How two quantum systems interact ?

[ronan1]

Hello

I don't understand how can two quantum systems are able to interact ?
Indeed, being in a superposition, they for examplle have no definite position before interaction, so what makes them interact ?

Some will say consciousness, but I would like another explanation if possible ?

It is especially troubling in the case of Relational Quantum Mechanics because it is stated that all of the interacting system can be seen as observer, in fact all quantum system. So what make a quantum system an observer ? the fact that it interact ?
So the question remains : How do they interact ?

Thank you

Ronan

 

[f95toli]

I suspect you are overthinking the problem. Quantum systems interact more or less in the same way as classical systems, i.e. via some form of coupling.
In many systems this coupling is essentially "classical" in the sense that it only depends on properties that you would recognize from from classical system (dipole moments etc).

Also, note that if you have two interaction quantum systems in a closed system the fact that they are coupled (i.e. the interaction part of the hamiltionian will give rise) obviously means that they in fact form ONE system.

Now, the "measurement problem" is, in fact, not an issue for a closed system. A measurement leading to a "collapse" will only be performed if the meter is in turn interacting with ANOTHER system with many degrees of freedom (i.e an enviroment).

Look at eq. 13 in the following article (which I have already referred to once today, but it is a good article).

http://www.arxiv.org/abs/quant-ph/0306072

 

[ronan1]

Thanks for your answer, I read the article but It doesn't seem to answer my question.

What do you mean by coupling ?
And how then the coupling is done ?

when you talk about two quantum system interacting in a closed system, what make them interacting ?
the fact that they are in closed system ?
if so, the whole universe should decohere and thus, no superposition should be present at any time, but the law of quantum physics are talking about superposition

or the fact that they are coupling ?Because we find some superposed system, it follows that some quantum systems are not always interacting, the question is:
what make them interacting and not interacting ?

It seems for me that it is a fundamental problem

 

[ronan1]

No one to answer ?

 

[f95toli]

Well, coupling is just a general term; two sub-systems are coupled if they somehow can "talk"; usually be exchanging energy.
Example: Take two, small, superconducting rings placed next to each other. Each ring is a quantum system that can be in two states corresponding to a current circulating clockwise or counter-clockwise. When you place two such rings next to each other they interact. This is simply due to the mutual inductance between them (same as in an ordinary transformer); i.e. it is just a "classical" effect where the so-called coupling strength will depend on parameters such as the distance, area of the loops etc.
There are many others forms of interaction, e.g. dipole-dipole interaction between particles (spin-spin coupling); systems can also interact indirectly by e.g. exchanging photons.
Now, real systems are always open which is why we have decoherence; it is also why large systems like you and me behave classically; if we want to see quantum effects in large systems (like the abovementioned rings) we have to work hard to isolate them as well as we can; thereby preventing them from interacting with the surrounding word.

 

[meopemuk]

If you want to describe an interacting quantum mechanical system (e.g., two particles interacting via potential V(r), where r = |\mathbf{r}_1 -\mathbf{r}_2|), then you should do the following:

1. Build the Hilbert space of the (2-particle) system as a tensor product of 1-particle spaces. States of the system are represented by vectors in this Hilbert space or by 2-particle wave functions like \psi(\mathbf{r}_1, \mathbf{r}_2)

2. Define the interacting Hamiltonian in the above Hilbert space. For example,

H = H_0 + V(r)

where H_0 is the sum of kinetic energies (operators) of the two particles.

3. Now the interacting time evolution of any initial state vector |\Psi \rangle is given by

|\Psi (t) \rangle = exp(\frac{i}{\hbar} Ht) |\Psi (0) \rangle

If you know this time evolution you can find the time dependence of expectation values of any observable, so you will know everything about the interacting system.

Eugene.

 

[ronan1]

Thank you for your answers!

I still have some questions:

Apparently, we need a classical view in order to do quantum physics, it seems strange to me.

Without a classical view we cannot create our prediction about the two rings ?
We need to know what are the possible future state (classical) in order to build the hilbert space ?

about the openess of systems :
the whole universe is a close system, no ?
So there should not be any decoherence ?

 

[vanesch]

Thank you for your answers!

I still have some questions:

Apparently, we need a classical view in order to do quantum physics, it seems strange to me.

Without a classical view we cannot create our prediction about the two rings ?
We need to know what are the possible future state (classical) in order to build the hilbert space ?

about the openess of systems :
the whole universe is a close system, no ?
So there should not be any decoherence ?

This is THE problem in quantum theory, and it gives rise to all the different interpretations, modifications and so on. No matter how you turn it, something weird roares up its head.

The "standard" Copenhagen interpretation indeed says that quantum dynamics is somehow limited to "microscopic" systems, and that at a certain point, the world "is classical". Apart from the vagueness of "where's the boundary", this introduces several conceptual problems, and the main one is of course the one you mention: the universe has no "outside observer". You can state that quantum theory is not applicable to large enough systems, which are then governed by classical physics, but the fact that they are just conglomerates of small systems which DO obey quantum physics makes this a strange view, unless we see both classical physics and quantum physics as limiting cases of a more profound theory. The last one is a very interesting option, but no matter how attractive it sounds, nobody has ever devised a way to build a reasonable theory that way - nevertheless - it is my personal opinion - is that a non-neglegible option, for a technical reason I won't go into detail, but which is called "the problem of time".

That said, the standard Copenhagen way is still the way everybody performs practical calculations: at a certain point, one considers a "transition to classical", and the question is: is this just a mathematical trick, or does this have anything to do with "nature".

So, as a short answer, yes, in a practical setting, we NEED a classical setting in order to do quantum calculations. When you are doing atomic or molecular physics, or when you are doing practical HEP calculations, that's no issue. However, when you go to more sophisticated situations, this quantum-classical transition starts to become a difficulty, and in any case it is a conceptual difficulty.

