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

[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."

 

[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"?)

 

[Academic]

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

 

[Academic]

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.

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

 

[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.

 

[Hoku]

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

 

[Academic]

Doesnt exist is a strong statement... I don't think he was a big fan of it and downplayed its significance.

 

[glengarry]

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

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.

 

[DrChinese]

i'm totally with einstein on this one.

lol.

 

[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?

 

[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.

 

[Dickfore]

"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.

So, there is no duality.

 

[Hoku]

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

 

[Dickfore]

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

What do you mean by 'duality'?

 

[Born2bwire]

I do not think that this is an accurate interpretation of what Feynman was trying to say. The impression I get a lot from Feynman is that he is very interested in describing physics in simple and clear terms. A lot of quantum mechanics is very confusing and Feynman 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, Feynman 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.

 

[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...

"...they begin to think that the wavefunction or amplitude is somehow associated with the photon.

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.

"...Keeping this principle in mind should help the student avoid being confused by things such as the "collapse of the wavefunction" and similar magic."

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.

 

[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.

 

[zonde]

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

 

[Dmitry67]

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

 

[Fredrik]

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.

 

[Fredrik]

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.

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.

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!

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".

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.

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.

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

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.

 

[Born2bwire]

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

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.

 

[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.

 

[zonde]

This way of thinking of QM is very natural when you take a path integral approach.

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?

 

[dx]

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.

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.

 

[dx]

That of course raises the question of why the Hamiltonian or canonical formulation of quantum mechanics speaks about states and generators of time evolution and so on. I'm not certain about the solution yet, but I think it is along the following lines: the space of states in classical mechanics, the phase space, is naturally regarded as the set of instantaneous dynamical state of systems, from a Newtonian standpoint. When we go to quantum mechanics, we carry over this type of thinking. But actually, mathematically, it is not at all necessary to look at phase space in this way. In fact, the lagrangian and hamiltonian pictures can be combined into a covariant picture, that talks about the whole spacetime history of the system. This viewpoint is called the 'covariant phase space formulation', and is, I think, the natural viewpoint when we describe quantum mechanics from the hamiltonian perspective. This is the reason why that formulation has the freedom of choosing between the 'Heisenberg picture', 'Schrodinger picture' and so on.

 

[Demystifier]

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.

I think Feynman is not the only guy that has this problem. In fact, most physicists have this problem, provided that someone pays attention to what they are saying.

 

[Fredrik]

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?

I would say it's for the detection event. The path integral doesn't describe properties of particles, or "what actually happens". It's just a tool that you can use to calculate probabilities of possible detection events.

 

[Fredrik]

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.

The issue of whether a wavefunction represents a system or an ensemble is just as present in the non-relativistic quantum theory of a single spin-0 particle. If you assume that it represents the system, some sort of MWI is pretty much inevitable. The alternative is to not make that assumption, and focus only on what we know, i.e. that QM predicts probabilities of possible results of experiments. That fact implies that the wavefunction represents the properties of an ensemble of identically prepared systems. That ensemble doesn't have anything to do with an indeterminate particle number. Suppose that you do an experiment to test a prediction of the non-relativistic single particle theory. You might want to run the same experiment thousands of times to get good statistics. The ensemble consists of the identical particles that participate in all those experiments.

I think everyone agrees that it's at least approximately correct to say that the wavefunction represents an ensemble in this sense. The controversy is about whether it represents something else as well. I think Feynman just wanted to avoid all those issues and focus on the stuff we know, i.e. that we have a set of rules that tells us how to calculate probabilities of possibilities. (It's funny that everyone in this thread seems to be saying "Feynman agrees with me").

 

[Zarqon]

The path integral doesn't describe properties of particles, or "what actually happens". It's just a tool that you can use to calculate probabilities of possible detection events.

This is a good point, and I think it also explains why the Feynman quote would cause more confusion than it solves. Most students (and most physicists!) really are interested when they start reading about physics to try to understand how the world really works, not merely being able to calculate a probability for the final outcome. Thus, what is basically a shut-up-and-calculate answer in the Feynman quote is not a satisfying one.

