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Consider a pole of 1 light second long in the ##y## direction (the vertical line(s) in the enclosed figure). It is moving in the ##-x## direction. According SR, the pole's length is not contracted because its length is not parallel to the propagation direction. However, given the time of flight of light, a signal from the pole's end will arrive 1 second later than a light signal from the pole's start. Given the pole is moving, one would expect an aberration of the pole's end. In the figure I have drawn a triangle, with the hypothenuse indicating the aberration angle ##\phi##. The horizontal line depicts the speed.
Both triangles in the figure are identical, the labeling of the sides is according to Lorentz's triangle that defines the ##\gamma## factor. The labeling of the sides of the lower triangle are obtained by dividing the labels of the upper triangle by the ##\gamma## factor.
When observing the moving pole in a rest frame one would expect that the hypothenuse is slanted to the left (think of mirror images of these figures). Choosing a frame where the pole is at rest, one would observe (by taking a picture) an aberration as shown in the figure. But SR does not predict this. It would predict no aberration.
Further, a peculiar issue is shown in the figure. The bottom triangle indicates that the vertical line is contracted by the ##\gamma## factor, which is not predicted by SR. The upper triangle does not suggest length contraction of the vertical line (the pole), but shows that the hypothenuse is dilated by the ##\gamma## factor.
I am trying to figure Lorentz's assertion of length contraction that explained the null result of MM and the above is a representation of one the light-arms involved.
Both triangles in the figure are identical, the labeling of the sides is according to Lorentz's triangle that defines the ##\gamma## factor. The labeling of the sides of the lower triangle are obtained by dividing the labels of the upper triangle by the ##\gamma## factor.
When observing the moving pole in a rest frame one would expect that the hypothenuse is slanted to the left (think of mirror images of these figures). Choosing a frame where the pole is at rest, one would observe (by taking a picture) an aberration as shown in the figure. But SR does not predict this. It would predict no aberration.
Further, a peculiar issue is shown in the figure. The bottom triangle indicates that the vertical line is contracted by the ##\gamma## factor, which is not predicted by SR. The upper triangle does not suggest length contraction of the vertical line (the pole), but shows that the hypothenuse is dilated by the ##\gamma## factor.
I am trying to figure Lorentz's assertion of length contraction that explained the null result of MM and the above is a representation of one the light-arms involved.