Why is Decoherence Needed in Quantum Mechanics?

[zonde]

I would like to understand why is decoherence needed in QM.
As I understand decoherence models irreversibility.
But if two quantum systems interact and resulting states are going in different directions they can't produce interference, right? Even if they do not interact with environment. So isn't it possible that isolated quantum system still undergoes irreversible evolution?

 

[Jilang]

A couple of strategically placed mirrors could make the process reversible though. So is it really irreversible?

 

[atyy]

I would like to understand why is decoherence needed in QM.
As I understand decoherence models irreversibility.

Decoherence is simply a part of QM in any interpretation. It comes for free.

But if two quantum systems interact and resulting states are going in different directions they can't produce interference, right? Even if they do not interact with environment. So isn't it possible that isolated quantum system still undergoes irreversible evolution?

In Copenhagen, it is unknown whether there is such a thing as an isolated quantum system. The wave function is just a tool to make predictions for observations, which necessarily means an interaction between the apparatus and the quantum system.

In Bohmian Mechanics and MWI, an isolated quantum system undergoes reversible evolution.

 

[zonde]

A couple of strategically placed mirrors could make the process reversible though. So is it really irreversible?

But do not mirrors represent environment?
And secondly in order to get observable interference mirrors would have to be place very precisely and for many identical interactions. So FAPP that won't happen unless you try to do this (in experiment).

 

[Jilang]

You asked if the process were reversible. The answer would be yes. Would it reverse spontaneously, not without the mirrors. Is there decoherence? I would say not.

 

[bhobba]

I would like to understand why is decoherence needed in QM.

It not a matter of being needed or not - its deducible from its basic axioms - no way around it.

What you MAY be asking is why its needed in interpretations and explaining collapse etc.

It isn't. In fact Ballentine specifically states it has no interpretational value at all and in his interpretation (the ensemble interpretation) it doesn't. However it has shed light on the so called measurement problem and because of that some interpretations take it on board eg Many Worlds, Consistent Histories, Bohmian Mechanics, Ignorance Ensemble to name a few. What it does is change how the measurement problem is viewed - now its not what causes collapse (collapse was never really part of QM anyway) but why do we get any outcomes at all; without going into what that means technically (it's the difference between an improper and a proper mixed state).

If you want to pursue it further here is THE book to get:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

It approachable after a first course in QM.

Thanks
Bill

 

[zonde]

Decoherence is simply a part of QM in any interpretation. It comes for free.

Let's take light. Obviously there are light sources that won't produce interference in double slit experiment. But once you have increased coherence of light say with bandpass filter how do you loose it?

 

[zonde]

What it does is change how the measurement problem is viewed - now its not what causes collapse (collapse was never really part of QM anyway) but why do we get any outcomes at all; without going into what that means technically (it's the difference between an improper and a proper mixed state).

Wikipedia says something similar:
"Specifically, decoherence does not attempt to explain the measurement problem. Rather, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive."
But I don't get it.
Let's take example. Beam of polarized light goes through polarization beam splitter at an angle. Later two resulting beams are detected with photodiodes. If I look at two beams after beam splitter they represent two coherent states. When a beam hits detector I get signal as photons are absorbed by electrons. I don't really see where decoherence comes into the picture and what it explains here.

If you want to pursue it further here is THE book to get:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

I don't want to go further. Basic understanding would be enough.

 

[Nugatory]

Let's take example. Beam of polarized light goes through polarization beam splitter at an angle. Later two resulting beams are detected with photodiodes. If I look at two beams after beam splitter they represent two coherent states. When a beam hits detector I get signal as photons are absorbed by electrons. I don't really see where decoherence comes into the picture and what it explains here.

The photons are absorbed by the electrons. But what happens to the electrons? The absorption of the photons is an interaction, so we'd expect the electrons to end up in a state which is also a superposition; and the electrons are part of the detector, so instead of having a detector which either detected or didn't detect, we'd have a detector that is in a superposition of detected and didn't detect. But we know that real-world detectors don't act that way.

Decoherence explains how a macroscopic object can (and usually does, unless we do heroic things to prevent it) behave classically, even though it is made up of a very large number of particles each individually doing weird quantum things.

