of someone who a priori assumes there is no such thing as "absolute motion". Of course if you posit there is no absolute motion, there would be no point in doing the experiment! The point is, these people thought there may indeed be "absolute motion" and the MM interferometer was implemented to test this idea.
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Dear Mr. Mathis,
Do not misunderstand me. We are both "correct", it's just that your analysis does not presuppose a stationary frame in which light always propagate with a certain velocity.
The mistake physics has made since then, however, is that despite the results of the experiment the concept of an underlying "grid" has not been foregone. The aether is still retained, pulses of light are still imagined to traverse these hypothetical "hypotenuses" between comoving source and receiver. The status quo has been to, instead of rejecting the aether, embracing mathematical abstractions that keep all the numbers coming out right. So, to save the diagonal aether trajectory there must be some amount of length contraction and time dilation as quantified by the Lorentz xformations.
You correctly point out that these xformations are derived by analyzing imaginary itineraries of light. I agree. Again they come from insisting upon the idea of an aether against all evidence, and against the very concept of relative motion itself! So we have, today, overly abstract mathematics because we are trying to force Nature to fit into our idea of an aether. The math is being contorted around a superfluous and unobservable hypothesis.
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Let's stick to your first paragraph. You say that I hypothesize that each man in the plane must have the same velocity relative to the observer. But I don't. My given is that the men have equal velocities relative to eachother and to the plane. Then I seek the velocities relative to the observer. I actually find that the men don't have equal velocities relative to the eye. I say that in plain language. I only find that they must return to home at the same time. Completely different. And my finding is not found by making any hypothesis, it is found by analyzing the logic and kinematics. I don't get the feeling you are actually reading my words, you are pre-judging the sentences based on something else, I don't know what.
The fact is, there is no way to create a fringe effect, except by making false assumptions or by creating bad diagrams.
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The assumption of the time was that the velocities of the men were equal with respect to the eye because the "eye" was actually a medium. Light was considered to be exactly like sound. If you perform the Michelson-Morley experiment with sound you will detect a "fringe effect", i.e. if you rotate such an apparatus (with tuning forks or some other sound apparatus) on a moving train you will detect "sound speed anisotropy".
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"My given is that the men have equal velocities relative to eachother and to the plane."
And this is exactly the problem. The plane is the apparatus. You are declaring the light pulse velocities to be equal with respect to the apparatus. But that was not consistent with the aether hypothesis of the time. The aether hypothesis of the 18th century stated that the light pulse velocities were equal with respect to the "eye" (stationary aether).
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You are arguing in circles. In the first email, you say that my problem is that I assume the men have equal velocities relative to the ether. In the next email you say that my problem is that I assume they don't, but that I should because that is what they thought in the 19th century. I can find no futher reply to that sort of polemic.
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Reread my 1st e mail, I did not state your specific problem in the 1st e mail.
However the 1st sentence of my 2nd e mail is:
Your error is that the velocity of each man in the plane relative to the observer must be the same.
And in my 3rd e mail:
The assumption of the time was that the velocities of the men were equal with respect to the eye because the "eye" was actually a medium.
And my 4th and most recent e mail, quoting you and giving my response:
"My given is that the men have equal velocities relative to eachother and to the plane."
And this is exactly the problem. The plane is the apparatus. You are declaring the light pulse velocities to be equal with respect to the apparatus. But that was not consistent with the aether hypothesis of the time. The aether hypothesis of the 18th century stated that the light pulse velocities were equal with respect to the "eye" (stationary aether).
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Sorry. I suppose I misread your second email. That sentence is ambiguous. My reading of it is valid, but it is clearly not the one you intended. I read it to mean that my error was that (in my explanation) the velocity of each man relative to the observer must be the same.
At any rate, all motion must be relative to a background, either in classical theory or relative theory. Relativity just makes that background local always. If you use a non-local background, you need a transform. So in this problem you must choose either the eye or the plane as the background. You say that the assumption in the 19th c. was that we choose the eye. The men are defined as equal from the start, relative to the ether. And my point in the various papers is that that is a stupid assumption from the beginning, one that leads to stupid diagrams. It is a stupid assumption even if you believe in the ether and don't believe in relativity. In my airplane example, I have an ether defined by the eye, and I don't use relativity to explain anything. But I still show, by simple logic, that the men must return to the same point at the same time, and be seen to do so from the eye. Neither classical mechanics nor relativists should expect a fringe.