Now, you might think that quantum mechanics is just a kind of statistical mechanics, and there's an underlying "all classical" dynamics which explains all this. This is not entirely impossible, but the underlying dynamics must be very strange if it is to reproduce several quantum predictions. That's what Bell's theorem tells us: there is no straightforward way to implement quantum dynamics with an underlying "classical" dynamics which respects in its inner workings Lorentz invariance, and in which we can still assume that we have statistically independent "free choices" in the experimental setup.
If you drop the "Lorentz invariance" part, you CAN find a "classically-looking" dynamics of some sorts, which is Bohmian mechanics, but, apart from the problem with Lorentz invariance, there are other strange things to Bohmian mechanics too.
So this is not a straightforward route either.

There is a (weird) view on quantum mechanics, though, which tries to stay entirely within the quantum realm. It is called the many worlds view, and in my personal opinion, it is the most coherent view on the quantum theory as we know it today - which doesn't mean that it will remain so for ever if the quantum formalism evolves. As such, everything is described with quantum theory. If observers then appear in superpositions of outcome states, it is simply postulated that the observers dedouble, and "live in different apparently classical worlds, with different outcomes". Although at first sight this sounds totally crazy, when you get used to the quantum formalism this makes entirely sense. The reason is that an observer which appears in a superposition of two states, will have that these states evolve both independently, without interaction, and that, if we look at each of them, things happen as if the state was alone, and is classical.
So if you strictly apply quantum theory, it seems that out of the formalism comes that we have several independent classical evolutions in parallel. If we say that subjective experience emerges from each classical evolution independently, then this simply means that there is one quantum world, but experienced as independent parallel classical worlds.
The difficulty is how to introduce probabilities into this scheme ; there are several approaches which do this, but they all have to make some extra hypotheses. Not everything is clear in this view either.

The "independence" of the different worlds is assured by decoherence. This is why quantum interference is observable for small systems, but often becomes invisible for larger systems.

Nevertheless, these musings are all "problems of principle". In practice, we all make sooner or later a transition to classical physics, by preference as soon as possible because calculations are so much easier in classical physics than in quantum physics.

 

[ronan1]

Ok, thanks for the explanation
So
It really seems that consciousness plays a role
Without being conscious to observe, Decoherence would have no meaning,
Indeed, there are no meanings to says that the rings interacts themselves as they are quantum systems without fixed behavior (position, momentum,...)
Only by looking at their state (or more correctly at their predicted behavior in relation to the apparatus) we can say that they finally interact, but if we don't nothing happen.

Because no conscious observer were there ?

But what make us observe ? Is it our brain, which is also a quantum system ?
It doesn't make sense.
So it should be something else:

Consciousness seems to be the only candidate living outside the material world.

Why this theory (consciousness cause collapse) is not taken seriously ?
Just because about the word "consciousness" ?
Or are there some drawbacks ?

 

[vanesch]

Indeed, there are no meanings to says that the rings interacts themselves as they are quantum systems without fixed behavior (position, momentum,...)

I think there's a confusion here. The interaction itself doesn't need any form of observation. Interaction is just the coupling of subsystems through a hamiltonian that acts on both systems. You don't need any "fixed behaviour" (I understand that you mean "classical state") in order to interact!

If the wavefunction of system 1 is |psi1> and the wavefunction of system 2 is |psi2> (this is a special case!), then the system wave function is |psi> =|psi1>|psi2>
Now, there can be a hamiltonian that describes the interaction between systems 1 and 2, and this can then, through the Schroedinger equation, evolve in a state:
|psi_later> = |psi5>|psi6> + |psi7>|psi8> + |psi9>|psi10>.

This is purely described by the interaction terms in the hamiltonian, which depend upon the charge, magnetic moment, ... of the two subsystems. There's no observation here, but there is interaction.

In the latter case, we say that systems 1 and 2 are now "entangled" because we cannot assign a single state to each of them, but only a superposition:
|psi_later> = |psi5>|psi6> + |psi7>|psi8> + |psi9>|psi10>
of combined states.

 

[ronan1]

Can we talk about interaction before decoherence (thus before observation) ?
It doesn't seem so,

If we take your definition of interaction (the one before decoherence), it is an interaction postulated by a classical view, thus a postulate from a conscious being, there is no such thing as classical state before observation.
So even by taking entanglement as interaction, you still have a classical (and thus conscious) description of the system.

It is in this respect that I think consciousness is needed.

So my question remains:
Are there some experimental evidence that consciousness don't play a role in the attribution of value to the quantum states ?
Or is the consciousness role denigrated because of the enigmatic status of consciousness ?

 

[vanesch]

Can we talk about interaction before decoherence (thus before observation) ?

Of course there is interaction before decoherence ! Decoherence is a specific result of interactions with complicated systems, but interactions are there all the time. They are the heart of the quantum-mechanical time evolution.

If you write down the hamiltonian of a 2-electron atom, you have 3 "subsystems" (the nucleus, considered as 1 single entity, and 2 electrons) which interact through the electrostatic force, eventually augmented with magnetic dipole interactions. You don't need any decoherence or whatever to have these 3 subsystems interact.

 

[ronan1]

So for you decoherence happen when there is interaction between enough complicated systems?
What is the defintion of a complicated system ?
It seems really arbitrary to define decoherence this way, isn't it ?

this definition looks like the way some people say that consciousness emerge from complicated processing in the brain.

Maybe there is a link ?

Thank you for your point of view

 

[reilly]

Of course we need a classical underpinning to QM; we live, mostly, in a classical world, we think about our physical world in largely classical terms -- classical physics is, in effect, part of our common heritage, and plays a very important role in language and concept.

Of course consciousness plays a role in physics -- without conscious physicists there would be no physics -- profound, huh? Most brain scientists believe that consciousness is a consequence of neural processing, which, by the way, is basically a classical phenomena. My sense is that, slowly to be sure, the physical ingredients of consciousness are being uncovered and understood.

