Consistent histories, 8

Relationship with other interpretations

The only group of interpretations of quantum mechanics with which RQM is almost completely incompatible is that of hidden variables theories. RQM shares some deep similarities with other views, but differs from them all to the extent to which the other interpretations do not accord with the “relational world” put forward by RQM.

Copenhagen interpretation

RQM is, in essence, quite similar to the Copenhagen interpretation, but with an important difference. In the Copenhagen interpretation, the macroscopic world is assumed to be intrinsically classical in nature, and wave function collapse occurs when a quantum system interacts with macroscopic apparatus. In RQM, any interaction, be it micro or macroscopic, causes the linearity of Schrödinger evolution to break down. RQM could recover a Copenhagen-like view of the world by assigning a privileged status (not dissimilar to a preferred frame in relativity) to the classical world. However, by doing this one would lose sight of the key features that RQM brings to our view of the quantum world.

Hidden variables theories

Bohm’s interpretation of QM does not sit well with RQM. One of the explicit hypotheses in the construction of RQM is that quantum mechanics is a complete theory, that is it provides a full account of the world. Moreover, the Bohmian view seems to imply an underlying, “absolute” set of states of all systems, which is also ruled out as a consequence of RQM.

We find a similar incompatibility between RQM and suggestions such as that of Penrose, which postulate that some processes (in Penrose’s case, gravitational effects) violate the linear evolution of the Schrödinger equation for the system.

Relative-state formulation

The many-worlds family of interpretations (MWI) shares an important feature with RQM, that is, the relational nature of all value assignments (that is, properties). Everett, however, maintains that the universal wavefunction gives a complete description of the entire universe, while Rovelli argues that this is problematic, both because this description is not tied to a specific observer (and hence is “meaningless” in RQM), and because RQM maintains that there is no single, absolute description of the universe as a whole, but rather a net of inter-related partial descriptions.

Consistent histories approach

In the consistent histories approach to QM, instead of assigning probabilities to single values for a given system, the emphasis is given to sequences of values, in such a way as to exclude (as physically impossible) all value assignments which result in inconsistent probabilities being attributed to observed states of the system. This is done by means of ascribing values to “frameworks”, and all values are hence framework-dependent.

RQM accords perfectly well with this view. However, the consistent histories approach does not give a full description of the physical meaning of framework-dependent value (that is it does not account for how there can be “facts” if the value of any property depends on the framework chosen). By incorporating the relational view into this approach, the problem is solved: RQM provides the means by which the observer-independent, framework-dependent probabilities of various histories are reconciled with observer-dependent descriptions of the world.

— Wikipedia on Relational quantum mechanics



2020.09.27 Sunday ACHK

Superposition always exists, 2

Decoherence means that the different components in the superposition do not interact with each other, but it does not mean that the components separate to form different macroscopic realities.


Just like when a 100-soldier army’s marching gets interrupted, the decoherent soldiers do not form a single army anymore, because their actions become out of sync.

However, they do not become 100 armies either.

Instead, they form a group of 100 random people in the street.

Although now they are out of sync with each other, all original soldiers still exist, forming the (new) average result; all or most of them have become part of the environment.


But it is an analogy only. It has an important distinction.

In quantum superposition, we discuss the relationships between different component states of the superposition. Those states exist not in physical space, but in a mathematical space.

In the army analogy, we discuss the relationships between the actions between different material items (solders in this case). Those material items exist in physical space.


The unselected eigenstates do not cooperate with other particles to form macroscopic realities.

Although the spirit of the statement is correct, the statement itself is incorrect in multiple senses.

First, an eigenstate is a quantum state. It interferes with other eigenstates, not other particles.

Second, although the “unselected” eigenstates seem to disappear, they actually still exist; they entangles with the environment, which includes the apparatus and measurement devices of that experiment.

— Me@2013.01.01

— Me@2020-02-26 06:49:46 AM


In “decoherence means that the different components do not interact with each other”, the meaning of “interact” is not defined yet.

The word should probably be “interfere”, instead of “interact”.

— Me@2020-02-25 10:44:23 PM


interference ~ superposition with pattern

Decoherence means that the phase differences between different components in a superposition are not constants anymore. It does not mean that there is no superposition anymore.

Superposition is always there.

What disappears is the interference pattern, not the superposition.

— Me@2019-09-20 06:48:55 AM



2020.02.26 Wednesday (c) All rights reserved by ACHK

Pointer state, 2

Eigenstates 3.2


Microscopically, a state can be definite or indefinite. Even if it is indefinite, the overlapping of superpositions of states of a lot of particles, or the superposition of a lot of system-microstates gives a definite macrostate.

