I Do Different Observers See Different Entangled States in Quantum Mechanics?

[Robert Shaw]

Alice and Bob are partial observers of states in a toy quantum Universe and widely discussed in the literature of Quantum Mechanics.

They see some states as separable and others as entangled. For Alice the partial measurement suboperator is diag(1,1,-1,-1) and Bob is diag(1,-1,1,-1).

Martians Ylc and Zog see the world differently. For Ylc adiag(1,1,1,1) and Zog adiag(1,-1,-1,1) ...antidiagonal matrices. Their eigenvectors are the maximally entangled states for Alice and Bob.

A state is prepared which is observed by Alice and Bob to be separable.

Ylc and Zog observe the same state and find it to be entangled.

This inconsistency between earthpersons and martians seems to be allowed in quantum mechanics.

Unless we invoke a rule that earthpersons cannot communicate with martians.

 

[AlexCaledin]

"Quantum theory is a procedure by which scientists predict probabilities that measurements of specified kinds will yield results of specified kinds in situations of specified kinds. It is applied in circumstances that are described by saying that a certain physical system is first prepared in a specified manner and is later examined in a specified manner."

http://www.informationphilosopher.com/solutions/scientists/stapp/Copenhagen_Interpretation.pdf

So, you must first specify how exactly the measurement is performed, on Earth or Mars, and only after that apply any QM.

 

[Robert Shaw]

"Quantum theory is a procedure by which scientists predict probabilities that measurements of specified kinds will yield results of specified kinds in situations of specified kinds. It is applied in circumstances that are described by saying that a certain physical system is first prepared in a specified manner and is later examined in a specified manner."

http://www.informationphilosopher.com/solutions/scientists/stapp/Copenhagen_Interpretation.pdf

So, you must first specify how exactly the measurement is performed, on Earth or Mars, and only after that apply any QM.

I think I like your answer, but I have doubts that you haven't addressed.

The term "specified manner" sounds reasonable and reassuring but is actually vague.

"I bought it at Aldi" so it's been prepared in a "specific manner".

"I weighed it on my bathroom scales" so it's been measured in a "specified manner".

Specifying the manner of preparation and measurement does not yield good physics.

We need to do more than "specify the manner"...

...but what more do we need!

 

[Demystifier]

For Alice the partial measurement suboperator is diag(1,1,-1,-1) and Bob is diag(1,-1,1,-1).
For Ylc adiag(1,1,1,1) and Zog adiag(1,-1,-1,1) ...antidiagonal matrices. Their eigenvectors are the maximally entangled states for Alice and Bob.

Where did you get this from? Some reference? Some calculation which you can present here?

 

[PeterDonis]

A state is prepared which is observed by Alice and Bob to be separable.

Ylc and Zog observe the same state and find it to be entangled.

Please show your work. As far as I know this is impossible; whether or not a state is entangled is an invariant property of the state, independent of who is observing it.

 

[stevendaryl]

Alice and Bob are partial observers of states in a toy quantum Universe and widely discussed in the literature of Quantum Mechanics.

They see some states as separable and others as entangled. For Alice the partial measurement suboperator is diag(1,1,-1,-1) and Bob is diag(1,-1,1,-1).

Martians Ylc and Zog see the world differently. For Ylc adiag(1,1,1,1) and Zog adiag(1,-1,-1,1) ...antidiagonal matrices. Their eigenvectors are the maximally entangled states for Alice and Bob.

A state is prepared which is observed by Alice and Bob to be separable.

Ylc and Zog observe the same state and find it to be entangled.

This inconsistency between earthpersons and martians seems to be allowed in quantum mechanics.

Unless we invoke a rule that earthpersons cannot communicate with martians.

I don't understand exactly what you're claiming here. Can we use the more traditional Dirac notation for entangled states?

If you have two maximally entangled spin-1/2 particles, then they can be described as being in the composite state:

\frac{1}{\sqrt{2}} ( |u_z\rangle |d_z\rangle - |d_z\rangle |u_z\rangle)

So that's a superposition of two states:

1. |u_z\rangle |d_z\rangle, in which the first particle is spin-up in the z-direction, and the other particle is spin-down
2. |d_z\rangle |u_z\rangle, in which the first particle is spin-down in the z-direction, and the other particle is spin-up

(Choosing any other direction leads to the same composite state, if the total spin is zero)

So what do you mean by saying that it's entangled for the Earthlings, but not the extraterrestrials, or vice-versa?