What is wrong in this reasoning about CPT symmetries?

Spatial inversion P preserves spin and inverses velocity. (See wikipedia,
at http://en.wikipedia.org/wiki/P-symmetry )

Motion or time inversion T inverses both spin and velocity (obvious, see also wikipedia,
at http://en.wikipedia.org/wiki/T-symmetry ).

Now, charge conjugation C preserves chirality. ( http://en.wikipedia.org/wiki/Charge_conjugation )
That means that either spin and velocity are both inverted or they are both preserved.

But: In either of these two cases, C cannot be equal to TP.
Now, C=TP is a deep theorem in physics!
What is wrong in this argument chain?

François
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 Nobody really says that C=PT, not in the sense that you get identical results from applying these two symmetries. In a classical world, C, P, and T are all symmetries by themselves. Meaning, you can take a physical process or an area of spacetime and apply C or P or T and you get a new valid process. In a quantum world, P is not a symmetry, because it takes valid weak-interaction processes into invalid processes. It is maximally violated by the weak interaction. CP is a lot better. The CPT theorem essentially states that you can take any valid process, apply C, P, and T (reverse spins and replace all particles with antiparticles), and you ALWAYS get a valid process.

 Quote by hamster143 Nobody really says that C=PT, not in the sense that you get identical results from applying these two symmetries. ... The CPT theorem essentially states that you can take any valid process, apply C, P, and T (reverse spins and replace all particles with antiparticles), and you ALWAYS get a valid process.
Oh, I understand. I have read so often that CP and T are either both broken or both
conserved that I thought that this means that CP equals T. Ok, that is wrong.
Thanks!

François

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