# How two quantum systems interact ?

1. Oct 16, 2007

### 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

Last edited: Oct 16, 2007
2. Oct 16, 2007

### 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 refered to once today, but it is a good article).

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

3. Oct 17, 2007

### ronan1

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

4. Oct 17, 2007

### ronan1

5. Oct 17, 2007

### 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.

Last edited: Oct 17, 2007
6. Oct 17, 2007

### 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.

7. Oct 18, 2007

### ronan1

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 ?

8. Oct 18, 2007

### vanesch

Staff Emeritus
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.

9. Oct 18, 2007

### 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 ?

Last edited: Oct 18, 2007
10. Oct 18, 2007

### vanesch

Staff Emeritus
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.

11. Oct 18, 2007

### 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 ?

Last edited: Oct 18, 2007
12. Oct 18, 2007

### vanesch

Staff Emeritus
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.

13. Oct 18, 2007

### 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

14. Oct 18, 2007

### 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

15. Oct 18, 2007

### 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

16. Oct 18, 2007

### vanesch

Staff Emeritus
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.

17. Oct 18, 2007

### reilly

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

18. Oct 19, 2007

### ronan1

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

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

Last edited: Oct 19, 2007
19. Oct 19, 2007

### vanesch

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

20. Oct 19, 2007

### 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