A good non-technical introduction, mentioned in many posts in this forum, is https://www.amazon.com/dp/0465067867/?tag=pfamazon01-20

 

[f95toli]

Don't get sidetracked by focusing too much on experiments in quantum optics. This is a very specific situation and it gets difficult to analyze because photons are so "weird".
If you want to understand how/why decoherence affects quantum systems you'd be better off looking at some other system. The easiest example is probably an electric RCL circuit:the oscillations of the LC circuit (which in QM terms is just a harmonic oscillator) are damped by the resistor. A full QM treatment of this which includes decoherence could e.g. be a hamiltonian consisting of a harmonic oscillator a^†a and a Lindbladian which accounts for the decay and is inversely proportional to the resistance.

This is formalism is incidentally the starting point for Jaynes-Cummings Hamiltonian which is used to model cavity/circuit QED experiments.

 

[stevendaryl]

It isn't. In fact Ballentine specifically states it has no interpretational value at all and in his interpretation (the ensemble interpretation) it doesn't.

I think it may be just buried in the assumptions. You might say something like

If a system is in state [itex]\psi[/itex] and you measure an observable corresponding to an operator [itex]O[/itex], then you will get [itex]\lambda[/itex] with probability [itex]|\langle \psi | \psi_\lambda \rangle|^2[/itex], where [itex]\psi_\lambda[/itex] is the projection of [itex]\psi[/itex] onto the subspace where [itex]O[/itex] has eigenvalue [itex]\lambda[/itex].
​

That doesn't seem to have anything whatsoever to do with decoherence. However, you need to ask the question: What does it mean to say that we have performed a measurement of the observable corresponding to operator [itex]O[/itex]? It seems to me that it means that you've set things up so that microscopic details (such as the value of some observable property of a particle) are amplfied to make a macroscopic difference (the presence or absence of a "click" on a Geiger counter, for instance). To really make sense of that, it seems that you need to know that macroscopic states are distinguishable, and don't interfere with each other the way that microscopic states do. And something like decoherence is involved in making macroscopic states distinguishable (so they "classical" for many purposes).

Of course, you can ignore the question of what it means to measure something, and just develop the theory under the assumption that observables are measurable.

 

[zonde]

The photons are absorbed by the electrons. But what happens to the electrons? The absorption of the photons is an interaction, so we'd expect the electrons to end up in a state which is also a superposition; and the electrons are part of the detector, so instead of having a detector which either detected or didn't detect, we'd have a detector that is in a superposition of detected and didn't detect.

As I understand decoherence does not solve problem of definite outcomes. Only disappearance of interference.
Speaking about states I believe that it's not exactly detector that has two states of detected and not detected but electrons instead. And the click state is represented by electrical pulse that have left detector and does not dissipate in environment (as we would not be able to make a record of that click).

But we know that real-world detectors don't act that way.

How do you know? In quantum world there are no superposition states, there are only superposition of states. If you say that in classical world you could see superposition state if there would be one because it's different that quantum world ... well it would seem quite strange reasoning. But I suppose it's related to cats.

 

[StevieTNZ]

How do you know? In quantum world there are no superposition states, there are only superposition of states. If you say that in classical world you could see superposition state if there would be one because it's different that quantum world ... well it would seem quite strange reasoning. But I suppose it's related to cats.

I always think that why we don't see a 'classical' system in superposition is because 'collapse of the wave function' has occurred.

 

[zonde]

I always think that why we don't see a 'classical' system in superposition is because 'collapse of the wave function' has occurred.

And what it is that we don't see? How does "'classical' system in superposition" look like?

 

[Nugatory]

QUOTE="zonde, post: 5076477, member: 129046"]As I understand decoherence does not solve problem of definite outcomes. Only disappearance of interference.
[/quote]
Yes, but that's enough to explain the lack of observed macroscopic weirdness (except in experiments where we have gone to great lengths to suppress interaction with the environment), and that's all that most people claim for decoherence. We still end up not knowing what the detector detected until we look, but we know that we have one or the other result with no interference between them.

