# Why is the number-flux four-vector frame-independent？

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GR191511
Recently I started studying 《A First Course in General Relativity》 and I came across a question in my book:
##\vec N =n\vec U##where n is number density,U is four-velocity,N is number-flux four-vector .The following sentence confused me:
In Galilean physics,number density was a scalar,the same in all frames(no Lorentz contraction),while flux was quite another thing:a three-vector that was frame dependent,since the velocities of particles are a frame-dependent notion.Our relativistic approach has unified these two notions into a single,frame-independent four-vector...
I wonder Why the number-flux four-vector is frame-independent？

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All four-vectos are frame independent

You should read page 88 (in the second edition) where it is explained what 'frame independent' means in this case

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GR191511, dextercioby and PeroK
2022 Award
I wonder Why the number-flux four-vector is frame-independent？
Because it's a four vector. They're frame independent by construction.

I think what you need to do is convince yourself that ##nU^a## actually represents something meaningful, and that it represents something meaningful whether ##U^a## is parallel to your frame's timelike axis or not. The usual way to go about it is to imagine a very large number of particles each with velocity ##U^a##. Then convince yourself that the number of particles crossing an infinitesimal plane depends on the number density ##n## and the velocity field ##U^a##, then convince yourself that the transformation properties of ##U^a## supply the right factors of ##\gamma## so that the transformed flux density behaves as you expect.

GR191511, PeroK and vanhees71
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