Little issue regarding physical states

For a single observer, the concept of Hilbert space is much more problematic than in quantum mechanics. To say that an observer, with his own preferred frame, has a Hilbert space with rays (pure states) is a great approximation, but not very precise. To begin with, the observer's Hilbert space is that of the observer. Then, the "same state" in other Hilbert spaces is not the same ray, but a state which is the result of applying a unitary transformation to the original observer's state. Thus, the observer cannot have a state in a different Hilbert space, but only a transformation of such state (which can be a mixed state).In summary, the QM postulate
  • #36
mikeyork said:
No. The op's question was about an invariant ray (state vector). I really don't understand how you don't get this distinction.
of course, whether the ray is time dependent or not depends on the chosen picture of time evolution. In the Heisenberg picture it's time-independent by definition.
 
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  • #37
vanhees71 said:
I've never seen that notation either, and I don't know what it should be good for, and I've also no clue how you come to conclude from what I wrote before, I'd suggest to use it.
#6 shows what it is good for.
 
  • #38
vanhees71 said:
of course, whether the ray is time dependent or not depends on the chosen picture of time evolution. In the Heisenberg picture it's time-independent by definition.
The OP was about a much more general frame transformation -- not just time evolution.
 

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