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Time-symmetric quantum mechanics and the Many-Worlds Interpretation

Time-symmetric quantum mechanics and the Many-Worlds Interpretation . Lev Vaidman. The Everett Interpretation of Quantum Mechanics: 50 years on 19 – 21 July 2007. The two-state vector formalism of quantum mechanics. The standard (one-state vector) description of a quantum system at time t.

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Time-symmetric quantum mechanics and the Many-Worlds Interpretation

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  1. Time-symmetric quantum mechanicsand the Many-Worlds Interpretation Lev Vaidman The Everett Interpretation of Quantum Mechanics: 50 years on 19 – 21 July 2007

  2. The two-state vector formalism of quantum mechanics

  3. The standard (one-state vector) description of a quantumsystem at time t We assume:

  4. The one-state vector description of a quantumsystem at all times:

  5. The time reversed description of a quantum system Backward Evolving Quantum State TheQuantum StateEvolving Backward

  6. The two-state vector description of a quantumsystem:

  7. Time symmetric description of a pre- and post-selected quantum system The two-state vector

  8. Measurements performed on a pre- and post-selected system described by the two-state vector: Strong measurement: The Aharonov-Bergmann-Lebowitz (ABL) formula: Weak measurement: The Aharonov-Albert-Vaidman effect: Weak value

  9. The three box paradox Where is the ball? ?

  10. The three box paradox It is in always !

  11. The three box paradox It is always in

  12. A single photon “sees” two balls Y. Aharonov and L. Vaidman Phys. Rev. A 67, 042107 (2003)  It scatters exactly as if there were two balls

  13. Weakly coupled (numerous) particles “see” two balls

  14. The tree of worlds picture of the MWI

  15. What is “a world” in the many-worlds tree picture? world, n I. Human existence; a period of this. II. The earth or a region of it; the universe or a part of it. OED The World is a name for the planet Earth seen from a human point of view, as a place inhabited by human beings. It is often used to mean the sum of human experience and history, or the 'human condition' in general. Wikipedia A world is the totality of (macroscopic) objects: stars, cities, people, grains of sand, etc. in a definite classically described state. The MWI in SEP A world is a branch of the Universal Wave Function consistent with the classically described state of macroscopic objects.

  16. The tree of worlds

  17. A world consist of: • "classical" macroscopic objects rapidly measured by the environment, • quantum objects measured only occasionally (at world splitting events), • weakly coupled quantum objects

  18. A world consist of: • "classical" macroscopic objects rapidly measured by the environment, • quantum objects measured only occasionally (at world splitting events), • weakly coupled quantum objects

  19. A world consist of: • "classical" macroscopic objects rapidly measured by the environment, • quantum objects measured only occasionally (at world splitting events) which described by the two-state vectors, • weakly coupled quantum objects

  20. Forward evolving branch of the universal wave function does not describe all we should know about a world. The (different) backward evolving state has to be added.

  21. Is this the two-state vector which describes the Universe?

  22. Is this the two-state vector which describes the Universe? No! The backward evolving quantum state is equal to the forward evolving state!

  23. Is this the two-state vector which describes the Universe? No! The backward evolving quantum state is equal to the forward evolving state!

  24. Is this the two-state vector which describes the Universe? No! The backward evolving quantum state is equal to the forward evolving state!

  25. Is this the two-state vector which describes the Universe? No! The backward evolving quantum state is equal to the forward evolving state!

  26. Forward evolving branch of the universal wave function does not describe all we should know about a world. ? The (different) backward evolving state has to be added. But, this backward evolving state has meaning only in this world. It does not exist in the physical world (Universe)

  27. The two-state vector description of a quantumsystem: in a particular world:

  28. The two-state vector description of a quantumsystem in the Universe:

  29. Forward evolving branches of the universal wave function do not describe all we should know about these worlds. The (different) backward evolving states have to be added. But, these backward evolving states have meaning only in every world separately. They do not exist in the Universe

  30. The multiverse: the tree of worlds The Universe: the trivial two-state vector

  31. Multiple Many-Worlds Interpretation The Universe is an equal-weight mixture of all quantum states of an orthonormal basis Like one side of the teleportation machine for universes S

  32. Multiple Many-Worlds Interpretation The Universe is an equal-weight mixture of all quantum states of an orthonormal basis Like one side of the teleportation machine for universes It is very, very symmetric. A backward evolving equal-weight mixture can be added The theory is not testable But it might provide a framework for (possibly testable) cosmological theory.

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