"How the world really works" is ultimately a lot more satisfying question to have answered, and is of course why we have such frequent debates on the interpretations of QM. Personally I enjoy these, and I don't think we could call it physics if we stopped asking questions after having the mathematical tools only.

 

[Demystifier]

"How the world really works" is ultimately a lot more satisfying question to have answered, and is of course why we have such frequent debates on the interpretations of QM. Personally I enjoy these, and I don't think we could call it physics if we stopped asking questions after having the mathematical tools only.

I agree with you, but I would like to see how then would you call it?

 

[Zarqon]

I agree with you, but I would like to see how then would you call it?

To clarify, I meant it in the good spirit that QM today still should be counted as physics and not pure math, as was disturbingly suggested in the beginning of the thread

Because today we do have people that ask questions on how to interpret QM that doesn't necessarily make sense asking on a purely mathematical level.

 

[Academic]

"doesn't necessarily" or "necessarily doesn't"? :)

 

[JDługosz]

"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.

I thought it meant the abrupt change of the state in Hilbert space to the eigenvector of the measurement operator that corresponds to the measured value. Namely, as being very different from the continuous and smooth evolution of the state over time.

Measuring the "position" is just a special case of that.

 

[Geigerclick]

To clarify, I meant it in the good spirit that QM today still should be counted as physics and not pure math, as was disturbingly suggested in the beginning of the thread

Because today we do have people that ask questions on how to interpret QM that doesn't necessarily make sense asking on a purely mathematical level.

It is a set of physical measuring tools in the language of math, but which leaves us who live in a reality which appears to sometimes contradict the math guessing as to the implications of these tools and their output.

 

[my_wan]

I can't ascribe to the idea that QM is not physics. The empirical data is king of all questions, and QM handles that fine. I do suspect (hope) that we are missing some basic connection that the formalism doesn't include, but that doesn't make it not physics.

I do find the "collapse of the wavefunction" hard to take seriously. Not the least of which because it's not that hard for another observer to be forced to consider me entirely in a superposition of states. Feynman emphasized the "final amplitude for the event" being a summation of a long series of amplitudes. Statistical ensembles are another construct where a large number of 'possible' states are superimposed as if a single state. Classically only one of these possible states represents the actual state of affairs, but in QM we are unable to reduce it to an actual state, like dice that takes a particular route to a particular outcome. So even if we take the wavefunction to be physically valid, it must still be formally smeared over a large ensemble of possible states without detailed knowledge of micro-states.

The fact that, in QM, possible states interfere with actual outcomes perhaps indicates some level of reality of a wavefunction. But that does not mean that the ensemble, which superimposes all possibilities over one another, is the actual state, any more than dice take all possible routes to an outcome. Only that for the dice, at the micro-level, there exist a waveform representation, rather than classical parts. There's still something quiet weird if the world we know is a persistent projection from something resembling Hilbert space, even if our model of it is a superposition of ensembles for which only a singular subset of these possibilities is real.

 

[JDługosz]

Years ago, I supposed and hoped that experience with trying to make "quantum computer" technology would shed light on the issue. Trying to keep an entangled system from collapsing is pretty much exploring the boundary conditions.

The underlying explanation appears to be "http://en.wikipedia.org/wiki/Decoherence" ". Basically, you see the superposition only if you make a measurement of the entire entangled system. If you measure part of it, you see a pure state. Once the particle interacts with "the environment" it rapidly diffuses to billions of atoms in a complex way, yet you only measure one or two particles.

Also, notice the experiments of a "quantum eraser" will restore the interference pattern.

The details of decoherence may be hard to grasp, but the idea is clear: you must measure the whole system. It's the same thing that gives you entanglement in the first place.

With a slight lay knowledge of QM, you can see roughly that the tensor product space contains vectors for both entangled parts, and you are measuring one and throwing away the other. The solution to the product space gives you a correlation between the two entangled particles, but does not state which specific state either particle is in. You cannot separate it into two separate particles with superposed states. So, the "rules" are that if you measure one particle you get a pure state. Saying it that way doesn't solve the measurement problem, but states it. But it is not mysterious: it states exactly when you see a collapsed state, and how that is contextual, and why collapse spreads like an epidemic.

