Proposed resolution of double-slit experiment paradox using Feynman path integral formalism. - Polidicks

[QUOTE][QUOTE][IMG]http://cdn.phys.org/newman/gfx/news/2014/twoslitexper.jpg[/IMG][/QUOTE]Scientists at the Raman Research Institute and the Indian Institute of Science, both in Bangalore, India, theoretically resolved this paradox by quantifying nonclassical path contributions in quantum interference experiments using the Feynman path integral formalism, which involves an integration over all possible paths that can be taken by the particle through the two slits, thereby calculating a quantum amplitude by replacing the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinite number of possible trajectories. This allows them to replace the approximate wavefunction with both slits open (ψAB = ψA + ψB) with an integral that includes both the classical paths – the nearly straight paths from the source to the detector through either slit – and the nonclassical, or looped, paths that make a small but finite contribution to the total intensity at the detector screen (ψAB = ψA + ψB + ψL). Read more at: [url]http://phys.org/news/2014-10-superposition-revisited-resolution-double-slit-paradox.html#jCp[/url] Source: [url]http://phys.org/news/2014-10-superposition-revisited-resolution-double-slit-paradox.html[/url][/QUOTE] We await the tl;dr from JohnnyMo1. Also, this is my first science specific SH post in a long, long, time.

The title alone confuses the shit out of me.

Very interesting. The actual quantum mechanics stuff behind it is still mind-melting to me, even with the whole probability density function crap. Please explain more, Johnnym0

The only thing I understand out of that is that we have a proposed explanation for the double-slit paradox, but any advances in QM theory are exciting because of what they may unlock in the near future (more discoveries/developments).

[QUOTE]Scientists at the [B]Raman[/B] Research Institute[/QUOTE]

[quote=Megadave]Scientists at the [b]Raman[/b] Institute[/QUOTE] [url]http://en.wikipedia.org/wiki/C._V._Raman[/url]

[QUOTE=Megadave;46133117]Raman[/QUOTE] [QUOTE]The Raman Research Institute was founded in 1948 by the Indian physicist and Nobel Laureate, Sir C V Raman, to continue his studies and basic research after he retired from the Indian Institute of Science. Sir C V Raman served as its director carrying on his personal research until his demise in 1970. It was funded personally by him and with donations from private sources.[/QUOTE] I thought it might've been named after [URL="https://en.wikipedia.org/wiki/Srinivasa_Ramanujan"]Ramanujan[/URL], one of the most brilliant Indian mathematicians to live, but it wouldn't have been shortened to just "Raman" then. fuck, ninja'd by Zones. If I'm gonna be ninja'd by anyone here, best by him I guess.

Particles can do this [IMG]http://journals.aps.org/prl/article/10.1103/PhysRevLett.113.120406/figures/2/medium[/IMG] instead of just be restricted to paths one would expect classically (like straight lines through the slits). That weird-ass curvy path does contribute but it's rare so the effects are small and difficult to measure. It's incorrect to simply add probability amplitudes of one slit being open at a time in interference problems.

[QUOTE=Falubii;46133316]Particles can do this [IMG]http://journals.aps.org/prl/article/10.1103/PhysRevLett.113.120406/figures/2/medium[/IMG][/QUOTE] Go home photon. You're drunk.

[QUOTE=Zephyrs;46133720]Go home photon. You're drunk.[/QUOTE] Do you know how fast you were going photon

[QUOTE=helpiminabox;46133786]Do you know how fast you were going photon[/QUOTE] Yes. But I have no idea where I am.

[QUOTE=helpiminabox;46133786]Do you know how fast you were going photon[/QUOTE]Maybe I wasn't moving, but just simultaneously occupying every point I have and will ever exist for an infinitely small instance of time.

[IMG]http://facepunch.com/image.php?u=244899[/IMG] Could not be more appropriate.

Forgive my relatively basic analogy here: From what I'm understanding here some of the photons interact with the matter of the slits, and when they do their trajectory changes as well as loosing some energy (Thus a change in wavelength) in order to change their trajectory? Sort of a diffractional slingshot effect?

[QUOTE=LoneWolf_Recon;46134227]Forgive my relatively basic analogy here: From what I'm understanding here some of the photons interact with the matter of the slits, and when they do their trajectory changes as well as loosing some energy (Thus a change in wavelength) in order to change their trajectory? Sort of a diffractional slingshot effect?[/QUOTE] I didn't get that impression. But I didn't read the paper because it costs money to view (which seems very archaic and against the open nature of science tbh).

[QUOTE=Empty_Shadow;46133811]Yes. But I have no idea where I am.[/QUOTE] I usually refrain from just posting to say something was funny, but this post coupled with the two posts before it made my evening.

[QUOTE=Empty_Shadow;46133811]Yes. But I have no idea where I am.[/QUOTE] Actually you would always know how fast a photon is going. If you knew which direction it was going then that could account for a certainty in it's momentum which would in turn mean you wouldn't know where it is. The joke is still funny I just need to seize the teaching opportunity.