The assumption that the velocities are equal relative to the eye leads to absurd local velocities (relative to the plane), ones that would conflict with commonsense data in the plane. That is why the boats analogy is so twisted. THe assumption is also absurd because it is immediately contradictory. It assumes the men have the same velocity relative to the ether, but that they don't. They do, in order to match a nebulous theory of propagation, but then they don't, in order to show a fringe. You see, if they have the same velocity relative to the ether, then they can't show a fringe. It is assumed that the directional difference will create a fringe, but if it does, then the absolute velocity relative to any point in the ether can't be the same. Since velocity is a vector, you can't define the velocity as equal, and then find that it is unequal. If you find that it is unequal, then your definition or assumption must have been wrong.
The real problem here is not the use of an ether, or no ether, since either with or without an ether there should be no fringe effect. The problem, as you point out, is that the 19th c. theorists assumed that light traveled like a sound wave, as a field wave. Contemporary physicists who accept relativity still believe that, since they can't figure out how else light can show a wave. But since light isn't a field wave, it should never have been expected to show a fringe. The M/M experiment was really a test of the field wave theory, not of the ether. I have shown that you can still do mechanics with or without an ether. You can do relativity with or without an ether. M/M was no proof or disproof of an ether, since you can't disprove an ether. An ether is a mathematical convenience, one you can take or leave. But M/M was a clear disproof of the field wave model of light, a disproof that contemporary physicists still haven't penetrated. That was the point of that paper and all my papers on M/M.
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" But I still show, by simple logic, that the men must return to the same point at the same time, and be seen to do so from the eye."
This is only true if the men do not have a constant velocity relative to the aether/eye, contrahyp.
"The assumption that the velocities are equal relative to the eye leads to absurd local velocities (relative to the plane), ones that would conflict with commonsense data in the plane."
If the data on the plane indicate the two men are traveling equal velocities then that's what they're doing. If the data on the plane indicate the two men are traveling unequal velocities, that is what they're doing. Neither set of data is "absurd" or more/less "commonsense". It is measured one way or the other. Or, in a thought experiment, it is stated as one way or the other. Michelson et. al, in their thought experiment, considered the men to not be moving at the same velocity relative to the plane, but rather at the same velocity relative to the eye/aether. This is consistent with the behavior of sound.
"THe assumption is also absurd because it is immediately contradictory. It assumes the men have the same velocity relative to the ether, but that they don't."
Incorrect. They have the same velocity relative to the aether but different velocities relative to the plane and each other.
"You see, if they have the same velocity relative to the ether, then they can't show a fringe."
Again, incorrect. Each light pulse travels a different distance but identical velocity through the aether. Each pulse sees itself traveling at c. But each one watches its destination mirror get dragged away at a different rate.
"The real problem here is not the use of an ether, or no ether, since either with or without an ether there should be no fringe effect. The problem, as you point out, is that the 19th c. theorists assumed that light traveled like a sound wave, as a field wave."
I agree completely, and I think you make excellent points about light "being itself" (for lack of a better way to summarize everything you've said". i.e. it's not a motion of something else, it is a motion of itself.
I also agree that the luminiferous aether was poorly conceived from the beginning. It went against centuries of empirical and theoretical ideas from Galileo to Newton to Mach. It attempted to overturn the principle that all motion is only relative. However that doesn't make their idea "impossible". There was no way to know, as a physicist (i.e. barring philosophical and metaphysical arguments) that light wasn't an undulation/wave of some fluid.
As you correctly point out, the experiment debunked the notion that light was some kind of "field wave". It debunked the concept that atoms sent out pulses of light like a buoy in the ocean sends out ripples, haphazardly and indiscriminately. An atom in the silvered mirror does not pulse and send out a little ripple that must wade through a medium. An atom in the SM pulses and sends a signal straight to an atom in the other mirror. It does not see a medium, there is no "extra distance" through the aether. The pulse traverses the length of the arm and back, period. Objectively that's all we have before us, a distance from the silvered mirror to the other mirror.
