I have been watching quantum mechanics documentaries and reading a layman's book called "The Quantum Universe". I believe I understand why the double slit experiments exclude a particle only model. However I do not understand why the particle portion of particle-wave duality is needed. When I google the title to this question I do not get an adequate explanation of why the particle side of wave-particle duality is needed I feel. I believe the explanations assert that a particle moves in a wave-like/probabilistic manner but what is the evidence that requires a particle even exist instead of the wave itself being the whole story?

Is it because elementary particles have quantized states? Can elementary 'waves' not simply exist in quantized states without a particle? I guess I would also like to know how a wave-only model would differ from string theory if you would not mind. My understanding is that string theory replaces particles with vibrating strings that seem an awful lot like quantized waves in my head.

Forgive me if this is duplicate, my googlefu did not reveal a duplicate.

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    $\begingroup$ I think you're getting confused by the terminology, but understand the concepts. Waves do exist in quantized states, and we call those quantized states particles! A particle doesn't mean a little ball, it just means some indivisible unit. A photon is a particle of light, but even so it's still a wave, just one that cannot be divided into smaller waves. $\endgroup$
    – gardenhead
    Commented Mar 11, 2020 at 14:43
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    $\begingroup$ @gardenhead A single photon is a single photon and no it’s not a little ball. It takes billions of coherent photons to create a light wave. A single photon is not a wave and does not resemble a wave. No one can physically describe what a light wave is without incorporating billions of individual photons. You cannot do it. $\endgroup$ Commented Mar 11, 2020 at 16:55
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    $\begingroup$ @BillAlsept this is not true, running the double slit experiment with a single photon source still produces wave interference. The point of wave-particle duality is that photons, electrons, etc are wave-particles, not waves or particles, they are always both at the same time, but depending on the particular experiment their behaviour is easier to understand as a wave or a particle. $\endgroup$
    – llama
    Commented Mar 11, 2020 at 21:51
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    $\begingroup$ @BillAlsept no, doing the double slit experiment with electrons does not produce photons, at least not in any way which is meaningful to the results of the experiment. Doing it with one electron at a time does result in an interference pattern due to self-interference of the electron, doing it with single photons does the same. See eg aapt.scitation.org/doi/abs/10.1119/1.4955173 $\endgroup$
    – llama
    Commented Mar 11, 2020 at 22:35
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    $\begingroup$ @BillAlsept: Re: "After a while many single impacts will slowly build up a fringe pattern": . . . meaning that each single impact exhibits wave-interference. No? (Otherwise you wouldn't get a fringe pattern, you'd just get one "spike" at each slit.) $\endgroup$
    – ruakh
    Commented Mar 12, 2020 at 0:40

6 Answers 6


Elementary particles are understood today as the quanta of quantum fields. The fields are ontologically primary and exist even when there are no particles, but a quantum field is not “a wave-only model” as is, say, a classical electromagnetic field.

Instead, a quantum field is a continuous field, existing everywhere in spacetime, of operators that create and destroy quanta with particle-like properties. Quantum fields are not just waves, nor just particles, but rather a mathematical hybrid for which our classical environment gives us no intuition. Fortunately, mathematics makes them understandable to some degree and we find that models using quantum fields, such as the Standard Model, are extremely accurate.

One single quantum field, extending throughout the universe, can explain all electrons and positrons. (Why are all electrons identical? Because they are quanta of the same field!) One more field can explain all photons. One more can explain all up quarks and antiquarks, etc. A mere seventeen quantum fields, interacting with each other, make up the current Standard Model and are the basis for the world we see, except for gravity.

  • $\begingroup$ Interesting, 17 quantum fields! With 4 fundamental forces, I had assumed 4 fields. An excitation of the EM field gives us electrons and positrons as well as photons? How to explain that electrons have mass and photons do not? $\endgroup$ Commented Mar 11, 2020 at 23:49
  • $\begingroup$ The 17 fields correspond to the 17 particles shown here. The Standard Model does not explain gravity. (General Relativity explains it as a classical field, not a quantum field.) So there are only 3 forces, not 4, in the SM and they are carried by the four “gauge bosons” in the fourth column. (The weak interaction involves two, the W and Z.) $\endgroup$
    – G. Smith
    Commented Mar 12, 2020 at 0:03
  • $\begingroup$ An excitation of the EM field is a photon. An excitation of the electron-positron field is an electron or a positron. These fields are completely different. The EM field is a vector field whose quanta are massless, chargeless, and have spin 0. The electron-positron field is a “spinor” field whose quanta have mass, charge, and spin 1/2. $\endgroup$
    – G. Smith
    Commented Mar 12, 2020 at 0:07
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    $\begingroup$ You may be interested in this paper entitled “There are no particles, there are only fields.” It has only a few equations and is not particularly “technical”. $\endgroup$
    – G. Smith
    Commented Mar 12, 2020 at 0:17
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    $\begingroup$ BTW, the “fields are primary” point of view is entirely mainstream, not something fringe-y. The Standard Model of particle physics is (ironically) a theory of interacting quantum fields. $\endgroup$
    – G. Smith
    Commented Mar 12, 2020 at 0:22

