Spin-spacetime EPR Gedanken-Experiment

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General relativity and various quantum gravity theories predict that the intrinsic quantum spin should bend the spacetime around it, breaking its spherical symmetry.[1][2][3][4] The Spin-spacetime EPR Gedanken-Experiment is a thought experiment to prove that such a spin-related deviation from spherical symmetry would violate relativistic causality.[5][6] To avoid a paradox, the measurable spacetime (which is associated with quantum spin) has to be spherically symmetric.[5][6] Thus, this spacetime version of the EPR experiment sheds important insights on the interface between quantum mechanics and general relativity.

Spin-spacetime EPR Gedanken-Experiment

Description of the Gedanken-Experiment[edit]

Fig 1. A time dilation (spacetime) version of the EPR experiment

The spacetime EPR experiment Gedanken-Experiment is performed with the following stages (as shown in Fig 1): An EPR pair of spin-½ particles, is prepared and distributed to Alice and Bob. Alice measures her particle with a Stern Gerlach setup. By orienting her magnets, Alice controls the orientation of both spins. She can set them to be parallel to any direction she desires (e.g., parallel to the X-axis or parallel to the Y-axis). Bob measures the time dilation effect around his spin-½ particle. To do that he uses extremely precise clocks placed symmetrically around his particle. If spin is an anisotropic source of gravity, then Bob can figure out which Stern-Gerlach orientation Alice chose. This creates a paradox - as it violates relativistic causality.

In conclusion it is asserted that the measurable spacetime around spin-½ particles must be spherically symmetric.[5][6]

Relation of the Gedanken-Experiment to an ordinary spin-spin EPR experiment[edit]

Fig 2. (a) An Ordinary EPR experiment. (b) A spin-spacetime EPR experiment.

In an ordinary EPR experiment Bob measures his particle with a second set of Stern-Gerlach magnets (see Fig. 2a). When Bob places his Stern-Gerlach magnets he orients them at a specific direction. The magnetic field of these magnets creates a back-action effect and alters the spin of his spin-1/2 particle. Due to the back-action effect Bob cannot infer the direction in which Alice had set his spin. This prevents a paradox with relativistic causality (as it prevents faster then light communication). However, in a spin-spacetime EPR experiment (see Fig 2. b) Bob is using precise clocks to measure the time-dilation effect of the spin. If Bob places his clocks in a symmetric configuration, there is no preferred axis and therefore it is not clear if there is any back-action in this type of measurement.[5] This is why the spin-spacetime EPR Gedanken-Experiment is currently used in active research.[5][6]

Implications of the Gedanken-Experiment to classical and quantum gravity[edit]

One of the difficulties of formulating a quantum gravity theory is that quantum gravitational effects only appear at length scales near the Planck scale, around 10−35 meter, a scale far smaller, and equivalently far larger in energy, than those currently accessible by high energy particle accelerators. Therefore, physicists lack experimental data which could distinguish between the competing theories which have been proposed[7][8][9] and thus thought experiment approaches are suggested as a testing tool for these theories.[10][11] [5][6] The spin-spacetime EPR Gedanken-Experiment can be used as a theoretical test for various quantum gravity theories - all of these theories should maintain relativistic causality. Thus, the Gedanken-Experiment restricts and could lead to modification of these theories.[5][6] To avoid a paradox, the measurable spacetime (which is associated with quantum spin) has to be spherically symmetric.[5][6]

See also[edit]

References[edit]

  1. ^ Lopez, Carlos A. "Extended model of the electron in general relativity." Physical Review D 30.2 (1984): 313.
  2. ^ Burinskii, Alexander (2007). "Kerr geometry as space–time structure of the Dirac electron". arXiv:0712.0577.
  3. ^ A. Burinskii, The Dirac-Kerr-Newman electron. Gravit. Cosmol. 14, 109 (2008).
  4. ^ Yuri.N., Obukhov, "Spin, gravity, and inertia", Physical review letters 86.2 (2001): 192.arXiv:0012102v1
  5. ^ Jump up to: a b c d e f g h Nemirovsky, J.; Cohen, E.; Kaminer, I. (30 Dec 2018). "Spin Spacetime Censorship". arXiv:1812.11450v2 [gr-qc].
  6. ^ Jump up to: a b c d e f g Nemirovsky, J.; Cohen, E.; Kaminer, I. (2019). The Principle of Spin-Spacetime Censorship (PDF). QUANTUM 2019. p. 174.
  7. ^ Becker, Becker, and Schwarz 2007, p. 296
  8. ^ Rovelli, Carlo (2008). "Quantum gravity". Scholarpedia. 3 (5): 7117. Bibcode:2008SchpJ...3.7117R. doi:10.4249/scholarpedia.7117.
  9. ^ On the quantization of the geometry of spacetime, see also in the article Planck length, in the examples
  10. ^ Bose, S.; et al. (2017). "Spin Entanglement Witness for Quantum Gravity". Physical Review Letters. 119 (4): 240401. arXiv:1707.06050. doi:10.1103/PhysRevLett.119.240401. PMID 29286711.
  11. ^ Marletto, C.; Vedral, V. (2017). "Gravitationally Induced Entanglement between Two Massive Particles is Sufficient Evidence of Quantum Effects in Gravity". Physical Review Letters. 119 (24): 240402. arXiv:1707.06036. doi:10.1103/PhysRevLett.119.240402. PMID 29286752.
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