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    A Time Dilation Paradox?

    (Quibble) Almost correct. Mathematically that should be: If ##Δx_A=0## then ##Δt_B>=Δt_A## and If ##Δx_B=0## then ##Δt_A>=Δt_B##. And then, if they insist on having them both in one scenario, then clearly: If ##Δx_A=Δx_B=0## then ##Δt_B>=Δt_A## and ##Δt_A>=Δt_B##, and thus...
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    Maxwell's distribution

    Good question. See Maxwell–Jüttner distribution.
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    Perspective on Relativity and Length Contraction

    Fwiw--not much apparently--I think you missed the point, but feel free not to lose any sleep over it :cool:
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    Perspective on Relativity and Length Contraction

    Nice diagram! Fwiw, note that : (*1) in the top figure, where Red touches the green car simultaneously with both hands, Green protests and says that Red is cheating because he does not touch his green car simultaneously. According to Green, Red touches the green car's front too late and the...
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    Derivation of Schwarzschild radius from escape velocity

    There's a nice comment about that on page 2-22 of http://www.eftaylor.com/pub/chapter2.pdf
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    Length contraction clarification

    It's pretty common jargon: https://www.google.com/search?q="spacetime+interval"&tbm=bks
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    How does Maxwell equation suggest that the speed of light is the same

    (Quibble) ... which will or will not falsify the postulates. I think that "validate" is too strong, as it might be interpreted as a synonym of "prove".
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    SR question

    No, more like, from a distance you look smaller to me, and I look smaller to you.
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    Problem with relativity

    Measured time differences increase by a factor gamma, but c.t' = c.t.gamma only for x=0 (see Wikipedia Time dilation) Measured distances decrease by a factor gamma, but x' = x/gamma only for t'=0 (see Wikipedia Length contraction) Combining these two clearly distinct situations with two events...
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    Four amateur questions about gravity and general relativity

    Nah. Gravity can be modeled with geometry. The former is physical and the latter is mathematical. The Sun has a LOT of mass.
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    Spacetime diagram drawing problem

    Lots of diagrams at https://en.wikipedia.org/wiki/Slope
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    Spacetime diagram drawing problem

    To get a slope 1/2 between the horizontal and a line, you do *not* bisect the 45 degrees angle. Instead you draw a line with slope 1/2, which means climbing 1 unit for every 2 units of horizontal displacement. That gives an angle of 26.6 degrees, not one of 22.5 degrees. See...
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    Spacetime diagram drawing problem

    Then you need Arctan(1/2) between the ct-axis and the ct'-axis, and thus 45 degrees -Arctan(1/2) between the ct'-axis and the light diagonal.
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    Spacetime diagram drawing problem

    Oops, I meant 45 degrees - Arctan(1/2) = 18.4 degrees.
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    Spacetime diagram drawing problem

    Try using an Arctan(1/2) = 26.6 degrees angle.
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    Bell’s spaceship paradox

    From the travelers point of view they don't accelerate the same way. The one in front moves away from the one behind. The thread breaks.
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    Trying to reconcile Lorentz Transformation and Length Contraction

    It means making a measurement that is simultaneous with the (x',t') = (0,0) event in my coordinates. You and the lamp post are moving in my frame, so I must make sure that I measure the distances to you and to the lamp post simultaneously. You are at distance x'=0 at my time t'=0, so I must...
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    Time moves forward, what if you move UP or DOWN? Does time stop?

    "Moving with the arrow of time" is just fancy speak for "growing older". As far as we know, we can't grow younger, hence the "arrow". It points "where" we go.
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    Ratio of proper clock rates?

    Worth a little texercise: \begin{align} \Delta x' &= x'_2 - x'_1 &\quad \Delta t' &= t'_2 - t'_1 \\ &= \gamma \ ( x_2 - v \ t_2 ) - \gamma \ ( x_1 - v \ t_1 ) & &= \gamma \ ( t_2 - \tfrac{v}{c^2} x_2 ) - \gamma \ ( t_1 -...
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    Ratio of proper clock rates?

    Thanks to its linearity, the Lorentz transformation works perfectly on coordinate differences between pairs of events.
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