Can elementary particles be explained adequately by a wave-only model?

The answer is no, not with the mathematical tools we have developed so far to describe data and observations.

The electron is the first elementary particle observed experimentally.

This single electron at a time double slit experiment


shows that single electrons exist ( frame $a$ with a footprint explainable as for a classical "particle"). It is the accumulation of electrons with the same boundary conditions that builds up a pattern of interference that imposes the need for a wave description in describing what an electron interacts as, that a particle attribute is not enough to explain the data. The probability hypothesis for quantum mechanical interactions, i.e. for the dimensions consistent with the Heisenberg Uncertainty Principe, is the way to explain interactions of elementary particles, and thus the particles themselves.

It is also good to contemplate this experimental picture as this bubble chamber picture


It shows beam particles entering from below , and one interaction with many particles coming out. We call them particles because their trace is the trace of a particle ,not a wave. The experiment has studied a large accumulation of such interactions, which will show the quantum mechanical interaction under study.

{ I am partly guessing it is a study $K^-$ interaction at 10 GeV/c in the 2 meter hydrogen bubble chamber. In this photo the curling track in the magnetic field is either a $π^+$, (or a $K^+$ the ionisation will distinguish the two masses but as there are only four charged tracks the incoming must be negative) which decays into a $μ^+$ and a neutrino, andfinally a positron with the accompanying neutrinos/ antineutrinos which cannot be seen }

In the mainstream mathematical model we have developed up to now assuming a wave nature for single particles is not possible. The wave nature appears in probability distributions, accumulation of data in the same boundary conditions, single particles behave as classical particles macroscopically.

There exist off the main stream theories and efforts to explain with a deterministic model the quantum mechanical probabilistic nature. One is Bohmian mechanics, but it cannot describe all observations , (it is using an underlying wave description). There are people still working on these lines, but have not been able to explain all the observations and data that the mainstream theory does.

  • $\begingroup$ It is not true that the current mainstream mathematical model makes it impossible to assign a wave nature to single particles. A single particle is an excitation of a wave. There are two points of view ("political parties" ?) concerning this question. Those most comfortable thinking about particles (particle physicists, high-energy physicists, ...) and those most comfortable thinking about wave excitations (optical physicists, solid state physicists, ...). But neither picture is right, and neither picture is wrong. They are both metaphors for objects our brains can't fathom. $\endgroup$
    – garyp
    Commented Mar 12, 2020 at 12:01

However I do not understand why the particle portion of particle-wave duality is needed.

One of the theories which fails if light was considered to be made of just waves is the photoelectric effect. Had light been just a wave, the energy of the light wave must be proportional to the brightness and hence the wave's amplitude. We could base our predictions as:

  1. The kinetic energy of emitted photoelectrons should increase with the light wave's amplitude.
  2. With increasing frequency of incident light, the rate of electron emission reflected in the photocurrent should also increase.

However, this is completely at odds with what we observe:

  1. The kinetic energy of photoelectrons increases with light frequency. It remains constant as light amplitude increases.
  2. Electric current remains constant as light frequency increases. It increases with light amplitude.
  3. Regardless of the amplitude, a light frequency too low does not produce any photocurrent -- this feature immediately implies a discrete version of energy transfer (thanks to J.G.).

The wave theory completely fails. What we hypothesize instead is that light comes as discrete particles with a defined energy - photons. That fits both the sets of observations.

The photoelectric effect introduced evidence that light exhibited particle properties on the quantum scale of atoms. At least, light can achieve a sufficient localization of energy to eject an electron from a metal surface.