[QUOTE=Falubii;46135389]Actually you would always know how fast a photon is going. If you knew which direction it was going then that could account for a certainty in it's momentum which would in turn mean you wouldn't know where it is. The joke is still funny I just need to seize the teaching opportunity.[/QUOTE] [sp]I knew that when I posted it but the joke was too good to let it go[/sp]

[QUOTE=Falubii;46135334]I didn't get that impression. But I didn't read the paper because it costs money to view (which seems very archaic and against the open nature of science tbh).[/QUOTE] Here's the arXiv preprint: [url]http://arxiv-web3.library.cornell.edu/pdf/1308.2022v2.pdf[/url]

Well shit you beat me to it, but I'm still gonna post the one from Phys Review Letters. Those fuckers shouldn't charge for this stuff. [url]http://ge.tt/7qXppG02/v/0[/url]

They thanked one of my professors for reading it over. Neato.

[QUOTE=JohnnyMo1;46135431]Here's the arXiv preprint: [url]http://arxiv-web3.library.cornell.edu/pdf/1308.2022v2.pdf[/url][/QUOTE] We still need you to put it into Layman's terms.

[QUOTE=Instant Mix;46133072]Very interesting. The actual quantum mechanics stuff behind it is still mind-melting to me, even with the whole probability density function crap. Please explain more, Johnnym0[/QUOTE] Basically what's going on is when we normally teach people about the double slit experiment, we talk about the wave function (which tells us the likelihood of finding the particle at each point in space). And we wave our hands and say, "Well basically we have the wave function of a particle going through one slit, and the wave function of a particle going through the other slit. And quantum mechanics is weird, so when both slits are open, it's like the particle goes through both slits and messes with itself. The wave function with both slits open is the wave function with slit A open plus the wave function with slit B open! Weird, right!?" The problem with that is that quantum mechanics is [I]even weirder[/I]. Particles can take paths that would look really strange in regular classical mechanics (like the second image in the link). [I]But[/I] when you look at the case where just one slit is open, for instance, it gets rid of the paths where a particle doubles back through another slit, since the slit is closed. The true overall wave function has to consider these paths! They're turning to analyzing the problem via Feynman's path integral formulation of quantum mechanics (which in short says that the chance of a particle going from point P to point O is the sum of the chances that it follows any conceivable path from P to O). If they can apply Feynman's path integral formulation to the case of both slits open simultaneously (or at least get some idea of how much "weird paths" contribute to the likelihood that a particle hits the screen in a certain place) they can determine how far off the standard approximation of "the wave function is the sum of single-slit wave functions" is. It looks like they want to do an experiment for three slits. I think this is why: If you do a double-slit experiment, you might have a path where the particle enters slit A, goes back through slit B, goes through slit A again and hits the screen. It's not immediately obvious how this would contribute to the wave function differently than the particle just going through slit A. But if you have three slits, you have paths like they illustrated where one photon goes through one slit, back through another, and out the third slit and to the screen. This is a rough guess but I think those contributions would be more noticeable.

Hard to imagine a single particle being projected foreword, and then changing it's trajectory so dramatically for no obvious reason. But hey, if we can accept particles being quantum entangled, I see no reason why we should refuse to see this as a possibility.

[QUOTE=JohnnyMo1;46136380]Basically what's going on is when we normally teach people about the double slit experiment, we talk about the wave function (which tells us the likelihood of finding the particle at each point in space). And we wave our hands and say, "Well basically we have the wave function of a particle going through one slit, and the wave function of a particle going through the other slit. And quantum mechanics is weird, so when both slits are open, it's like the particle goes through both slits and messes with itself. The wave function with both slits open is the wave function with slit A open plus the wave function with slit B open! Weird, right!?" The problem with that is that quantum mechanics is [I]even weirder[/I]. Particles can take paths that would look really strange in regular classical mechanics (like the second image in the link). [I]But[/I] when you look at the case where just one slit is open, for instance, it gets rid of the paths where a particle doubles back through another slit, since the slit is closed. The true overall wave function has to consider these paths! They're turning to analyzing the problem via Feynman's path integral formulation of quantum mechanics (which in short says that the chance of a particle going from point P to point O is the sum of the chances that it follows any conceivable path from P to O). If they can apply Feynman's path integral formulation to the case of both slits open simultaneously (or at least get some idea of how much "weird paths" contribute to the likelihood that a particle hits the screen in a certain place) they can determine how far off the standard approximation of "the wave function is the sum of single-slit wave functions" is. It looks like they want to do an experiment for three slits. I think this is why: If you do a double-slit experiment, you might have a path where the particle enters slit A, goes back through slit B, goes through slit A again and hits the screen. It's not immediately obvious how this would contribute to the wave function differently than the particle just going through slit A. But if you have three slits, you have paths like they illustrated where one photon goes through one slit, back through another, and out the third slit and to the screen. This is a rough guess but I think those contributions would be more noticeable.[/QUOTE] The weird paths should be phase-shifted. I have no idea if they can measure that without breaking the interference though.

