# Possible explanation for the wave-particle duality ?

#### probert84

Hi everyone,

today I had a thought coming across my mind when I woke up, and I think it might be an explanation for the particle-wave duality.

Now, when we are talking about a particle, one thing that has to be mentioned is the uncertainty principle. If you divide space into equal volumes for ex. imagine a 3D grid of cubes, and you put a particle in it, you can assign a number to each cube, which represents the probability of that particle being in that cube. If we consider a moving particle this probability will represent a change rather than a constant value. If the particle is moving towards a cube, this number is positive because the chance that it can be found in that cube is increasing, and when its moving away from a cube then the number is negative. Take every cube, and assign a probability for each cube, and lets call the sum of these a probability field.

I think that the phenomenon what we experience as a wave is caused by this. Its not the particle that is interfering but the probability field of the particles possible paths.

For example where you see dark areas in the double slit experiment, this can be caused by the possible paths of the same particle interfering with each other.

When you fire a photon, in the moment of the launch it has a chance to pass each slit, say it goes through each slit 50 times from a 100 experiments. This means 50% of the possible paths are divided between the two slits. The paths are different in length, and because of this after the particle passes the slit there will be a shift in the phase of probability changes. On dark areas there are several paths of the particles interfering with each other so, that they sum up to 0. For ex a path that represents particle 'X' coming from slit 'A' towards a dark point adds 0.5 chance to the volume (the cube), while on the other possible paths from slit 'B' particle 'X' has already left the same volume with 0.5 chance. The end result the incoming(+0.5) and leaving (-0.5) particle paths is a chance of 0, meaning that there cannot be a change in that volume.

You can also view this from a geometric perspective. Before you launch a particle count all the possible paths were it can go through. Separate them and assign each one to a separate 3 dimensional space. Each particle (or better to say each possibility of the particle) in every one of these 3 dimensional spaces interfere with all other particles in a 4 dimensional space (consisting of the sum of the 3 dimensional ones ) and the interference pattern is we see is caused by this.

In our 3 dimensional space what really happens is not that the particle goes through two slit at the same time and it interferes with itself, it passes only one slit and doesn't interfere with anything, its just the possible paths that are limited for it, and it simply does not cover those places that are impossible for it to go through.

The interference does not happen between particles, it happens between probabilities, and the particle is not a wave, rather because the imperfect way how we examine it makes it for us to seem as a wave of probability.

Now I can't prove this with equations, and the idea just came across my mind somehow, and I wonder if it could be true ? What do you think ?

Related Quantum Physics News on Phys.org

#### stevendaryl

Staff Emeritus
Well, the fact that gets in the way of interpreting wave functions as probability distributions is that they are complex numbers, rather than real numbers, which leads to interference effects that are not easily understood in terms of ordinary probability distributions.

#### probert84

I dont get it, does the fact that wave functions operate with complex numbers imply that the explanation I gave is wrong ? Or you say its just not easy to validate because of this ?

#### DennisN

Hi probert84, and welcome to Physics Forums!

Do you know about the classical wave mechanics treatment of the double slit experiment?

Assignment for you:

The appearing fringes (maxima) on the screen depends on a couple of parameters. Which?

See: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html

I'm particularly interested in what λ is.

#### Cthugha

The interference does not happen between particles, it happens between probabilities, and the particle is not a wave, rather because the imperfect way how we examine it makes it for us to seem as a wave of probability.
It is not really the imperfect way of examination that causes it, but it is well known since at least the 1960's that interference does not happen between particles in the naive sense.

See the quote below. It is taken from "100 years of light quanta", which is the 2005 Nobel prize lecture given by Roy J. Glauber, who was awarded the prize for his contributions to quantum optics and optical coherence.

"It is worth recalling at this point that interference simply means that the probability amplitudes for alternative and indistinguishable histories must be added together algebraically. It is not the photons that interfere physically, it is their probability amplitudes that interfere— and probability amplitudes can be defined equally well for arbitrary numbers of photons."

#### probert84

@Cthugha:

Actually I'm not a physics expert, I only studied it in high school and one semester in uni. I don't know why I had this thought in the morning, but when I woke up this was the first thing that came across my mind, and I felt I had to check it out if it makes sense. I didn't know that this is basically known since the 1960's, but it seems that I stumbled upon the same conclusion somehow. The way I learned it was that it is still unclear if atomic stuffs are particles or waves.