If a state is definite, it is corresponding to one single system-macrostate directly.

I am referring to the physical definition, not the mathematical definition.

— Me@2012-12-31 09:28:08 AM


If a microstate is definite, it is called an “eigenstate”. It is corresponding to one single system-macrostate directly.

However, the microstate is NOT the macrostate. The microstate is just corresponding to that macrostate.

— Me@2019-09-20 07:02:10 AM


In quantum Darwinism and similar theories, pointer states are quantum states, sometimes of a measuring apparatus, if present, that are less perturbed by decoherence than other states, and are the quantum equivalents of the classical states of the system after decoherence has occurred through interaction with the environment. ‘Pointer’ refers to the reading of a recording or measuring device, which in old analog versions would often have a gauge or pointer display.

— Wikipedia on Pointer state


In quantum mechanics, einselections, short for environment-induced superselection, is a name coined by Wojciech H. Zurek for a process which is claimed to explain the appearance of wavefunction collapse and the emergence of classical descriptions of reality from quantum descriptions.

In this approach, classicality is described as an emergent property induced in open quantum systems by their environments. Due to the interaction with the environment, the vast majority of states in the Hilbert space of a quantum open system become highly unstable due to entangling interaction with the environment, which in effect monitors selected observables of the system.

After a decoherence time, which for macroscopic objects is typically many orders of magnitude shorter than any other dynamical timescale, a generic quantum state decays into an uncertain [in the sense of classical probability] state which can be decomposed into a mixture of simple pointer states. In this way the environment induces effective superselection rules. Thus, einselection precludes stable existence of pure superpositions of pointer states. These ‘pointer states’ are stable despite environmental interaction. The einselected states lack coherence, and therefore do not exhibit the quantum behaviours of entanglement and superposition.

Advocates of this approach argue that since only quasi-local, essentially classical states survive the decoherence process, einselection can in many ways explain the emergence of a (seemingly) classical reality in a fundamentally quantum universe (at least to local observers). However, the basic program has been criticized as relying on a circular argument (e.g. R. E. Kastner). So the question of whether the ‘einselection’ account can really explain the phenomenon of wave function collapse remains unsettled.

— Wikipedia on Einselection


Here I simply review the basic approach to ‘deriving’ einselection via decoherence, and point to a key step in the derivation that makes it a circular one.

— Ruth E. Kastner


We should not derive einselection via decoherence. Instead, they should be regarded as different parts or different presentations of the same theory.

In other words, “einselection” and “decoherence” are synonyms.

— Me@2019-09-21 05:53:53 PM


There has been significant work on correctly identifying the pointer states in the case of a massive particle decohered by collisions with a fluid environment, often known as collisional decoherence. In particular, Busse and Hornberger have identified certain solitonic wavepackets as being unusually stable in the presence of such decoherence.

— Wikipedia on Einselection



2019.09.22 Sunday (c) All rights reserved by ACHK


A physics statement is meaningful only if it is with respect to an observer. So the many-world theory is meaningless.

— Me@2018-08-31 12:55:54 PM

— Me@2019-05-11 09:41:55 PM


Answer me the following yes/no question:

In your multi-universe theory, is it possible, at least in principle, for an observer in one universe to interact with any of the other universes?

If no, then it is equivalent to say that those other universes do not exist.

If yes, then those other universes are not “other” universes at all, but actually just other parts of the same universe.

— Me@2019-05-11 09:43:40 PM



2019.05.11 Saturday (c) All rights reserved by ACHK

The problem of induction 3.2

The meaning of induction is that

we regard, for example, that

“AAAAA –> the sixth is also A”

is more likely than

“AA –> the second is also A”


We use induction to find “patterns”. However, the induced results might not be true. Then, why do we use induction at all?

There is everything to win but nothing to lose.

— Hans Reichenbach

If the universe has some patterns, we can use induction to find those patterns.

But if the universe has no patterns at all, then we cannot use any methods, induction or else, to find any patterns.


However, to find patterns, besides induction, what are the other methods?

What is meaning of “pattern-finding methods other than induction”?

— Me@2012.11.05

— Me@2018.12.10



2018.12.10 Monday (c) All rights reserved by ACHK

The problem of induction 3


In a sense (of the word “pattern”), there is always a pattern.


Where if there are no patterns, everything is random?

Then we have a meta-pattern; we can use probability laws:

In that case, every (microscopic) case is equally probable. Then by counting the possible number of microstates of each macrostate, we can deduce that which macrostate is the most probable.