With all due respect, my strong sense is that the Copenhagen interpretation described by vanesch is not the one most of us use. That is, as I've mentioned many time, the key is Born's notion about probability densities = absolute value squared of the wave functions. With Sir Rudolph Peierls, Nobel Prize winner, and hero of the early days of QM, I believe that probabilities describe states of mind, knowledge in particular -- classical or quantum makes absolutely no difference. Collapse is ,simply, they way our knowledge changes from the possibility of many outcomes to the actual outcome. This approach is Occam simple. And note: everything we know about the physical world is stored in our brain, that is we are talking knowledge -- that's all we got. When we deal with any experiment, all we have is our knowledge -- communications from other experimenters show up as knowledge in our brains, as does the state of experimental apparatus. The thought of some type of classical-quantum boundary strikes me as fanciful, if not downright mystical; perhaps in th 1920s such an idea was plausible. But, in those days people did not have the extensive practical and theoretical knowledge of probability and statistics we have today.And, as still is the case today, most physicists and statisticians do not talk much. As Professor Ed Jaynes commented sometime ago, physicists are way out of date when it comes to prob and stat. I concur after roughly 30 years of work, among other things, as an economist and business statistician. The views I express are not unknown by statisticians, and at least a few physicists as well.

Note that the knowledge approach has no problems with dealing with the Universe as a whole. It's not that hard to figure out, and I'll leave it to the readers to do so. By the way, I can think of few things as "unOccam" as the multi-worlds approach -- strikes me as the efforts of 19th century romanticists trying to cope with the quantum world.

Interactions? Read up on the Heisenberg equations of motion for interacting particles, and the answer to the original question of this thread will be clear.
Regards,
Reilly Atkinson

 

[ronan1]

Reilly: "Of course we need a classical underpinning to QM"
Why so ?
Why should not we able to think in term of Quantum mechanisms ?

When you say: "My sense is that, slowly to be sure, the physical ingredients of consciousness are being uncovered and understood. "
I think you don't really know what you are talking about because, consciousness is far from being explainable.
Consciousness does not supervene logically on the physical, Zombie are logically possible and this make impossible for a material theory to explain consciousness. That is for sure !

Now, quantum physics tell us some weird thing, one of them is the fact that quantum systems are in superposition and I have difficulties to understand how superposed systems can interact each other according to classical interactions.

A little funny notes about what you say here:
"without conscious physicists there would be no physics -- profound, huh?" FALSE :)
Imagine all physicist as zombies, they still do physics and other (non phsyicist like me) can still see the results of their physics (with no need to understand the physics)


Please tell me where I can find an article about Heisenberg equations which talk about interacting particles and define what is the interactions.

Thanks

 

[vanesch]

Collapse is ,simply, they way our knowledge changes from the possibility of many outcomes to the actual outcome.

But you know that there is a difficulty here: when did the wavefunction 'got into its right basis' ? When looking at the double-slit experiment, at a certain moment, the wavefunction is split in two components, one going through the left slit, and one going through the right slit. Clearly, this is NOT the point were we can consider the wavefunction as some "probability wave". If we convert things to a probability density at this point, things turn out wrong (we won't get an interference pattern). So clearly, we cannot just at any moment consider that wavefunctions are "carriers of probability, which is all in our minds". Now, when the light gets onto the screen, suddenly what we weren't allowed to do, namely, to consider the wavefunction as a generator of probability density, suddenly is what one has to do. So something PHYSICAL must have happened from the moment where the wavefunction was a wavefunction WITHOUT any probability interpretation (at the level of the slits), into a wavefunction which is a "mere description of our knowledge" at the screen.

What happened, was that the photon's "position was measured". True, but what did it mean ? It means it hit a photocathode (for instance). As such, this is an interaction between a photon and an electron. But can't we describe that quantum-mechanically ? If we do, we still have a wavefunction, but this time of the photon plus the electron. In what way is such a thing fundamentally different from the photon that interacts with the electrons in the slit material ? Why did the photon wavefunction at the slit count as such, and couldn't be counted as a probability density, and why is suddenly our wavefunction after interaction with electrons in a photocathode to be taken as a "measurement" and hence as a "change of the knowledge of our mind" ?

This is what is the "fuzzy barrier" between the "classical" world (the one where wavefunctions taken squared, are seen as probability densities, which then, of course, "collapse" when new information is extracted) and the "quantum" world where the wavefunction CANNOT be seen as a probability density (at the passage of the slits) because otherwise we simply get out bad results.

So you cannot simply say that when we take quantum theory as a "machine that provides information from a wavefunction" because at some point, we cannot do that, and at another point, we have to do so.

 

[reilly]

But you know that there is a difficulty here: when did the wavefunction 'got into its right basis' ? When looking at the double-slit experiment, at a certain moment, the wavefunction is split in two components, one going through the left slit, and one going through the right slit. Clearly, this is NOT the point were we can consider the wavefunction as some "probability wave". If we convert things to a probability density at this point, things turn out wrong (we won't get an interference pattern). So clearly, we cannot just at any moment consider that wavefunctions are "carriers of probability, which is all in our minds". Now, when the light gets onto the screen, suddenly what we weren't allowed to do, namely, to consider the wavefunction as a generator of probability density, suddenly is what one has to do. So something PHYSICAL must have happened from the moment where the wavefunction was a wavefunction WITHOUT any probability interpretation (at the level of the slits), into a wavefunction which is a "mere description of our knowledge" at the screen.

I'm doing a partial response; time limitations and all that.

Now, I don't understand the problem you discuss. Seems to me that the |wave function|^^2 evaluated at any point in either slit gives the probability density of finding the electron, say, at that particular point. Further, I can determine the conditional probability that an electron reaches the screen at some point, given it's probability structure at the slits -- one slit, the other slit, or both; that is, we're talking initial conditions. I just don't see your issue. So I'd like to get a better idea, if you would be so kind.
Regards,
Reilly

 

[ronan1]

Hello!
It seems that you ignore my answers and questions, why so?
You are as lost as I am ?

You just answer me believing your answer are perfect while for me they don't seem satisfactory,

At the beginning I wanted an explanation of quantum system interaction which would avoid consciousness but nobody could give me a correct explanation except that interaction is here all the time and when interaction are strong, decoherance occur. But these interaction are in fact described in term of classical view even before decoherence!