Before the discovery of decoherence, there was nothing in theory to explain why Schrodinger's cat would be either in a dead state or a live state, but never in a superposition of the two before someone opened the box. The best answer most interpretations could come up with was:

I always think that why we don't see a 'classical' system in superposition is because 'collapse of the wave function' has occurred.

That was a less than completely satisfying answer because there's nothing in the theory that explains why some interactions have to collapse the wave function and others don't. Yes, it's true that the wave function collapse happens at the boundary between the quantum and classical worlds, but because "classical" was defined as where the wave function collapse happens, that answer explained little. What made the cat "classical"? Suppose we ran the experiment with an oyster? Or a bacterium? Or just the detector and the cyanide vial?

Decoherence basically says that the ordinary unitary evolution of a quantum system interacting with its environment will produce results that are experimentally indistinguishable from collapse, but without requiring an arbitrary division into classical and quantum and a near-magical non-unitary collapse at the boundary.

 

[zonde]

Yes, but that's enough to explain the lack of observed macroscopic weirdness (except in experiments where we have gone to great lengths to suppress interaction with the environment),

Can you give reference for experiment where we have gone to great lengths to suppress interaction with the environment and observe macroscopic weirdness?

Before the discovery of decoherence, there was nothing in theory to explain why Schrodinger's cat would be either in a dead state or a live state, but never in a superposition of the two before someone opened the box. The best answer most interpretations could come up with was:

That was a less than completely satisfying answer because there's nothing in the theory that explains why some interactions have to collapse the wave function and others don't. Yes, it's true that the wave function collapse happens at the boundary between the quantum and classical worlds, but because "classical" was defined as where the wave function collapse happens, that answer explained little. What made the cat "classical"? Suppose we ran the experiment with an oyster? Or a bacterium? Or just the detector and the cyanide vial?

Decoherence basically says that the ordinary unitary evolution of a quantum system interacting with its environment will produce results that are experimentally indistinguishable from collapse, but without requiring an arbitrary division into classical and quantum and a near-magical non-unitary collapse at the boundary.

So from this I take that decoherence is attempt to make QM unequivocal. So it has more to do with consistency of theory than some specific observations.

 

[bhobba]

Can you give reference for experiment where we have gone to great lengths to suppress interaction with the environment and observe macroscopic weirdness?

http://physicsworld.com/cws/article/news/2010/mar/18/quantum-effect-spotted-in-a-visible-object

Thanks
Bill

 

[zonde]

Don't get sidetracked by focusing too much on experiments in quantum optics. This is a very specific situation and it gets difficult to analyze because photons are so "weird".

Photons are not weird (at least not weirder than matter). People who try to model photons the same way as matter particles are weird.

 

[f95toli]

Can you give reference for experiment where we have gone to great lengths to suppress interaction with the environment and observe macroscopic weirdness?So from this I take that decoherence is attempt to make QM unequivocal. So it has more to do with consistency of theory than some specific observations.

The fact that you are not already aware of these experiments sort of proves my point. Both pop-science and intro courses to QM tend to focus way too much on e..g the double slit experiment and largely ignore just about every interesting experiment that has been done since Aspects work on the Bell inequalities. It is of course true that this is a key experiment in QM, but it is ALSO true that is a very difficult experiment to understand in detail . Most of the recent work in QM (over the past 30 years or) has focused on other types of systems, e.g. trapped ions, atoms and artificial two-level systems such as solid state qubits (quantum dots, superconducting circuits etc). This latter development has to a large extent been what has motivated the development of a relatively simple framework for handling decoherence; this is simply because decoherence is much more noticeable (and important) in these systems, the underlying mechanisms are much easier to understand than in optics and the coherence can also be dramatically increased by careful design (choice of material etc) so understanding it is of considerably practical importance.

Photons are not weird (at least not weirder than matter). People who try to model photons the same way as matter particles are weird.

