# Does a particle really try every possible path?

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 :-)

Nugatory
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".

Bystander
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.

Nugatory
Mentor
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.

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.

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?

Nugatory
Mentor
So what happens when we bring it up to a double slit experiment and the particle becomes a wave, the a particle again?

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.

Fabian Ballar, vanhees71 and bhobba
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!

naima
Gold Member
In the path integral are there ftl paths?

Larry Pendarvis
bhobba
Mentor
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,

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

bhobba
Mentor
In the path integral are there ftl paths?

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

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

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!

phinds
Gold Member
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!

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.

More likely you misunderstood what was said/written.

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?

bhobba
Mentor
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/dp/0465036678/?tag=pfamazon01-20&tag=pfamazon01-20

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

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Thanks. I will certainly look into the book and watch the videos.

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

From: http://simple.wikipedia.org/wiki/Planck_time

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

?

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

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

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.

phinds
Gold Member
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?
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.

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?
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

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.

phinds
Gold Member
Would you mind explaining what you mean? Why a misstatement? I could, in theory, travel at the speed of light, couldn't I?
No, you most emphatically could not. Nothing with mass can travel at c.

naima
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.
The propagator gives the amplitude x(t')|x(t)
Does Feynmann say that we can avoid paths going forward and backward in time and get the correct result?

bhobba
Mentor
The propagator gives the amplitude x(t')|x(t) Does Feynmann say that we can avoid paths going forward and backward in time and get the correct result?

Did you see post 9?

Why do you think it would allow particles travelling back in time or FTL?

Are you trying to handle amti-particles? That was Feynmans particular way of looking at it - I dont think its an inherent part of the formalism.

Thanks
Bill

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stevendaryl
Staff Emeritus
Well, your post #9 didn't say anything about restricting the integral over $x_i$ so that $|\frac{x_i - x_{i-1}}{\delta t_i}| < c$