Then I asked why consciousness is avoided, and I get an answer from Reilly who seems to don't know what is the fundamental problem of consciousness (its non logical superveniance over the physical)Could you answer my last posts as well as this one ?Thank you

 

[vanesch]

At the beginning I wanted an explanation of quantum system interaction which would avoid consciousness but nobody could give me a correct explanation except that interaction is here all the time and when interaction are strong, decoherance occur. But these interaction are in fact described in term of classical view even before decoherence!

I don't understand why you insist that interactions are described in terms of a classical view.

 

[ronan1]

Describe me the interaction between the 3 sub systems of the 2 electrons atom please,

I think you will need to use the fact that they are three indepedant system intreracting via forces. But quantum theory tell us that they are not independant and it is an error to separate them.

So the only way to describe their interaction is to use classical view, but this is a false description.

I want to have a quantum view about interaction but it seems that the only answer is : coupling.

Have you a better description that "coupling" ?Thanks

 

[f95toli]

Hello!
But these interaction are in fact described in term of classical view even before decoherence!

No, the interactions are not described in terms of a "classical view". The point I was trying to make was that if two systems interact classicaly they will also interact in QM.
This is hardly suprising. Take the two rings again as an example. When they are "quantum" (before they decohere or a measurement it performed) they will couple due to the mutual inductance and this interaction will give rise to non-classical effects such as superpositions etc. Now, if there is a lot of decoherence (i.e. we are in a "classical limit") they are of course still coupled (the mutual inductance is still there) but now the interaction will only give rise to "classical" effects.

Look in section III of this paper and you will see an example of how a complettely "classical" type of reasoning can be used to model coupling even in QM (in this case one of the abovementioned rings and an electric resonator).

http://www.arxiv.org/abs/0704.0727

Eq.10 shows the coupling strength which is the same in the both the classical and QM regime (and only contains "classical" parameters, but only in the latter case will it give rise to non-classical effects since it is only in the quantum limit that the ring and the resonator are "quantum".

 

[vanesch]

Further, I can determine the conditional probability that an electron reaches the screen at some point, given it's probability structure at the slits -- one slit, the other slit, or both; that is, we're talking initial conditions. I just don't see your issue.

Point is, that "left slit", "right slit", or "both" is not what the probability structure of the wavefunction at that point gives us. The probability structure (of the conditional events) is: 50% left ; 50% right. This is what you get when you look at the probability structure of the wavefunction (take | |^2) at the slits.

As such, applying Bayes' theorem, we find that:

P(screenpoint 1) = P(screenpoint 1 | slit A) P(slit A) + P(screenpoint 2 | slit B) P(slit B).

You know as well as I do that this doesn't work in QM because you wouldn't get interference.

 

[ronan1]

When they are "quantum" (before they decohere or a measurement it performed) they will couple due to the mutual inductance "they will couple due to the mutual inductance"

but what is inductance ?
To describe inductance, you will need to use a classical view: It is at this point that for me it is strange: It is like we describe the world as a quantum state and thus nothing permit us to divide it in interacting independant systems (such as two rings) but it is what we do and it seems to work!


It seems for me that in QM there is really no such thing as interaction (interaction need independent systems), there is only one system, isn't it ?

 

[vanesch]

Describe me the interaction between the 3 sub systems of the 2 electrons atom please,

I think you will need to use the fact that they are three indepedant system intreracting via forces. But quantum theory tell us that they are not independant and it is an error to separate them.

?? Quantum mechanics doesn't say that "it is an error to separate them". You can very well consider "separated states" in quantum mechanics ; they are called "product states" and are the opposite to "entangled states". Now, it is sufficient to know what happens to product states in which the entities ARE separated, to know how things will evolve in all generality. That is because the product states span the entire state space, and that it is sufficient, by linearity, to know what happens to a set of basis states, to know what will happen to anything (the famous superposition principle and the unitarity of time evolution).

So, we CAN consider the 3 systems as separated in certain states (product states), and we CAN say what will happen to them. Technically, this means that we write out the Hamiltonian in such a basis of product states.
That is SUFFICIENT to know what will happen in all generality.
And now comes the crux: if we do that, we see that product states don't remain product states if the subsystems interact (through the hamiltonian). They can start out as product states (separated systems), but they will evolve, most of the time, into entangled states.

At no point, we needed an explicitly classical description. However, what we do, usually, is to write the quantum interactions formally in the same way as would the classical interactions of a similar classical system. But we're not obliged to do so, and we don't always. The proof is that spin has no classical counterpart, for instance. Nevertheless, we can write spin-spin interactions.

We could go into more technical detail if you want to.

 

[ronan1]

Ok so interactions are happenning all the times (the shrodinger equation evolve), there nothing classical in it
but sometimes it decohere making the value to be fixed for an instant (what we call classical)

Ok I think I see the pictures but It seems that it is what I saw before asking my question.

For example take the electromagnetic force which attract an electron toward a proton: it is defined by their properties (such as position) isn't it ?
But in a quantum state the propreties are not defined, so the schrodinger equation will make the system (eletron-proton) evolving according to all the possible position.

is it right ?

So the answer to my question "How two quantum systems interacts ?" is:

they interact by the fact that they have definite propriety : be a proton or be a electron for example

But I is not: the fact to be an electron and a proton is a consequence of quantum interactions of other particles and so on in the past.

What the was the interaction which makes them electron and proton ?
In order to no that we need to go back in time ans see the universe as a whole.
But taking the universe as a whole, there is even not such thing as ring or electron, isn't it ?

So what are interactions ?

I don't know if you see what I want to know or maybe I don't see correctly the picture of quantum mechanics
But I feel that I see the picture and that quantum mechanics cannot told us how system interacts before decoherence.

 

[vanesch]

Ok so interactions are happenning all the times (the shrodinger equation evolve), there nothing classical in it
but sometimes it decohere making the value to be fixed for an instant (what we call classical)

The first part is ok, the second, not. "decohere" doesn't mean: making the value to be fixed for an instant! So let's leave "decohere" for a moment aside. We'll concentrate on the following aspect:

For example take the electromagnetic force which attract an electron toward a proton: it is defined by their properties (such as position) isn't it ?
But in a quantum state the propreties are not defined, so the schrodinger equation will make the system (eletron-proton) evolving according to all the possible position.

