Wave/Particle Duality: Helical Paths & Planar Projections

[Bach33]

With respect to wave/particle duality, is it correct to think of a particle traveling a wave path? And if so, given that no orientation with respect to an observer of that wave is generally considered, is the "wave" that is referred to then more accurately the planar projection of a helical path?

 

[Drakkith]

With respect to wave/particle duality, is it correct to think of a particle traveling a wave path?

No. The wavefunction is used to predict various aspects of a particle, such as position or momentum, but not its path through space. Particles are certainly not traveling with an up and down or side-to-side motion.

 

[Bach33]

Thank you for answer. I know this can get complicated fast, but I see "photon helicity" referred to, including diagrams that show helical path? Also, and this may seem a stretch to include in the discussion as it is not part of the textbook descriptions, but it is fair to say that at most scales it is correct to say that the particle is traveling a helical path i.e., to the extent that it has a position on the Earth that is rotating and orbiting and transiting in the galaxy etc. -- so it would seem tidy if that feature didn't suddenly change at atomic scale, especially when the "wave" character is so fundamental...?

 

[berkeman]

I know this can get complicated fast, but I see "photon helicity" referred to, including diagrams that show helical path?

Where? We require links to the reading you have been doing, and we require that the links be from reputable sources (see the PF Rules page under INFO at the top of the page).

With respect to wave/particle duality

That paradigm has been redacted in the last few dozen years (or more). It was used in the early days of trying to understand the "new" science of quantum mechanics, but nowadays is not used in mainstream science. I'll see if I can find some links for you to check out...

 

[Drakkith]

Thank you for answer. I know this can get complicated fast, but I see "photon helicity" referred to, including diagrams that show helical path?

Those are not showing a path. Those are showing either the way the magnetic and electric field vectors behave in an EM wave, or something having to do with the interplay between angular momentum and the direction of travel or momentum or something (I'm not entirely sure, as I'm not very familiar with this specific topic). In either case the helicity isn't showing the particle traveling in a helical manner.

Also, and this may seem a stretch to include in the discussion as it is not part of the textbook descriptions, but it is fair to say that at most scales it is correct to say that the particle is traveling a helical path i.e., to the extent that it has a position on the Earth that is rotating and orbiting and transiting in the galaxy etc. -- so it would seem tidy if that feature didn't suddenly change at atomic scale, especially when the "wave" character is so fundamental...?

No, because nothing about these paths is helical. They are complex and chaotic, changing over time in ways that aren't easily predicted thanks to their timescales and the combined gravitational interaction of countless numbers of objects.

Once again I'll stress that the 'wave' aspect of quantum physics is not about particles traveling in wave-like motions. It is about the fact that certain behaviors or properties of particles is described and predicted by a type of wave equation, called a wavefunction. That is, by an equation that is similar to that which describes waves in classical physics. But the results of the wavefunction are not paths.

 

[Bach33]

Thank you for your answer, appreciate it.

 

[berkeman]

Thank you for your answer, appreciate it.

I'm pretty sure that you are thanking me, and not @Drakkith since my reply was way better than his...

(in the future, when replying to one particular post out of several that replied to you, use the "Reply" link in the lower right of the post that you are replying to)

Or to quote/reply to just part of a post, click-drag to select what you want to quote and select "Reply" from the pop-up.

 

[berkeman]

I'll see if I can find some links for you to check out...

Here is a relevant link. Please ignore the line thing through his username thing. I just means that the user is uh, retired. Yeah, retired.

https://www.physicsforums.com/threads/is-wave-particle-duality-really-wrong.887652/

 

[PeterDonis]

I see "photon helicity" referred to, including diagrams that show helical path?

"Helicity" is basically another name for "spin", and has nothing to do with a particle's path through spacetime.

 

[Bach33]

Here is a relevant link. Please ignore the line thing through his username thing. I just means that the user is uh, retired. Yeah, retired.

Thanks

 

[Bach33]

No, because nothing about these paths is helical. They are complex and chaotic, changing over time in ways that aren't easily predicted thanks to their timescales and the combined gravitational interaction of countless numbers of objects.

I see what you mean here. But is it correct to say "nothing about these paths is helical"? If I'm standing on the surface of the Earth that is rotating and orbiting, surely my trajectory is helical in some reference frame? And similarly, at the next scale up the Earth's trajectory is helical from some observer's viewpoint. In fact, is there any other single trajectory that applies across the board to every object in space, granted not in every reference frame, but in at least some reference frame?

