Entanglement swapping and Bohmian mechanics

[Morbert]

As I have said plenty of times, (2) is mathematically derived from (1). There is no physical meaning to that derivation.

I'm not asking you for physical meaning. That comes after. First we need basic linear algebra.

Ma says something more specific than "(2) is mathematically derived from (1)". He says (2) is a rewriting of (1). Do you accept this?

 

[Sambuco]

Because if you execute a BSM on photons 2 and 3, you do get one of the Bell States of i).

Yeahhhhh!!!!!! That's the key! Before the BSM on photons 2 and 3, the state of the entire system is:

i) |Ψ〉1234 (before BSM) = |Ψ−〉12⨂|Ψ−〉34 = 1/2(|Ψ+〉14⨂|Ψ+〉23 − |Ψ−〉14⨂|Ψ−〉23 − |Φ+〉14⨂|Φ+〉23 + |Φ−〉14⨂|Φ−〉23)

which does not show any entanglement between photons from the pairs (1,2) and (3,4). After the BSM, only one of these terms remains. For example, if Victor measures |Φ+〉23, the state of the entire system after the BSM is:

|Ψ〉1234 (after BSM) = |Φ+〉14⨂|Φ+〉23

Lucas.

 

[Morbert]

@DrChinese I suspect what is happening is when you see me ask whether you accept Ma's words when he says (2) is a rewriting of (1), you are jumping ahead and interpreting this as me asking whether you accept Ma is saying photons 1 and 4 were secretly entangled all along.

I.e. You're misunderstanding the physical significance of a state expansion and thereby refusing to acknowledge state expansions.

 

[DrChinese]

@DrChinese I suspect what is happening is when you see me ask whether you accept Ma's words when he says (2) is a rewriting of (1), you are jumping ahead and interpreting this as me asking whether you accept Ma is saying photons 1 and 4 were secretly entangled all along.

Funny you say that.

In Ma's (1), photons 1 and 4 are not entangled. In Ma's (2), photons 1 and 4 are entangled in all 4 Bell State terms. So... how is (2) a rewriting of (1)? Because they make contradictory assertions, right? Are they "secretly entangled" or not?