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There is a simple inference to formula for time dilation on Wikipedia. On this simple inference they take two scenarios:

  1. Observer on the moving frame where the height is represented by letter "H"
  2. Observer on a "stationary" frame where the height is also represented by "H"

My question is: how is possible to assume that on the two scenarios the height is a constant "H" and don't get any king of space transformation?

I have been calculate the same but without assume the "H" constant and get: $$ \Delta T' = \frac{\frac{H'}{c}}{\sqrt{1 - \frac{v^2}{c^2}}}$$ where H' is the height of object viewd from a "stationary" frame.
If H'=H than the formula become the traditional: $$ \Delta T' = \frac{ \Delta T}{\sqrt{1 - \frac{v^2}{c^2}}}$$

So my question is: "How can I assume that the height doesn't change with velocity?
in other words... how is H'=H ?"

Remember: The theory of relativity says about lengh contraction, so is totaly valid think about height contration (or dilatation).

Why is the height constant with velocity and length not?

aguiadouro
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1 Answers1

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If you have two mirrors opposite of each other and move them parallel to their orientation, there is no reason to assume why their distance should vary. In fact, you can do this experiment by installing two guard rails at constant distance and move the mirrors by sliding in between the guard rails (like a sliding door). Clearly, their distance cannot change as the mount is stationary, but the rest of the experiment remains the same.

infinitezero
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