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I'm in the middle of reading 'The Great Equations' by Robert P. Crease (good book) and I've just got to the chapter on E=mc^2. The chapter covers Einstein's original thought experiment. You know, the one with the mirrors and the stationery / moving observers. I've worked through the maths associated with the experiment and as you'd expect the suggested formula does fall out of the end.

Many, many years ago, at school, we were always taught to feed the results of any calculations back into the starting point of the calculation to make sure that they make sense. Here the starting point is the diagram used to introduce the starting values. Feeding V=0 back into the mirror's experiment is straight forward enough, but what happens when you plug V=c back in ?

The default presentation of the diagram associated with this experiment already appears to represent the situation where V=c. ie. twice the distance between the mirrors, matches the distance travelled by the moving observer. This being the case, the original diagram represents the limits of the experiment, where V=c, and the distance travelled by the moving observer can never be more than the distance shown on the diagram.

If this is the case, then it seems to me that the limit of the time dilation factor, that can be derived from this thought experiment, is d/sqrt(2d^2), d/sqrt(2)d, 1/sqrt(2), or approx. 0.71. A smaller value would necessitate half the distance travelled by the moving observer to be greater than the distance between the mirrors. For this, the traveller would have to travel faster than c.

This obviously doesn't agree with the final formula. Where am I going wrong ? How would V=c be represented in the diagram ?

Many, many years ago, at school, we were always taught to feed the results of any calculations back into the starting point of the calculation to make sure that they make sense. Here the starting point is the diagram used to introduce the starting values. Feeding V=0 back into the mirror's experiment is straight forward enough, but what happens when you plug V=c back in ?

The default presentation of the diagram associated with this experiment already appears to represent the situation where V=c. ie. twice the distance between the mirrors, matches the distance travelled by the moving observer. This being the case, the original diagram represents the limits of the experiment, where V=c, and the distance travelled by the moving observer can never be more than the distance shown on the diagram.

If this is the case, then it seems to me that the limit of the time dilation factor, that can be derived from this thought experiment, is d/sqrt(2d^2), d/sqrt(2)d, 1/sqrt(2), or approx. 0.71. A smaller value would necessitate half the distance travelled by the moving observer to be greater than the distance between the mirrors. For this, the traveller would have to travel faster than c.

This obviously doesn't agree with the final formula. Where am I going wrong ? How would V=c be represented in the diagram ?

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