Of course they are weird: they are intrinsically quantum mechanical. They are also much more difficult to handle mathematically than e..g a two-level system since you can't even write down a SE. This makes them extremely counter-intuitive.
If you want to get a better understanding of decoherence it is therefore much better to start with a classical system (e.g. a electrical or mechanical resonator or a two-level system) that behaves "classically" when it interacts with the environment, but can be made to exhibit QM effects when sufficiently isolated ( by cooling to down to very low temperatures etc). Some useful models for these can even by analyzed with just some simple algebra (decaying Rabi oscillations in a two-level system coupled to a heat bath)

 

[lucas_]

When you see chairs and tables. They are collapsed. Yet when you see atoms and molecules. They are not collapsed. So how do you reconcile the two? Can we say the position eigenstates are collapsed while the Hamiltonians are uncollapsed.. but how could the atoms/molecules in position collapsed eigenvalues still respond to the environmental hamiltonians?

 

[StevieTNZ]

me up with was:

That was a less than completely satisfying answer because there's nothing in the theory that explains why some interactions have to collapse the wave function and others don't. Yes, it's true that the wave function collapse happens at the boundary between the quantum and classical worlds, but because "classical" was defined as where the wave function collapse happens, that answer explained little. What made the cat "classical"? Suppose we ran the experiment with an oyster? Or a bacterium? Or just the detector and the cyanide vial?

I think you are reading more into my, I admit short, response. I speech marked 'classical' and refer to a 'classical' system as Newtonian Mechanics would (although in principle these are also quantum systems). I don't believe collapse happens at the boundary of classical and quantum worlds; there is no division in quantum theory. I was merely stating that because we see everyday items in definite states that 'collapse of the wave function' (however it may occur, and I say collapse to say 'so we see a definite result [it does not mean the system is not still in superposition and we are only seeing one of its states]).

 

[Nugatory]

When you see chairs and tables. They are collapsed. Yet when you see atoms and molecules. They are not collapsed. So how do you reconcile the two? Can we say the position eigenstates are collapsed while the Hamiltonians are uncollapsed.. but how could the atoms/molecules in position collapsed eigenvalues still respond to the environmental hamiltonians?

When you see chairs and tables and other macroscopic objects, they are not "collapsed" - their state is a mixture that can only be described with a density matrix, and it is neither a pure state nor an eigenstate of any physically interesting operator.

The macroscopic object has an enormous number of internal degrees of freedom and therefore an enormous number of accessible states, and it moves at random among them. It just so happens that the overwhelming majority of those states are ones in which the object is located within a few atomic diameters of one position, so that's where we'll find it.

As an analogy, you could think about a volume of gas in a container. It contains some enormous number of molecules, all doing their own quantum mechanical thing, collapsing their wave functions into position eigenstates (Could I ask the specialists here to please withhold their maledictions for a moment?) when they interact with their neighbors and then evolving into new states in which their position is no longer certain. Despite all that quantum mechanical weirdness, on average the number of molecules interacting with the walls with container per unit time will be constant, so the pressure on the walls will be constant and consistent with the ideal gas law ##pV=nRT##. You would not, however, conclude that the gas is in a single pure state that is an eigenstate of some operator that gives you the pressure; instead you would conclude that any measurement of the pressure is going to yield a value that is very close to the expectation value.

 

[bhobba]

When you see chairs and tables. They are collapsed. Yet when you see atoms and molecules. They are not collapsed.

Seeing and not collapsed doesn't make any sense since seeing is an observation.

Thanks
Bill

 

[atyy]

When you see chairs and tables. They are collapsed. Yet when you see atoms and molecules. They are not collapsed. So how do you reconcile the two? Can we say the position eigenstates are collapsed while the Hamiltonians are uncollapsed.. but how could the atoms/molecules in position collapsed eigenvalues still respond to the environmental hamiltonians?

In the Copenhagen interpretation, whenever you see something, the wave function will collapse. The tables and chairs and the atoms are equally collapsed. It turns out that in many cases, if one wishes to include the environment in one's description, decoherence causes apparent collapse of the atoms to the energy eigenstate. When you make the observation, then the atom collapses to an energy eigenstate.

Schlosshauer, http://arxiv.org/abs/quant-ph/0312059 (p14): When the interaction with the environment is weak and ##\hat{H}_{S}## dominates the evolution of the system (that is, when the environment is “slow” in the above sense), a case that frequently occurs in the microscopic domain, pointer states will arise that are energy eigenstates of ##\hat{H}_{S}## (Paz and Zurek, 1999)

Paz and Zurek, http://arxiv.org/abs/quant-ph/9811026: We investigate decoherence in the limit where the interaction with the environment is weak and the evolution is dominated by the self Hamiltonian of the system. We show that in this case quantized eigenstates of energy emerge as pointer states selected through the predictability sieve.