[QUOTE=Kardia;46136401]Hard to imagine a single particle being projected foreword, and then changing it's trajectory so dramatically for no obvious reason. But hey, if we can accept particles being quantum entangled, I see no reason why we should refuse to see this as a possibility.[/QUOTE] You can actually motivate it with some fairly simple reasoning about double-slit experiments and probability. You've got the usual double slit setup: the chance that the particle hits a point O on the screen is the chance that it goes through slit A and then goes to point O plus the chance that it goes through slit B and then to point O. If you had, for instance, two walls each with three slits cut out of them instead, the chance of a particle going through slit A1 and then slit A2 and then to O, plus the chance of it going through A1 then slit B2 and then to O, plus... etc. etc. We can think of empty space as "a double-slit experiment with an infinite number of walls with an infinite number of slits cut into them." (~deep~) So the chance of your particle going from your source to O through empty space is the chance of it traveling to some point nearby, then another, then another, ad infinitum until it reaches O. This traces out some path in space. You have to account for all of them to know the total chance of the particle reaching O. Mind you, some of these weird paths don't contribute anything, or don't contribute very much, to the probability of the particle reaching a point. [editline]2nd October 2014[/editline] [QUOTE=Tamschi;46136693]The weird paths should be phase-shifted. I have no idea if they can measure that without breaking the interference though.[/QUOTE] That's true, but wouldn't you get phase shifted weird paths in single-slit diffraction as well? e.g. The particle goes through the slit, backwards through it, meanders partway back to the source, and goes through again and to the screen. Or do they miraculously cancel? I haven't actually used the path integral formulation in any detail.

Wow! This changes everything(?)

[QUOTE=JohnnyMo1;46136813] That's true, but wouldn't you get phase shifted weird paths in single-slit diffraction as well? e.g. The particle goes through the slit, backwards through it, meanders partway back to the source, and goes through again and to the screen. Or do they miraculously cancel? I haven't actually used the path integral formulation in any detail.[/QUOTE] Were you taught it in undergrad? We've only dealt with your typical matrix mechanics; a little bit sad that I've not formally learned Feynman path integrals. Perhaps it'll pop up in honours... my uni is quite heavily condensed matter and quantum optics focused after all (one of my professors is starting an honours course in GR next year, though; apparently it may be a result of me having hassled him about it so much :v: ). A university on the other side of the city from me did a triple slit experiment recently (can't remember if it was with electrons or photons). Apparently the interference pattern that was produced was really crazy and consisted of 'vortices'. Sounded interesting.

[QUOTE=sltungle;46136969]Were you taught it in undergrad? [/QUOTE] Nope, that's why I never really did much with it. All I've gotten is from glancing over Shankar and Zee. I think for most physicists it's pretty unnecessary, just an interesting footnote. I find it sort of weird that Zee build up QFT from it instead of canonical quantization. I feel like canonical quantization is more elegant and lends itself to intuition better.

[QUOTE=JohnnyMo1;46136380]Basically what's going on is when we normally teach people about the double slit experiment, we talk about the wave function (which tells us the likelihood of finding the particle at each point in space). And we wave our hands and say, "Well basically we have the wave function of a particle going through one slit, and the wave function of a particle going through the other slit. And quantum mechanics is weird, so when both slits are open, it's like the particle goes through both slits and messes with itself. The wave function with both slits open is the wave function with slit A open plus the wave function with slit B open! Weird, right!?" The problem with that is that quantum mechanics is [I]even weirder[/I]. Particles can take paths that would look really strange in regular classical mechanics (like the second image in the link). [I]But[/I] when you look at the case where just one slit is open, for instance, it gets rid of the paths where a particle doubles back through another slit, since the slit is closed. The true overall wave function has to consider these paths! They're turning to analyzing the problem via Feynman's path integral formulation of quantum mechanics (which in short says that the chance of a particle going from point P to point O is the sum of the chances that it follows any conceivable path from P to O). If they can apply Feynman's path integral formulation to the case of both slits open simultaneously (or at least get some idea of how much "weird paths" contribute to the likelihood that a particle hits the screen in a certain place) they can determine how far off the standard approximation of "the wave function is the sum of single-slit wave functions" is. It looks like they want to do an experiment for three slits. I think this is why: If you do a double-slit experiment, you might have a path where the particle enters slit A, goes back through slit B, goes through slit A again and hits the screen. It's not immediately obvious how this would contribute to the wave function differently than the particle just going through slit A. But if you have three slits, you have paths like they illustrated where one photon goes through one slit, back through another, and out the third slit and to the screen. This is a rough guess but I think those contributions would be more noticeable.[/QUOTE] Even with this explanation I barely understand it. Quantum Mechanics is one of the few things I've ever seen that's so mindboggling it makes me feel stupid, and I'm thoroughly impressed by the people who can put it in Layman's terms. :v: [editline]3rd October 2014[/editline] To me Quantum Physics looks like "here's all the shit you thought you knew. Confusing, yet logical isn't it? WRONG, HERE'S QUANTUM PHYSICS" followed by a complete overhaul of how everything works.