A quasi-analogy of wave-particle duality?

[Matty521]

TL;DR Summary

I am asking a question while also giving my understanding. I am going to compare a rock falling vertically into still pond to wave-particle experimental evidence. Further conclusions abound the more acceptable the conditions mirror QM experiments.

One Major question I have about wave-particle duality of say a photon... Could we describe it like a rock falling vertically into a still pond. Around this point of contact we establish a circular wall which detects the contact of the wave. Two things are evident here: the rock keeps on moving downward through the pond as the energy of its impact ripple throughout the surface of the pond, and this is an analogue of QM observation. So then when the wave hits the circular detector, the rock stops moving downward and it is focused perpendicularly at some point along the wave that hits the detector, at whichever point. Furthermore, when the point at which, along the wave, the "rock" is found to be, the pond becomes instantly still. Is this a way to describe the experimental evidence of the nature of wave-particle duality? Also, if instead of the pond quit rippling and there only being a rock, can we say that the energy of the rock falling downward is then diverted in the same direction as the rock was initially traveling, effectively swapping places?

 

[Demystifier]

No, wave-particle duality is nothing like that.

If you want an analogy, here is one. Consider a water wave and a surfboard carried by the wave. The water wave and the surfboard are very much analogous to wave and particle in the Bohmian formulation of quantum mechanics.

 

[Matty521]

No, wave-particle duality is nothing like that.

If you want an analogy, here is one. Consider a water wave and a surfboard carried by the wave. The water wave and the surfboard are very much analogous to wave and particle in the Bohmian formulation of quantum mechanics.

It seems like you are referencing pilot wave theory. First and foremost, there is no definitive interpretation of the WP duality. In fact it is quite frustrating and strongly concerning that most who attempt to answer my questions on the subject are biased to their own interpretation. It feels a lot like discussing religious issues rather than scientific facts.

However, it it is well documented that complimentary is what is the case. I believe that pilot wave theory tries to state otherwise. As is, generally when there is no quantization of a photon, it's essentially anywhere in a specified region. In essence the photon becomes infinitely (theoretically) divided to being in an infinite (theoretically) amount of places. This explains how a photon can interfere with itself, which pilot wave theory cannot.

In the case of the double slit experiment, the reason why there is an interference pattern is because the photon is quantized at two possible locations. This effectively then reduces the wave to 2 half photons. It has been demonstrated that photons behave this way in other experiments as well. So then, when this phenomenon occurs, the two half photons return into a wave again, as we lose the information of their quantization. Then, upon hitting the detector, the wave then fully disappears, one photon is chosen to exist somewhere governed by probability and chance.

I would also like to add, a recent experiment which shows that it is possible for a photon to be observed in a non-binary state, where it is somewhat a wave and somewhat a particle. Regardless, I am still absorbing all the information to learn how to best describe the strange results of these experiments. Even still, I am impartial investigating facts to create the most comprehensive view possible with the addition of the least amount of complexity.

I appreciate the discussion!

 

[PeroK]

It seems like you are referencing pilot wave theory. First and foremost, there is no definitive interpretation of the WP duality. In fact it is quite frustrating and strongly concerning that most who attempt to answer my questions on the subject are biased to their own interpretation. It feels a lot like discussing religious issues rather than scientific facts.

However, it it is well documented that complimentary is what is the case. I believe that pilot wave theory tries to state otherwise. As is, generally when there is no quantization of a photon, it's essentially anywhere in a specified region. In essence the photon becomes infinitely (theoretically) divided to being in an infinite (theoretically) amount of places. This explains how a photon can interfere with itself, which pilot wave theory cannot.

In the case of the double slit experiment, the reason why there is an interference pattern is because the photon is quantized at two possible locations. This effectively then reduces the wave to 2 half photons. It has been demonstrated that photons behave this way in other experiments as well. So then, when this phenomenon occurs, the two half photons return into a wave again, as we lose the information of their quantization. Then, upon hitting the detector, the wave then fully disappears, one photon is chosen to exist somewhere governed by probability and chance.

I would also like to add, a recent experiment which shows that it is possible for a photon to be observed in a non-binary state, where it is somewhat a wave and somewhat a particle. Regardless, I am still absorbing all the information to learn how to best describe the strange results of these experiments. Even still, I am impartial investigating facts to create the most comprehensive view possible with the addition of the least amount of complexity.

I appreciate the discussion!

This is largely nonsensical, I'm sorry to say. Quantum Theory explains the experimental results that represent "wave-particle duality".

You can't have half a photon!

 

[DrChinese]

You can't have half a photon!