  • $\begingroup$ I disagree with this interpretation: "One of the theories which fails if light was considered to be made of just waves is photoelectric effect." Maxwell's equations in general and Helmholtz' wave equation in particular say nothing of the interaction with elementary particles; it does describe interaction with a pure charge but an electron, for example, is not just a pure charge for it has other elementary properties as well such as spin, etc. $\endgroup$
    – hyportnex
    Commented Mar 11, 2020 at 13:11
  • $\begingroup$ @hyportnex - you should be careful about picking a fight with everybody's favorite physicist. and the committee that granted him a Nobel prize for this explanation of the photo-electric effect. "There may be other explanations" is always going to be true. However, the explanations that are most predictive of future experiments are the ones we prefer. $\endgroup$ Commented Mar 11, 2020 at 17:19
  • $\begingroup$ @Paul_Sinclair I am not picking fight with anybody neither do I disagree with SR, QM, QED, whatever, I only think that our way of explaining physics by ignoring that Maxwell's equations are not necessarily really made for that situation is misleading. $\endgroup$
    – hyportnex
    Commented Mar 11, 2020 at 17:26
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    $\begingroup$ Another point you should mention: regardless of amplitude, a light frequency too low produces no current at all. $\endgroup$
    – J.G.
    Commented Mar 11, 2020 at 17:54
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    $\begingroup$ This is taught in schools but is in fact wrong. One can explain all features of the photoelectric effect by quantizing matter, treating light classically, and using time-dependent perturbation theory. c.f. citeseerx.ist.psu.edu/viewdoc/… The calculation is also found in Griffiths QM book. $\endgroup$
    – Kuma
    Commented Mar 12, 2020 at 4:54

Yes and no.

The standard model, a quantum field theory, is the most complete description of particles and their interactions. Though physicists don't normally think about it quite like this (e.g. see G. Smith's answer), a quantum field theory is simply the theory of high dimensional fields with quantized excitations (i.e. wave packets) that can exist in superposition. A quantized wave acts like a classical particle on length scales that are much larger than the wavelength. So "yes" in the sense that, at the foundation, the theory is a wave only theory.

However, one could argue that particles are necessary due the fact that the the wave excitations are quantized, and further that the interaction of the quanta can be discrete, e.g. in particle creation and annihilation. Feynman thought of particles as "any bits of energy that come in lumps." Under that definition, the lumpyness of the field excitations and their interactions make the particles abstraction essential. But still, ontologically, we think of the particles themselves as wave packets of the fields in the modern view.

  • $\begingroup$ What “high dimensional fields” are you referring to? The quantum fields in the Standard Model live in 4D spacetime. $\endgroup$
    – G. Smith
    Commented Mar 12, 2020 at 23:09
  • $\begingroup$ Each point in spacetime can be seen as having many degrees of freedom (one for each flavor of particle). In that sense, the sm is the theory of one very high dimensional field, or several high dimensional fields (ex. one for gluons, one for the electroweak sector, etc...). $\endgroup$ Commented Mar 13, 2020 at 1:19
  • $\begingroup$ in other words, I'm using dimension synonymously to degree of freedom $\endgroup$ Commented Mar 13, 2020 at 1:30

No. As anna v has explained we only ever observe particles. We do not observe waves, but we use them to calculate the probabilities for where particles might be found. Actually, they are not even waves. To take the simplest case, the "wave function" for a plane wave state is actually a helix in a complex valued configuration space. The helix rotates in time, creating the illusion of waves on the real and imaginary axes.

"wave function" of a plane wave state

The reason for apparent wave effects is buried deep in the mathematics of probability theory and Hilbert space, and involves a higher level of mathematics than is commonly taught to physicists. However, it does make completely clear that there cannot be any physical wave, or indeed any physical field. This is just how calculations have to be performed in order to preserve the probability interpretation for a system in which probabilities result from indeterminacy, not from unknowns, or hidden variables.

I have given a full conceptual discussion in Light After Dark II: The Large and the Small and a rigorous mathematical treatment in Light After Dark III: The Mathematics of Gravity and Quanta


Sort of, yes.

The many-worlds interpretation of quantum mechanics essentially says that there aren't actually any particles, just the quantum waves and our observations of them - the "particles" are just our limited observations of a small slice of the complete quantum waveform. As a result, you could say that they're a wave-only explanation of fundamental particles, since the particles don't "actually" exist.

Here's a Youtube video explaining it in a bit more detail.


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