But I don't understand why this isn't caused by the lack of our ability of perfect observation. Because it's like when you are sitting in a fast moving car, and watching the landscape, and you see the trees blurred. The trees are not blurred for real, it's just how we receive information about them, and the 'particle wave' is just a picture, just like the blurry tree, and we should not mix up the picture with the object.

Also I wonder if this refers to other phenomena related to the particles, like the structure of the electron shell for example ?

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#### DennisN

, and the 'particle wave' is just a picture, just like the blurry tree, and we should not mix up the picture with the object. (my bolding)
That's good thinking, IMO .

But I don't understand why this isn't caused by the lack of our ability of perfect observation. Because it's like when you are sitting in a fast moving car, and watching the landscape, and you see the trees blurred. The trees are not blurred for real, it's just how we receive information about them [...]
You mentioned the uncertainty principle in post #1. Here's a nice demonstration of it:

Also I wonder if this refers to other phenomena related to the particles, like the structure of the electron shell for example ?
If "this" means "quantum mechanics", then, yes, absolutely. But I still would like to know what λ means in post #4.

#### probert84

That's wavelength, I thought it was obvious, so that's why I didn't say anything about it.

#### DennisN

That's wavelength, I thought it was obvious, so that's why I didn't say anything about it.
Excellent. And what happens at the screen in the double-slit experiment when you change the wavelength of the light you use?

#### probert84

well you get different interference patterns on different wavelength if this is what you are trying to get to, but does this contradict with my original assumption somehow ?

#### DennisN

well you get different interference patterns on different wavelength if this is what you are trying to get to, but does this contradict with my original assumption somehow ?
I don't know yet - that's what I'm trying to find out . You mentioned basically only "space" and "particles" in your description, so I wanted to know if you were aware that different wavelengths (and different types of particles with different masses) means different interference patterns.

#### probert84

I don't think that wavelength makes a difference here, because different wavelength means different energy density, and therefore it interacts differently. It would certainly mean that I'm wrong if particles with different energy level looked identical, because then the interference patterns should look identical too, but since even the single particles look differently there has to be a difference in the interference patterns as well.

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#### Maui

The interference does not happen between particles, it happens between probabilities, and the particle is not a wave, rather because the imperfect way how we examine it makes it for us to seem as a wave of probability.

No, this is wrong. You can see why in the video posted by DennisN in this thread. Basically, the stuff the universe is made of is not classical and it's quite easy to see in easy to do experiements. The above video highlights the issue as well. There isn't all that much that's unclear about how and why stuff happens at the quantum level, it's just that it's unexpected that stuff there isn't solid, with fixed properties and resists attemps at applying objectivity to it. Why should an objective universe be made out of stuff that lacks objectivity? There are hypothesises but none is quite there.

Though modern physics is generally agnostic on these isssues, there isn't even one objective and noncontextual particle in this universe and this is a good indication that something is deeply wrong with our understanding of physical reality. What you propose above is not tenable as the two aspects of 'particles' - the unlocalized wavelike nature with frequency and wavelength cannot be bundled together with the particle properties that are detected virtually all the times and they are both equally real and equally important for the existence of particles as they are known. There also seems to be some deep relationship between questions and answers and it has been like that since the dawn of mankind. It's as if there are questions because there are answers. So we definitely shoudn't stop asking, knowledge even has a rather distinctive role in the quantum world.

#### bhobba

Mentor
But I don't understand why this isn't caused by the lack of our ability of perfect observation.
You are putting the cart before the horse.

The uncertainly relations are a consequence of the the principles of QM - not its cause.

What is known these days is QM is simply one of the two most reasonable generalized probability models that can be used to describe physical systems, the other being standard probability theory:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Also the so called wave particle duality, while talked about a lot at the beginners level of QM is, from the more advanced standpoint, seen to not be strictly correct:
'So there is no duality – at least not within quantum mechanics. We still use the “duality” description of light when we try to describe light to laymen because wave and particle are behavior most people are familiar with. However, it doesn’t mean that in physics, or in the working of physicists, such a duality has any significance.'

Its used at the beginner level to motivate things in a semi-historical way, but once you understand QM you realize its just that - of historical interest - the modern theory doesn't view it that way. Quantum objects are neither particle or wave - they are quantum stuff described by the probability calculus of quantum theory - without detailing exactly what that is - the links I posted will give the detail.

