Does a particle really try every possible path?

[ChrisVer]

It's purely a mathematical reformulation - it doesn't mean it literally takes all paths.

When you try and visualise this stuff is when you run into problems.

Thanks
Bill

Try visualizing it you get problems: Well that depends on the person I guess... I find it an extreme beautiful idea and easy to "visualize"..
And in general many things are just mathematical. I mean, you have an unknown region, where you don't know what is happening because you can't observe it. It's amazing that you can say "everything happens" but also "everything ends up in what I measure".

In his space-time approach Feynman calculates the propagator (x,0) -> (x',t) as an integral of e^{i S(q)/hbar where S(q) is the classical action along the path.
The paths have to be continuous, to start at (x,0) and to end at (x',t) and that is all.
Nothing about speed of light.
The question was can we think that the particle explore all these paths. My answer is that this is a wrong and useless conception. the particle would have to explore a part of them with a ftl speed.

What exactly are you trying to say here?

 

[naima]

I wanted to say that path integral is the integral along ALL paths.

 

[Atomic squire]

Would you mind explaining what you mean? Why a misstatement? I could, in theory, travel at the speed of light, couldn't I?

Well, no matter can travel at or above the speed of light without disintegrating, even in theory. The particles that create the field that holds together the quarks that make up protons and neutrons move only at the speed of light, so traveling at that speed would basically cancel out the movement and destroy the field. Thus, sir atom turns to quark mush.

 

[PeterDonis]

The particles that create the field that holds together the quarks that make up protons and neutrons move only at the speed of light

No, they don't. The particles that create the field are virtual particles (more precisely, in the appropriate approximation, the field can be viewed as being mediated by virtual particles--but there are field phenomena that cannot be modeled in this approximation), and virtual particles have a nonzero amplitude to travel faster than light. (They also have a nonzero amplitude to move slower than light even if they are massless--for example, virtual photons have a nonzero amplitude to move slower than light. Virtual particles that move in a way that violates the usual energy-momentum relation for their particle type are called "off-shell", and they must be included to get the right answers out of the path integral.)

 

[PeterDonis]

since ftl paths can't exist, neither can the paths in the Feynman integral.

I'm not sure this is correct. As I understand it, in the general form of the path integral you cannot restrict the paths to only non-FTL ones. Feynman, IIRC, explained it as being due to all the energies being positive; restricting to non-FTL paths amounts to restricting the 4-momentum to a finite interval, and all the energies being positive means only positive frequencies, and known properties of the Fourier transform say that a function with a Fourier transform with only positive frequencies that vanishes outside a finite interval must be identically zero. So to have a non-vanishing path integral at all with only positive energies, you need to include FTL paths.

I understand that the above does not require that the Feynman-Stueckelberg interpretation of virtual particles moving outside the light cone as moving "backwards in time" is correct. But AFAIK the need to include FTL paths in the path integral does not depend on a particular interpretation.

 

[bhobba]

Well, no matter can travel at or above the speed of light without disintegrating, even in theory

I agree with Peter.

There are some parts of your post I can't really make sense of, but the above is incorrect.

The reason particles can't travel above the speed of light (they can travel at the speed of light if massless) has to do with space time geometry and is a consequence of the fact regardless of how fast you are traveling the speed of light is always the same. As Wheeler says forward is always forward and since a beam of light always moves away from you at the speed of light you can't catch up to it, hence an object traveling slower than the speed of light can't reach that speed.

Of relevant to this thread however is that the path integral formalism is formulated for ordinary QM, and although it not usually emphasised, classical mechanics is not local and based on the Galilean transformations (see page 8 - Landau - Mechanics) so any path or speed is allowed. In QFT things are different and we have virtual particles (they don't really exist - they are simply an artefact of the perturbation formalism used) that do all sorts of crazy things like going FTL etc - bit since they aren't real who cares.

Thanks
Bill

 

[bhobba]

I'm not sure this is correct. As I understand it, in the general form of the path integral you cannot restrict the paths to only non-FTL ones.

Sure - as far as I understand it one must consider all contributions of the propagator - even FTL ones - but arent they called off-shell and not real?

Thanks
Bill

 

[Joel A. Levitt]

How do you define PARTICLE?
How do you understand the FTL transmission of information observed in recent entanglement experiments?

 

[PeterDonis]

the path integral formalism is formulated for ordinary QM

It may have originally been formulated for ordinary QM, but it certainly works for quantum field theory (with appropriate changes). Zee's Quantum Field Theory in a Nutshell has a good review.

as far as I understand it one must consider all contributions of the propagator - even FTL ones - but arent they called off-shell and not real?

"Off shell" means "not obeying the appropriate energy-momentum relation". Plenty of non-FTL paths are also off-shell.

As for "not real", either a path is in the integral or it isn't. What does "real" have to do with it?