 

[lucas_]

In the Copenhagen interpretation, whenever you see something, the wave function will collapse. The tables and chairs and the atoms are equally collapsed. It turns out that in many cases, if one wishes to include the environment in one's description, decoherence causes apparent collapse of the atoms to the energy eigenstate. When you make the observation, then the atom collapses to an energy eigenstate.

Schlosshauer, http://arxiv.org/abs/quant-ph/0312059 (p14): When the interaction with the environment is weak and ##\hat{H}_{S}## dominates the evolution of the system (that is, when the environment is “slow” in the above sense), a case that frequently occurs in the microscopic domain, pointer states will arise that are energy eigenstates of ##\hat{H}_{S}## (Paz and Zurek, 1999)

"When the interaction with the environment is weak".. is this referring to isolated quantum system or everyday object?

If the object is already in eigenstates of position, is it still available to be perturbed such that the pointer states will change to energy eigenstates?

In systems (irregardless of decomposition) where the pointer states are energy eigenstates. What would be the effect of different values of the pointer states of energy eigenstates from the environment on the system.. would this make the electrons become higher in orbital or would it just contribute to more vibrational degree of freedom in the molecules (making it hotter for instance)?

Paz and Zurek, http://arxiv.org/abs/quant-ph/9811026: We investigate decoherence in the limit where the interaction with the environment is weak and the evolution is dominated by the self Hamiltonian of the system. We show that in this case quantized eigenstates of energy emerge as pointer states selected through the predictability sieve.

 

[zonde]

The fact that you are not already aware of these experiments sort of proves my point.

I don't think so. Of course there are experiments where we have gone to great lengths to suppress interaction with the environment. But the key part here is "observable macroscopic weirdness". I would say that the closest to that "observable macroscopic weirdness" would be double slit type experiment with buckyball molecules and later experiments with even larger molecules. But you don't do double slit experiments with chairs on everyday basis. So the point that the classical world lacks observable quantum weirdness because of decoherence isn't self obvious.

Both pop-science and intro courses to QM tend to focus way too much on e..g the double slit experiment and largely ignore just about every interesting experiment that has been done since Aspects work on the Bell inequalities. It is of course true that this is a key experiment in QM, but it is ALSO true that is a very difficult experiment to understand in detail . Most of the recent work in QM (over the past 30 years or) has focused on other types of systems, e.g. trapped ions, atoms and artificial two-level systems such as solid state qubits (quantum dots, superconducting circuits etc). This latter development has to a large extent been what has motivated the development of a relatively simple framework for handling decoherence; this is simply because decoherence is much more noticeable (and important) in these systems, the underlying mechanisms are much easier to understand than in optics and the coherence can also be dramatically increased by careful design (choice of material etc) so understanding it is of considerably practical importance.

Yes, you have made a point that decoherence is common concern for experimentalists so it's well studied. So even if I am interested about decoherence "as a measurement" it clarifies things a lot. Thanks.

Of course they are weird: they are intrinsically quantum mechanical.

You automatically without the slightest doubt apply the same laws to photons as you apply them to matter particles. And then you claim that photons are weird. That sort of proves my point.
But you know that there are some key differences between photons and matter particles, right? You can't study photons directly or at least not the way you can matter particles. And then photons move at speed of light, so time for photons is not really defined according to special relativity.

 

[f95toli]

I don't think so. Of course there are experiments where we have gone to great lengths to suppress interaction with the environment. But the key part here is "observable macroscopic weirdness". I would say that the closest to that "observable macroscopic weirdness" would be double slit type experiment with buckyball molecules and later experiments with even larger molecules. But you don't do double slit experiments with chairs on everyday basis. So the point that the classical world lacks observable quantum weirdness because of decoherence isn't self obvious.

