Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Does a particle really try every possible path?

  1. Jan 17, 2015 #1
    Hi,

    I'm reading that a particle located at any given point can, in the next moment, be at any other given point in the universe. My understanding is that this is a correct interpretation of quantum physics.

    So, my question is, how does the particle 'decide' where actually to be in the next moment, and why there rather than anywhere else? My current understanding is that it has something to do with the path of least action, which I've interpreted as it takes the 'easiest' route between the two points.

    Assuming I'm correct so far, does this mean that the particle does NOT actually go to every point in the universe (even though it has to potential to do so), but actually only goes (or 'contemplates' going) to a relatively few points in the nearby area, which provides it with enough information to then 'know' which path is the 'easiest' to take?

    My understanding is that this is similar to all the possible routes I could take on a trip from my house to the shop at the end of the street. I could get to the shop via Pluto or via a galaxy billions of light years away, but I don't, because I only have to contemplate walking a greater distance from the shop in the opposite direction before I give up on that path and go a shorter route, excluding my trip to Pluto from my plans. Would it be correct therefore to say that particles are efficient?

    Am I totally confused? Thanks :-)
     
  2. jcsd
  3. Jan 17, 2015 #2

    Nugatory

    User Avatar

    Staff: Mentor

    We have no way of knowing whether the particle actually tries every path. For that matter, it's not clear what it means to talk about a particle "trying" anything; it's not like a rat in a maze trying every path to get at the cheese.

    It would be more accurate to say "You can calculate the probability of the particle being at any position by doing the right calculations with the every possible path and combining them in the right way".
     
  4. Jan 17, 2015 #3
    Thanks. So, would I be right in saying that the probability of a particle's next position being right next to its previous position has the highest probability, which is why particles don't jump around the universe from moment to moment but generally end up where we'd logically expect them to.
     
  5. Jan 17, 2015 #4

    Nugatory

    User Avatar

    Staff: Mentor

    Pretty much, yes. In fact, if you calculate the "expectation value" of the position, which is what you'd get if you set up an arbitrarily large number of systems the same way, then measure the position of the particle for each one and take the average... You'll get the result that classical mechanics and what we'd logically expect of non-quantum particles predicts.
     
  6. Jan 18, 2015 #5
    So what happens when we bring it up to a double slit experiment and the particle becomes a wave, the a particle again? What do the calculations look like for that particle making it though the slits in some form or another and arriving on the other side?
     
  7. Jan 18, 2015 #6

    Nugatory

    User Avatar

    Staff: Mentor

    That's not how the double-slit experiment works; the particle is never either a particle or a wave. Search this forum for some discussion of why "wave-particle duality" is misleading for more informatiuon.

    The sum-over-all-paths approach produces the right answer when you include all the possible paths through both slits and include none of the paths that are blocked by the screen.
     
  8. Jan 19, 2015 #7
    Thanks all.

    So, on this basis, would I be right in saying that something which at first glance appears quite mind-blowing i.e. that a particle—being more a 'cluster of probability' than a solid bit of stuff—can jump from one place to any other place in the universe in one unit of Planck time, is actually about as mind-blowing as me saying that I myself could be anywhere in the universe at the next moment from now. In other words, not at all—it really is still possible, but is just so vastly improbable that it may as well be described as impossible for all practical purposes. If this is the case, it seems that so much of the initial confusion and 'spookiness' of this aspect of QM disappears, to my mind at least!
     
  9. Jan 19, 2015 #8

    naima

    User Avatar
    Gold Member

    In the path integral are there ftl paths?
     
  10. Jan 19, 2015 #9

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    One unit of plank time, particles jumping from one place to another - where are you getting this stuff from?

    When not measured what a quantum particle is doing is anyone's guess.

    Here is the detail of the path integral formalism

    You start out with <x'|x> then you insert a ton of ∫|xi><xi|dxi = 1 in the middle to get ∫...∫<x|x1><x1|......|xn><xn|x> dx1.....dxn. Now <xi|xi+1> = ci e^iSi so rearranging you get ∫.....∫c1....cn e^ i∑Si.

    Focus in on ∑Si. Define Li = Si/Δti, Δti is the time between the xi along the jagged path they trace out. ∑ Si = ∑Li Δti. As Δti goes to zero the reasonable physical assumption is made that Li is well behaved and goes over to a continuum so you get ∫L dt.

    Now Si depends on xi and Δxi. But for a path Δxi depends on the velocity vi = Δxi/Δti so its very reasonable to assume when it goes to the continuum L is a function of x and the velocity v and you get the principle of least action because nearby paths generally cancel.

    Strictly speaking its actually a hidden variable formulation - the path is the hidden variable - but of a very novel type.

    Certainly particles are not jumping around the place in plank time.

