Special Relativity and reference frames

AI Thread Summary
The discussion focuses on a mathematical problem related to special relativity, specifically the equation (\Deltax')2 = (\Deltax)2 - c2(\Deltat)2. The poster seeks guidance on how to approach proving that this equation holds true across all reference frames. It is suggested that the solution involves using Lorentz transformations to relate the coordinates (x', t') and (x, t). The key goal is to demonstrate that the differences in spacetime intervals remain invariant under these transformations. Understanding the relationship between time and space in different frames is crucial for solving this problem.
authenticgeek
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Here's a statement that I'm supposed to solve:

(\Deltax')2 = (\Deltax)2 - c2(\Deltat)2

And the accompanying text: "Show that (the equation above) is the same for all reference frames in special relativity"

I consider myself somewhat decent with your basic special relativity calculations but I'm having trouble starting this one. I'm not interested in an answer as much as a gentle nudge in the correct direction.

What is this question asking for, mathematically? I don't even know where I should be ending up...
 
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It's asking you to assume (x',t') and (x,t) are related by a Lorentz transformation and show that (delta t')^2*c^2-(delta x')^2=(delta t)^2*c^2-(delta x)^2.
 

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