Is it allowed to have the zeroth-component of a four-velocity be negative? This is referring to V_0 for a curved space metric with signature −+++.

motsetjela 2022-08-12 Answered
Is it allowed to have the zeroth-component of a four-velocity be negative?
This is referring to V 0 V^0 for a curved space metric with signature + + + -+++ .
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Answers (1)

Uriel Whitehead
Answered 2022-08-13 Author has 8 answers
The four velocity is
U μ = d x μ d τ
where τ is the proper time. U 0 < 0 implies that d t d τ < 0, i.e. the particle is moving backwards in time. There is an out of date interpretation, popularised by Feynman, that a particle moving backward in time can be thought of as an antiparticle moving forward in time, but this has fallen out of favour because it causes a great deal of unnecessary confusion. Normally the situation you describe is considered unphysical since the energy of the particle would be negative and unbounded from below.

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