# Consistent histories, 5

consistent histories ~ quantum decoherence

— Me@2012.04.08

# 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

# 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

.

.

.

# 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

# 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

# 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

# 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

# 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

# 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

# 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

# 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

# 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

# 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

# State

On the assumption that all interactions are local (which is backed up by the analysis of the EPR paradox presented below), one could say that the ideas of “state” and spatiotemporal contiguity are two sides of the same coin: spacetime location determines the possibility of interaction, but interactions determine spatiotemporal structure. The full extent of this relationship, however, has not yet fully been explored.

— Wikipedia on Relational quantum mechanics

2012.11.11 Sunday ACHK

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

2012.11.09 Friday ACHK

# Black hole complementarity 2

Instead, an observer can only detect the information at the horizon itself, or inside, but never both simultaneously. Complementarity is a feature of the quantum mechanics of noncommuting observables, and Susskind proposed that both stories are complementary in the quantum sense.

Interestingly enough, an infalling observer will see the point of entry of the information as being localized on the event horizon, while an external observer will notice the information being spread out uniformly over the entire stretched horizon before being re-radiated. To an infalling observer, information and entropy passes through the horizon with nothing strange happening. To an external observer, the information and entropy is absorbed into the stretched horizon which acts like a dissipative fluid with entropy, viscosity and electrical conductivity.

— Wikipedia on Black hole complementarity

2012.10.30 Tuesday ACHK

# Black hole complementarity

Leonard Susskind proposed a radical resolution to this problem by claiming that the information is both reflected at the event horizon and passes through the event horizon and can’t escape, with the catch being no observer can confirm both stories simultaneously.

— Wikipedia on Black hole complementarity

2012.10.28 Sunday ACHK

# Consistent histories, 2

Single-world interpretation, 8

The interpretation based on consistent histories is used in combination with the insights about quantum decoherence. Quantum decoherence implies that irreversible macroscopic phenomena (hence, all classical measurements) render histories automatically consistent, which allows one to recover classical reasoning and “common sense” when applied to the outcomes of these measurements.

— Wikipedia on Consistent histories

2012.04.14 Saturday ACHK

# Single-world interpretation, 7

One consequence is that every observation can be thought of as causing the combined observer-object’s wavefunction to change into a quantum superposition of two or more non-interacting branches, or split into many “worlds”.

— Wikipedia on Many-worlds interpretation

That is incorrect.

Let’s consider the double-slit experiment. For simplicity, we regard the event “a person reads the device reading” as a classical event.

Before installing the measuring device, we do not know which slit a photon goes through. The photon state is in a superposition of eigenstates:

| photon > = a | left > + b | right >

(According to the meaning of probability, |a|^2 + |b|^2 = 1.) In other words, if we send enough such kind of photons through the double-slit apparatus, we get the interference pattern.

After installing the measuring device, we know which slit a photon goes through. According to the Copenhagen interpretation, when the photon passes through the double-slit apparatus, the photon-state “collapses” to one of the two eigenstates, such as | left >. However, a more accurate point of view is that, according to the quantum decoherence interpretation, the photon-and-device state becomes a superposition of a lot of eigenstates. Most of such eigenstates are corresponding to the macrostate of passing-through-the-left-slit, |left>_macro_state.

The above many-worlds-interpretation statement assumes that there is a |right>_macro_state.

It is true in a sense that, since the photon-and-device involves a lot of particles, there are so many eigen-microstates. Some are certainly corresponding to the |right>_macro_state.

It is false in a sense that the weighting of the |right>_macro_state is so small that such macrostate is not meaningful in a macroscopic context, for example:

| photon-and-device > = 10^23 |left>_macro_state + 0.001 |right>_macro_state + other possible macrostates

— Me@2012-04-07 11:03:12 AM

It turns out that the usual rules for combining quantum mechanical and classical descriptions violate the principle of locality without violating causality.

Causality is preserved because there is no way for Alice to transmit messages (i.e. information) to Bob by manipulating her measurement axis. Whichever axis she uses, she has a 50% probability of obtaining “+” and 50% probability of obtaining “-“, completely at random; according to quantum mechanics, it is fundamentally impossible for her to influence what result she gets.

Furthermore, Bob is only able to perform his measurement once: there is a fundamental property of quantum mechanics, known as the “no cloning theorem”, which makes it impossible for him to make a million copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results. Therefore, in the one measurement he is allowed to make, there is a 50% probability of getting “+” and 50% of getting “-“, regardless of whether or not his axis is aligned with Alice’s.