As you cogently point out, modern physicists have incongruously retained the debunked "field wave" model of light! Instead of developing a different model:
http://www.youtube.com/watch?v=J-NB5vg7woM
they retained this model, and the subsequent imaginary trajectories of light trough the aether (pythagorean trajectory in the perpendicular arm, (L/c+v)+(L/c-v) trajectory in the parallel arm). In retaining these trajectories they had to alter L to bring their debunked model into line with experiment, so in comes gamma.
Their conclusion: our model of light wasn't wrong, we just didn't account for the velocity-dependent contraction we just now made up a posteriori.
So I agree with the conclusions you draw, and I understand your point, but your presentation wrt the field wave theory of the pre-interferometer era is not fair to these theorists. As much as we may object to their "field wave" hypothesis there was no empirical reason for them to a priori reject it outright (although I'd argue there was reason for heavy doubt). The MM experiment was a definitive empirical refutation of any concept of absolute motion. It laid this idea to rest for good, no longer should there be any debates that there is such a thing as absolute motion or absolute rest, the MM experiment turned a debate that waxed a bit too philosophical for there to be a broad scientific consensus on into an unambiguous empirical result. For that Michelson/Morley do indeed deserve some credit, your presentation does not analyze the experiment in a fair or accurate scientific context. Their hypothesis was not mathematically contradictory (it was mostly opposed, by any that did oppose it, on philosophical and metaphysical grounds).
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The data on the plane could not indicate they were traveling unequal velocities, given this problem. That is my point. The experiment needs to address that fact, and it can't. It just buries it under a bad diagram. If the velocities are equal from the eye, they can't be equal in the plane. But they must be equal in the plane, so they can't be equal from the eye. The 19th c. physicists thought, "If they can't be equal from the eye, there must be a fringe effect." But that was a false assumption, since, even though the velocities are unequal from the eye, the final position is equal, from both eye and plane. Since that is how the interferometer was set up, it couldn't find a fringe effect even with unequal velocities measured from the eye.
I am sure we must both be tired of saying the same things over and over. I am not "incorrect" about anything here. I appear to be stating things in a way you don't approve of, or don't agree with, or don't understand, but that is a different matter. At any rate, I would prefer to move on.
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"The data on the plane could not indicate they were traveling unequal velocities, given this problem. That is my point. The experiment needs to address that fact, and it can't."
This is simply untrue. If the velocities of the men are equal with respect to the eye they are unequal with respect to the plane. This is simply an irrefutable kinematic fact. There is nothing contradictory or impossible going on in such a thought experiment. This is precisely what the experiment was trying to determine, if the velocities were constant with respect to the apparatus (plane) or with respect to a hypothetical eye (aether).
"The 19th c. physicists thought, "If they can't be equal from the eye, there must be a fringe effect." "
No, the 19th c. physicists thought the OPPOSITE. If the velocities ARE equal from the eye, there must be a fringe effect. Since there was no fringe effect, the conclusion is that the velocity with respect to the hypothetical eye is not constant. In effect, the plane behaves as if the eye were not there at all, and the conclusion was by many that there was indeed no aether there at all.
Actually to be thorough there is the 3rd route, which physics has unfortunatly decided to go, and that is in retaining the aether and stating the the velocity is constant wrt the eye AND wrt the plane, quite a magic trick that modern physics has pulled off.
"I am sure we must both be tired of saying the same things over and over. I am not "incorrect" about anything here."
You have made 2 incorrect statements in this past e mail. You have contradicted a basic fact of kinematics and you have stated that the postulate of Michelson et. al was the opposite of what it actually was.
It is not a matter of my inability to understand or my personal preference for your mode of communication. You are in error and I am striving to help you see it. Had I not such high respect for much of your work and your thinking in general I would not take such effort.
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Once again, I disagree: it is your inability to understand me, as you make clear again here. You twist everything I say to fit your own understanding, and fail to see that I am seeing things here that you are not. But I am finished. I don't have time to trade infinite emails with everyone who writes me.