Where if not all microstates are equally probable?

Then it has patterns directly.

For example, we can deduce that which microstate is the most probable.

— Me@2012.11.05



2018.11.19 Monday (c) All rights reserved by ACHK

Relational quantum mechanics

EPR paradox, 10


Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and has since been expanded upon by a number of theorists. It is inspired by the key idea behind special relativity, that the details of an observation depend on the reference frame of the observer, and uses some ideas from Wheeler on quantum information.


Relational solution

In RQM, an interaction between a system and an observer is necessary for the system to have clearly defined properties relative to that observer. Since the two measurement events take place at spacelike separation, they do not lie in the intersection of Alice’s and Bob’s light cones. Indeed, there is no observer who can instantaneously measure both electrons’ spin.

The key to the RQM analysis is to remember that the results obtained on each “wing” of the experiment only become determinate for a given observer once that observer has interacted with the other observer involved. As far as Alice is concerned, the specific results obtained on Bob’s wing of the experiment are indeterminate for her, although she will know that Bob has a definite result. In order to find out what result Bob has, she has to interact with him at some time {\displaystyle t_{3}} in their future light cones, through ordinary classical information channels.

The question then becomes one of whether the expected correlations in results will appear: will the two particles behave in accordance with the laws of quantum mechanics? Let us denote by {\displaystyle M_{A}(\alpha )} the idea that the observer {\displaystyle A} (Alice) measures the state of the system {\displaystyle \alpha} (Alice’s particle).

So, at time {\displaystyle t_{2}}, Alice knows the value of {\displaystyle M_{A}(\alpha )}: the spin of her particle, relative to herself. But, since the particles are in a singlet state, she knows that

{\displaystyle M_{A}(\alpha )+M_{A}(\beta )=0,}

and so if she measures her particle’s spin to be {\displaystyle \sigma }, she can predict that Bob’s particle ( {\displaystyle \beta } ) will have spin {\displaystyle -\sigma }. All this follows from standard quantum mechanics, and there is no “spooky action at a distance” yet. From the “coherence-operator” discussed above, Alice also knows that if at {\displaystyle t_{3}} she measures Bob’s particle and then measures Bob (that is asks him what result he got) — or vice versa — the results will be consistent:

{\displaystyle M_{A}(B)=M_{A}(\beta )}

Finally, if a third observer (Charles, say) comes along and measures Alice, Bob, and their respective particles, he will find that everyone still agrees, because his own “coherence-operator” demands that

{\displaystyle M_{C}(A)=M_{C}(\alpha )} and {\displaystyle M_{C}(B)=M_{C}(\beta )}

while knowledge that the particles were in a singlet state tells him that

{\displaystyle M_{C}(\alpha )+M_{C}(\beta )=0.}

Thus the relational interpretation, by shedding the notion of an “absolute state” of the system, allows for an analysis of the EPR paradox which neither violates traditional locality constraints, nor implies superluminal information transfer, since we can assume that all observers are moving at comfortable sub-light velocities. And, most importantly, the results of every observer are in full accordance with those expected by conventional quantum mechanics.

— Wikipedia on Relational quantum mechanics



2018.10.22 Monday ACHK

Pointer state

Eigenstates 3


In quantum Darwinism and similar theories, pointer states are quantum states that are less perturbed by decoherence than other states, and are the quantum equivalents of the classical states of the system after decoherence has occurred through interaction with the environment.

— Wikipedia on Pointer state


In calculation, if a quantum state is in a superposition, that superposition is a superposition of eigenstates.

However, real superposition does not just includes states that make macroscopic senses.


That is the major mistake of the many-worlds interpretation of quantum mechanics.

— Me@2017-12-30 10:24 AM

— Me@2018-07-03 07:24 PM



2018.07.03 Tuesday (c) All rights reserved by ACHK

Quantum Computing, 2

stcredzero 3 months ago

A note for the savvy: A quantum computer is not a magic bit-string that mysteriously flips to the correct answer. A n-qubit quantum computer is not like 2^n phantom computers running at the same time in some quantum superposition phantom-zone. That’s the popular misconception, but it’s effectively ignorant techno-woo.

Here’s what really happens. If you have a string of n-qubits, when you measure them, they might end up randomly in [one] of the 2^n possible configurations. However, if you apply some operations to your string of n-qubits using quantum gates, you can usefully bias their wave equations, such that the probabilities of certain configurations are much more likely to appear. (You can’t have too many of these operations, however, as that runs the risk of decoherence.) Hopefully, you can do this in such a way, that the biased configurations are the answer to a problem you want to solve.