 

[PeterDonis]

How do you define PARTICLE?

A particular type of excitation of a quantum field.

How do you understand the FTL transmission of information observed in recent entanglement experiments?

Reference, please?

 

[Mark Harder]

In the path integral are there ftl paths?

"ftl" ?

 

[StevieTNZ]

"ftl" ?

faster than light

 

[Mark Harder]

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.

It seems to me, a non- physicist with an admittedly rudimentary knowledge of, but some experience using, QM, that these "weird" notions in QM are really physical interpretations, as in the "Copenhagen Interpretation", of an essentially mathematical framework for predicting physical observations. Intuitive understandings of classical mechanics were relatively easy to make. Waves and fields could be pictured. Even spacetime curvature can be pictured. But these intuitive pictures couldn't be extended to include quantum realities, so new physical explanations had to be invented. The Copenhagen interpretation is one of these. Perhaps out of ignorance, I am skeptical of these pictures. Someday, I will learn more QM and perhaps I will arrive at a physical intuition that satisfies me.

 

[bhobba]

As for "not real", either a path is in the integral or it isn't. What does "real" have to do with it?

Hmmmm. Actually that's a good point.

Thanks
Bill

 

[bhobba]

I agree w/ all of bhobba's statements

I suspect I have goofed here. Peter has corrected me, and its exactly in the area I often stress - namely what is real.

Even in QFT you include FTL and other normally not allowed things - that they are not classically allowed and in that sense are not real doest mean didly squat as far as what is included in the path integral.

Thanks
Bill

 

[Mark Harder]

How do you define PARTICLE?
How do you understand the FTL transmission of information observed in recent entanglement experiments?

Does entanglement require the transmission of information, or is it a statement about what happens when 2 quantum systems originate from the same event? My understanding is that the experiments that demonstrate entanglement involve particles that interact locally, then each carries information depending on the state of the other as the partners move apart, a process that does not occur ftl.

 

[bhobba]

Does entanglement require the transmission of information

No it does not.

Its a statement about correlations like if you have a pair of different coloured socks - put on one and you know what colour the other is automatically - Google Bertlmann's socks.

Thanks
Bill

 

[Mark Harder]

No it does not.

Its a statement about correlations like if you have a pair of different coloured socks - put on on and you know what colour the other is automatically - Google Bertlmann's socks.

Thanks
Bill

Thanks, Bill. BTW, what does "Ballentine" refer to, a textbook?

 

[phinds]

I suspect I have goofed here. Peter has corrected me, and its exactly in the area I often stress - namely what is real.

Even in QFT you include FTL and other normally not allowed things - that they are not classically allowed and in that sense are not real doest mean didly squat as far as what is included in the path integral.

Thanks
Bill

I vaguely remember reading that early in my readings on QM but it seemed unreasonable and didn't stick. Thanks for pointing that out

 

[bhobba]

Thanks, Bill. BTW, what does "Ballentine" refer to, a textbook?

Yes.

IMHO the finest textbook on QM available - but of course that is just an opinion - although many on this forum also hold it in high esteem:
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

Be warned however - it's advanced.

If you are just starting out I recommend Susskinds book:
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

Thanks
Bill

 

[brianhurren]

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.

this works if you model the double slit experiment using boolean logic as well. I was curious as to weather I could treat a double slit as an OR gate. the output of the OR gate is the sum of the two binary streams entering each input (which there are two of). if you plot the relative positions of the '1's in the output in relation to each other you get something resembling an interference pattern. So it is the sum of the superposition of the two inputs. It seams that the universe is very 'logical'

 

[Ken Natton]

To the OP. Hi, gerbilmore, I operate very much at your level and not at the level of most of the contributors to this thread in terms of my understanding of this stuff, but I have a perspective to offer that might assist you. It isn’t specifically about what you raised in your original post, rather more general about understanding this probabilistic – formally it is called ‘stochastic’ – approach employed by these chaps.

So one of the best, easiest to grasp examples I encountered was the matter of electrical resistance. The phenomenon of electrical resistance was known and fairly well understood before the QM guys put a deeper explanation on exactly what causes it. So you can get tables that will tell you what the resistance of a given length of copper wire of a given gauge will be. Quantum physics can explain the phenomenon in terms of the interactions between the electrons flowing through the wire that constitute the electrical current and the electrons of the atoms that actually make up the piece of wire. Now, it is impossible to exactly predict every interaction that will take place, not just because of the limitations of human science or the sheer scale of the exercise, but because, at a fundamental level, there is a degree of a random nature to it. But it is possible to take the probabilistic approach and come up with a theoretical calculation that matches the already known experimental data. And that really is the heart of the point about the probabilistic approach. It is all about coming up with theoretical methods of calculating that which can be experimentally verified. In many cases, the experimental results were known first and the challenge was to come up with a theoretical method of achieving the same results. That, I think is what lies behind the infamous maxim of theoretical physicists – ‘shut-up and calculate’. And perhaps this is the point about a particle taking every path between two points. It isn’t that it does, only that we don’t know and can’t know what path it does take, but we can calculate the probabilities and come up with a worthwhile result by so doing.