I disagree. Experiments that show that you can put objects such as micromechanical resonators (essentially just vibrating beams, large enough that you can see them in an optical microscope, see Bill's link above) or large (mm sized) electrical circuits into quantum superposition is -in my view- an even better example. Buckyballs are large, but they are still microscopic single molecules. Note also that the question about the possibility of macroscopic quantum coherence (MQC) and/or tunneling (MQT) was not really settled until the mid 80s when e.g. experiments on MQT in Josephson junctions settled the question. See e.g. the writings by Legget.

You automatically without the slightest doubt apply the same laws to photons as you apply them to matter particles. And then you claim that photons are weird. That sort of proves my point.
But you know that there are some key differences between photons and matter particles, right? You can't study photons directly or at least not the way you can matter particles. And then photons move at speed of light, so time for photons is not really defined according to special relativity.

I am fully aware of the differences (one of the things I work on is creating single photon emitters in the microwave regime), and the differences you mention are exactly what makes photons "weird" (as in "quantum weirdness") in m view. I have never met anyone who works on QM and/or quantum optics who did not share that view. It is even difficult to pin down what a single photon is (a friend if mine wrote a review article about single photon sources a few years ago, he ended up writing a whole page about what he actually meant by "single photon")
But you also need to remember the "technical" problems you encounter when dealing with photons. They are much more difficult to handle even theoretically than say a two-level system (e,.g. no SE) and it is also more difficult to understand conceptually; there is no equivalent to a Bloch sphere for a photon so there is no straightforward way to visualize the evolution and certainly not the effects of decoherence. This is my main reason for believing that there is too much focus on the double-slit experiment in intro QM.

 

[zonde]

I disagree. Experiments that show that you can put objects such as micromechanical resonators (essentially just vibrating beams, large enough that you can see them in an optical microscope, see Bill's link above) or large (mm sized) electrical circuits into quantum superposition is -in my view- an even better example. Buckyballs are large, but they are still microscopic single molecules.

Micromechanical resonator is bigger but the quantum weirdness part is far from obvious in this experiment - http://www.nature.com/nature/journal/vaop/ncurrent/full/nature08967.html
I did not find where is interference measured (needed for the claim that there is superposition of macroscopically discernible states). And besides it makes sense to say that quantum particle in this experiment is phonon.
So this experiment completely fails to demonstrate the point about macroscopic weirdness. I will stick to buckyball double-slit as better example.

I am fully aware of the differences (one of the things I work on is creating single photon emitters in the microwave regime), and the differences you mention are exactly what makes photons "weird" (as in "quantum weirdness") in m view. I have never met anyone who works on QM and/or quantum optics who did not share that view. It is even difficult to pin down what a single photon is (a friend if mine wrote a review article about single photon sources a few years ago, he ended up writing a whole page about what he actually meant by "single photon")
But you also need to remember the "technical" problems you encounter when dealing with photons. They are much more difficult to handle even theoretically than say a two-level system (e,.g. no SE) and it is also more difficult to understand conceptually; there is no equivalent to a Bloch sphere for a photon so there is no straightforward way to visualize the evolution and certainly not the effects of decoherence. This is my main reason for believing that there is too much focus on the double-slit experiment in intro QM.

Well, because time is not defined for photons there shouldn't be any evolution for photons and any evolution should be on the side of matter particles. So photons just as well could be classical particles with any "advanced" properties actually belonging to matter and being just "encoded/decoded" in/from photon ensembles rather than individual photons.

I know little about microwave photons however so I imagine there could be other peculiarities.

 

[lucas_]

The photons from CMBR are everywhere and can't be shielded and said to decohere things to position eigenstates. But how come one can perform double slit experiment or the c60 buckyball... won't the CMBR photons interact with them or are they somehow shielded from this, and how?.

 

[craigi]

The photons from CMBR are everywhere and can't be shielded and said to decohere things to position eigenstates. But how come one can perform double slit experiment or the c60 buckyball... won't the CMBR photons interact with them or are they somehow shielded from this, and how?.

The C60 beam is shielded by metal.

It's very easy to shield against microwaves. The CMBR is of very liitle concern.