So then, if you have a quantum computer in such a setup, you can run it a bunch of times, and if everything goes well after enough iterations, you will be able to notice a bias towards certain configurations of the string of bits. If you can do this often enough to get statistical significance, then you can be pretty confident you’ve found your answers.

— An Argument Against Quantum Computers

— Hacker News



2018.05.17 Thursday ACHK

Superposition always exist

A Non-classical Feature, 2

superposition ~ linear overlapping

~ f(ax + by) = a f(x) + b f(y)

Reality is a linear overlapping of potential realities, although different components may have different weightings.

Superposition always exists, if it exists at the beginning of a process.

So the expression “the wave function collapses and the superposition ceases to exist” does not make sense. 

Superposition always exist; interference (pattern) does not.

For a superposition to have an interference pattern, the two (for example) component eigenstates need to have a constant phase difference.

In other words, they have to be coherent.

superposition without an interference pattern

~ microscopically decoherent component states

~ macroscopically a classical state

— Me@2016-09-01 4:42 AM

2016.11.27 Sunday (c) All rights reserved by 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

Single-world interpretation, 7.2

Quantum Mechanics 3

Under the many-worlds interpretation, the Schrodinger equation, or relativistic analog, holds all the time everywhere. An observation or measurement of an object by an observer is modeled by applying the wave equation to the entire system comprising the observer and the object. 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”. Since many observation-like events have happened, and are constantly happening, there are an enormous and growing number of simultaneously existing states.

If a system is composed of two or more subsystems, the system’s state will be a superposition of products of the subsystems’ states. Once the subsystems interact, their states are no longer independent. Each product of subsystem states in the overall superposition evolves over time independently of other products. The subsystems states have become correlated or entangled and it is no longer possible to consider them independent of one another. In Everett’s terminology each subsystem state was now correlated with its relative state, since each subsystem must now be considered relative to the other subsystems with which it has interacted.

— Wikipedia on Many-worlds interpretation

This is insightful, but incorrect. Please refer to my previous post “Single-world interpretation, 7” for details.

The main theme is that the macroscopic reality can never be an eigen-quantum-state. Instead, the macroscopic reality is the resultant effect of the superposition of eigen-quantum-states. For example, without quantum superposition, there would be no Principle of Least Action in classical mechanics.

— Me@2012-12-28 12:52:12 PM

In particular, Sidney explains that our world is a quantum world and any phenomena that look classical are approximate or derived. So it’s really nonsensical to ask for an “interpretation of quantum mechanics”. Instead, one should really discuss the “interpretation of classical physics” and its derivative appearance from the quantum framework.

Of course, Sidney was well aware of the fact – and made this fact explicit – that the people who have problems with these concepts have those problems simply because they believe that underneath quantum mechanics, there is still some classical physics operating.

— Sidney Coleman: Quantum mechanics in your face

— Lubos Motl

2012.12.28 Friday (c) All rights reserved by ACHK

Single-world interpretation, 6.2.2

Information lost, 5

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

This environment theory is not totally accurate. For example, in the photon double slit experiment, during the wave function collapse, 

sqrt(2) | left > + sqrt(2) | right >

–> | left >    ,

| right > as the unchosen choice, or the lost information, goes to the environment.      

However, the macroscopic reality of | photon goes left > requires not only the state of the photon but also the state of its environment, including the lost information | right >_micro. Just the lost information itself is not enough to form a macroscopic reality.

— Me@2012.04.03

2012.11.16 Friday (c) All rights reserved by ACHK

機會率哲學 1.6

這段改編自 2010 年 4 月 3 日的對話。

In fact, the spectrum of interpretations in quantum mechanics has a close analogue in probability theory. The “wave function is real” view is analogous to the “frequentist” view of probability theory where probabilities describe “random pheonomena” like rolling dice or radioactive decays and the “wave function represents what you know about the system” view is analogous to the Bayesian view where probability is just a consistent way of assigning [likelihoods] to propositions independent of whether they have anything to do with a “random process.”

— Bayesian Probability Theory and Quantum Mechanics

— John Baez






— Me@2012.11.03

致讀者:我於去年(2011)已經搞清了「機會率」的真正意義。如果你想知道,請參閱本網誌 quantum probability (量子機率)和 single-world interpretation(單重宇宙) 類的文章。你將會得到部分答案。


— Me@2012.11.03

2012.11.03 Saturday (c) All rights reserved by ACHK