First time posting in this section. I understand that this question could possibly be an old and common question about Lorentz Transformation, however I failed to find useful discussions or instructions online.(adsbygoogle = window.adsbygoogle || []).push({});

Assuming that there're 2 frames ##S, S'## where ##S'## moves along the ##x_{+}## axis of ##S## at constant speed ##v##. The frames coincide at ##<0,0,0,0>## (as well as their rectilinear coordinate axes) for a starting event ##P## and then measure ##<x, y, z, t>## and ##<x', y', z', t'>## respectively for event ##Q##.

According to Lorentz Transform I shall have:

##x'=\gamma \cdot (x-vt)##

##t'=\gamma \cdot (t-\frac{vx}{c^2})##

where ##\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}##

Now that ##\frac{dx'}{dx} = \gamma## which indicates that ##\frac{dx'}{dx}## is independent of the direction of ##v## along the ##x## axis. However it doesn't make sense to me here. If I introduce a 3rd frame ##S''## which moves along the ##x_{-}## direction of ##S## at a constant speed ##v##, then should I get ##\frac{dx''}{dx}=\gamma## as well and further ##dx'' = dx'## (which should NOT hold bcz ##S'## and ##S''## are dynamic to each other)? Did I make a mistake in the calculation?

I'm quite confused for how "some degree of symmetry" (for relation of ##dx, dx', dx''## above) could be achieved if Lorentz Transformation is true. Any help will be appreciated :)

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# How to determine which frame measures "larger" dx?

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