consistent histories ~ quantum decoherence
— Me@2012.04.08
2015.04.14 Tuesday (c) All rights reserved by ACHK
Category Archives: quantum decoherence
Logical Fatalism
Logical Fatalism and the Argument from Bivalence
Another famous argument for fatalism that goes back to antiquity is one that depends not on causation or physical circumstances but rather is based on presumed logical truths.
The key idea of logical fatalism is that there is a body of true propositions (statements) about what is going to happen, and these are true regardless of when they are made. So, for example, if it is true today that tomorrow there will be a sea battle, then there cannot fail to be a sea battle tomorrow, since otherwise it would not be true today that such a battle will take place tomorrow.
The argument relies heavily on the principle of bivalence: the idea that any proposition is either true or false. As a result of this principle, if it is not false that there will be a sea battle, then it is true; there is no in-between. However, rejecting the principle of bivalence—perhaps by saying that the truth of a proposition regarding the future is indeterminate—is a controversial view since the principle is an accepted part of classical logic.
— Wikipedia on Fatalism
Quantum superposition can solve logical fatalism:
Macroscopic time is due to quantum decoherence.
The future is a coherent (constant phase difference) superposition of eigenstates.
That’s why classical probability can be regarded as part of quantum theory.
Quantum decoherence gives classically consistent histories.
— Me@2012.04.08
— Me@2015.03.26
2015.03.27 Friday (c) All rights reserved by ACHK
Quantum decoherence 7
There is no room for a physical collapse or, on the contrary, for an ad hoc privileged role of conscious observers; the wave functions only predict the probabilities but they can be calculated for any set of consistent histories, regardless of whether the systems look conscious, unconscious, macroscopic, or microscopic; the only “collapse” that occurs is the rapid diagonalization of the density matrix in the preferred basis by the interactions with the environment; however, the “unrealized” diagonal entries of the matrix (probabilities of outcomes that won’t come true) are never “physically” set to zero because their interpretation always remains probabilistic, even when the classical approximation becomes acceptably accurate[.]
— Decoherence is a settled subject
— Lubos Motl
2015.02.19 Thursday ACHK
Logical arrow of time, 6
The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference of prediction and retrodiction.
In a prediction, the deduction direction is the same as the physical/observer time direction.
In a retrodiction, the deduction direction is opposite to the physical/observer time direction.
.
— guess —
If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really doing a prediction.
However, it may not be possible for such an observer to exist. Me@2018-02-02 09:37:48 PM
— guess —
.
— Me@2013-10-25 3:33 AM
.
.
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2013.10.29 Tuesday (c) All rights reserved by ACHK
T-symmetry 10
Uncertainty principle, 5.2 | Universal wave function, 12.2 | Reductionism 5
The uncertainty principle states the limit of reductionism. Science is based on reductionism, which assumes we can investigate part of the universe. So the uncertainty principle, in effect, states the limit of science.
— Me@2011.11.29
You need to be a meta observer to get all the information of the universe in order to see the macroscopic time symmetry. However, by definition, the universe cannot have any meta.
— Me@2013-08-17 6:52 PM
The arrow of time is due to macroscopic states, aka incomplete pieces of information about the microstates. The microscopic state information keeps losing to the environment.
— Me@2013-08-14 6:58 PM
2013.08.18 Sunday (c) All rights reserved by ACHK
Conscious time
Cumulative concept of time, 15
In 1895, in his novel, The Time Machine, H.G. Wells wrote, “There is no difference between time and any of the three dimensions of space except that our consciousness moves along it.”
— Wikipedia on Spacetime
Consciousness “moves” from the past to the future because consciousness is a kind of reflection.
To be conscious, one has to access its own states. But only the past states are available. Accessing one’s own now-here state is logically impossible, because that creates a metadox (paradox).
— Me@2013-06-26 02:28:51 PM
We can remember the past but not the future because the past is part of the future; the whole contains its parts, but not vice versa.
— Me@2011.08.21
2013.06.29 Saturday (c) All rights reserved by ACHK
Eigenstates 2.3
So, after all, what is the meaning of “a quantum eigenstate”?
One way to resolve the circular definition is to define
a definite state
as
a state whose measurement result can be predicted with 100% certainty provided that the initial condition is given with 100% accuracy
Another way to resolve the circular definition is to realize that
1. a classical state, as a macroscopic definite state, is experimental or observational;
2. a quantum eigenstate, as a microscopic definite state, is conceptual.
A classical state is what we, as macroscopic observers, can see directly.
A quantum eigenstate is what we cannot see. Moreover, it is not absolute. For the same system, there are more than one choice of state vector bases, in the sense that different sets of measurements can get different sets of eigenstates.
