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When you envision the vertical bars, the mirror is not moving away from them. They are in the same frame.
Relative to the bars or light waves, the mirror is in the same place when the bottom of a bar contacts it as it is when the top of that bar contacts that mirror. No matter the relative velocity of the moving frame the mirror is not moving away from the light waves.
3. The angle of reflection equals the angle of incidence.It is a good rule of thumb to just add “for all observers” to any rule of physics when in the environment of special relativity. So in this case: The angle of reflection equals the angle of incidence for all observers.
But the mirror is moving away from the light waves if you're viewing the mirror as moving within your frame.
QuoteBut the mirror is moving away from the light waves if you're viewing the mirror as moving within your frame.If the mirror is moving away from the light waves under any circumstance, the mirror is moving at a speed greater than light. We all know that is not allowed.
In the case of the mirror, the mirror is moving away from the light which is closing in on it. The mirror is moving to the right at a high percentage of c, while the light is chasing it at c. The bottom of the wavefront of the light will catch the bottom of the mirror first and begin to reflect off that at the location where it hits it. The mirror continues to move to the right for some distance before the top of the wavefront of the light catches up with it and reflects off it. The effective angle of the mirror will thus, from the point of view of the wavefront of the light that hits it, be different from the actual angle of the mirror.
Within the moving frame containing the Michelson Morley experiment the mirror was stationary in relationship to the light contacting it. Then, judged from the position of the mirror in the relatively moving frame, the speed of the light when it contacted the mirror was c. The speed of the light when it contacted the mirror was always c notwithstanding the relative velocity of the frame which contained the experiment and the mirror because c is constant and the same for all observers. Therefore, there was no difference in the manner light contacted the mirror for any observer.
Alternatively, the relative velocity of the frame had absolutely no influence on the experiment or the angle of the mirror as observed from within the moving frame. The moving frame had a certain velocity relative to one rest frame, a different velocity relative to another rest frame and so on. Judged form within the relatively moving frame the angle of the mirror in the experiment was not different for each possible rest frame. However, because the contraction factor is unique for each relative velocity the angle of the mirror was unique as judged from each unique rest frame.
Of importance is that in the Michelson Morley experiment the angle of the mirror was constant and the angle necessary for the experiment to be operational judged by the observer in the frame with it, no matter the relative velocity of the frame in relationship to any rest frame. But, the relative velocities of the moving frame were different and the angles of the mirror were not the same as the angle judged from within the moving frame, which was the angle necessary for the experiment to be operational, when judged from frames that were at relative rest. Therefore, the experiment which was operational judged from within the moving frame was not operational judged from frames which were at relative rest. In the arena of special relativity either the experiment is operational or the experiment is not operational, not both.
But it isn't constant - if you measure the speed of light relative to you (and your measuring equipment), it will always be c, but if you try to measure it for something in a different frame from yourself (and your measuring equipment), it will not be constant and it will also be different in different directions.
The angle of the mirror is always correct for all frames, so there is no problem with it at all. As the length of one arm contracts, the mirror's angle changes to match, and so does the effective angle of the mirror in relation to how the light interacts with it.
QuoteBut it isn't constant - if you measure the speed of light relative to you (and your measuring equipment), it will always be c, but if you try to measure it for something in a different frame from yourself (and your measuring equipment), it will not be constant and it will also be different in different directions.Here are the words of Einstein himself. This is on line at http://www.bartleby.com/173/Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920Section XIV. The Heuristic Value of the Theory of RelativityParagraph 1“OUR train of thought in the foregoing pages can be epitomised in the following manner. Experience has led to the conviction that, on the one hand, the principle of relativity holds true, and that on the other hand the velocity of transmission of light in vacuo has to be considered equal to a constant c. By uniting these two postulates we obtained the law of transformation for the rectangular co-ordinates x, y, z and the time t of the events which constitute the processes of nature. In this connection we did not obtain the Galilei transformation, but, differing from classical mechanics, the Lorentz transformation.”
Paragraph 3“Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of the space-time variables x, y, z, t of the original co-ordinate system K, we introduce new space-time variables x', y', z', t' of a co-ordinate system K'. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or, in brief: General laws of nature are co-variant with respect to Lorentz transformations.”
QuoteThe angle of the mirror is always correct for all frames, so there is no problem with it at all. As the length of one arm contracts, the mirror's angle changes to match, and so does the effective angle of the mirror in relation to how the light interacts with it.Copy an image of the instrument into an application that allows you to only change the width of the image as the Theory of Special Relativity hypothesizes. The angle of the mirror is increased when the contraction is increased. The angle of incidence is decreased and the angle of reflection is increased (in respect to the “normal”). That is a violation of the law of reflection caused by length contraction on the moving frame as observed from relative rest.
Paragraph 4“This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature. If a general law of nature were to be found which did not satisfy this condition, then at least one of the two fundamental assumptions of the theory would have been disproved. Let us now examine what general results the latter theory has hitherto evinced.”So, Einstein said that contraction occurred which changed the angle of the mirror which violated a natural law and as such a general law of nature was found which did not satisfy this condition and at least one of the two fundamental assumptions of the theory was disproved.
In this paragraph Einstein is chucking out some aspect(s) of Galilean relativity which don't match up with reality, favouring the Lorentz transformation instead. The bit you've underlined simply says that light travels at c, and that is not disputed.
That appears to say that you can translate between frames by applying the Lorentz transformation and the same law will then apply in the new frame.
If you measure it from within its own frame, the mirror is always at 45 degrees. If you measure it from some other frame and see the mirror as having some other angle, you know that you either have to apply the Lorentz transformation to what you're seeing to convert it into a form which allows you to see it as if you are in the same frame as the mirror (in which case it will be at 45 degrees) or you have to analyse what's going on with the interaction between light and mirror in the way that I have described in previous posts - the effective angle of the mirror is the real angle of the mirror as far as the light is concerned, so it behaves accordingly.
If you analyse what's going on carefully, the mirror reflects light correctly because the actual angle of a moving mirror is not the angle that counts - it's the angle which the light "thinks" the mirror is at that counts, because that represents the angle of the mirror which the light experiences.
QuoteIf you measure it from within its own frame, the mirror is always at 45 degrees. If you measure it from some other frame and see the mirror as having some other angle, you know that you either have to apply the Lorentz transformation to what you're seeing to convert it into a form which allows you to see it as if you are in the same frame as the mirror (in which case it will be at 45 degrees) or you have to analyse what's going on with the interaction between light and mirror in the way that I have described in previous posts - the effective angle of the mirror is the real angle of the mirror as far as the light is concerned, so it behaves accordingly.Could you please clarify “you know that you either have to apply the Lorentz transformation to what you're seeing to convert it into a form which allows you to see it as if you are in the same frame as the mirror”
QuoteIf you analyse what's going on carefully, the mirror reflects light correctly because the actual angle of a moving mirror is not the angle that counts - it's the angle which the light "thinks" the mirror is at that counts, because that represents the angle of the mirror which the light experiences. Please clarify this as well.