 

[andrewr]

lol.

I am pretty sure the meaning of "collapse of the wavefunction" includes something that even Feynman doesn't dispute -- and that is that the probability of finding an item in a location it *wasn
t* found in (eg: after the experiment is over) is no longer predicted accurately by the probability amplitude previously calculated. That is, the probability field is no longer associated with that item.

A probability interpretation indicates where something *can* be found (possibly) -- but the point of using the word "collapse" is that something that existed before (a prediction of probability) is no longer valid.

looking at previous posts, isn't it obvious that Feynman's interpretation can be made indefensible simply by taking an overly-literalist interpretation of his statement ??
eg: If the probability field is not even associated with the photon, then it obviously can't predict anything about the photon. So, clearly, since Feynman means something by his words...

associated:
1. To join as a partner, friend, or companion.

He can only mean what he says as a matter of degree -- not as an absolute. Clearly, the wavefunction is a companion of the path of the photon, and thus loosely associated with the photon's journey (even a super-set partially overlaps any individual case.)

Funny, even the QM book I just bought from the college bookstore uses the phrase... "Wavefunction collapse" ...
Of course the author is from our competitor weed college, oops... I mean REED college REED college...

 

[jVincent]

The collapse of the wave function is real, Just like the collapse of the probability in a coin toss experiment is real. People just get confused about what it means, and start talking about it like it's some magical operation.

Consider the coin toss. At one instance the probability of getting heads or tails is 50/50 and the very next instance, there is a 100% probability that the coin ended up heads. It's magic, it weird and it's pretty much boring if you don't try to confuse people about what you mean.
What Feynman is talking about is that people confuse the wave function (a tool to predict probability) with the actual photon, and that the student should keep the distinction in mind.

A coin isn't in a state of 50/50 before we toss it, but this is the state we need if we want to describe it.

 

[Dmitry67]

Collapse can't be real, as is shown in the Wgner's friend experiment.

 

[Phrak]

I'll have to paraphrase something written by Feynman, as I can't find nor recall the source. It goes something like "If you try to understand it, it will drive you crazy." I know the word 'crazy' was included.

This worked for him. Don't try to see behind the curtain, but fill in some gaps, and call it QED.

 

[Ken Natton]

I’m not so sure if there is much point in answering your assessment Phrak, the thing that I am certain of is that Feynman doesn’t need me to defend him. However, I do find your assessment somewhat cursory and maybe not fully aware of the history – I’m thinking particularly of the period after the war at the time of the Shelter Island and Pocono conferences. I don’t know if you’re familiar with it Phrak, but there is a website called ‘Web of Stories’ that includes lots of fascinating interviews with some of the prominent people themselves. I have not found anything of Feynman there (although there are plenty of Feynman clips on YouTube), but one of the people I have found most fascinating to listen to on Web of Stories is Freeman Dyson. He is the man that demonstrated to everyone else that Schwinger and Feynman were getting similar results because they were really doing the same thing by different routes, founded on the very different personalities of the two men. In the series of Freeman Dyson videos, check out no 58 ‘Richard Feynman and his work’ but more particularly the series from no. 69 'Summer school in Michigan; Schwinger’s talks' to no. 76 'Linking the ideas of Feynman, Schwinger and Tomanaga. '

Certainly, Feynman tended to live on his instincts and fly by the seat of his pants. Dyson mentions how Feynman knew nothing of Quantum Field Theory and didn’t want to know. He could get to the same point by a much easier route. But far from not looking behind the curtain, Feynman was the arch peeker behind the curtain specifically to short-cut the systematic approach, and he did a great deal more than ‘fill in some gaps’.

 

[Phrak]

Ken Natton. Yes, 'filling in the gaps' was a poor turn of phrase.

The subject here is wavefunction collapse. Feynman chose not to be distracted by this question. This is the curtain I refer to.

"I think it is safe to say that no one understands Quantum Mechanics. (Richard Feynman)
One does not, by knowing all the physical laws as we know them today, immediately obtain an understanding of anything much.
[...]
The more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that." Richard Feynman, Quantum Mechanics"