That's always the case... although you can manipulate half a photon in some exotic situations. A H/V polarizing beamsplitter can split a diagonally polarized photon into 2 halves (one H, one V). Those can be routed wherever, and then rejoined later to create the original diagonal polarized photon. (Admittedly, this is not an everyday experiment.)

http://www2.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/eberlybellsineq.pdf

In even more exotic situations, you could join an H component originating from one photon, and a V component from another independent photon - creating a new photon. (There would be a number of additional constraints to make this occur.)

Regardless, you never observe half a photon. Either one, or none. Or two, if you perform down conversion.

 

[Demystifier]

You can't have half a photon!

Physically not, but is it possible mathematically? It boils down to the question is there a square root $(a^{\dagger})^{1/2}$ of the creation operator $a^{\dagger}$? If such an operator existed, then its action on the vacuum would create half a particle (such as photon).

I suspect that such an operator does not exist even mathematicaly, but I'm not sure. Can someone prove it?

 

[Demystifier]

This explains how a photon can interfere with itself, which pilot wave theory cannot.

Yes it can.

 

[Demystifier]

In fact it is quite frustrating and strongly concerning that most who attempt to answer my questions on the subject are biased to their own interpretation.

Unlike you, who are not biased at all to your own interpretation.
https://en.wikipedia.org/wiki/Psychological_projection

 

[vanhees71]

That's always the case... although you can manipulate half a photon in some exotic situations. A H/V polarizing beamsplitter can split a diagonally polarized photon into 2 halves (one H, one V). Those can be routed wherever, and then rejoined later to create the original diagonal polarized photon. (Admittedly, this is not an everyday experiment.)

http://www2.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/eberlybellsineq.pdf

In even more exotic situations, you could join an H component originating from one photon, and a V component from another independent photon - creating a new photon. (There would be a number of additional constraints to make this occur.)

Regardless, you never observe half a photon. Either one, or none. Or two, if you perform down conversion.

If you have a polarizing beam splitter and a single photon going through, the photon usually is not "split in two" but the one photon as whole goes either in one or the other direction with the probabilities given by the prepared polarization state of the photon. That's what really distinguish a true single-photon state from a coherent state: You can have only one photon not "two half photons".

What the polarizing beam splitter does is to entangle the polarization with the momentum of the single (sic!) photon.

That forced Born to reinterpret Schrödinger's wave function as a probability amplitude rather than a classical field describing an electron as a "smeared charge distribution". Note, however, that there's no 1st-quantization description of photons, i.e., there are no wave function descriptions of photons in the sense of non-relativistic wave functions for massive particles.

 

[DrChinese]

If you have a polarizing beam splitter and a single photon going through, the photon usually is not "split in two" but the one photon as whole goes either in one or the other direction with the probabilities given by the prepared polarization state of the photon.

Just as in a double-slit setup with which-slit information not obtained, a photon traversing a PBS does not go in one direction or the other. There is in fact something that emerges from both output ports, and those outputs can be manipulated, guided, rotated, etc. and then later be recombined to recreate the original diagonal polarization. This is not much different than a Mach-Zehnder Interferometer in many ways.

Of course, one and only one photon can be detected at any point... you never see 2 half-photons. I choose to see this as indicating probability amplitudes have some kind of "reality" in the same sense that particles traverse both slits in a double slit setup. But that is just my opinion.

 

[vanhees71]

That's of course "quasi right". If the photon is not detected, after the slit you have a single-photon state where the polarization and momentum of the photon is entangled, and there's a certain probability to find this photon at either detector placed in the corresponding directions wrt. (and far enough from) the beam splitter. Nevertheless it's with certainty one and only one photon.

 

[Matty521]

If you have a polarizing beam splitter a

That's always the case... although you can manipulate half a photon in some exotic situations. A H/V polarizing beamsplitter can split a diagonally polarized photon into 2 halves (one H, one V). Those can be routed wherever, and then rejoined later to create the original diagonal polarized photon. (Admittedly, this is not an everyday experiment.)

http://www2.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/eberlybellsineq.pdf

In even more exotic situations, you could join an H component originating from one photon, and a V component from another independent photon - creating a new photon. (There would be a number of additional constraints to make this occur.)

Regardless, you never observe half a photon. Either one, or none. Or two, if you perform down conversion.

What the polarizing beam splitter does is to entangle the polarization with the momentum of the single (sic!) photon.

That forced Born to reinterpret Schrödinger's wave function as a probability amplitude rather than a classical field describing an electron as a "smeared charge distribution". Note, however, that there's no 1st-quantization description of photons, i.e., there are no wave function descriptions of photons in the sense of non-relativistic wave functions for massive particles.