The concept of “quantum eigenstates” exists because we insist to express quantum states in terms of daily-life (classical (macroscopic) physics) language.
— Me@2013.06.22
2013.06.22 Saturday (c) All rights reserved by ACHK
Eigenstates 2.2
But there is a problem. The definition of “quantum eigenstate” seems to be circular:
an eigenstate = a definite state = a classical state
a quantum eigenstate = a microscopic state corresponding to a macroscopic (classical) state
The phrase “quantum eigenstates” is defined in terms of “classical states”. However, classical states exist only because of the decoherence of quantum states of a lot of particles. The universe is fundamentally quantum, not classical. The classical world exists only as an approximation to the quantum universe.
Also, we cannot define a quantum eigenstate as a collapsed quantum state, because in reality, there is no wave function collapse. Collapse is only an illusion due to quantum decoherence.
So, after all, what is the meaning of “a quantum eigenstate”?
— Me@2013.06.18
2013.06.18 Tuesday (c) All rights reserved by ACHK
Eigenstates 2.1
A (macroscopic) classical state is due to the decoherence of quantum states of a lot of particles.
A quantum state is a quantum eigenstate or a superposition of quantum eigenstates.
a classical state = a macroscopic definite state
a quantum eigenstate = a microscopic definite state
a definite state = a state whose measurement result can be predicted with 100% certainty
— Me@2013.06.16
2013.06.17 Monday (c) All rights reserved by ACHK
Causal diamonds
Quantum mechanics is a set of rules that allows an observer to predict, explain, and/or verify observations (and especially their mutual relationships) that he has access to.
An observer has access to a causal diamond – the intersection of the future light cone of the initial moment of his world line and the past light cone of the final moment of his world line (the latter, the final moment before which one must be able to collect the data, is more important in this discussion).
No observer can detect inconsistencies within the causal diamonds. However, inconsistencies between “stories” as told by different observers with different causal diamonds are allowed (and mildly encouraged) in general (as long as there is no observer who could incorporate all the data needed to see an inconsistency).
— Raphael Bousso is right about firewalls
— Lubos Motl
2013.04.08 Monday ACHK
The most quantum state
A classical state is the most quantum state, because once position is definite, the momentum uncertainty is infinite.
— Quantum Mechanics 2009
— LIU Renbao
2013.02.05 Tuesday (c) All rights reserved by ACHK
Schrodinger’s cat
You should not apply a single-particle wavefunction to Schrodinger’s cat. Instead, you should either use classical physics or use a wavefunction for all the particles of the cat.
— Me@2013-01-23 10:25:00 AM
The uncertainty in Schrodinger’s cat’s life or death problem is classical uncertainty, not quantum uncertainty. For an observer outside the box, the cat is in a mixed state, not just a superposition of quantum eigenstates. The probability in a mixed state is classical, not quantum.
— Me@2013-01-27 09:59:13 AM
2013.01.27 Sunday (c) All rights reserved by ACHK
Eigenstates
an eigenstate = a microscopic “definite” state = a microscopic-classical state = a microscopic state corresponding to a macroscopic state
a microscopic state = a quantum state = an eigenstate or a superposition of eigenstates
A superposition state is not corresponding to any particular macroscopic state.
a macroscopic state = a definite state = a classical state
A macroscopic-classical state, in turn, is a superposition of a lot of microscopic states. A classical state is a superposition of a lot of quantum states.
— Me@2013-01-22 09:26:31
2013.01.23 Wednesday (c) All rights reserved by ACHK
Decoherence is continuous
On the other hand, he must make sure that the splitting of the worlds occurs as soon as decoherence is over. But the “moment” when decoherence is over isn’t sharply defined. Decoherence is never “absolute”. Decoherence is a continuous process that becomes “almost totally complete” after a certain time scale but it is never complete.
— Hugh Everett’s many worlds interpretation of QM
— Lubos Motl
2013.01.22 Tuesday ACHK
Quantum observer 1.2
Single-world interpretation, 7.4
…
What if I have a microscopic measuring device, B, as a “quantum observer”?
If a particle A is in a superposition of eigenstates, another particle B, as a micro-observer, can also be in a superposition of eigenstates, before or after the observation.
An observation on A by B is an interaction between A and B.
If after the observation/interaction, B is in a superposition, what would B see? Would it see A as in a superposition? Or would it see A as in one of the eigenstates?
It depends on whether you regard individual eigenstates of the resulting B as individual particles “B1, B2, …” in multiple “worlds”, or you regard the superposition of all eigenstates of the resulting B as one single particle in this single universe. In other words, it depends on how you use the label “B”.