Here is a much better way of looking at QM from some guy that lectures on it at MIT:
http://www.scottaaronson.com/democritus/lec9.html
'As a direct result of this "QWERTY" approach to explaining quantum mechanics - which you can see reflected in almost every popular book and article, down to the present -- the subject acquired an undeserved reputation for being hard. Educated people memorized the slogans -- "light is both a wave and a particle," "the cat is neither dead nor alive until you look," "you can ask about the position or the momentum, but not both," "one particle instantly learns the spin of the other through spooky action-at-a-distance," etc. -- and also learned that they shouldn't even try to understand such things without years of painstaking work.

The second way to teach quantum mechanics leaves a blow-by-blow account of its discovery to the historians, and instead starts directly from the conceptual core -- namely, a certain generalization of probability theory to allow minus signs. Once you know what the theory is actually about, you can then sprinkle in physics to taste, and calculate the spectrum of whatever atom you want. This second approach is the one I'll be following here.'

Thanks
Bill

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#### vanhees71

Gold Member
I couldn't agree more with what bhobba says in the previous post. It's very misleading to talk about "wave-particle duality" after nearly 90 years of the resolution of this paradox of "old quantum theory". Nowadays we have "modern quantum theory", which was developed in 1925/26 more or less independently in three equivalent forms by (1) Born, Heisenberg and Jordan, (2) Dirac, and (3) Schrödinger.

The little youtube movie is astonishingly misleading, although usually Lewin's lectures on YouTube are excellent. Lewin doesn't do a specifically quantum-theoretical experiment here (except in the sense that (nearly) everything "classical" is understood as an approximation to something that can be also described by quantum theory).

What he does is the classical diffraction experiment with coherenc monochromatic light. Quantum theoretically this light is described as a coherent excitation of the quantized electromagnetic field, i.e., a coherent state. It's very well described approximately by good old classical Maxwell electromagnetism.

The uncertainty principle as usually derived from quantum theory has nothing to do with our ability to measure position or momentum with arbitrary precision. It is a statement about the incompatibility of these two observables. It simply says that one cannot prepare a particle in a state in which both its position and its momentum are determined with arbitrary precision. Here it is important to note that quantum theory tells us that if a particle is prepared in some state, this only implies that we know probabilities for the outcome of measurements, except the state is such that the measured observable has a determined value.

Position and momentum of a particle are never determined. There's always a finite width in the probability distribution for both of them, which is quantified by their standard deviations $\Delta x$ and $\Delta p$, as usual in statistics. Then Heisenbergs uncertainty principle reads
$$\Delta x \Delta p \geq \frac{\hbar}{2},$$
where $\hbar=h/(2 \pi)$ is the modified Planck constant. This tells us that in any state the particle can be prepared in that both, $\Delta x$ or $\Delta p$, can never vanish and that, if the position is determined at a high precision, i.e., if $\Delta x$ is small, then $\Delta p$ must be at least as large as to fulfill the uncertainty relation.

#### Maui

I couldn't agree more with what bhobba says in the previous post. It's very misleading to talk about "wave-particle duality" after nearly 90 years of the resolution of this paradox of "old quantum theory". Nowadays we have "modern quantum theory", which was developed in 1925/26 more or less independently in three equivalent forms by (1) Born, Heisenberg and Jordan, (2) Dirac, and (3) Schrödinger.

This is also misleading as people hardly have any idea how to think of the outside world in terms of physical objects as excitations of corresponding fields. You are just moving the paradox to a more general and wider context, aren't you?

#### bhobba

Mentor
This is also misleading as people hardly have any idea how to think of the outside world in terms of physical objects as excitations of corresponding fields. You are just moving the paradox to a more general and wider context, aren't you?
This is bog standard QM - nothing to do with fields.

Also Vanhees is talking about the formalism of QM. That, for a long time now, independent of any interpretation, has shown the wave-particle duality is well - wrong.

Thanks
Bill

#### Maui

This is bog standard QM - nothing to do with fields.

Also Vanhees is talking about the formalism of QM. That, for a long time now, independent of any interpretation, has shown the wave-particle duality is well - wrong.

Thanks
Bill

The formalism is a calculational tool and does not provide even a rough approximation what an electron(or any other quantum particle) is. It 'solves' the paradox by not even addressing it(it could be solved by a theory of quantum gravity however).

But I believe his point was different and involved QFT(I could be wrong).

#### bhobba

Mentor
The formalism is a calculational tool and does not provide even a rough approximation what an electron(or any other quantum particle) is.
First you need to prove it is 'more' than the formalism tells us.

