# There is no such thing as 'collapse of the wavefunction' - Feynman

1. May 27, 2010

### dx

I found this passage interesting and illuminating: (from Feynman's book 'QED')

".. In this example, complex numbers were multiplied and then added to produce a final amplitude for the event, whose square is the probability of the event. It is to be emphasized that no matter how many amplitudes we draw, add, or multiply, our objective is to calculate a single final amplitude for the event. Mistakes are often made by physics students at first because they do not keep this important point in mind. They work for so long analyzing events involving a single photon that they begin to think that the wavefunction or amplitude is somehow associated with the photon. But these amplitudes are probability amplitudes, that give, when squared, the probability of a complete event. Keeping this principle in mind should help the student avoid being confused by things such as the "collapse of the wavefunction" and similar magic."

2. May 27, 2010

### glengarry

This is just one of the myriad reasons why I advocate moving QM out of the realm of physics and into the realm of pure mathematics. We should call it "The Statistical Theory of Measurement." But wait a minute... why do we need the term "of measurement" involved? I mean, what kind of statistical theory does not concern the measurements of things? Let's just call it "Statistics"! But don't we already have such a subject matter? Why yes, I think we do!

(Can you tell that I am just sick to death, along with Feynman, of all of these ridiculous "interpretations" about "what it all means"?)

3. May 27, 2010

"No such thing" is different than "avoid being confused"

4. May 27, 2010

huh? Its physics because it describes observations. Pure mathematics doesn't describe observations, if it did it wouldn't be 'pure'.

5. May 27, 2010

### LostConjugate

Collapse is just a word we use to describe the function going from a wave function to a dirac delta. It is like a slinky or an accordion, collapsing. Nothing measurable is actually collapsing yes, so don't wear your hard hat.

6. May 27, 2010

### Hoku

So is Feynman saying that the wave/particle duality doesn't actually exist?

7. May 27, 2010

Doesnt exist is a strong statement... I dont think he was a big fan of it and downplayed its significance.

8. May 27, 2010

### glengarry

No it does not "describe observations". I can't even comprehend what that phrase is supposed to mean. The ony thing that it "describes" is that a given measurement will result a certain percentage of the time, over an infinite number of trials.

And I'm not saying that there is absolutely zero correlation between QM and the world of physical reality. I'm just saying that the nature of QM is not at all what the typical human being understands physical theorization to be all about. My advocacy of this separation is simply to avoid the interpretive free-for-alls that are the hallmark of contemporary theoretical physics, to the detriment of developing actual spacetime models of physical reality (based upon the language of differential geometry) that we can all come to agree upon.

I'm totally with Einstein on this one.

9. May 27, 2010

### DrChinese

lol.

10. May 27, 2010

### jostpuur

I understand that wave function amplitudes, when squared, give probabilities for events... but I still feel pretty confused about the wave function collapse. Now, what did I do wrong?

11. May 27, 2010

### Hoku

"Wave function collapse" is simply the terminology that describes the change of state from wave to particle. To say there IS no collapse is to say that there is no duality. Period.

12. May 27, 2010

### Dickfore

So, there is no duality.

13. May 27, 2010

### Hoku

Duality is verifiable. This just goes to show that even highly respected physicist can be blinded by their own biases.

14. May 27, 2010

### Dickfore

What do you mean by 'duality'?

15. May 28, 2010

### Born2bwire

I do not think that this is an accurate interpretation of what Feynmann was trying to say. The impression I get a lot from Feynmann is that he is very interested in describing physics in simple and clear terms. A lot of quantum mechanics is very confusing and Feynmann is always quick to try and clear up misconceptions. However, I think that in his simplifications, people often take his short statements out of context. In this case, Feynmann is not saying anything to denigrate the idea of a collapsing wavefunction. He is just stating that students often get confused with the "magical" properties of quantum mechanics (the properties that are contrary to our observations of the classical macroscopic world) and that the collapse of the wavefunction is one such topic that often evokes such confusion.

With regards to the collapse of the wavefunction, there is experimental evidence of this. The Heisenberg Uncertainty Principle can be thought of as being one after effect of this (Griffith's explores this route though I do not think that we can say that that this is a strong indication as the derivation of the principle does not introduce such notions but conceptually Griffith's uses it to help explain how it comes about). Another consequence has to do with the time evolution of a system. If we have a system that has a probability of moving to another state, say we have an excited atom that will drop down to the ground state with a lifetime of T, then repeated measurements of the system will affect this probability. That is because each measurement resets the system by collapsing the wavefunction, preventing it from evolving. Repeated measurements have been experimentally shown to actually extend the lifetime of the system. So there are valid reasons to find the wavefunction collapse an attractive phenomenon.

EDIT: Also realize that his book, "QED," was written for the lay audience. So his use of the word "magic" is again simply there to describe how the average person would view the physics of the quantum world and not to actually deride the theory itself.