 

[my2cts]

Not having read but a few of the previous 82 posts I will give my answer the original question.
The quantum particle is described by a wave function which obeys a wave equation.
That wave function will use every 'path' to get to its destination. The amplitude there is the sum of all amplitudes reaching the position.
This is just a form of the Huygens principle.
That is not to say that the wave function IS the particle, so it is inaccurate to say that the particle uses or even tries every path.

 

[Atomic squire]

No, they don't. The particles that create the field are virtual particles (more precisely, in the appropriate approximation, the field can be viewed as being mediated by virtual particles--but there are field phenomena that cannot be modeled in this approximation), and virtual particles have a nonzero amplitude to travel faster than light. (They also have a nonzero amplitude to move slower than light even if they are massless--for example, virtual photons have a nonzero amplitude to move slower than light. Virtual particles that move in a way that violates the usual energy-momentum relation for their particle type are called "off-shell", and they must be included to get the right answers out of the path integral.)

I certainly have to improve my overly generalized approximation. Also, what is meant by a "nonzero amplitude"?

 

[bhobba]

IAlso, what is meant by a "nonzero amplitude"?

In Quantum Field Theory an important object is the propagator which is a complex number whose square gives the probability of something happening - such is known as an amplitude. Non zero amplitude means there is a probability of that happening.

Thanks
Bill

 

[Atomic squire]

In Quantum Field Theory an important object is the propagator which is a complex number who square gives the probability of something happening - such is known as an amplitude. Non zero amplitude means there is a probability of that happening.

Thanks
Bill

An excellent explanation, but how do scientists observe that the nonexistent "particles" can move faster than the speed of light if they are, by definition, nonexistent? Do they measure fluctuations in the field associated with them, or do they arrive at the conclusion with mathematics?

 

[PeterDonis]

how do scientists observe that the nonexistent "particles" can move faster than the speed of light if they are, by definition, nonexistent?

Who said they were nonexistent? The quantum fields exist, and as I said before, the "particles" are just particular states of the quantum fields.

As for measuring them moving faster than light, we don't, and nobody has said we do. What we have said is that, in order to get the right answers out of the path integral, you have to include states of the quantum field that, under the particle interpretation, correspond to particles moving faster than light. But that is an interpretation, and that's all it is. It doesn't mean you can actually measure a particle moving faster than light, and it doesn't mean information can travel faster than light.

Do they measure fluctuations in the field associated with them, or do they arrive at the conclusion with mathematics?

Yes. ;) Two important measurements of "field fluctuations" of this type are the Lamb shift and the Casimir effect. The mathematical argument is basically what I said above, about what is required to get the right answers with the path integral.

 

[Joel A. Levitt]

A particular type of excitation of a quantum field.
Reference, please?

 

[Joel A. Levitt]

Peter Donis:

Would you please provide a more detailed response to "How do you define PARTICLE?"

Requested Reference Re: Recent experimental demonstrations of the FTL transmission of information between entangled entities --

Challenging preconceptions about Bell tests with photon pairs
Authors: V Caprara Vivoli, P Sekatski, J -D Bancal, C C W Lim, B G Christensen, A Martin, R T Thew, H Zbinden, N Gisin, N Sangouard
Journal: Phys. Rev. A 91, 012107 (2015)

 

[naima]

Not having read but a few of the previous 82 posts I will give my answer the original question.
The quantum particle is described by a wave function which obeys a wave equation.
That wave function will use every 'path' to get to its destination. The amplitude there is the sum of all amplitudes reaching the position.
This is just a form of the Huygens principle.

I completely agree with you.
When we have a non relativistic lagrangien with energy = m v^2 /2 we have no problem to integrate on all paths. Things become more difficult if energy = \frac{m c^2}{\sqrt{1-v^2/c^2} } . The integral is ill defined for paths on which there is a point where v = c.
A naive solution would be to say: avoid those paths because a massive particle cannot reach v=c. We could also avoid path where speed is not continuous and so on.
Feynman found the good answer. If we Fourier transform this integral we go from space time to momenta energy and proposes a contour around the poles. This is very technicall but it succeeds.

So we need no cut off , no v < c.

A problem still remains. Suppose yhat we have a particle in a box. its wave function is null outside the box. At time 0 i destroy the box. The propagator is not null outside the future cone of the box But relativity says that a particle which was in a region will remain in the future cone of this region.
Read faster than light? in wiki to solve te problem