When we use probabilities to describe say flipping a coin we know why that's done - the more that's going on is lack of knowledge about the initial conditions such as the forces involved. It seems natural to think of QM the same way - but the fact is there is zero reason to suppose any kind of deeper layer like the forces in flipping of the coin. It may be nature is just like that - or not. We simply do not know, and without experiments to decide its a pretty useless question really.

Thanks
Bill

#### DennisN

Clarification:
I never spoke of any wave-particle duality, and neither did Lewin. I was trying to extract what the OP knew about 1) the uncertainty principle and 2) the double-slit experiment(s), introduce variations on the DSE, e.g. with massive particles, and then gently lead him towards quantum mechanics. And whenever I ever say "particle" I of course mean "quantum mechanical object" or "quanta". The name of these things does not matter very much to me.

The little youtube movie is astonishingly misleading, although usually Lewin's lectures on YouTube are excellent. Lewin doesn't do a specifically quantum-theoretical experiment here (except in the sense that (nearly) everything "classical" is understood as an approximation to something that can be also described by quantum theory).
I don't see why Lewin's demonstration is astonishingly misleading as an introduction. I never said it was the start and end of "all you want to know about quantum mechanics" .

It simply says that one cannot prepare a particle in a state in which both its position and its momentum are determined with arbitrary precision.
Regarding diffraction experiments, can't the particle source + a narrow slit be seen as a preparation, and can't the screen location where the particle hits be seen as a subsequent measurement? Is there a problem with this? And would you get diffraction with a very narrow slit if not the uncertainty relation was true?

The Heisenberg uncertainty principle demonstrated with an electron diffraction experiment
http://iopscience.iop.org/0143-0807/31/5/027/
Giorgio Matteucci, Loris Ferrari and Andrea Migliori

Abstract:
An experiment analogous to the classical diffraction of light from a circular aperture has been realized with electrons. The results are used to introduce undergraduate students to the wave behaviour of electrons. The diffraction fringes produced by the circular aperture are compared to those predicted by quantum mechanics and are exploited to present and discuss the Heisenberg uncertainty principle.

I want to strongly underline that I'm not trying to get into any argument about interpretations at all - I just want to know if narrow slit diffraction is a good introduction to the HUP or not. (I might aswell say that regarding interpretations I'm personally in a superposition between agnostic/ensemble).

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#### vanhees71

Gold Member
Clarification:
The Heisenberg uncertainty principle demonstrated with an electron diffraction experiment
http://iopscience.iop.org/0143-0807/31/5/027/
Giorgio Matteucci, Loris Ferrari and Andrea Migliori

Abstract:
An experiment analogous to the classical diffraction of light from a circular aperture has been realized with electrons. The results are used to introduce undergraduate students to the wave behaviour of electrons. The diffraction fringes produced by the circular aperture are compared to those predicted by quantum mechanics and are exploited to present and discuss the Heisenberg uncertainty principle.

I want to strongly underline that I'm not trying to get into any argument about interpretations at all - I just want to know if narrow slit diffraction is a good introduction to the HUP or not. (I might aswell say that regarding interpretations I'm personally in a superposition between agnostic/ensemble).
This is not about interpretations. This is about the use of proper language, particularly for beginners in learning quantum theory! The idea that an electron is a wave described by the Schrödinger wave equation was abandoned very soon from experimental evidence. Doing an experiment like the one proposed in the above cited paper using one electron at a time clearly demonstrates that there is no interference pattern whatsoever, but this interference pattern occurs only if the experiment is repeated with equally prepared electrons (i.e., an ensemble of electrons) many times. The position of any single electron is unpredictable but it leaves only one spot on the screen not an interference pattern or else "smeared" distribution.

This observation/thought experiment has lead Born to the probabilistic interpretation of the meaning of the wave function, which resolves this apparent paradox, called wave-particle duality, in the "old quantum theory". The understanding of this point is critical particularly for beginners of quantum theory, and it should not be made even more difficult to comprehend by refering to outdated historical ideas like "wave-particle duality" or "orbits of electrons" in the Bohr-Sommerfeld model of atoms, etc.

