Eckard
I found some Feynman material, but decided I probably would not understand it, so I will await your explanation, especially in the context of your essay figs.
As cautioned in your blog, one needs to be sure that references are to SR as defined by Einstein, and not presumed to be 1905, which is not SR.
The null result was not explained by Einstein, apart from the fact that he was wrong anyway. In effect, they just ignored it. The knee jerk reaction was, apart from instinctively finding it difficult to accept, to hypothesise dimension alteration. But the simple fact is that relativity does not rely on that. Here is a quote. The significance of this being it is the first time that the two main errors are formalised, and note the ignoring of the Michelson result.
Poincaré, 1900, page 20:
"It is the case that, in reality, that which we call the principle of relativity of motion has been verified only imperfectly, as shown by the theory of Lorentz. This is due to the compensation of multiple effects, but:...2. For the compensation to work, we must relate the phenomena not to the true time t, but to a certain local time t' defined in the following fashion.
Let us suppose that there are some observers placed at various points, and they
synchronize their clocks using light signals. They attempt to adjust the measured
transmission time of the signals, but they are not aware of their common motion, and
consequently believe that the signals travel equally fast in both directions. They perform observations of crossing signals, one travelling from A to B, followed by another travelling from B to A. The local time t' is the time indicated by the clocks which are so adjusted. If V = 1/√Ko is the speed of light, and v is the speed of the Earth which we suppose is parallel to the x axis, and in the positive direction, then we have: t' = t − v x/V2."
Poincaré, 1900, page 22:
"Suppose T is the duration of the emission: what will the real length be in space of the perturbation?...The real length of the perturbation is L = (V - v')T. Now, what is the apparent length?...the local time corresponding to that is T(1-vv'/V2). At local time t', it is at point x, where x is given by the equations: t ' = t − vx/V2,
x = v'T + V(t - T), from which, neglecting V2:
x = [v'T + V(t - T)](1 + v/V)...The apparent length of the perturbation will be, therefore, L' = Vt' - (x - vt') = (V - v')T(1 +v/V) = L(1 + v/V)."
The main errors in this are:
1 A conflation of light which is used as a timing reference, and is hence deemed to be constant for that reason, and observational light which is just a moving physical entity and therefore has to have its speed calibrated with respect to something.
2 The start of the misuse of the Voigt/Doppler concept of local time, which relates to frequency, ie over time. Although he does in the second para speak of perturbation, but later on this condition is dropped, and everything acquires its own local time.
3 The misconception of distance/length/space. This is not a function of time, it is a spatial differential which does not of itself exist, and can only be identified between two physically existent states which are existent at the same time.
Because we then have this generic nonsense, where Poincaré failed to understand the true relationship of measuring systems, the devices utilised to effect calibration, and the actual conceptual references underpinning those systems. Clocks 'tell' the time, they are not the time. Rulers 'tell' the distance, they are not the distance.
Poincaré, 1902, para 90:
"...that treatises on mechanics do not clearly distinguish between what is experiment, what is mathematical reasoning, what is convention, and what is hypothesis....
1. There is no absolute space, and we only conceive of relative motion; and yet in most cases mechanical facts are enunciated as if there is an absolute space to which they can be referred.
2. There is no absolute time. When we say that two periods are equal, the statement has no meaning, and can only acquire a meaning by a convention.
3. Not only have we no direct intuition of the equality of two periods, but we have not even direct intuition of the simultaneity of two events occurring in two different places.
4. Finally, is not our Euclidean geometry in itself only a kind of convention of language? Mechanical facts might be enunciated with reference to a non-Euclidean space which would be less convenient but quite as legitimate as our ordinary space; the enunciation would become more complicated, but it still would be possible.
Thus, absolute space, absolute time, and even geometry are not conditions which are imposed on mechanics."
Which leads to this nonsense, note how the logic fails as of "but under one condition" (start para 2). Synchronised watches are synchronised, they do not cease to be so because of movement:
Poincaré, 1904, page 6:
"The most ingenious idea is that of local time. Let us imagine two observers, who
wish to regulate their watches by means of optical signals; they exchange signals,
but as they know that the transmission of light is not instantaneous, they are careful
to cross them. When station B sees the signal from station A, its timepiece should
not mark the same hour as that of station A at the moment the signal was sent,
but this hour increased by a constant representing the time of transmission. Let
us suppose, for example, that station A sends it signal at the moment when its
time-piece marks the hour zero, and that station B receives it when its time-piece
marks the hour t. The watches will be set, if the time t is the time of transmission,
and in order to verify it, station B in turn sends a signal at the instant when its
time-piece is at zero; station A must then see it when its time-piece is at t. Then
the watches are regulated."
"And, indeed, they mark the same hour at the same physical instant, but under
one condition, namely, that the two stations are stationary. Otherwise, the time
of transmission will not be the same in the two directions, since the station A, for
example, goes to meet the disturbance emanating from B, whereas station B sees
before the disturbance emanating from A. Watches regulated in this way, therefore,
will not mark the true time; they will mark what might be called the local time,
so that one will gain on the other. It matters little, since we have no means of
perceiving it. All the phenomena which take place at A, for example, will be
behind time, but all just the same amount, and the observer will not notice it since
his watch is also behind time; thus, in accordance with the principle of relativity
he will have no means of ascertaining whether he is at rest or in absolute motion."
You will of course notice all these elements which re-appear in Einstein 1905. And as explained in my post on my blog, it is wrong. M&M were wrong, I suspect simply because they either did faulty calculations &/or their equipment was good, for its day, but not good enough. This is what you are looking at. But in terms of identifying the flaw in relativity, that is a red herring. The faults are actually so simple, ie the misuse of x=vt, and the conflation of existent reality with light reality.
Paul
