A silly question I'm sure about Feynman's many paths

[Demystifier]

Remember CI doesn't so much assert the absence of e.g. pilot waves or even multiple worlds. It rather insists on agnosticism about these theological speculations. It is the same as SR's agnosticism about the unobservable luminiferous aether, or science's general agnosticism about God & friends. Assertions about the nature of reality beyond the observable is a departure from the domain of science.

Let me ask you a personal question:
Do you believe that the universe existed even before humans (or animals) have started to observe it? Or are you completely agnostic about that?

 

[Demystifier]

(2) You don't need to know the wave function over all space to compute the propagator. You just need the second derivative of the wave function - or more accurately the second derivative of its amplitude (for the quantum potential) and of its phase (for the \nabla\cdot{\bf v} in the Jacobian J) at the points along the track. In a practical numerical method, these can be calculated by sending a particle down the trajectory {\bf v} = \nabla S (i.e. following the streamlines of the quantum probability current) and then evaluating the required derivatives numerically using finite differencing or whatever. There is a whole community of physical chemists (believe it or not) who do precisely this to solve chemistry problems.

You mean like this?
http://prola.aps.org/abstract/PRL/v82/i26/p5190_1

 

[zenith8]

You mean like this?
http://prola.aps.org/abstract/PRL/v82/i26/p5190_1

Exactly like that, yes. I think Wyatt wrote a book on it as well.

PS: Thanks for filling in for me while I was asleep..

 

[Demystifier]

PS: Thanks for filling in for me while I was asleep..

It was my pleasure.

By the way, what do you think about #49?

 

[zenith8]

By the way, I've seen nice citations on weirdness of QM in this thread, so here is another one:
"If you really believe in quantum mechanics, then you can't take it seriously."
(Robert Wald)

In this spirit, I would say that Copenhagenians are those who really believe in QM, while Bohmians are those who take it seriously. Or is it just the opposite? :-)

You ask, what do I think of #49 (quoted above)?

I don't know, I think Wald's quote is a bit glib.

The fact of the matter is that we all know that QM provides statistical data on the results of experiments - one hardly needs the 'Copenhagen interpretation' to tell you that.

So basically there is a group of people who are interested in why QM does this, and there is another group who don't care (the instrumentalist people who use QM to build things - fair enough), and there is a third very vocal group who not only don't care but actively try to suppress any attempt to find out. Why they do this is beyond me. It makes rational discussion about - for example - the meaning of paths in the various kinds of path integral (the subject of this thread as defined by the OP) almost impossible without having these people throw their toys out of their pram.

In the end, I prefer some quotes about the Copenhagen interpretation from the Cambridge lecture course I referred to earlier:

"A philosophical extravaganza dictated by despair." (Schroedinger)

"It is now well-known that Copenhagen cannot be reconstructed as a coherent philosophical framework - it is a collection of local, often contradictory, arguments embedded in changing theoretical and sociopolitical circumstances.. ..riddled with vaccillations, about-faces and inconsistencies." (historian Mara Beller)

"One would expect proponents of Copenhagen were in possession of some very strong arguments, if not for inevitability, at least for high plausibility. Yet a critical reading reveals that all the far-reaching, or one might say far-fetched, claims of inevitability are built on shaky circular arguments, on intuitively appealing but incorrect statements, on metaphorical allusions to quantum 'inseparability' and 'indivisibility' that have nothing to do with quantum entanglement and nonlocality."
(historian Mara Beller)

"[Copenhagen QM is] an idea for making it easier to evade the implications of quantum theory for the nature of reality" [David Deutsch, albeit for the wrong reasons]

By the way, have you noticed we seem to be the last two left standing. Don't tell me we've won an argument for once?

 

[Demystifier]

By the way, have you noticed we seem to be the last two left standing. Don't tell me we've won an argument for once?

It's too early to say. Let us give them 24 hours more.

 

[jambaugh]

Pardon my absence I had a long reply but had to be somewhere yesterday. As you (zenith8) point out this is not the thread to continue the long debate on interpretations. I intend to start a new thread to continue it.

BTW Dr. Beller is a better historian than student of QM. One expects that as CI or any interpretation is developed there will be contradictions over time and difficulty in expressing revolutionary concepts. You see the same in the unfolding of the aetherless relativistic theory of electromagnetism. Note Poincare derived the E=mc^2 formula, and other researchers had various other versions E=2/3mc^2 etc.