The same holds for the movie by Lewin: Here it is suggested the observed interference pattern from a classical electromagnetic wave (or if you insist on expressing it in the correct quantum language a coherent state of the electromagnetic field) in a double-slit experiment would prove anything specifically quantum mechanical. It's not even easy to produce single-photon states, but if you do such experiments, as is standard nowadays in quantum-optics labs, with true single-photon states again you find the analogous crucial probabilistic properties of the quantum-mechanical state as you find them in the case of the diffraction experiments with (massive) particles.

Concerning the Heisenberg uncertainty principle, I think the refraction experiments are fine. It's easily understood as a property of the solution of wave equations. In quantum theory the single-particle wave function however has a probabilistic meaning and does not describe some kind of smearing of the single particle it is describing. About both, position and momentum, we can only make probabilistic assertions, they are not determined. The hole in the above scattering experiment at a circular opening in a screen restricts the position of the particles at the moment when they fly through the screen and according to the uncertainty relation, the probability distribution for the momentum perpendicular to the screen becomes the broader the smaller the circular opening is and vice versa. This is mathematically well understood by the Fourier properties used to solve the Schrödinger equation for this experimental setup but has to carefully be interpreted in the sense of Born's probabilistic rule.

This minimal interpretation you must make to make contact of the abstract mathematical formalism of quantum theory ("kinematics" and "dynamics" as inherent in the Schrödinger equation) with the observation/experiment in Nature with single electrons. I'm convinced that you avoid a lot of trouble with the proper understanding of quantum mechanics at the beginners (undergraduate) level, if you consequently and from the very beginning present the issue in this "modern" (if you call something discovered in 1925/26 modern :-)) understanding of the subject.

#### DennisN

Ok, vanhees71, I understand and agree with what you wrote above.

Doing an experiment like the one proposed in the above cited paper using one electron at a time clearly demonstrates that there is no interference pattern whatsoever, but this interference pattern occurs only if the experiment is repeated with equally prepared electrons (i.e., an ensemble of electrons) many times. The position of any single electron is unpredictable but it leaves only one spot on the screen not an interference pattern or else "smeared" distribution.
And that was actually my next planned step for the OP, so I might aswell do it right now:

Double-slit experiment (with electrons, Hitachi):
http://www.hitachi.com/rd/portal/research/em/doubleslit.html

To the original poster: On this page there is a small clip showing the build-up of an interference pattern from many single electrons, one at a time. Direct link to the clip: http://rdg.ext.hitachi.co.jp/rd/moviee/doubleslite-n.wmv

Note: at the end of the page they regretfully mention "electron waves" once - please ignore that.

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#### Maui

First you need to prove it is 'more' than the formalism tells us.

When we use probabilities to describe say flipping a coin we know why that's done - the more that's going on is lack of knowledge about the initial conditions such as the forces involved. It seems natural to think of QM the same way - but the fact is there is zero reason to suppose any kind of deeper layer like the forces in flipping of the coin. It may be nature is just like that - or not. We simply do not know, and without experiments to decide its a pretty useless question really.

Thanks
Bill

Electrons have frequencies and wavelengths and some critical medical devices rely on this feature to save lives. The formalism is just that - formalism. It is not the world out there and will one day be replaced by an even better formalism as has happened before. So the wave nature is just as real as any other aspect of quantum systems.

#### vanhees71

Gold Member
Electrons have frequencies and wavelengths and some critical medical devices rely on this feature to save lives. The formalism is just that - formalism. It is not the world out there and will one day be replaced by an even better formalism as has happened before. So the wave nature is just as real as any other aspect of quantum systems.
No, physics is about observations and their description in mathematical theories (or more modestly models) that link observations to general principles that were established by earlier observations.

So what is the observation that establishes the idea that "electrons have frequencies and wavelengths". If you refer to the functioning of the electron microscope, it is understandable by standard modern quantum theory. There is no need for wave-particle duality as in the double-slit experiment!

No, physics is about observations and their description in mathematical theories (or more modestly models) that link observations to general principles that were established by earlier observations.

So what is the observation that establishes the idea that "electrons have frequencies and wavelengths". If you refer to the functioning of the electron microscope, it is understandable by standard modern quantum theory. There is no need for wave-particle duality as in the double-slit experiment!
I think you have to realise that there are the theoretical physicists who work stuff out and who come up with the theories which might be right or wrong and all of which seem to have a tendency to change as time progresses.
On the other hand there are the applied physicists who use those aspects of the theories which are useful for them to carry out their tasks and develop their technologies. Depending on what they do an applied physicist might find it most productive to treat electrons as waves just as he/she would treat members of the em spectrum as waves.

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