Single-world interpretation, 6.5

If this is the case, then wave function is deterministic. There is no free will. The free will is due to the ongoing superposition of eigenstates. Locally, we see superposition of “a and b” collapse to (such as) a. Globally, we also see b “goes to” the environment. Nothing is lost in a sense that no information is lost.

Then what happens when you make a choice by collapsing a wave function?

Free will, like wave function collapse, is a local illusion.

Since information cannot be lost, we always exist.

— Me@2011.11.20

2012.02.25 Saturday (c) All rights reserved by ACHK

Single-world interpretation, 6.2

In the Many-worlds interpretation (MWI), when we say that “a + b” collapses to “a”, there is a shift of definition of “you”.

MWI is in one sense correct: choice b version of you still exists. But the trick is that he is not in another universe. He is in the environment of this universe.

And perhaps in reverse, you are also part of the environment of him.

— Me@2011.11.20

2012.02.22 Wednesday (c) All rights reserved by ACHK

Single-world interpretation, 5

Wave function collapse is a process of losing the superposition information to the environment.

— Me@2011.11.20

The unchosen choices are lost to the environment.

— Me@2011.11.21

Nature never forgets about any correlations: …

— Lubos Motl

The alternative “universes” are in this universe’s environment.  

— Me@2012.01.27

2012.01.28 Saturday (c) All rights reserved by ACHK

Principle of least action, 5

Principle of least time, 3

Single-world interpretation, 4

In 1948, Feynman discovered the path integral formulation extending the principle of least action to quantum mechanics for electrons and photons. In this formulation, particles travel every possible path between the initial and final states; the probability of a specific final state is obtained by summing over all possible trajectories leading to it. In the classical regime, the path integral formulation cleanly reproduces Hamilton’s principle, and Fermat’s principle in optics.

— Wikipedia on Lagrangian mechanics

2012.01.21 Saturday ACHK

Universal wave function, 4

Single-world interpretation, 4

That is, components of the wavefunction are decoupled from a coherent system, and acquiring phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue.

— Wikipedia on Quantum decoherence

The universal wave function is deterministic?

— Me@2011.11.20

2011.12.07 Wednesday ACHK

Single-world interpretation, 2

The correct meaning of Hugh Everett’s thesis should not be “many-(different)-worlds interpretation”. Instead, it should refer to the fact that the whole universe is described by a single wavefunction, which is a superposition a lot of eigenstates. Also the wavefunction of the universe can never collapse since there is no “environment” for it to have decoherence with. 

Macroscopically, a lot of, if not all, the eigenstates are corresponding to one single classical reality, e.g.

1 + 1 + 2 = 4

1 + 3 + 0 = 4

So there are no multiple (different) universes. Even if the universe is a superposition of several distinct macrostates, the wavefunction cannot collapse to a single macrostate, because there is no “environment” for it to lose information to.

— Me@2011.10.06

— Me@2011.10.18

2011.10.18 Tuesday (c) All rights reserved by ACHK

Single-world interpretation

Everett’s thesis introduction reads:

    Since the universal validity of the state function description is asserted, one can regard the state functions themselves as the fundamental entities, and one can even consider the state function of the entire universe. In this sense this theory can be called the theory of the “universal wave function,” since all of physics is presumed to follow from this function alone.

The universal wave function is the wavefunction or quantum state of the totality of existence, regarded as the “basic physical entity” or “the fundamental entity, obeying at all times a deterministic wave equation”.


Ray Streater writes:

    The idea of the wave-function of the universe is meaningless; we do not even know what variables it is supposed to be a function of. […] We find the laws of Nature by reproducible experiments. The theory needs a cut, between the observer and the system, and the details of the apparatus should not appear in the theory of the system.

Hugh Everett’s response

    If we try to limit the applicability so as to exclude the measuring apparatus, or in general systems of macroscopic size, we are faced with the difficulty of sharply defining the region of validity. For what n might a group of n particles be construed as forming a measuring device so that the quantum description fails? And to draw the line at human or animal observers, i.e., to assume that all mechanical aparata obey the usual laws, but that they are not valid for living observers, does violence to the so-called principle of psycho-physical parallelism.

— Wikipedia on Universal wavefunction

2011.10.16 Sunday ACHK