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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

Time-symmetric quantum mechanicsand the Many-Worlds Interpretation

Lev Vaidman

The Everett Interpretation of Quantum Mechanics: 50 years on 19 – 21 July 2007

slide3

The standard (one-state vector) description of a quantumsystem at time t

We assume:

slide5

The time reversed description of a quantum system

Backward Evolving Quantum State

TheQuantum StateEvolving Backward

slide8

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

slide9

The three box paradox

Where is the ball?

?

slide10

The three box paradox

It is in

always !

slide11

The three box paradox

It is always in

slide12

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

slide15

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.

slide18

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
slide19

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
slide20

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
slide24

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.

slide26

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

No! The backward evolving quantum state is equal to the forward evolving state!

slide27

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

No! The backward evolving quantum state is equal to the forward evolving state!

slide28

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

No! The backward evolving quantum state is equal to the forward evolving state!

slide29

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

No! The backward evolving quantum state is equal to the forward evolving state!

slide30

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)

slide33

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

slide34

The multiverse: the tree of worlds

The Universe: the trivial two-state vector

slide35

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

slide36

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.