Category Archives: an observer | a causal diamond

Eigenstates 2.2

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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

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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

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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

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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

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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

Quantum observer 1.2

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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

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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

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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

State

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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

Black hole complementarity 2

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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

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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

Black hole information paradox, 2

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It shouldn’t be so surprising that unitarity survives completely while causality doesn’t. After all, the basic postulates of quantum mechanics, including unitarity, the probabilistic interpretation of the amplitudes, and the linearity of the operators representing observables, seem to be universally necessary to describe physics of any system that agrees with the basic insights of the quantum revolution.

On the other hand, geometry has been downgraded into an effective, approximate, emergent aspect of reality. The metric tensor is just one among many fields in our effective field theories including gravity.

— Black hole information puzzle

— Lubos Motl

2012.04.25 Wednesday ACHK

Consistent histories, 2

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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

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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

2012.04.09 Monday (c) All rights reserved by ACHK

EPR paradox, 3

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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.

— Wikipedia on EPR paradox

In fact, a theorem proved by Phillippe Eberhard shows that if the accepted equations of relativistic quantum field theory are correct, it should never be possible to experimentally violate causality using quantum effects (see reference [6] for a treatment emphasizing the role of conditional probabilities).

— Wikipedia on Delayed choice quantum eraser

2012.04.08 Sunday ACHK

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

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

Wheeler’s delayed choice experiment

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Quantum decoherence 5.3
 
 
In the delayed choice experiment, the wave function of the system (the photons and the environment) is also in a superposition of eigenstates, not just the wave functions of the individual photons are.

All the past is there, but our present measurement “chooses” which part to see. 

— Me@2011.10.21
 
 
The chosen part must be a consistent story, according the quantum mechanics.

The chosen part is what we called “an observer”.

— Me@2018-01-22 09:35:02 PM
 
 
 
2011.11.20 Sunday (c) All rights reserved by ACHK