Do mean cosmic rays? If so, there aren't many of them. The probabilty of a cosmic ray interaction with the C60 is so low to be negligble. In the rare event that a cosmic ray does hit a C60 molecule, it'll blow the molecule apart and it won't contribute to the interference pattern, but the others will.

 

[bhobba]

The photons from CMBR are everywhere and can't be shielded

They can be shielded.

Thanks
Bill

 

[stevendaryl]

When you see chairs and tables. They are collapsed. Yet when you see atoms and molecules. They are not collapsed. So how do you reconcile the two? Can we say the position eigenstates are collapsed while the Hamiltonians are uncollapsed.. but how could the atoms/molecules in position collapsed eigenvalues still respond to the environmental hamiltonians?

I have a complaint about the claim "We see that [the wavefunctions of] chairs and tables are collapsed". It seems obvious that it's true, but think about what it would mean to be otherwise.

In quantum mechanics, the behavior of a superposition (or mixture--there is a technical difference which isn't important here) is completely determined by the behavior of the corresponding pure states. Suppose you set things up so that there is a consequence of being in one state or another:

1. If the system is in state [itex]|A\rangle[/itex], then consequence [itex]C_A[/itex] happens.
2. If the system is in state [itex]|B\rangle[/itex], then consequence [itex]C_B[/itex] happens.

Then if the consequence itself is governed by quantum-mechanical laws, then we conclude:

If the system is in a superposition/mixture of states [itex]|A\rangle[/itex] and [itex]|B\rangle[/itex], then the consequence will be a superposition/mixture of [itex]C_A[/itex] and [itex]C_B[/itex]​

So how does this apply to tables and chairs? Well, suppose you have a folding chair, and for simplicity, we consider two states, either "open" or "folded". So you take a notebook and walk into the room where the chair is, resolved to record what you see:

1. If it is open, you write "open".
2. If it is folded, you write "folded".
3. If it is in a superposition or mixture of these two states, you write "both"

Well, according to QM if you yourself are governed by quantum mechanics, then you'll never write "both". Instead, what will happen is:

1. If it is open, afterward the notebook will contain the word "open"
2. If it is folded, afterward the notebook will contain the word "folded"
3. If it is in a superposition or mixture, afterward the notebook will be in a superposition or mixture of having the word "open" and having the word "folded"

There is no possibility of your writing the word "both" in the notebook (at least not if we assume that you always write "open" if it's open, and "folded" if it's folded)

Another way to say it is that the three possible consequences: write "open", write "folded", write "both" are contradictory; if the first two happen, then the third will never happen.

Note: this is assuming that you yourself are governed by quantum mechanical laws. Some interpretations of quantum mechanics treat observers as special cases. But in these interpretations, observing the chair causes its wavefunction to "collapse". So you wouldn't write "both" in that interpretation, either.

 

[atyy]

Well, according to QM if you yourself are governed by quantum mechanics, then you'll never write "both". Instead, what will happen is:

1. If it is open, afterward the notebook will contain the word "open"
2. If it is folded, afterward the notebook will contain the word "folded"
3. If it is in a superposition or mixture, afterward the notebook will be in a superposition or mixture of having the word "open" and having the word "folded"

There is no possibility of your writing the word "both" in the notebook (at least not if we assume that you always write "open" if it's open, and "folded" if it's folded)

How do we know from QM that the notebook being in a superposition of "open" and "folded" is not "both"?

For example, for spins, ##|x\rangle = |u\rangle+|d\rangle##

 

[stevendaryl]

How do we know from QM that the notebook being in a superposition of "open" and "folded" is not "both"?

For example, for spins, ##|x\rangle = |u\rangle+|d\rangle##

I think it's pretty obvious that the word "both" is not a superposition of the words "open" and "folded". But you could redo the experiment, with the plan of writing "Mixed" instead of "both". If the word "both" is a superposition of "open" and "folded", then the word "Mixed" can't also be the same superposition.

 

[atyy]

I think it's pretty obvious that the word "both" is not a superposition of the words "open" and "folded". But you could redo the experiment, with the plan of writing "Mixed" instead of "both". If the word "both" is a superposition of "open" and "folded", then the word "Mixed" can't also be the same superposition.

So there is a possibility that one would see the superposition if open and folded, and write "both"?