Category Archives: quantum decoherence

Quantum cosmology

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… the universe is the sum total of all that is in existence. Physically, a (physical) observer outside of the universe would require the breaking of gauge invariance, and a concomitant alteration in the mathematical structure of the theory. Similarly, RQM conceptually forbids the possibility of an external observer. Since the assignment of a quantum state requires at least two “objects” (system and observer), which must both be physical systems, there is no meaning in speaking of the “state” of the entire universe.

This is because this state would have to be ascribed to a correlation between the universe and some other physical observer, but this observer in turn would have to form part of the universe, and as was discussed above, it is impossible for an object to give a complete specification of itself. Following the idea of relational networks above, an RQM-oriented cosmology would have to account for the universe as a set of partial systems providing descriptions of one another. The exact nature of such a construction remains an open question.

— Wikipedia on Relational quantum mechanics

2012.03.27 Tuesday ACHK

Consistent histories

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Physicists including your humble correspondent always preferred to keep the normal logic. I really don’t understand how one could work with von Neumann’s strange rules. The consistent histories, the most complete framework to interpret quantum mechanics today, imply that exactly those quantum histories (sequences of projection operators at different times) for which the classical rules of logic work – the consistent histories themselves – are allowed.

— John von Neumann: 104th birthday

— Lubos Motl

2012.03.18 Sunday ACHK

Wheeler–DeWitt equation

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Well, in some sense, the Wheeler-DeWitt equation is nothing else than Einstein’s equations that you encountered elsewhere – potentially simplified and reduced in a minisuperspace formulation.

But if something like the Wheeler-DeWitt equation is the only equation that defines what can happen in a quantum gravity system, your task actually becomes harder, not easier. You must artificially reparameterize your physical states according to a new observable (e.g. the total volume of the Universe at some “moment”) that will play the role of your time (recall that there’s no preferred choice of coordinates in general relativity) – and with this new “gauge-fixed” choice of your time, you will find out that the Wheeler-DeWitt “H=0” equation becomes non-trivial.

— Why and how energy is not conserved in cosmology

— Lubos Motl

Bryce DeWitt first published this equation in 1967 under the name “Einstein–Schrodinger equation”; it was later renamed the “Wheeler–DeWitt equation”.

…

Solutions to the Wheeler-DeWitt equation have therefore been interpreted as the Universal wave function.

This property is known as timelessness [disambiguation needed]. The reemergence of time requires the tools of decoherence and clock operators.

— Wikipedia on Wheeler–DeWitt equation

Timelessness is a property of the Wheeler-deWitt equation in canonical quantum gravity.

— Wikipedia on Timeless

2012.03.08 Thursday ACHK

Free will theorem, 2

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Block time, 3

There are logically flawed conclusions in the show made out of various careless arguments, too. For example, it’s being said that one must adopt “eternalism” – all of the spacetime, whether it is in the past or in the future – is equally real. But such a conclusion is once again sloppy. Nothing like that follows from relativity. And in fact, relativity combined with quantum mechanics implies things like the “free will theorem” which pretty much refutes eternalism.

— The Fabric of the Cosmos II

— Lubos Motl

If we consider the universal wave function, there is no collapse, then the block time is allowed.

— Me@2011.11.19

2012.03.04 Sunday (c) All rights reserved by ACHK

Definite

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Universal wave function, 14

Quantum decoherence makes the macroscopic world appear definite.

In fact, Nature is fundamentally a superposition of definite states.

So the world, either microscopic or macroscopic, is definite in a sense that the universal wave function is evolving deterministically; and

is indefinite in a sense that it is not in a particular eigenstate.

— Me@2011.11.19

2012.02.27 Monday (c) All rights reserved by ACHK

Everett’s relative-state formulation

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Universal wave function, 13

Everett noticed that the unitary, deterministic dynamics alone decreed that after an observation is made each element of the quantum superposition of the combined subject-object wavefunction contains two “relative states”: a “collapsed” object state and an associated observer who has observed the same collapsed outcome; what the observer sees and the state of the object have become correlated by the act of measurement or observation. The subsequent evolution of each pair of relative subject-object states proceeds with complete indifference as to the presence or absence of the other elements, as if wavefunction collapse has occurred, which has the consequence that later observations are always consistent with the earlier observations. Thus the appearance of the object’s wavefunction’s collapse has emerged from the unitary, deterministic theory itself. (This answered Einstein’s early criticism of quantum theory, that the theory should define what is observed, not for the observables to define the theory). Since the wavefunction appears to have collapsed then, Everett reasoned, there was no need to actually assume that it had collapsed. And so, invoking Occam’s razor, he removed the postulate of wavefunction collapse from the theory.

— Wikipedia on Everett’s relative-state formulation

2012.02.26 Sunday ACHK

Single-world interpretation, 6.5

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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

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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

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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

Planck spacetime box, 2

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Onion self 3.2 | 洋蔥自我 3.2 | Inner and outer, 3 |

Planck scale 3 | Hidden variable, 2 | T-duality, 3

If the quantum jump is an illusion or an approximation to the reality of events at a quantum level, then maybe events at the quantum level are actually deterministic and we could, in principle, determine the outcome of a quantum measurement. This all boils down to what is happening in the quantum “foam” at the smallest Planck Scale.

– Andrew Thomas, 19th March 2007

[guess] Then the hidden variable is related to the universal wave function and the planck-scale physics.

[guess] The universal wave function is related to the planck-scale physics.

— Me@2012-01-22 11:33:47 AM

2012.01.22 Sunday ACHK

Principle of least action, 5

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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