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arXiv:1205.1584 · Physics Letters B

Everything is entangled

Roman V. Buniy, Stephen D. H. Hsu

Published Sep 25, 2012• 15 citations
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Abstract

We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other – the reduced density matrix describing any pair is likely to be separable.

DOI
10.1016/j.physletb.2012.09.047

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We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other – the reduced density matrix describing any pair is likely to be separable.
We investigate the fate of big-bang singularity and coherence between distinct clock states in a quantum cosmological setting within the Page-Wootters framework. With a canonically quantized plane-symmetric Bianchi I universe, we employ Dirac factorization of the Wheeler-DeWitt constraint and obtain a Schrodinger-like equation which is first-order in an internal clock variable. By constructing its solution as a Gaussian wave packet in the expanding branch, we derive the corresponding conditional state and probability density of the universe. We find that the conditional probability density vanishes in the zero-volume limit, indicating resolution of the big-bang singularity within this probabilistic framework. Another prespective of the study is provided by the construction of density matrix from the conditional states associated with different clock readings and the remaining degree of freedom. By tracing out the remaining subsystem, we obtain the reduced density matrix and analyze the resulting coherence as a function of separation between different clock states. These results provide a relational characterization of singularity resolution and demonstrate how the spectral properties of the quantum state govern the temporal coherence between different clock states in the Page-Wootters description.
Entanglement can be understood as an extraordinary degree of correlation between states of quantum systems – a correlation that cannot be given an explanation in terms of something like a common cause. Entanglement can occur between two or more quantum systems, and the most interesting case is when these correlations occur between systems that are space-like separated, meaning that changes made to one system are immediately correlated with changes in a distant system even though there is no time for a signal to travel between them. In this case one says that quantum entanglement leads to non-local correlations, or non-locality. More precisely, entanglement can be defined in the following way. Consider two particles, A and B, whose (pure) states can be represented by the state vectors ψA and ψB. Instead of representing the state of each particle individually, one can represent the composite two-particle system by another wavefunction, Ψ AB. If the two particles are unentangled , then the composite state is just the tensor product of the states of the components: Ψ AB = ψ A ⊗ ψ B; the state is then said to be factorable (or separable). If the particles are entangled, however, then the state of the composite system cannot be written as such a product of a definite state for A and a definite state for B. This is how an entangled state is defined for pure states: a state is entangled if and only if it cannot be factored: Ψ AB ≠ ψ A ⊗ ψ B.
It is shown that every zero-temperature Bose-Einstein condensate is a highly entangled state, as a consequence of the fact that the particles in a condensate are distributed over space in a coherent way. In particular, any two regions within a condensate of finite particle number are entangled. This entanglement does not depend on the distance between the two regions. Criteria for the presence of entanglement are derived in the context of interference experiments. For separable states there is a trade-off between fluctuations in particle number and interference visibility.
Key Areas of the Consciousness Physics Research Project (Phase II)•The Temic Big Bang Cosmology (also called the Temifa Big Bang Cosmology)•CEN (consciousness-energy): The cenforms•Mathematical Frameworks for the following and their subsections: oEntanglement Is Fundamental to the Universe: The Temic Principle of Consciousness Entanglement (the Beginning)oGravity: A consequence of Big Bang expansion/explosion by Fundamental Consciousness, a natural forceoThe Temic Theory of GravityoThe Temic Big Bang Principle: A generalization of the Big Bang in the Standard Big Bang ModeloThe Temic Uncertainty Principle: A generalization of Heisenberg's Uncertainty PrincipleoThe Temic Superposition Principle: A generalized version of the superposition principleoThe Temic Principle of Consciousness-Energy Conservation: A generalized version of the principle of conservation of energyoThe Temic Wave-Particle Duality: A generalization of the Wave-Particle Duality of MatteroQuantization of ConwavesoObjectivity, Observation, Measurement, and SubjectivityoThe Temic Principle of CoherenceoThe Temic Principle of Conscious PerceptionoThe Temic Relativity Principle: Reality Is Both Local and Non-Local•The Periodic Table of Lifeforms on Earth (PTL)•CEN: The Theory of Everything•Nature of existence and space-time in Consciousness Mechanics•Further Predictions of The StudyoApplications
The reduced density matrix ${\ensuremath{\rho}}_{r}(x,{x}^{\ensuremath{'}})$ of the transverse biphoton state beyond the near zone is found to be real on and only on diagonals in the plane of the photon's transverse coordinates $(x,{x}^{\ensuremath{'}})$. This remarkable feature is found to occur at any distances of photon propagation with diffraction spreading completely taken into account. The functions of the reduced density matrix at two orthogonal diagonals, ${\ensuremath{\rho}}_{r}(x,x)$ and ${\ensuremath{\rho}}_{r}(x,\ensuremath{-}x)$, are considered as the only two complementary single-particle distributions generated by the reduced density matrix. The ratio of widths of these two distributions is interpreted as the new entanglement parameter Rdiag{R}_{\mathrm{diag}}Rdiag​ which is found to be very close to and completely compatible with the Schmidt entanglement parameter KKK.