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

The two-state vector formalism of quantum mechanics

The standard (one-state vector) description of a quantum system at time t We assume:

The one-state vector description of a quantum system at all times:

The time reversed description of a quantum system Backward Evolving Quantum State The Quantum State Evolving Backward

The two-state vector description of a quantum system:

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

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

The three box paradox Where is the ball? ?

The three box paradox It is in always !

The three box paradox It is always in

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

Weakly coupled (numerous) particles “see” two balls

The tree of worlds picture of the MWI

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. II. The earth or a region of it; the universe or a part of it. I. Human existence; a period of this. world, n OED 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 What is “a world” in the many-worlds tree picture? A world is a branch of the Universal Wave Function consistent with the classically described state of macroscopic objects.

The tree of worlds

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

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

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

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.

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

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

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

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

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

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) ?

The two-state vector description of a quantum system: in a particular world:

The two-state vector description of a quantum system in the Universe:

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

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

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

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. The theory is not testable A backward evolving equal-weight mixture can be added But it might provide a framework for (possibly testable) cosmological theory.