    Thanks
    Bill
     
  11. Jan 19, 2015 #10

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    No. Generally nearby paths cancel, but for stationary action they in fact reinforce, and since ftl paths cant exist, neither can the paths in the Feynman integral.

    Thanks
    Bill
     
  12. Jan 19, 2015 #11
    I wasn't saying I was right, I was asking the question. So I don't mean jump I mean 'travel' ... essentially do whatever a particle does to get from A to B, where A is its starting point and B is anywhere else in the universe. And by one unit of Planck time I'm referring to the shortest possible time between two events. Maybe I'm mistaken, but this is my understanding of things. I'm currently reading this book:

    http://en.wikipedia.org/wiki/The_Quantum_Universe

    Sorry, but everything else you've written makes no sense to me right now!
     
  13. Jan 19, 2015 #12

    phinds

    User Avatar
    Gold Member
    2016 Award

    Your understanding of how fast a particle could move from one place to another would allow faster than light travel. This is impossible. If someone told you that quantum objects travel from any point to any other point in one Plank Time they were either kidding you or making things up. More likely you misunderstood what was said/written. Some quantum objects, the photon for example, travel AT the speed of light but none travel faster and massive ones, the electron for example, travel slower.
     
  14. Jan 19, 2015 #13
    Seems to be the case, hence my questioning :)

    So, let me revisit my question:

    With reference to the double slit experiment, would I be right in saying that something which at first glance appears quite mind-blowing i.e. the suggestion that a particle (as a wave) takes every possible route from the source to the screen, is as mind-blowing as me saying that I too could take every possible route from my house to the local shop (some of which may go via Pluto or another galaxy were I to travel at the speed of light). In other words, not at all mind-blowing—yes, it really is still possible according to the laws of physics, but most physically possible journeys between my house and the local shop are just so vastly improbable that they may as well be described as impossible for all practical purposes. If this is the case, it seems that so much of the initial confusion and 'spookiness' of this aspect of QM disappears, to my mind at least!

    Can you see what I'm getting at?
     
  15. Jan 19, 2015 #14

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    That book is a popularisation. Brian Cox tries hard to explain QM, but without math you always run into problems. I have a copy and he makes a reasonable fist of it - but perfect it aren't - or rather in trying to express these concepts without math issues will always arise. QM does not say everything that can happen does happen. Feynman's parth integral formulation does not say particles literally takes all possible paths - it says they mathematically behave like they take all possible paths.

    I strongly suggest you study Susskinds book instead:
    https://www.amazon.com/Quantum-Mechanics-The-Theoretical-Minimum/dp/0465036678

    It requires some math but it is correct.

    There are also associated video lectures:
    http://theoreticalminimum.com/

    When you have gone through that book you should be able to understand what I posted.

    None of the generally accepted theories of physics require a shortest possible unit of time - its continuous.

    Thanks
    Bill
     
    Last edited by a moderator: May 7, 2017
  16. Jan 19, 2015 #15
    Thanks. I will certainly look into the book and watch the videos.

    As an aside...
    From: http://simple.wikipedia.org/wiki/Planck_time

    "Theoretically, this is the shortest time measurement that is possible."

    ?
     
  17. Jan 19, 2015 #16

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    Last edited by a moderator: May 7, 2017
  18. Jan 19, 2015 #17

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    That article shows a common misunderstanding of the uncertainly principle. It does not put a limit on measurement precision - rather its a statistical statement about measurements of similarly prepared systems.

    In our most powerful and experimentally verified theory, Quantum Field Theory, time is continuous.

    Thanks
    Bill
     
  19. Jan 19, 2015 #18
    Thanks. I recognise there subject matter is highly complex, but there's so much contradictory information out there; it's hard to know what to believe! The videos look like a great immediate starting point though - much appreciated.
     
  20. Jan 19, 2015 #19

    phinds

    User Avatar
    Gold Member
    2016 Award

    I agree w/ all of bhobba's statements but I think I do see what you are getting at and yes, other than your mis-statement about your being able to travel at the speed of light, you are right. These weird things are possible (but one at a time, not all together ... it's a statistical thing) but almost all paths are so utterly improbably that they can be ignored for all practical purposes. I'm not sure that changes the weirdness of QM but it's also clear that you have a distorted view of QM so it may well change what YOU view as the weirdness of QM.
     
  21. Jan 19, 2015 #20
    Thanks. I'll get there! :)
    Would you mind explaining what you mean? Why a misstatement? I could, in theory, travel at the speed of light, couldn't I?
    That's true. My understanding of QM began, many years ago, quite by accident, with http://en.wikipedia.org/wiki/What_the_Bleep_Do_We_Know!? (hey, we all have to start somewhere!). I now realise that simplifying things can strip a great deal of meaning and lead to all sorts of wrong thinking. I'm aware that QM is weird, but you're right, it's perhaps not as weird as I first thought.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Does a particle really try every possible path?
  1. Particle Path (Replies: 1)

Loading...