There are quantum states in which the position of the electron and the proton are well-defined: they are called "position states". All states an electron can be in, is a superposition of well-defined position states. So it is sufficient to look ONLY at position states, to determine the interactions.
So let's consider "Coulomb interaction". We now consider the special state of the electron in position r1, and the proton in position r2, and moreover, we consider the special product state where they both have their "position" property independently.
We write that state as |el-r1> |pr-r2> (as the product of individual electron and proton states). Well, the set of states {|el-r1> |pr-r2>} for all position couples {r1, r2} IS A BASIS of the total set of states of the electron-proton system. As such, it is sufficient to know the interaction of the systems in these states, and here we have two separate well-defined systems, which, moreover are in well-defined positions. The Coulomb interaction ON THIS STATE is written as H_int = - e^2 /|r1 - r2| (you recognize the same FORM of the interaction energy as for the classical system, but it is applied to a quantum state).

As it is sufficient to know the hamiltonian on a basis to know it everywhere, the interaction is completely fixed now, even for states that are NOT of the form |el-r1>|pr-r2> (but are build up as a superposition of such states).

So the answer to my question "How two quantum systems interacts ?" is:

they interact by the fact that they have definite propriety : be a proton or be a electron for example

"be an electron and be at a specific position r1": the quantum state |el-r1>

What the was the interaction which makes them electron and proton ?
In order to no that we need to go back in time ans see the universe as a whole.
But taking the universe as a whole, there is even not such thing as ring or electron, isn't it ?

This brings up 2 questions. Why wouldn't you want to consider in a quantum-mechanical context that there are electrons and protons but why is this not a problem for you when you do classical mechanics ? If you look at a purely classical question: "there's a weight on a rope and a pulley and..." do you also object that in order to know that there is a rope, we have to go to the origin of the universe to find out how it came that there was a rope ?

But the second point is: in fact, in quantum field theory we can (at least in principle) see indeed electrons as specific manifestations of the state of another system, which is a quantum field.

But I feel that I see the picture and that quantum mechanics cannot told us how system interacts before decoherence.

I wonder what you understand under the word "decoherence"...

 

[ronan1]

For classical mechanics, you can go back at the beginning of the universe and thus explain the rope state but in quantum mechaincs you cannot!

this is this way because of decoherence:

Decoherence is just the passage between a superposition of value (position for example) to a specific value

In QM, when you look at the universe as a whole, you cannot anymore talk about indepedent systems and interactions

It is only because we observed at some time the universe that we are seeing separate entities

Interactions become explainable in this context but not when you look at the whole universe.

My question can be reformulated:
How two quantum systems inside the whole universe interact when we see the universe as a quantum system ?

But how two quantum systems be treated inside the whole universe if we see this whole universe as one quantum system ?

Is my question answerable ?

 

[vanesch]

For classical mechanics, you can go back at the beginning of the universe and thus explain the rope state but in quantum mechaincs you cannot!

this is this way because of decoherence:

Decoherence is just the passage between a superposition of value (position for example) to a specific value

Not at all: that's not what decoherence says. As we have seen, a quantum subsystem (and we take it that the quantum universe is composed by an agglomerate of subsystems, in the same way as a classical universe has subsystems in it) can have different quantum states, and some of them have "classically-looking properties", but most of them don't. By this, I mean that a state of a subsystem which is a particle, for instance, can have "classically-looking" states which are "position states", but it can also be in other states, which are SUPERPOSITIONS of these classically-looking states.

In a similar way, composed systems can be in "product" states (where each individual subsystem has its own quantum state), but they can also be in "entangled" states, which are superpositions of product states.

But you see: ALL quantum states are eventually superpositions of product states of classically-looking states. So it is sufficient to know the interaction on product states of classically-looking states of subsystems, and we know entirely how the interaction works on ALL states (using unitarity of the time-evolution).

Now, it turns out that if you take a complicated system with many subsystems (say, a volume of air, with all its molecules and so on), and a "macroscopic system", such as a big ball, that, no matter what quantum state we're into start with, the interactions make the overall state VERY QUICKLY evolve into a state which looks as follows:

|ball in classically-looking state 1> |air state 1> + |ball in classically-looking state 2> |air state 2> + ...

with the air 1 and air 2 ... states complicated states, but essentially orthogonal, and remaining so. Moreover, once this split is obtained, these states evolve mostly independently and don't mix anymore. This means the following: after some time, it could in principle be that |ball in classically-lookingstate 1> |air state 1> evolves into something like |ball in classically-looking state 3>|air state 2>, while
|ball in classically-looking state 2>|air state 2> evolves into
|ball in classically-looking state 4>|air state 2>.

This would then mean that suddenly we can factor out |air state 2>, and we would have that a classically-looking state 3 and 4 appear in a superposition, giving rise to quantum interference phenomena.

Well, this is what is in principle possible, but doesn't happen, and that phenomenon is called "decoherence".

It comes down to saying that |ball in classically-looking state 1> |air state 1> will lead its own life, and that |ball in classically-looking state 2> |air state 2> will lead its own life etc...

But they all appear one next to each other in the "universe wavefunction".
The many-worlds interpretation then simply says that these are different classical worlds which live one next to another in a single quantum universe, and that the decoherence phenomenon comes down to a practical "split" of a classical world into several.

In other views, one gives other interpretations to this "sum of independently evolving states".

But no matter what, decoherence allows us to just consider ONE of these states and to PRETEND that this is all that there is to is, as such neglecting all the other terms ; because we know (decoherence) that they won't influence on the evolution of this single term.

 

[ronan1]

OK, I agree with your definition of decoherence, It is what I knew before and what I say in the precedent post except this wrong simplification of decoherence is still valid :

For classical mechanics, you can go back at the beginning of the universe and thus explain the rope state but in quantum mechaincs you cannot!

this is this way because of decoherence

In QM, when you look at the universe as a whole, you cannot anymore talk about indepedent systems and interactions

It is only because we observed at some time the universe that we are seeing separate entities

Interactions become explainable in this context but not when you look at the whole universe.

My question can be reformulated:
How two quantum systems inside the whole universe interact when we see the universe as a quantum system ?