That's always the case... although you can manipulate half a photon in some exotic situations. A H/V polarizing beamsplitter can split a diagonally polarized photon into 2 halves (one H, one V). Those can be routed wherever, and then rejoined later to create the original diagonal polarized photon. (Admittedly, this is not an everyday experiment.)

http://www2.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/eberlybellsineq.pdf

In even more exotic situations, you could join an H component originating from one photon, and a V component from another independent photon - creating a new photon. (There would be a number of additional constraints to make this occur.)

Regardless, you never observe half a photon. Either one, or none. Or two, if you perform down conversion.

I am really glad you mentioned it then gave me a complete interpretation of what is happening. I was using this precise experiment to show that a photon acts like 2 half photons. I was under the impression that the amplitude of the individual photon was reduced by a factor of 2 creating the sense of seeing two half photons. Perhaps there is a better way to say this then...

What I am actually trying to say is there is only one photon, but as if in the double split experiment, one photon in one slit is real, and the other is "imaginary." Because we don't know which is real, the real and the imaginary interact with each other to create an interference pattern. Somewhere along the way both one then hits the detector as the photon we all know and love.

As an analogy I would like to say it is like dividing the photon in half. And putting it in two locations. Or in other words, the more possible places the photon may be at a given region (say a circle of radius r), we can relate it's probability at being in one location within the region proportionate to "(photon)/pi(r)^2". For a photon moving freely, we can, at least in imaginary terms, interpret this as the photon dividing itself exponentially as it travels through time, where r also increases with respect to time.

I know there is no classical sense of describing the photon itself when discussing it as a wave and vise versa. So I suppose unless we want to discuss the viability of a 5'th dimension (two unique 3space regions partially overlapping), I guess it's best to speak in terms of the photon not being split, but as one being real and the other existing in an imaginary universe. Although I do wonder, if for this phenomenon alone, could we simply use this 5th dimension as purely imaginary?

 

[Matty521]

Unlike you, who are not biased at all to your own interpretation.
https://en.wikipedia.org/wiki/Psychological_projection

Hey I am working on a hunch and as much as I am trying to build on it, I am testing its validity to ensure that I am not biased.

Sometimes one can make an objection through quantitative analysis and rational qualification, and likewise be able to identity it as something they consiously will not emulate. There is truth, and if one speaks the truth, how can they be wrong? It's kind of hard to generalize others in this fashion and always be correct...But ya, it was helpful cause no one is perfect, and it's easy to be blind to whichever aspect of our psychology we do not understand... In this case, it did give me a new window to look through, so I appreciate that.

 

[Matty521]

I am really glad you mentioned it then gave me a complete interpretation of what is happening. I was using this precise experiment to show that a photon acts like 2 half photons. I was under the impression that the amplitude of the individual photon was reduced by a factor of 2 creating the sense of seeing two half photons. Perhaps there is a better way to say this then...

What I am actually trying to say is there is only one photon, but as if in the double split experiment, one photon in one slit is real, and the other is "imaginary." Because we don't know which is real, the real and the imaginary interact with each other to create an interference pattern. Somewhere along the way both one then hits the detector as the photon we all know and love.

As an analogy I would like to say it is like dividing the photon in half. And putting it in two locations. Or in other words, the more possible places the photon may be at a given region (say a circle of radius r), we can relate it's probability at being in one location within the region proportionate to "(photon)/pi(r)^2". For a photon moving freely, we can, at least in imaginary terms, interpret this as the photon dividing itself exponentially as it travels through time, where r also increases with respect to time.

I know there is no classical sense of describing the photon itself when discussing it as a wave and vise versa. So I suppose unless we want to discuss the viability of a 5'th dimension (two unique 3space regions partially overlapping), I guess it's best to speak in terms of the photon not being split, but as one being real and the other existing in an imaginary universe. Although I do wonder, if for this phenomenon alone, could we simply use this 5th dimension as purely imaginary?

Btw, being skeptical is a great to hear! There are 3 possibilities for my theory.

1) Impossible. - I learn a lot of new things
2) Possible - I learn a lot of new things
3) Correct - I learn a lot new things

 

[PeroK]

Btw, being skeptical is a great to hear! There are 3 possibilities for my theory.

1) Impossible. - I learn a lot of new things
2) Possible - I learn a lot of new things
3) Correct - I learn a lot new things

You'd learn something by studying quantum mechanics.

 

[Matty521]

You'd learn something by studying quantum mechanics.

Well I am learning through investigating, which is my point. I am working my way through it by forming hypotheses, and asking questions. I understand it in broad terms, but I am trying to understand it a bit more specifically. As well, I don't want to have a model of fundamental reality that is shown to not exist, so it's personally helpful to prune what dead branches, which I have little way to determine myself.

Appreciate the understanding

 

[fresh_42]

Temporarily closed for moderation.

 

[berkeman]

Problematic thread has been cleaned up and will remain closed. Thank you for your contributions.