
Black Holes + Wormholes = Quantum Answers - jonbaer
http://www.npr.org/blogs/13.7/2013/07/29/206652461/black-holes-wormholes-quantum-answers
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ivan_ah
The links to the original papers:

older one:
[http://arxiv.org/abs/1005.3035v1](http://arxiv.org/abs/1005.3035v1)

recent one: [http://arxiv.org/abs/1306.0533](http://arxiv.org/abs/1306.0533)

Very cool. The paper suggests a connection between the non-local properties of
EPR pairs and the non-local properties of wormholes that connect distant
regions of space time.

EPR pair = Einstein-Podolsky-Rosen pair, e.g.

    
    
        |Phi〉 = |0〉⊗|0〉+ |1〉⊗ |1〉.               (1)
    

The vectors to the left of ⊗ represent the state of Alice, the vectors to the
right of the ⊗ represent Bob's state. The + in the equation refers to the
notion of quantum superposition.

There is nothing mysterious about quantum superposition. You know how y=sin(x)
and y=cos(x) are both solutions to y''+y=0? Well then any linear combination
of sin and cos is also a solution:

    
    
        y  = a*sin(x)  +  b*cos(x).
    

Similarly, in QM, a quantum states |v〉is described by linear combinations of
some reference vectors |0〉and |1〉

    
    
        |v〉 = a|0〉+ b|1〉.
    

For example, the vector |+〉=|0〉+ |1〉 points half-way between the direction
|0〉and |1〉. However, we cannot describe |Phi〉as the tensor product of two
local descriptions:

    
    
        |0〉⊗|0〉+ |1〉⊗ |1〉 ≠ (a|0〉+ b|1〉) ⊗ (c|0〉+ d|1〉)  for any a,b,c,d \in C.
    

Because |Phi〉, the quantum state of an EPR pair cannot be written in terms of
local descriptions. We say EPR pairs are non-local. The equation of the state
|Phi〉(see equation (1) above) is a description of the combined state of Alice
and Bob.

Their states are entangled. If upon measuring Alice's state we find it to be
|0>, then we know immediately that Bob's state is also |0>. Because of the
entanglement, the collapse in the superposition on Alice's side immediately
causes a collapse of the superposition on Bob's side. Note that Bob's collapse
will occur IMMEDIATELY, and no matter how far Bob's system is from Alice's.
This is what the authors Einstein, Podolsky and Rosen called "spooky action at
a distance."

Now imagine you have have a whole bunch of physical systems prepared so their
state is an EPR pair. Alice has the left halfs of the EPR pairs, Bob has all
the right halfs. Now Alice's systems collapse into a black hole and Bob's
systems collapse into their own black hole. The connection that will exist
between these black holes appears to be similar to the wormholes connecting
black holes ("Einstein-Rosen bridge"s), which have been studied in general
relativity.

------
ivan_ah
A comment on the idea by John Preskill:
[http://quantumfrontiers.com/2013/06/07/entanglement-
wormhole...](http://quantumfrontiers.com/2013/06/07/entanglement-wormholes/)