But how two quantum systems be treated inside the whole universe if we see this whole universe as one quantum system ?

Is my question answerable ?

 

[vanesch]

For classical mechanics, you can go back at the beginning of the universe and thus explain the rope state but in quantum mechaincs you cannot!

Why ? What's the difference ?

In order to explain the existence of a rope in classical mechanics "from the beginning", you have to postulate a certain begin state (and hence all its constituents) of the universe, and its interactions (time evolution). Well, you can do exactly the same thing in quantum mechanics: you postulate an initial wavefunction (and hence all its subsystems) and interactions. What's different ?

 

[ronan1]

The difference is that decoherence happened in order to make you aware of the rope and thus because of the irreversibility of decoherence you can not go back at the begginning of the universe to explain the reality of the rope !

and if you considere that no decoherence occur, you cannot even talk about rope

If you suppose that no decoherence occur before and that the time you see the rope was the ONLY time decoherence (lets call it D) occur, then it was by pure chance that the rope appear and in fact everything, even you

because if you go back at the wavefunction of the universe, it evolve in so many direction that you can get anything: any world (in the many world interpretation) at the time D occur. So your rope could have been a flying elephant (pink if you want) !


It seems completely crazy but without decoherence before D the world can be anything (almost at least) at the time of D

and with multiple decoherences before D, then we need to explain why decoherence happened before.

For my orginal question, could we say that even if interaction happen all the time, they get concretized only after decoherence ?

thus making a definition for interaction in quantum realm:
interaction = way in which the whole system evolves
and not:
interaction = exchange of energy between a and b
which would be the classical definition (or the after D defintion)

Now, "way in which the system evolves" seems to not be satisfactory
we can not even describe it

Is it the only chance?

What about Bohmian mechanics or its possible future derivatives ?
What would they say about it ?
Do you kow ? would it be more easy to grasp ?

 

[vanesch]

because if you go back at the wavefunction of the universe, it evolve in so many direction that you can get anything: any world (in the many world interpretation) at the time D occur. So your rope could have been a flying elephant (pink if you want) !

Absolutely. In MWI, we consider that there's a "world" (a term in the wavefunction) with a rope, and that there's also another "world" (another term in the wavefunction) with a pink flying elephant, and there's a world where the dinosaurs didn't get extinct, and there's a world where the solar system never formed etc...

You happen to observe the one with the rope. That's simply 'the place where you are'. In the same way as you happen to be on planet earth, and not in some other remote galaxy, and that you are living in this period, and that you didn't live in Julius Caesar's time.

It seems completely crazy but without decoherence before D the world can be anything (almost at least) at the time of D

But also AFTER decoherence! Decoherence only means that the guy who sees the rope won't be bothered by the guy who sees the pink elephant and that the guy who sees the pink elephant won't be bothered by the guy who sees the rope ; that no experiment ever by one will indicate the presence or not of the other. Which, in its turn, means that you can just as well forget about the others.

Before decoherence, there were interference phenomena possible, while after decoherence they became so complicated to realize that they are essentially impossible.

For my orginal question, could we say that even if interaction happen all the time, they get concretized only after decoherence ?

Not really. You could probably say however that observations only get concretized after decoherence (most of the time, observations imply decoherence in a way).

thus making a definition for interaction in quantum realm:
interaction = way in which the whole system evolves
and not:
interaction = exchange of energy between a and b
which would be the classical definition (or the after D defintion)

Yes, that's correct: interaction determines the way the whole system evolves. However, it is based upon energy exchange which can be written down in explicit "separated system" states, which is enough to determine the time evolution (interaction) for all states.

Now, "way in which the system evolves" seems to not be satisfactory
we can not even describe it

But of course we can describe it! Why do you think we can't ? That's what the quantum formalism is for.

What about Bohmian mechanics or its possible future derivatives ?
What would they say about it ?
Do you kow ? would it be more easy to grasp ?

For people who cannot get loose of the classical Newtonian paradigm, it can help them get a picture of quantum theory that can ease their mind

 

[ronan1]

But of course we can describe it! Why do you think we can't ? That's what the quantum formalism is for.

When you ll describe it you will use object such as pink elephant and rope (or rings, or 2 electron atom) So you will need to choose one universe among many and not the whole multiverse

Thus you will not describe the whole world but an arbitrary one!


Also, decoherence happened many times before you observe for the first time, so you finally cannot live in any world but some specific ones
This make the thing wierd: it is like finnaly the world need something else to evolve: decoherence and thus the MWI is not satisfactory : it needs an explantion why do we choose one special world and why we cannot go back to a precedent decoherence to change completely the world from a rope to a pink elephant


What is the cause of these precedent decoherences ?
complicated interactions ? : not very satisfactory

Not really. You could probably say however that observations only get concretized after decoherence (most of the time, observations imply decoherence in a way).

observation getting concretized ? What do you mean ?
there is no observation before decoherence
It would make more sense that this the interactions which are in superposition (as the systems are in superposition) that get concretized (one of them).

By saying that the interaction "chosen" is concretized it means that the interaction actually takes place. It seems for me more correct that saying that observation are concretized.

For people who cannot get loose of the classical Newtonian paradigm, it can help them get a picture of quantum theory that can ease their mind

In which way ?
Do they say that the world is evolving completely deterministcaly
but that we cannot access the variables which would permit us to make precise prediction ?

 

[vanesch]

When you ll describe it you will use object such as pink elephant and rope (or rings, or 2 electron atom) So you will need to choose one universe among many and not the whole multiverse

Thus you will not describe the whole world but an arbitrary one!

Yes, you will be limited to only a part in the whole "universe" description. But that will also be the case in, say, a classical, infinitely large Newtonian universe, where you will only be able to describe a lump of the total (infinite) universe. You'll have to be satisfied with that part which is related to your "neighbourhood" (even if that extends for 15 billion light years, that's still a small spec in an infinite universe).

Also, decoherence happened many times before you observe for the first time, so you finally cannot live in any world but some specific ones

Indeed. Note that you have the same problem with classical thermodynamical irreversibility. If you have hot water, you don't know whether it was ice before or not.