The identification of particle B as the superposition of all its eigenstates is more reasonable, because that is compatible with the meaning of the word “observer” in ordinary quantum mechanics. In ordinary quantum mechanics, an observer is a measuring device. A measuring device is a macroscopic object, following classical physical laws. If we have to express the classical laws in terms of quantum mechanics, we say that each classical state of that macroscopic object is a superposition of a lot of quantum states of a lot of the constituent particles.
Classical objects follow the Principle of Least Action, which is due to the superposition of a lot of microstates of the particles. If there is no quantum superposition, there is no Principle of Least Action. Classical mechanics does not work.
— Me@2013.01.14
2013.01.17 Thursday (c) All rights reserved by ACHK
Quantum observer 1.1
In ordinary quantum mechanics, observers or measuring devices are macroscopic. So they are classical, in the sense that each of them is always in a macroscopic-eigenstate, aka “a macrostate“. A classical object would not be in a macroscopic superposition, in the sense that there would not be in a superposition of macroscopic-eigenstates. Macroscopic reality is always definite, unless you are talking about future events.
Then, would the macroscopic reality actually be a superposition of microscopic eigenstates?
Yes, it is. That is a logical implication from quantum mechanics. However, that makes no experimental difference, since those microstates of a lot of particles constitute a single macrostate.
In conclusion, a macrostate is not a superposition of macroscopic eigenstates. And although it is a superposition of microscopic eigenstates, it makes only conceptual difference but no experimental difference even if we ignore this fact. So for a classical observer, we do not have to consider whether it is in a superposition or not.
How about the observed particle? Would it be in a superposition?
It can and probably is.
However, superposition is a logical implication only. It cannot be observed directly using a macroscopic measuring device. Also, by using a macroscopic measuring device, aka “a classical observer“, to measure or observe a microscopic event, we will always collapse the wave function of the observed system (due to the decoherence effect), yielding a definite macroscopic result (which is corresponding to one of the eigenstate components in the original microscopic superposition).
What if I have a microscopic measuring device as a “quantum observer”?
— Me@2013-01-16 10:53:06 AM
2013.01.16 Wednesday (c) All rights reserved by ACHK
Phe-nomenon
Universal wave function, 19 | Reductionism 4
Impartial/All is the Noumenon, which is logically impossible for any single observer to observe directly, unless the observer is the whole of the universe. But “self-observation” is meaningless.
— Me@2012.04.07
Because “state” is expressed in RQM as the correlation between two systems, there can be no meaning to “self-measurement”.
— Wikipedia on Relational quantum mechanics
The Noumenon is a logical implication. It cannot be observed directly. It can be observed partially only, through senses, or phenomena. An observation is an interaction between the observer and the observed.
To really “observe” the Noumenon, all we can do is to observe as many phenomena as possible. In other words, we consider as many observer-observed pairs as possible.
— Me@2013.01.14
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
nomenon = all
phe- = part
noumenon = all aspects of the universe
phenomenon = part of the reality of the universe
— Me@2012.04.07
2013.01.14 Monday (c) All rights reserved by ACHK
Everett’s relative-state formulation, 2
The relative-state interpretation makes two assumptions.
The first is that the wavefunction is not simply a description of the object’s state, but that it actually is entirely equivalent to the object, a claim it has in common with some other interpretations.
The second is that observation or measurement has no special role, unlike in the Copenhagen interpretation which considers the wavefunction collapse as a special kind of event which occurs as a result of observation.
— Wikipedia on Many-worlds interpretation
2013.01.12 Saturday ACHK
Coherent quantum superpositions 1.2
remain secret = is not lost to the environment yet
— Me@2013-01-03 11:07:30 AM
The no-cloning theorem is a result of quantum mechanics that forbids the creation of identical copies of an arbitrary unknown quantum state.
— Wikipedia on No-cloning theorem
[guess]
conservation of information
= you can only move, but not copy, a piece of information
Classical information can be copied because “identical” classical systems are not really identical if we consider their microscopic details. One macrostate can be corresponding to a lot of microstates, e.g.
4 = 1 + 1 + 2
4 = 1 + 3 + 0
copy one macrostate = find another microstate which is corresponding to the same macrostate
Whether two states are “identical” depends on the resolution of the observer.
[guess]
— Me@2013-01-03 11:07:30 AM
2013.01.04 Friday (c) All rights reserved by ACHK
Coherent quantum superpositions
Decoherence was worked out in great detail by Los Alamos scientist Wojciech Zurek, Zeh and others over the following decades. They found that coherent quantum superpositions persist only as long as they remain secret from the rest of the world.
— from Max Tegmark; John Archibald Wheeler (2001). “100 Years of the Quantum”. Scientific American 284 (2003): 68–75
— Wikipedia on Quantum entanglement
That means the superposition information is not lost to the environment yet.
— Me@2012.12.31
2013.01.03 Thursday (c) All rights reserved by ACHK
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