Four-velocity of massless particle

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Discussion Overview

The discussion revolves around the concept of four-velocity for massless particles, particularly whether it can be defined or normalized. Participants explore the relationship between four-velocity and four-momentum in the context of massless particles.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether the four-velocity of a massless particle is defined.
  • Another participant asserts that while the world line of a massless particle has a tangent vector, it is a null vector and cannot be normalized.
  • A different participant suggests that the four-momentum vector for a massless particle, being a null vector, may imply that a four-velocity vector could exist in the limit as mass approaches zero, although both components would be infinite.
  • Some participants discuss the relationship between four-momentum and four-velocity, noting that for timelike four-momentum, the four-velocity can be expressed as four-momentum normalized to one, but this does not hold for null four-momentum.

Areas of Agreement / Disagreement

Participants express differing views on the definition and normalization of four-velocity for massless particles, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants highlight the limitations of normalizing null vectors and the implications of mass approaching zero, but do not resolve these issues.

sweet springs
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is defined or not? Thanks.
 
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Since it is the tangent vector of the particle's world line normalised to one, no. The world line of the particle still has a tangent vector, but it is a null vector and therefore cannot be normalised.
 
Thanks a lot.
 
Let me rethink about it. 4-momentum vector for massless particle is also a null vector. We may regard 4-momentum vector as 4-velocity vector multiplied by mass m.
So 4-velocity vector as 4-momentum vector divided by m may be able to exist even in the limit of m to be zero. Normalizable to one but both time and space componebts are infinit. How do you think of that ? Best.
 
sweet springs said:
We may regard 4-momentum vector as 4-velocity vector multiplied by mass m.

For a timelike 4-momentum, yes, because the mass m is just the norm of the 4-momentum, so expressing 4-momentum as 4-velocity times m is just another way of saying that the 4-velocity is the 4-momentum normalized to one.

For a null 4-momentum, you can't do that, because, as Orodruin said, you can't normalize a null 4-vector.
 
Thanks. Now I know better.
 

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