Please note that my question is not a duplicate, it is not about the speed of light, my question is only technical about the four velocity vector for light, its definedeness, value and constantness.
I have read these questions:
What is the time component of velocity of a light ray?
Where Izhov says:
Four-velocity actually isn't well-defined for light.
And where ClassicStyle says in a comment:
The four velocity of light is perfectly well defined. You just can't use proper time to parameterize the world line. Four velocity is just the tangent vector to a world line
Are components of the velocity of light equal to $c$?
https://en.wikipedia.org/wiki/Four-vector
The four-velocity defined here using the proper time of an object does not exist for world lines for objects such as photons travelling at the speed of light
Why is light affected by time dilations in space-time curvatures
Where Safesphere says in a comment:
The magnitude of the 4-velocity of light is always zero (see my comment above).
The (always) non-zero time component of the 4-velocity of light does NOT mean that light moves in time. To calculate the 4-velocity of light, we have to use a different affine parameter instead of proper time, because the proper time of light is always zero.
Now this is confusing. Light must have a four velocity vector, but it seems to be either well defined or not, and it seems to have a magnitude of 0 or c and it seems to be always constant or not.
Questions:
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Which one is right, is the four velocity of light well defined or not?
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Is the magnitude of the four velocity vector for light always constant?
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Is the magnitude 0 or c?
Best Answer
From "A First Course in General Relativity":
The immediate problem for the case of a photon is that it does not have a frame. Schutz makes this explicit here:
So, by the above, the answer to your first question is: the four-velocity is not defined for photons.