 

[Bach33]

Also...
If I need to accept that particles are not traveling any waveform trajectory, I’m wondering, is there any trajectory that can be associated with particle movement? Is it a straight-line or geodesic?
Also, I see that pilot wave theory is still alive as a possible approach to quantum gravity – I’m wondering if proponents of this theory would take a more literal view of a wave trajectory for the particle?

 

[vanhees71]

Thank you for answer. I know this can get complicated fast, but I see "photon helicity" referred to, including diagrams that show helical path? Also, and this may seem a stretch to include in the discussion as it is not part of the textbook descriptions, but it is fair to say that at most scales it is correct to say that the particle is traveling a helical path i.e., to the extent that it has a position on the Earth that is rotating and orbiting and transiting in the galaxy etc. -- so it would seem tidy if that feature didn't suddenly change at atomic scale, especially when the "wave" character is so fundamental...?

You must never think about photons as being classical particles. That's always wrong. Rather think of a very specific kind of an electromagnetic wave (technically speaking a one-photon Fock state of the electromagnetic quantum field). The electromagnetic wave carries energy, momentum, and angular momentum. The helicity is the projection of the wave's angular momentum to the direction of its momentum. There are two helicity values for a single photon, i.e., $\hbar$ and $-\hbar$. These eigenstates of the helicity are described as the quantum version of what you might know as left- and right-circular polarized electromagnetic waves from classical electromagnetism/optics.

 

[gentzen]

Also, I see that pilot wave theory is still alive as a possible approach to quantum gravity – I’m wondering if proponents of this theory would take a more literal view of a wave trajectory for the particle?

Note that pilot wave theory, aka Bohmian mechanics, is an interpretation of QM, not "a possible approach to quantum gravity". Let me say three things:
(1) Even quantum gravity does not rule out Bohmian mechanics.
(2) Your though when calling it "a possible approach to quantum gravity" may be that the definite particle positions of Bohmian mechanics could solve the gravity problem caused by superpositions of macroscopic states. However, that is not the case, as far as I know. And even if it could help, it would be much more subtle and indirect than you expect.
(3) Even so Bohmian mechanics is a valid interpretation, it is subtle to understand why it is valid and consistent with QM and experiments. For the typical student, the hopes that Bohmian mechanics would provide a shortcut for understanding the counterintuitive aspects of QM will probably be disappointed. Still, it can be discussed in the Quantum Interpretations and Foundations subforum (and only there).

 

[Delta2]

Particles in Quantum Mechanics don't have exact well defined motion paths, like in classical mechanics.

 

[Bach33]

Note that pilot wave theory, aka Bohmian mechanics, is an interpretation of QM, not "a possible approach to quantum gravity". Let me say three things:
(1) Even quantum gravity does not rule out Bohmian mechanics.
(2) Your though when calling it "a possible approach to quantum gravity" may be that the definite particle positions of Bohmian mechanics could solve the gravity problem caused by superpositions of macroscopic states. However, that is not the case, as far as I know. And even if it could help, it would be much more subtle and indirect than you expect.
(3) Even so Bohmian mechanics is a valid interpretation, it is subtle to understand why it is valid and consistent with QM and experiments. For the typical student, the hopes that Bohmian mechanics would provide a shortcut for understanding the counterintuitive aspects of QM will probably be disappointed. Still, it can be discussed in the Quantum Interpretations and Foundations subforum (and only there).

Thanks

 

[Bach33]

Particles in Quantum Mechanics don't have exact well defined motion paths, like in classical mechanics.

Thanks

 

[Drakkith]

I see what you mean here. But is it correct to say "nothing about these paths is helical"? If I'm standing on the surface of the Earth that is rotating and orbiting, surely my trajectory is helical in some reference frame? And similarly, at the next scale up the Earth's trajectory is helical from some observer's viewpoint.

I should have clarified that I meant that none of those paths are ideal helices. They can be helix-like to varying degrees of accuracy when viewed from certain reference frames, but how closely the resembled ideal helices varies widely. This isn't because there's something special with helices and motion, it's simply because objects tend to make a series of elliptical orbits within larger elliptical orbits under the influence of gravity. But even that isn't entirely true, as perfect ellipses are idealized orbits that don't exist in real life. They are the result of 2-body approximations we use because they are easy and they work well enough in many circumstances.

So orbits and motions in space under gravity are neither ideal helices nor ideal ellipses nor any other shape.

 

[Bach33]

I should have clarified that I meant that none of those paths are ideal helices. They can be helix-like to varying degrees of accuracy when viewed from certain reference frames, but how closely the resembled ideal helices varies widely. This isn't because there's something special with helices and motion, it's simply because objects tend to make a series of elliptical orbits within larger elliptical orbits under the influence of gravity. But even that isn't entirely true, as perfect ellipses are idealized orbits that don't exist in real life. They are the result of 2-body approximations we use because they are easy and they work well enough in many circumstances.