This make the thing wierd: it is like finnaly the world need something else to evolve: decoherence and thus the MWI is not satisfactory : it needs an explantion why do we choose one special world and why we cannot go back to a precedent decoherence to change completely the world from a rope to a pink elephant

Well, we cannot go back in thermodynamics either. But you still seem to be attached to the idea that nothing can evolve if it is not expressed in classical terms of some sort.
What is true however, is that there needs to be something "else" that explains why we observe THIS world (the one with the rope) and not THAT world (with the elephant). But that's an old philosophical problem, called heacceity: what makes "me" "me" ? Why am I here, and not there ? Why this world and not that world ?

So the question is not strictly quantum-mechanical. Only the extravagantness of certain interpretations of quantum theory makes one think of what was tacitly taken for granted in more conventional and classical views.

What is the cause of these precedent decoherences ?
complicated interactions ? : not very satisfactory

I think this is because you think that decoherence is some special happening ; it isn't.
When two particles interact, the overall quantum state can be an entanglement of two particles. When the 2-particle system is entangled like this, you cannot have interference anymore with one single particle. We can, as such, say that one particle "decohered" with the other one. Say that two particles are a proton and an electron, and that they are conscious (who knows ). They can have two "states of awareness": being "spin up" and being "spin down" (probably related to their mood or something...).
You can have a state which is |up>|down> for instance, where the electron has one state of awareness (up) and the proton has one state of awareness (down).
But now, they interact, and they get into a state like |up>|down> + |down>|up>. Well, this means now that there are now TWO states of awareness for the electron, one where there is an "electron-awareness" that is "up" and another "electron awareness" that is "down". And there are two proton-awarenesses too. Well, the electron awareness that is "up" will live in a world where there is also a proton in a state "down", while the electron awareness that is "down" will live in a world where there is also a proton in state "up".

So in a way, the "world" of the electron has "decohered" in two worlds, one in which it is aware of being "up" and one in which it is aware of being "down", with corresponding proton states and everything.

But it's not really a decoherence here, because the state |up>|down> + |down>|up> can easily evolve into something like |up> |up> for instance. That's a thinkable quantum evolution. As such, the two "worlds" namely "updown" and "downup" will INTERFERE to make one single world "upup". |up>|down> doesn't lead its own life "irreversibly and independently of |down> |up>.

However, if you play the same game with 10 000 different particles, then there is already much less chance that |up>|down>|down>|up> ... |up> will interfere again with |up> |up> ... |down>, because most of the time, at least one of the factors will remain orthogonal. The more different systems that are composed, the less likely that it becomes that under time evolution, they will interfere. So if you have a state with 10^23 different systems (different air molecules for instance), chances that they will interfere again are very remote indeed, and will practically not happen. So the terms are now "separated for ever". This is when interaction gives rise to decoherence.

observation getting concretized ? What do you mean ?
there is no observation before decoherence
It would make more sense that this the interactions which are in superposition (as the systems are in superposition) that get concretized (one of them).

By saying that the interaction "chosen" is concretized it means that the interaction actually takes place. It seems for me more correct that saying that observation are concretized.

An interaction is not "chosen". It happens, irrespectively of whether we call it an observation or not. Observation is then just "being aware of one of the terms". And others will be aware of different outcomes, but they are simply not "you" but a copy of "you".

In which way ?
Do they say that the world is evolving completely deterministcaly
but that we cannot access the variables which would permit us to make precise prediction ?

Yes.

 

[ronan1]

An interaction is not "chosen". It happens, irrespectively of whether we call it an observation or not. Observation is then just "being aware of one of the terms". And others will be aware of different outcomes, but they are simply not "you" but a copy of "you".

You seems to be sure of the correctness of MWI, but it is not the only one interpretation, haecceity is deeper in MWI than in other interpretation

because MWI doesn't forbiden you to jump to another world !
while in a classical view, it forbiden you because it is said that there is one world.

The difference between classical thermodynamics and QM is that if you know the beginning of the universe you can predict the whole world while in QM, you can not!

I think this is because you think that decoherence is some special happening

Ok so for you it happens all the time, universes are splititng constantly, it is again MWI and it doesn't solve anything except that you can think quantum mechnicaly
with MWI you think only in QM but you have a big problem explaining why there is a classical view and why I am in this world AND WHY I CANNOT CHANGE WORLD !

Yes.

So Bohm interpretation doesn't have any problem that we mentioned !
It is true that as currently stated it don't work but there is still a possibility (apparently Bell's theorem have been refuted recentely, isn'it ?)

 

[vanesch]

You seems to be sure of the correctness of MWI, but it is not the only one interpretation, haecceity is deeper in MWI than in other interpretation

No, I'm not "sure" about the MWI interpretation. I've often said that I find it the interpretation that is closest in spirit to the actual formalism of quantum theory, and I still stand by that point. I do not consider that it is any "true" view of reality. I'm agnostic about what reality really is.

But MWI is the only framework in which decoherence makes any sense. If you have any other view on the measurement process (such as collapse), then you don't need any consideration of decoherence. Decoherence is what gives MWI a leg to stand on.

So in order to even discuss sensibly about decoherence, one has to place oneself in an MWI viewpoint. In other views, there's a deus ex machina that "ends" quantum mechanics and in one way or another makes you transit into a classical world, and there's no need (or no meaning to) decoherence.

because MWI doesn't forbiden you to jump to another world !

Do you sometimes jump into experiencing being another person ? Do you "change bodies" sometimes ? Why do you (as a subjective experience) experience *this* body and not another body ? Classical mechanics doesn't forbid you to jump into experiencing another body. The same reason that makes you "stick to your body" is probably also applicable to why you stick to your own world in MWI.

The difference between classical thermodynamics and QM is that if you know the beginning of the universe you can predict the whole world while in QM, you can not!

Well, quantum-mechanically, you CAN predict the whole world (wavefunction). You can only not predict what world a specific "you" will experience. But if you pick out a world (a term in the wavefunction) you can tell that a person living in that world will experience this and that.

