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I have the following question about wave-particle duality:

Are particles really just waves with short wavelengths?

If this is correct, would it then be accurate to say:

"everything in the universe is a wave, but when a wavelength is short, it acts like our macroscopic conception of a particle. However, on a quantum level, everything is really just a wave"

For years, I have thought about it like I stated above and it makes perfect sense to me. Indeed, the de-Broglie relation $$\text{wavelength} = \frac{h}{mv}$$ shows that all matter exhibits wave like properties seems to confirm my understanding that they are "really" just waves with short wavelengths.

But I ask the question because I hear quotes like "we don't know if things are particles or waves" and "our brains can't comprehend it", etc. I want to make sure I am not missing something.

The following quote also seems to justify the interpretation I have given above:

"If the distance between wave peaks is much smaller than the size of an object, the object will block the waves. But if the distance between wave peaks is much larger than the size an object, the waves will go around the object."

Thus anytime we use the word "particle" really it would be a wave with a very short wavelength given by the DeBroglie formula.

Any input would be appreciated.

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    $\begingroup$ Hi, please try to avoid inflammatory wording ("...is a lie") in your questions. $\endgroup$ Sep 17, 2021 at 13:21
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    $\begingroup$ Both waves and particles can easily be considered useful models which allow us to analyze and predict system behavior. $\endgroup$ Sep 17, 2021 at 13:22
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    $\begingroup$ The problem with "this is not an exact quote from source but same idea" is that you may have misunderstood the quote and thus have the wrong (i.e. not same) idea. $\endgroup$ Sep 17, 2021 at 14:35
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    $\begingroup$ “I lie to myself all the time. But I never believe me.” [Hinton]. $\endgroup$ Sep 17, 2021 at 15:01

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Well, one can argue that there is no duality what so ever but that all particles are simply excitations of some quantum fields. For example, I do not think that it makes sense to say things like "an electron is both a wave and a particle at once" since after all it is neither classical wave nor classical particle but an excitation of the electron field and that's it.

The idea of wave particle duality is still useful though. It simply has to be used with more care. For example it makes sense to say:

"Under certain conditions, electrons may create interference patterns that are similar to the patterns observable for classical waves."

or

"Under other conditions, electrons can be scattered by a target and behave just like classical point particles."

The argument about the wave length etc. that you are making is a statement about the energy scales of the specific situation at hand. This energy scale determines which - if any - classical analogon (i.e. wave or particle) comes closest to the behaviour of your quantum system.

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Are particles really just waves with short wavelengths?

No, the wavelength of a particle characterizes the probability distribution, it is the probability that displays wave interference properties, no the particle in space.

This accumulation of single electrons through a double slit :

singlelect

An important version of this experiment involves single particles. Sending particles through a double-slit apparatus one at a time results in single particles appearing on the screen, as expected. Remarkably, however, an interference pattern emerges when these particles are allowed to build up one by one .

Each particle has the footprint of a dot.

I want to make sure I am not missing something. Any input would be appreciated.

You are missing that at the micro level quantum mechanical wave equations are about probability of detection, whereas classical waves are distributions in space.

Buildup of interference pattern from individual particle detections

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  • $\begingroup$ I was thinking about this as well. 1)The wave nature is the probabilistic wave before detection and 2)The particle nature is when the wave function collapses to a single point upon detection. This is understood mathematically but conceptual why this occurs is still a mystery. I suppose under the Copenhagen interpretation of quantum mechanics, wave-particle duality makes sense in this situation. However under other interpretations (many worlds) everything would remain a wave. Thankyou, your response has helped me clarify my ideas. $\endgroup$
    – Morphyl
    Sep 18, 2021 at 0:49
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This is a good question.

Wave-particle duality is a physical reality of quantum systems. Insofar as we can encapsulate this by a principle, we can 'understand' it (based on the results of experiments described in [1]) to be a consequence the (bizarre yet absolutely fundamental and unavoidable) assumption that particles do not follow paths, which is the physical content of the 'Heisenberg Uncertainty Principle'. This is the really incomprehensible thing about quantum mechanics.

This is the basis for the end of classical mechanics and the main motivating principle, along with the assumption of that classical mechanics still exists in some to-be-defined 'classical limit', for setting up the formalism of quantum mechanics that we find.