So orbits and motions in space under gravity are neither ideal helices nor ideal ellipses nor any other shape.

I see that I was applying rather crude observations to something rather more nuanced. But is that to say that we cannot make any generalisations about the trajectories that objects make in the universe? Not to labour the point (and I appreciate your comments), but “orbits” and I would add “helices” do seem to generally feature at all scales? In one sense this seems to have drifted from the underlying deeper QM considerations, but then perhaps not so much? Side note: The reason I’m perhaps biased toward seeing helices everywhere is because I’m working on a geometry constructed with minimal information input (e.g., no assuming straight-line as primitive) and fractally layered helices appear in the construction.

 

[Drakkith]

But is that to say that we cannot make any generalisations about the trajectories that objects make in the universe? Not to labour the point (and I appreciate your comments), but “orbits” and I would add “helices” do seem to generally feature at all scales?

Depends on what exactly you mean by this. A subatomic particle (treated classically, not quantum in this context), a basketball, a planet, and a star all behave the same under the influence of gravity, meaning they all accelerate at the same rate when placed near the same gravitational source. So things certainly scale in this sense.

But when we go to different forces things don't scale at all. Or, rather, the issue isn't about scaling, it's about applicability. The motion of bodies through space under gravity is very different than motion of an electron in a metal lattice for example, or a gas molecule bouncing around in the atmosphere. While the large scale motion of these might appear to be helical, when we zoom in we find that it is anything but.

Also note that an 'orbit' is a thing that is specific to objects under the influence of gravity. An electron is not orbiting a nucleus in an atom, it occupies an orbital, not an orbit. The two terms are superficially similar, but the details are very different. The electron actually occupies a stationary state (or a close approximation of it in everything but a lone 1s orbital), and you would be hard pressed to even say that the electron is moving at all.

 

[Bach33]

Depends on what exactly you mean by this. A subatomic particle (treated classically, not quantum in this context), a basketball, a planet, and a star all behave the same under the influence of gravity, meaning they all accelerate at the same rate when placed near the same gravitational source. So things certainly scale in this sense.

But when we go to different forces things don't scale at all. Or, rather, the issue isn't about scaling, it's about applicability. The motion of bodies through space under gravity is very different than motion of an electron in a metal lattice for example, or a gas molecule bouncing around in the atmosphere. While the large scale motion of these might appear to be helical, when we zoom in we find that it is anything but.

Also note that an 'orbit' is a thing that is specific to objects under the influence of gravity. An electron is not orbiting a nucleus in an atom, it occupies an orbital, not an orbit. The two terms are superficially similar, but the details are very different. The electron actually occupies a stationary state (or a close approximation of it in everything but a lone 1s orbital), and you would be hard pressed to even say that the electron is moving at all.

Thank you for your comprehensive answer.

 

[PeroK]

I see that I was applying rather crude observations to something rather more nuanced. But is that to say that we cannot make any generalisations about the trajectories that objects make in the universe? Not to labour the point (and I appreciate your comments), but “orbits” and I would add “helices” do seem to generally feature at all scales?

A helix is just a circle with uniform translation normal to the plane of the circle. You can say circlular paths, hence helical paths, are common in physics. But, to demand that there is something universal about circular paths is to regress to the physics before Kepler.

In the Newtonian theory of gravitation the fundamental shapes are the conic sections, one of which is the ellipse, and a circle being a special case of the ellipse.

In that sense, the circle or helix is the simplest case in many applications. But only a special case of generally more complex trajectories.

 

[Bach33]

In that sense, the circle or helix is the simplest case in many applications. But only a special case of generally more complex trajectories.

From that statement it seems reasonable to investigate the converse view that the helix is the trajectory associated with a fundamental underlying geometry, and the more complex trajectories of the real physical environment are the special cases that depart from that. This is the proposition that my model of that “fundamental underlying geometry” is supporting.

 

[PeroK]

From that statement it seems reasonable to investigate the converse view that the helix is the trajectory associated with a fundamental underlying geometry, and the more complex trajectories of the real physical environment are the special cases that depart from that. This is the proposition that my model of that “fundamental underlying geometry” is supporting.

No comment!

 

[PeterDonis]

From that statement it seems reasonable to investigate the converse view that the helix is the trajectory associated with a fundamental underlying geometry, and the more complex trajectories of the real physical environment are the special cases that depart from that. This is the proposition that my model of that “fundamental underlying geometry” is supporting.

This is personal theory and is off limits here.

Thread closed.