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It is well established that any massless particle, by special relativity, must travel at the speed of light, e.g. Special relativity and massless particles.

Accordingly, this means that massless particles move at the speed of light in every reference frame and experience 'infinite' time dilation with the Lorentz factor equaling 1/0.

In Quantum Mechanics, the evolution of an energy eigenstate which is governed by a time invariant Hamiltonian evolves as $ e^{-i \hat{H}t/\hbar }|\psi_0\rangle$. The first part of my question is: is it possible for a massless particle to change eigenstates at all (or would that only apply to energy eigenstates)? For example, could a photon change chirality without interacting with another particle or would this violate special relativity?

Second, if one can entangle a massive particle with a massless particle, say the angular momentum state of a hydrogen atom to the helicity of an interacting photon (forgive me if this is inaccurate), then can the massless speed of light particle still have its state changed after interaction via entanglement if the state of the massive particle is altered? Wouldn't this contradict special relativity or does this just re-iterate that entanglement is noncausal and/or does not have 'real' hidden variables?

So to reiterate and clarify the question:

1: a massless speed of light particle becomes entangled with another particle via interaction or emission or some process.

2: this massless particle escapes and travels at the speed of light experiencing infinite time dilation.

3: the particle entangled with the massless one is then measured or its state altered.

4: the state change or wavefunction collapse of the entangled particle leads to a change in the massless particle's state via the entanglement (as measured by probabilities of it being in a certain state).

If 1-4 are true this would imply that the massless, speed of light particle just 'evolved' with time in that it changed state. This seems to create a contradiction between special relativity and QM. The reconciliation of this contradiction for such an example is the answer I am looking for.

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Knowledge Quench
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    Have you learnt any Quantum Field Theory? Its very purpose is to reconcile Quantum Mechanics with Special Relativity. – Feel My Black Hole Aug 05 '19 at 23:24
  • Changing the state of a quantum system always requires some interaction with the environment, be it massive or massless. Can you elaborate where you see issues? (I.e., what should an answer address?) – Norbert Schuch Aug 06 '19 at 08:18
  • @NorbertSchuch Agreed, but from another point of view the 'change of state' can occur after the interaction via entanglement and wavefunction collapse of an entangled particle. – Knowledge Quench Aug 06 '19 at 16:50
  • @Feel My Black Hole, nope, but thanks for the pedantic response. Regardless of the formalism describing this interaction, there still seems to be a contradiction in that a speed of light particle is changing. The reconciliation of this contradiction is the answer I am looking for. – Knowledge Quench Aug 06 '19 at 16:50
  • @KnowledgeQuench Sure, but that requires just as much interaction to produce the entanglement in the first place. I'm afraid I don't get your question. – Norbert Schuch Aug 06 '19 at 18:13
  • @KnowledgeQuench The formalism is important. It is well known that non-relativistic Quantum Mechanics and Special Relativity are incompatible. So, of course contradictions can arise. But, if you want to resolve these contradictions, then you need to study Quantum Field Theory. – Feel My Black Hole Aug 07 '19 at 01:13
  • @NorbertSchuch I don't know if you saw the edits in the original comment above, but that example scenario is about as clear and succinct of an explanation of the question as I can think of. The idea would be that the interaction with the particle entangled with the massless particle would not be causally connected with the massless particle. – Knowledge Quench Aug 07 '19 at 16:26
  • @FeelMyBlackHole, ok, well then would you mind showing how in QFT the example descibed above or a similar one would not create a contradiction? That would be a great answer to this question. – Knowledge Quench Aug 07 '19 at 16:28

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