If we then agree to work with quantum mechanics, and if we agree (of course even some textbooks unbelievably actually disagree with this next thing) that the wave function of a single free particle of definite energy $E$ and definite momentum $\mathbf{p}$ is $$\Psi(\mathbf{r},t) = A e^{- \frac{i}{\hbar} E t + i \frac{i}{\hbar} \mathbf{p} \cdot \mathbf{r}}$$ (this can be found by solving the free-particle Schrodinger equation, and assuming $A$ is a normalization constant, note using a normalization constant here might really puzzle people but of course it makes sense) then the 'wavelength' is the length of the vector $\vec{\lambda}$ in $\mathbf{r}+\vec{\lambda}$ such that the above wave repeats itself, i.e. $\vec{\lambda}$ should satisfy $$e^{\frac{i}{\hbar} \mathbf{p} \cdot \vec{\lambda}} = 1 \ \ \to \ \ \frac{1}{\hbar} \mathbf{p} \cdot \vec{\lambda} = 2 \pi \ \ \to \ \ \lambda = \frac{2 \pi \hbar}{p} = \frac{h}{mv}. $$ So quantum mechanics (done properly) accounts for the 'de Broglie wavelength' that just makes no sense from a classical perspective. In other words, the Heisenberg Uncertainty Principle stated above coupled with the basic principles of quantum mechanics directly leads to the 'de Broglie wavelength'.

To be clear, the 'particles' are actually 'point particles', not 'waves' at least in any usual sense. If they were 'waves' in any usual sense then these waves would themselves have to be made up from degrees of freedom that themselves would just behave like particles so it would simply make no sense. It is absolutely fundamental to understand that they are point particles whose motion possesses wave-like properties (due to the bizarre non-existence of paths). The 'wave function' written above governs the probability distribution for the motion of a free point particle through space, it's wave-like properties capture the 'wave-like' properties of a particle which doesn't follow well-defined path as best we can.

If we invoke special relativity then one can further show that all particles absolutely must be 'point particles' and not miniature 'rigid bodies' (i.e. extended objects but with no new degrees of freedom which if it worked would bypass the problem with 'waves' and the extra degrees of freedom). While the 'rigid body' model fails because it contradicts special relativity, the obvious idea is to try to modify it to be in accordance with special relativity, i.e. a 'relativistic rigid body' if that makes sense.

Indeed a method does exist to bypass this issue: the idea is to embed a 'relativistic surface' into space-time. It's called (bosonic) 'string theory', and one can show such strings have no internal degrees of freedom only degrees of freedom orthogonal to the string in space-time (only if we use a 'sting' and not a higher surface called a 'brane'). Obviously this is still a work in progress, and at least on an experimental level so far not at all what wave-particle duality is about, so from the perspective of point particle physics, we must assume they are particles whose motion has wave-like properties.

On a mathematical level, over 90 years ago people proved (I wont check the precise earlier references) and Heisenberg placed in his book ([1], Appendix 11) the equivalence between the 'point particle' model of quantum mechanics, and the 'quantum field' model of quantum mechanics, explicitly referring to it as the mathematical counterpart to the physical notion of wave-particle duality. In more modern terms he just showed the equivalence of first and second quantization, which is unfortunately very commonly completely misunderstood with people often claiming something along the lines of 'everything is fundamentally just quantum fields'.

Indeed wikipedia says the following regarding wave-particle duality relevant to this:

Werner Heisenberg considered the question further. He saw the duality as present for all quantic entities, but not quite in the usual quantum mechanical account considered by Bohr. He saw it in what is called second quantization, which generates an entirely new concept of fields that exist in ordinary space-time, causality still being visualizable. https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality

References:

  1. Heisenberg, "The Physical Principles of Quantum Theory", 1st Ed. (1930).
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    $\begingroup$ The reason that particles in QM are pointlike is because we cannot measure something that small? And saying that particles are pointlike is just a model and we don't actually know the size of the particles themselves? Is that true or not? $\endgroup$
    – Tachyon
    Sep 17, 2021 at 14:07
  • $\begingroup$ The real answer is that this is very complicated. On a mathematical level, we have to assume a degree of freedom we are modelling is point-like so that we are dealing with a single degree of freedom. Obviously when we apply this e.g. to an electron orbiting an atom it's just a model, but on a fundamental level the goal is to work with the smallest building blocks we can which in conventional (i.e. non-string) physics has to be point-like (due to the special relativity argument above). This directly brings the famous 'infinities' into physics. As of now this is an unavoidable limitation. $\endgroup$
    – bolbteppa
    Sep 17, 2021 at 14:13
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    $\begingroup$ To be clear, if we don't assume a fundamental particle is point-like, and instead assume it is 'extended' in some fashion (which we all believe is really the case in reality as it makes no sense to be point-like in the real world), it completely contradicts the special relativity argument I mentioned above, but contradicting special relativity is one of the biggest sins one can commit given how unbelievably successful it is, so there is an inherent issue here that we'd like to just ignore except QFT throws those infinities in ones face so unavoidably, so there is something deep going on here. $\endgroup$
    – bolbteppa
    Sep 17, 2021 at 14:18
  • $\begingroup$ A good classical illustration of the contradictions that occur is given here. $\endgroup$
    – bolbteppa
    Sep 17, 2021 at 14:25

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