Relativistic force

  • #1
hi,
i was tryin to learn some relativistic particle dynamics and came across reltivistic force
[tex]m\frac{d^{2}x}{d\tau^{2}}[/tex],how does this help in transforming forces between reference frames?i dnt understand how this wrks since the vale of velocity changes with time
 
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Answers and Replies

  • #2
Bill_K
Science Advisor
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Lostinthought, this is the most useful way to write F = ma in special relativity because it's manifestly covariant. That is, the position vector x = (x, ct) is a 4-vector. The mass m is a scalar, and the proper time τ is a scalar. Therefore dx/dτ and d2x/dτ2 are also 4-vectors, and when you write F = m d2x/dτ2 you know that F will be a 4-vector too.

If you tried to express the same equation in terms of the coordinate time derivative d/dt you would not only have to deal with explicit factors of γ, but even a term involving dγ/dt.
 

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