Let's assume there's a classical universe, in which classical beings evolve biologically into sentient beings. You cannot predict what "you" will experience. You CAN maybe predict what the being that is sitting there under the tree is experiencing. But you cannot predict that that being will be "you". In the same way, ideally, in QM, you CAN predict what a being in a specific world (decohered term in the wavefunction) will experience. But you cannot predict that that world will be YOURS.

Ok so for you it happens all the time, universes are splititng constantly, it is again MWI and it doesn't solve anything except that you can think quantum mechnicaly
with MWI you think only in QM but you have a big problem explaining why there is a classical view and why I am in this world AND WHY I CANNOT CHANGE WORLD !

Yes. But that's not proper to quantum theory per se.

So Bohm interpretation doesn't have any problem that we mentioned !
It is true that as currently stated it don't work but there is still a possibility (apparently Bell's theorem have been refuted recentely, isn'it ?)

Bohmian mechanics works very well. Bell's theorem is not refuted - it is misunderstood by those who think they refuted it. They refuted something Bell's theorem never claimed.

Bohmian mechanics is not "harmed" by Bell's theorem as in Bohmian mechanics, you allow for superluminal causal effects explicitly: the measurement at Alice's has a direct causal influence on Bob's measurement, even if they are 2 lightyears apart. As such, Bohmian mechanics is not compatible with relativity - which is the main reason why many people don't find it inspiring to work in it. But in an ether view, you can get rid of relativity too, and that's what Bohmian mechanics does: it is a strictly pre-relativistic, Newtonian view, with sufficient "fiddle terms" that make all effects of relativity and quantum theory appear. But it works.
There where Bohmian mechanics really becomes terribly ugly, is in quantum field theory. Nevertheless, there are (after-the-fact) ways of introducing in Bohmian mechanics even effects that mimick quantum-field theory results.

The point is, that Bohmian mechanics is never an "inspiration" for further work. It can accommodate what has been discovered in quantum theory. But it works.

 

[ronan1]

Do you sometimes jump into experiencing being another person ? Do you "change bodies" sometimes ? Why do you (as a subjective experience) experience *this* body and not another body ? Classical mechanics doesn't forbid you to jump into experiencing another body. The same reason that makes you "stick to your body" is probably also applicable to why you stick to your own world in MWI.

That's right :)

Bohmian mechanics works very well. Bell's theorem is not refuted - it is misunderstood by those who think they refuted it. They refuted something Bell's theorem never claimed.

Ok, Bell theorem does not apply to Bohmian mechanics.
Is Bohmian Mechanics not a local hidden variable theory ?

The point is, that Bohmian mechanics is never an "inspiration" for further work. It can accommodate what has been discovered in quantum theory. But it works.

Why not an inspiration ?
Bohm found inspiration in it : "Wholeness and the implicate order"
It is also a good way to view Quantum mechanics, quite intuitive.

What about relational quantum mechanics ?
It says that basically decoherence is just a matter of point of view.

let put an example:

O1, O2 and S are three quantum system
O1 study S,
O2 study O1+S

according to O1,
S = a|up> +b|down> (a^2+b^2)=1

according to O2 :
O1+S = |O1 up>|up> + |O1 down>|down> (|O1 up> being the state of O1 observing S=up and same for down)

But in fact when O1 observe S
S= up or S= down
let say that O1 actually observe S=up

Now O2 observe O1+S , will he find :
O1+S = |O1 up>|up> ?

and if he observe S alone, will he find:
O1+S = |up> ?

So it is not completely relational as something seem to be there no matter who measure it: S=up
?

Thank you for the discussion, I think I get in some way a better picture of QM even if I feel like something is missing :p

maybe the question about relational quantum mechanics should be put in another thread.

 

[vanesch]

That's right :)
Ok, Bell theorem does not apply to Bohmian mechanics.
Is Bohmian Mechanics not a local hidden variable theory ?

No, it is not local, in the sense that interactions are immediate and at a distance (and don't even diminish with distance). It's pretty close to Newtonian mechanics, except that we now also have a wavefunction living in multi-dimensional space which dictates the forces, and not just the positions of the particles.

Why not an inspiration ?
Bohm found inspiration in it : "Wholeness and the implicate order"
It is also a good way to view Quantum mechanics, quite intuitive.

It is a very good way to get intuition for non-relativistic, ONE-PARTICLE spinless quantum mechanics. Spin is a horror in Bohmian mechanics (although it comes out quite nicely in the end).

What about relational quantum mechanics ?
It says that basically decoherence is just a matter of point of view.

To me, relational quantum mechanics = many worlds + solipsism.

The solipsism part then makes that we can get away with the "many" in the many worlds. But that's just my opinion. It is not shared by everybody

I would like to add something I like to stress when talking about interpretations of quantum mechanics. This is my personal opinion, but I think it helps putting things in perspective. I think that we don't have the final theory of the universe yet. If history is some lesson, before we have it, it is probably wrong to speculate about whatever properties it might have as an extrapolation of what we already have. I'm not even sure we'll ever have it, and even if we have it, whether we will know that we have it. As such, I think that hoping to know how nature really really is, is idle business. Nature might be totally different than what we might now think it is like at its most fundamental level. It might retain certain aspects we've discovered already, but it might also be totally different. As such, any "reality" we might deduce from our current theories is probably "wrong" anyways. Maybe "reality" is less weird than we deduce from our current theories, but it might also be even much more strange and weird than what are now our wildest fantasies if history is any guide.
So in a certain way, our guess about reality anyway being "wrong" at the most fundamental level, we might as well make the best guess we can that goes with our current theories - realizing the relativity of its value.

This is why I prefer MWI: it is closest to the spirit of the actual quantum formalism, and it helps one get a feeling for it. It's all I ask about a "view" or an "interpretation" of a theory: help me get some "picture", some "feeling" for it. I don't lie awake about its philosophical and moral implications, given that it is probably wrong anyways, and that I haven't gotten any better guess than that. I think it is an error to try to think up grandiose world views that adhere to our intuition and butch up the formal side of things for that. But I think it is just as well misguided to think that our current theories already touch the "final truth". This is just preliminary guesswork. And that's probably a permanent situation.