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arXiv:1604.02589 · Fortschritte der Physik

Copenhagen vs Everett, Teleportation, and ER=EPR

Leonard Susskind

Published Jun 1, 2016• 76 citations
arXivHTMLPDF

Abstract

Quantum gravity may have as much to tell us about the foundations and interpretation of quantum mechanics as it does about gravity. The Copenhagen interpretation of quantum mechanics and Everett's Relative State Formulation are complementary descriptions which in a sense are dual to one another. My purpose here is to discuss this duality in the light of the of ER=EPR conjecture.

DOI
10.1002/prop.201600036

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Quantum gravity may have as much to tell us about the foundations and interpretation of quantum mechanics as it does about gravity. The Copenhagen interpretation of quantum mechanics and Everett's Relative State Formulation are complementary descriptions which in a sense are dual to one another. My purpose here is to discuss this duality in the light of the of ER=EPR conjecture.
Of all the many rival interpretations of quantum mechanics, none is more important or influential than the Copenhagen interpretation. Unfortunately, there is no one Copenhagen interpretation of quantum mechanics. If one uses the expression, and everyone does, one should not think of the Copenhagen interpretation as a single consistent interpretation of the theory. Philosophers of physics tend to use the expression ‘the Copenhagen interpretation of quantum mechanics’ as a label covering a variety of different interpretations all of which either originate with Niels Bohr or were invented by him, his colleagues and guests at the Institute for Theoretical Physics in Copenhagen beginning in the middle 1920s. Perhaps one should say that the Copenhagen interpretation in this diffuse sense goes back farther than this, back even before the rise of the new quantum mechanics. Heisenberg tells the story of a boat trip he, Bohr, and some friends took from Copenhagen to the island of Fyn around the time when the then new quantum mechanics was being developed. Bohr, ‘full of the new interpretation of quantum theory’, talked of ‘the difficulties of language, of the limitations of all our means of expressing ourselves’ and of how these limitations had been expressed ‘in the foundation of atomic theory in a mathematically lucid way’. ‘Finally,’ Heisenberg ends the story, ‘one of the friends remarked drily, “But, Niels, this is not really new, you said exactly the same ten years ago”
Everett's Relative State Interpretation (aka Many Worlds Interpretation) has gained increasing interest due to the progress understanding the role of decoherence. In order to fulfill its promise as an intellectually economic realistic description of the physical world, two postulates are formulated. In short they are 1) for a system with continuous coordinates x\mathbf xx, discrete variable jjj, and state ψj(x)ψ_j(\mathbf x)ψj​(x), the density ρj(x)=∣ψj(x)∣2ρ_j(x)=|ψ_j(x)|^2ρj​(x)=∣ψj​(x)∣2 gives the distribution of the location of the system with the respect to the variables xxx and jjj; 2) an equation of motion for the state iℏ∂tψ=Hψi\hbar \partial_t ψ= Hψiℏ∂t​ψ=Hψ. The contents of the standard (Copenhagen) postulates are derived including the quantum probabilities (Born's rule).
We unify the ER = EPR conjecture with the Many-Worlds Interpretation (MWI) by constructing a transfinite, bijective functor between the poset of entangled Everett branches and the space of Einstein-Rosen bridges. Leveraging the fact that the branching cardinality is at least ℶ1\beth_1ℶ1​ (the cardinality of the continuum), we employ the axiom of choice and Cantor's transfinite recursion to define a one-to-one correspondence Φ:B×B→Ω\Phi: \mathcal{B} \times \mathcal{B} \to \OmegaΦ:B×B→Ω, where B\mathcal{B}B is the set of orthogonal branches and Ω\OmegaΩ the set of non-traversable ER bridge geometries. The mapping preserves unitarity, respects the no-communication theorem, and yields three falsifiable predictions: (i) a geometric correction to the decoherence functional, (ii) a generalised Ryu-Takayanagi formula for branch entanglement entropy, and (iii) a topological obstruction to non-Hausdorff branch merging. This work fills a precise gap in the literature and provides a rigorous mathematical foundation for ER = EPR in the Everett multiverse.
After summarising a previously given analysis of Bohr's reply to Einstein, Podolsky and Rosen (EPR), this chapter endorses the claim made by Everett himself that Everettian quantum mechanics `in a certain sense bridges the positions of Einstein and Bohr'. On the one hand, it shows how Everett's theory provides a reconstruction of Bohr's viewpoint of complementarity as applied to the EPR case and a justi�cation of his criticism of EPR's `criterion of reality'. On the other hand, it includes a notion of physical reality that is independent of any observational context, and suggests a remaining shortcoming of Bohr's reply.