Again the comparison between SR and CIQM has important parallels. SR rejects the aether not because it is disproved but because it is irrelevant. This is a positivist position exactly in keeping with the CI of QM which rejects the objective state of reality for the same reason. You can find legion "kooks" out there claiming to "disprove Einstein" with their pet reinvention of the aether. They make the same predictions as SR and can't understand why they are not raised up on the shoulders of the physics community for their brilliant insight. I see Bohm's interpretation and Everett's as important for the development of CI as they point out that (up to a point) ontological interpretations are possible. I see it as the same as the emergence within mathematics of geometry as an abstract topic instead of a natural science. The demonstrations of models of Geometry sans the parallel postulates show that Euclidean geometry is not inevitable but rather one of a larger class. These models did not supplant the Euclidean case as natural science their appearance rather show that natural science is not the proper context to study geometry. One is in the context of logic rather than science and one is thus free to choose axioms freely (within the constraint of consistency).

Likewise the various divergent ontological interpretations of QM point out the inappropriateness of viewing QM in the context of ontology. It is a description of phenomena not of reality. This is unarguable and that is the essence of CI.

Oops... I intended to make a quick comment but got worked up. I'll save further comments for another thread.

 

[Demystifier]

These models did not supplant the Euclidean case as natural science their appearance rather show that natural science is not the proper context to study geometry.

But we have a very physical theory - general relativity - that tells us that geometry may be an important part of a natural science. In particular, it is possible to decide by an experiment whether the universe is curved or not.

By the way, you haven't answered my questions in #51.

 

[zenith8]

Pardon my absence I had a long reply but had to be somewhere yesterday. As you (zenith8) point out this is not the thread to continue the long debate on interpretations. I intend to start a new thread to continue it.

Go on, we're waiting. Or did they already move it to Philosophy?

Zenith

 

[jambaugh]

Sorry it took so long. (Busy busy busy!)https://www.physicsforums.com/showthread.php?p=2274454#post2274454"

I got to run.

 

[maverick_starstrider]

Lol. I love how this post has gone on for 4 pages and the OP has not replied since the first post and probably have no idea what was being said since the second post.

 

[jaketodd]

Ok, I have not read all four pages of posts so this may have already been addressed. From what I did read, the paths the particle takes (Feynman) are probability waves (probability given by amplitude) and the amplitudes interfere, some cancel out. I remember the words of one post: "a probability with a direction." And I remember someone else saying that's a good interpretation.

My question now is: These waves with amplitude travel in different directions, so they are not superimposed on each other, so how can they cancel out or interfere at all? So I would say that the electron does not take all these many paths. Instead I would favor the idea that it is a singular wave of probabilities that propagates through space and manifests as a particle according to a formula that takes into account how many thing(s) it runs into (the more, the more likely for collapsing to a particle and sooner), how far away from the source of the electron wave those thing(s) are (the closer, the more likely the manifestation of a particle there), and some degree of randomness.

 

[jambaugh]

Ok, I have not read all four pages of posts so this may have already been addressed. From what I did read, the paths the particle takes (Feynman) are probability waves (probability given by amplitude) and the amplitudes interfere, some cancel out. I remember the words of one post: "a probability with a direction." And I remember someone else saying that's a good interpretation.

My question now is: These waves with amplitude travel in different directions, so they are not superimposed on each other, so how can they cancel out or interfere at all? So I would say that the electron does not take all these many paths. Instead I would favor the idea that it is a singular wave of probabilities that propagates through space and manifests as a particle according to a formula that takes into account how many thing(s) it runs into (the more, the more likely for collapsing to a particle and sooner), how far away from the source of the electron wave those thing(s) are (the closer, the more likely the manifestation of a particle there), and some degree of randomness.

Much of how you are characterizing this is interpretation dependent. What QM says operationally is that the wave functions add linearly and thence interference patterns in the wave function of e.g. an electron can be setup e.g. via double slit experiment. If you then in that experiment measure the position of an electron prior to and posterior to "passage through the double slits" and in addition configure the experiment so as not to allow measurement of "which slit the electron passed through" then you will get a probabilistic prediction for the final position measurement expressed using the interfering wave function.

When you do multiple experiments you can confirm the probabilistic prediction via the distribution pattern of the many electron position measurements. You thus see an interference pattern in the distribution of electron position measurements.
This is all the theory predicts. We argue about what the theory implies vis-à-vis interpretation debates which also delve into the semantics of what we mean by "the electron".

Is the electron some type of field modeled by our wave-function said field behaving non-locally when it collapses during a position measurement? Is the electron a point particle guided by a Bohm pilot wave represented by the wave-function? Is the electron a point particle passing through different slits in different sub-universes? Is "an electron" shorthand for a systematic class of phenomena wherein a certain mass and charge leaves one device and enters another and should we view questions such as "which slit the electron passed through" as ill posed given that in this instance no measurements are being made which would distinguish cases? Different interpretations answer this in different ways.

Pick your favorite.