# What is the difference between interaction and measurement?

1. Feb 5, 2012

### Xilor

Hello, as far I understand wavefunction collapse (or decoherence or whatever stops particles from acting as waves) is initiated through something referred to as a measurement. These measurements are thought of as interactions.
Now the question I have is, why are some interactions measurements while others are not without any obvious physical differences?

For example, photons when used as a measuring tool do collapse the wavefunction permanently, but photons exchanged between parts of a particle do not. (molecules have shown interference patterns while they definitely require electromagnetism to stay together).

Also the influence of other molecules does seem to collapse the wavefunction (the screen that the particles are fired towards), but not always since mirrors do not.

From all the wavefunction collapse mechanisms that I've heard of, they all involve electromagnetism, but not all electromagnetic effects seem to be able to collapse the wavefunction. Why?
If the answer to this is actually still unknown, is there any sort of list out there that shows exactly which kinds of interactions have been shown to be able or unable to collapse wavefunctions?

2. Feb 5, 2012

### juanrga

i)
Particles do not act as waves but as particles.

ii)
Decoherence and quantum collapse are two completely different processes.

iii)
Measurements and non-measurements are evidently physically different. That is why to measure something you build an measurement apparatus, although an apple in the garden outside the lab is interacting with your system as well (e.g., via gravitational force)

iv)
A part of a particle is not a measuring apparatus, how could measure? somewhat as a part of a car is not the same than a car.

Electromagnetism plays an important role because is the more important interaction for ordinary matter. Gravitation is very relevant for large masses and the other interactions more relevant at nuclei scale.

3. Feb 5, 2012

### strangerep

The whole notion of wavefunction collapse is merely part of an old interpretation of QM, but not an essential part of the theory (i.e., the math which predicts statistical results of experiments).

A more productive way to think of "measurement" is as an interaction between an object system S and an apparatus A. An interaction between S and A constitutes a useful "measurement" of some dynamical variable for S if the interaction is such that the initial state of S is correlated with the final state of A. Typically, A can have some set of final states, and we associate a number with each such state. The number is then interpreted as the measured "value" for S of the physical quantity (dynamical variable) represented by the (class of) apparatus A.

Ballentine gives a useful discussion of this in ch 9.

The answer has been well-known for decades: collapse of the wavefunction is not an essential part of QM. Unfortunately, it is often far too convenient to explain scenarios by invoking it rather than to slog through the math. :-(

4. Feb 6, 2012

### jk22

Measurement is supposed to disturb the system.

Now if I have a composite system |a>|b> and I measure only the first subsystem with an operator A does this disturb the second subsystem ?

If I suppose |a> were an eigenstate of A, then endstate of a measurement by A is |a>|b> or |a>|b'> were |b'> were an unknown state ?

5. Feb 6, 2012

### Xilor

Well it doesn't have to be called a measurement but in any interpetation of quantum mechanics there is some sort of interaction which causes the interference pattern to dissappear. What seperates those interactions from interactions that don't is what I'm searching for.

I'm not really following this, especially the part about states and numbers. But from what I do seem to understand: How are the object and the apparatus organised in larger systems that are seemingly more than the sum of their parts? Why don't some interactions correlate the states together (gravity/electromagnetic fields which change spin/mirrors)?

Also, now I'm wondering if an assumption I had made was incorrect. When a particle is measured and, is it possible for that particle to go in superposition again after that measurement? Does that happen inmediatly?

Doesn't every interpretation without realism involve some sort of way for superpositions to cease existing? Even those with realism have some mechanism to stop a particle from acting like it's on a wave.

6. Feb 6, 2012

### ZealScience

I think that such interactions between particles can only contribute to a composite systems, where the state is still a combination of eigenstates, instead of a well defined state.

Measurements are processes that determine the state of a system. Like magnetic field that can determine spin, or polarizer that determines polarization.

7. Feb 6, 2012

### StevieTNZ

Anything used to measure a quantum system only gets entangled with the system. You can say it interacts, in this case. Measure, well, according to QM, no.

8. Feb 6, 2012

### lugita15

But then can't you equally well construct the wave function of the S-and-A system? The whole reason there is still disagreement about the measurement problem is that you can always enlarge your system and still have a valid wave function. Von Neumann in his famous Mathematische Grundlagen der Quantenmechanik (AKA the "bible" of QM) rigorously proved that it makes no experimental difference how you split the world into an observed system and a measuring device. Hence the notion of a "Von Neumann chain".