16. May 28, 2010

### Hoku

Born2bwired, it's optimistic and kind of you to speak in defense of Feynman. Unfortunately, I'm not sure I agree with your assessment of his intentions. Let's pick apart this passage a little...
This quote alone is saying, quite clearly, that the photon is not associated with a wavefunction. In other words, the photon has no wave properties. If there are no wave properties, there is no duality and, consequently, no collapse.
This quote has two points indicating that the author doesn't accept wavefunction collapse. 1) the context of his quotations indicate that he doesn't take the idea seriously. 2) whenever a scientist compares something to "magic" or "mystical", they are insulting it.

17. May 28, 2010

### Demystifier

The point that Feynman wanted to make is that IF the wave function is NOTHING but the probability amplitude, THEN there is nothing mysterious about the collapse. And that is fine. This is essentially the statistical ensemble interpretation of QM.

But this raises a new question. If wave function is nothing but a probability amplitude, then wave function has nothing to do with an individual particle. And if the wave function is all that QM is about, then QM says nothing about an individual particle. But in experiments we OBSERVE individual particles. So QM says nothing about what we observe in individual experiments. But if QM says nothing about it, does it mean that QM is not complete? And if so, can we have a more complete theory? That is why the Feynman remark does not remove all the problems.

18. May 28, 2010

### zonde

If Feynman wasn't taking "collapse of the wavefunction" seriously what he used in it's place?
Maybe "reduction of the wavefunction"?

19. May 28, 2010

### Dmitry67

Is it possible that he was one of the first MWI-ers?

20. May 28, 2010

### Fredrik

Staff Emeritus
I think his point was that QM should be viewed as a set of rules that tells us how to calculate probabilities of possible results of experiments. This way of thinking of QM is very natural when you take a path integral approach. The approach based on wavefunctions talks about how the "state" of the system changes with time, and that paints a very different picture, a picture that I feel is misleading. Feynman was really smart, so he must be thinking the same thing I am.

Edit: I see now that Demystifier already said essentially the same thing.

Last edited: May 28, 2010
21. May 28, 2010

### Fredrik

Staff Emeritus
Pure mathematics doesn't make predictions about results of experiments. So what you're proposing is to take the most successful theory in the history of science and change it into something that fails to qualify as a theory.

Statistics is about probabilities due to ignorance. QM is not. This is what Bell inequality violations are telling us. There's also a very beautiful mathematical fact that I don't fully understand yet: The axioms of probability theory can be derived from theories in which the set of observables have the structure of a commutative C*-algebra, but if you start with a non-commutative C*-algebra instead, you end up with a quantum theory instead of a statistical theory. So QM is definitely something different than statistics. It's a generalization of statistics.

I suppose you could call it "generalized statistics".

I disagree with your "in other words". He could just be thinking that the wavefunction isn't a representation of the properties of a single photon, but of the statistical properties of an ensemble of identically prepared photons. It's understandable that he didn't want to go into details about that.

I think the path integral approach is as far as you can get from the MWI. The main assumption of the MWI is precisely what he's protesting against here, that the wavefunction represents the properties of the system.

Last edited: May 28, 2010
22. May 28, 2010

### Born2bwire

Not that I have ever read. I really think that people are just trying to get far more out of this statement then there is. Again, this is "QED" which is a very simplified book to give some kind of idea about Feynman's path integral quantum electrodynamics. This was written more or less for the average Joe. I think that if Feynman really was insinuating what some of the posters think he is then he would be more explicit in his many textbooks on the subject that he wrote for students. I have gone through his famous Lecture texts and his "Path Integral" text and do not recall such a statement.

23. May 28, 2010

### jostpuur

Isn't it paradoxical, that when Feynman is trying to give some relief to the confusion of students, with some helpful comment, the helpful comment itself is so ambiguous that it becomes a subject of interpretation.

24. May 28, 2010

### zonde

But with this path integral approach you don' talk about single photon either, right? It's path integral for ... ensemble? ... or whole experimental setup? Or sill something else?

25. May 28, 2010

### dx

I think the main point he was trying to make is quite clear and unambiguous. In non-relativistic quantum mechanics, or low-energy quantum mechanics, we are always dealing with systems with fixed numbers of particles, usually only one. So, when we calculate amplitudes in these situations, the auxiliaruy function on spacetime that we introduce, psi(x,t), is interpreted as somehow being associated with that particle, as being showhow it's 'state'.

But, when you look at quantum mecanics from a more general and natural point of view, i.e. high-energy physics, we see that it is a misunderstanding to associate the amplitudes with single particles as 'states'; this is because in principle, if arbitrarily high energies are accessible, then processes whose probailities are encoded in the amplitude can involve the production destruction and transformation of an arbitrarily large number of particles of arbitrarily types. The is no longer a single particle, with a single spacetime history, whose 'state' can be described by the amplitude. The point is to keep in mind that the central quantity, the amplitude, should be thought of as associated with a whole event, not objects like particles. The objects come in when we calculate the amplitude, i.e. by considering all possible processes that could result in that event. The number of particles, type of particles, etc. that can take part in these processes is not at all definite.

Last edited: May 28, 2010