9. Feb 6, 2012

### strangerep

It depends on whether an interaction preserves or destroys the coherence (correlation)
between the different sources contributing to the interference pattern.

In QM, a composite systems is modelled as a tensor product of its component systems.
That's essentially what Ballentine does when explaining this stuff in ch 9.

You're still not thinking of superpositions as determining statistical properties only.

(Sorry, it's not practical for me to reproduce all of Ballentine's arguments here. If you're really interested in QM, I can guarantee that his textbook would be a good investment...)

Of course. That's how the analysis proceeds -- using a tensor product construction as mentioned above. Measurement is really all about correlations in the combined $S\otimes A$ system. I think this is why N. D. Mermin was motivated to introduce an interpretation that "the only proper subjects of physics are correlations among different parts of the physical world."

Cf. http://arxiv.org/abs/quant-ph/9801057 and http://arxiv.org/abs/quant-ph/9609013 .

10. Feb 6, 2012

### lugita15

I find the term "statistical interpretation" highly misleading. Pretty much the only people who subscribe to a genuinely statistical interpretation of QM are the Bohmians, who view the wave function not as something fundamental but as merely a way to calculate the probability due to the classical uncertainty associated with large systems. I think the self-described adherents of a "statistical" interpretation really believe in Many Worlds: the distinction between actual physical parallel universes and a mere conceptual ensemble of universes is largely a matter of taste, not a very meaningful scientific or philosophical difference.

11. Feb 6, 2012

### strangerep

I find it the opposite -- but I'm not sure how to discuss this constructively without knowing your background. Have you studied Ballentine's textbook?

Well, I'm reasonably sure Ballentine is neither Bohmian nor Many Worlds. And I'm absolutely that I'm not. I'm a hard-core pragmatist who doesn't waste time on any parts of "interpretations" which cannot be confirmed or distinguished by experiment.

12. Feb 6, 2012

### lugita15

Not the whole book, but yes I have read of most of what he says about interpretation, including his arguments against wave function collapse.
I'm not claiming that Ballentine would self-identify as a many-worlder, what I'm saying is that he and those like him have been led by a desire to interpret QM statistically toward a position that is more or less the Many Worlds Interpretation. Pretty much everyone agrees that quantum mechanics is a probabilistic theory; the question is in part how do you interpret this probability. Ballentine subscribes to a broadly frequentist interpretation of probability (he makes a distinction between frequency and propensity, but to me that's largely splitting hairs). It's hard to distinguish Everett's MWI from the combination of the beliefs:
1. The laws of physics are fundamentally probabilistic in nature.
2. Probablity is fundamentally frequentistic in nature.
You can try making a distinction between many worlds as a physical reality and many worlds as a conceptual construct, but that's like arguing about whether the equator is a "real" line or not: it's irrelevant for most scientific or philosophical discussion.
I would think that absolute pragmatism leads to a Bayesian, not frequentist, interpretation of probability. And Bayesian probability leads naturally to some variant of the Copenhagen interpretation (although other interpretations like consciousness-causes-collapse and Bohmian mechanics are also compatible with a Bayesian view).

13. Feb 6, 2012

### strangerep

I don't see that this is necessarily the case, since successive experiments just improve the distribution being used as a prior. In any case, I've yet to hear of any experiment that can distinguish between the Bayesian and frequentist versions of probability (provided one understands a suitable notion of math limit in the latter case).

But this sub-discussion is gradually diverging from the main topic of this thread, so it would be impolite of me to pursue this any further here.

14. Feb 7, 2012

### Xilor

Would you say that this difference between interaction and measurement is then mainly something that depends on which interpretation of quantum mechanics you're using?

Btw, one important experiment cold maybe make it clearer but I'm not sure what the results are or if it has ever been peformed. What if you use some molecule in the double-slit experiment and fire a photon (or a bunch of them) at it in such a way that the photon bounces off into space or somewhere else where it can't be measured at least. What happens? Does the interference pattern appear?

15. Feb 7, 2012

### strangerep

If by "you", you mean me, then I'm afraid I find it too difficult to respond to questions of the kind that put words in my mouth. Not much more I can usefully say until you take a look at Ballentine ch9 and determine whether you understand it.

16. Feb 7, 2012

What is the difference between interaction and measurement?
That depends on the model. There are models where interaction is defined through unitary evolution, while "measurement" is defined by a stochastic process including nonunitary quantum jumps. In these models the distinction is clear.

17. Feb 14, 2012

### jk22

Do you have an example of non unitary quantum measurement (initial and final state) ?

18. Feb 14, 2012