# Is it wrong to say that an electron can be a wave?

In QM it is sometimes said that electrons are not waves but they behave like waves or that waves are a property of electrons. Perhaps it is better to speak of a wave function representing a particular quantum state.

But in the slit experiment it is obvious to see that electrons really are a (interfered) wave. So can you say that an electron is a wave? And is that valid for other particles, like photons? Or is it wrong to say an electron is a wave because it can be also a particle, and because something can't be both (a behaviour and a property)?

• I don't think it's worth being an answer, but it might be useful to you. You should read about wave-particle dualism. "And is that valid for more particles like photons?" It's valid for every particle, de Broglie got a Nobel prize for this theory, and two guys shared a Nobel prize for experiment. Nota bene for electrons, photons were described as such 1st, landing Nobel for Einstein for photo-electric effect, which proved they exhibit particle like behaviour. BTW, saying that something is in Physics is not a very good idea, theories remain valid for certain applications. E.g. Newton laws. Feb 22, 2016 at 3:55

What is a wave? From sound and water waves we come to an association with sine and cosine variational behavior. Wave equations are differential equations whose elementary solutions are sinusoidal .

In water waves and sound waves and even electromagnetic waves what is "waving", i.e. has a sinusoidal variation with time and space, is the energy of the wave, represented by its amplitude.

When dimensions become very small, compatible with h, the Planck constant the individual "particles" electrons etc., can be described sometimes like classical billiard balls, and at the same time they exhibit a randomness, which when accumulated displays interferences and other wave characteristics. This single electron at a time double slit experiment shows both effects. The individual electrons leave a point on the screen which seems random. The accumulation gives a probability distribution that has sinusoidal variations.

One can only give a probability for the electron to appear at the (x,y) of the screen, which depends on the quantum mechanical solution of the boundary value problem "electron scattering from two slits"

So it is not a classical particle behavior because even though the energy is carried by the single electron, its (x,y) is controlled by a probability distribution; and it is not the classical wave, i.e. a single electron that is "waving" its mass all over the screen interference pattern. Each electron is a quantum mechanical entity.

• Still its hard to understand that the electron leaves a point randomly and creating a probabilty distributrion while often is spoken about interference. So there isn't any interference? Feb 21, 2016 at 19:48
• @Marijn There is interference, that's what the images show: an interference pattern.
– Kyle
Feb 21, 2016 at 22:40
• @Marijn: Electrons don't interfere; probability amplitudes interfere.
– user36790
Feb 22, 2016 at 1:45
• @Marijn The electron does not create a probability distribution. If you want a probability distribution of number of births per month, how would you find it? You would go to the census and copy the number of births per month and make a histogram. One baby does not create a distribution. The collective birth date has a distribution 1.bp.blogspot.com/-9OuW0uvl3EA/UEqA5mHOseI/AAAAAAAADqM/… . The electron does not create the (x,y) distribution, the collection of electron does. Feb 22, 2016 at 4:40
• @Marijn: That's why it's so weird. There is obviously interference, yet each particle also collapses to a single point when it hits the film. Which means that when the interference occurs each particle is travelling alone thus not being interfered with by anything else. Each particle, in essence, interferes with itself. Every so often people would come up with new interpretations of this phenomena. It used to be said that each electron's probability distribution act as a wave thus interfere with itself. Now it is said that electrons are just excitations in the electric field Feb 22, 2016 at 8:28

Electrons are neither particles nor waves - they are electrons. We say they behave as particles or waves because we are familiar with macroscopic objects having these properties and want to provide a kind of "feel" for what they are in terms we can easily understand. We are the ones that select the experiment that shows aspects of their behaviour. They do not change from particle to wave and back again. Our experiments change.

• can we extend this to other "entities", like neutrinos and quarks? I mean, can we say that according to nonrelativistic Quantum Mechanics the concept of particle is meaningless?
– set5
Apr 12, 2016 at 5:25

Yes. No! Both! Neither?

The electron is an excitation of the QED quantum field, which is not quite compatible with the classical notion of either fields or particles. All you can do is draw analogies to either of these. Both analogies are sometimes just wrong, as in, they suggest different behaviour from what electrons actually do in experiments. However, they also predict some behaviour that agrees with experiment. And in the end that's all physics is about: finding models/analogies which allow you to predict the outcome of some experiments.

All of these models are wrong in a sense, but that doesn't mean you should never use them: just be aware that there are limits beyond which you get nonsense. It clearly is useful to think about the electron as a particle when you're designing a cathode ray tube. It is not really useful to think of it as a particle when you're trying to understand the spectra of atoms... OTOH, a wave description works quite nicely here!

However, it is a sensible standpoint to say the electron will never be a wave, only its probability. Or perhaps better: (a particular kind of -)charge is a wave, but is quantised to something particle-like called electrons.

I rather like Dirk Bruere's approach: an electron is an electron, full stop.

Even here there's a wrong but useful model.

• that's how physics is done, but it's not what physics is about, physics is about understanding the universe and its mechanisms in a reproducible manner. It's a subtle, but important distinction. The alternative is saying mathematics is about abascuses. Feb 23, 2016 at 16:23
• @Racheet: “mathematics is about abascuses” would be like saying physics is about synchrotrons/telescopes/diffractometers etc., which indeed it is not. But I persist: physics is about models. Some of these are very specific like the Bohr Model; the more interesting ones are very general like the Standard Model or the theories of relativity. But they are all models – understanding the mechanisms of the universe means nothing else but constructing models of parts of the universe, and comparing them to the real thing. Feb 23, 2016 at 16:32

In the micro world particles like electron has dual nature .In some experiments it behaves like waves such as diffraction of electrons by a single slit but in other experiments like compton scattering or photoelectricity it behaves like particle. In wavelike representation of electrons by a quantum mechanical wave function can explain the diffraction and interference of electrons.

The rules of how electrons move are analogous to waves because an internal state is cyclic and different possible paths are summed showing an interference pattern.

That's not the same as saying that electrons themselves are waves. The formulas for waves are used to explain where to find an electron.

Dual split experiment showed e- can show wave like properties. When electrons were fired from a gun at a barrier with two slits on it the electrons exhibited a wave like pattern on the EM sensor behind the barrier, showing three distinct bands. Showing refraction occurred and hence electrons behaved like waves.

The electron can be whatever we want it to be, we create the mathematical models in which the electron is a part of, so we can dictate the rules under which the electrons behave;

Quantum Mechanics is just a mathematical model, that includes mathematical objects like, "the electron" that we use to make predictions about the physical world. Just like we use numbers and fields, abstract objects like "electrons" are purely mathematical in nature, and we don't necessarily examine whether or not they "exist", because "existence" is a purely philosophical subject that's outside of the scope of the practice of physics.

In this way, we are free to dream of objects that can exhibit all kinds of "weird" properties, like the ones that particles have in Quantum Mechanics, that don't necessarily "exist" in a philosophical sense, but as long as our models work, we can keep on adding more and more layers of abstractions, because its our model, and we can make it whatever we want it to be! As long as it can make accurate predictions about the real world;

When we say that Gravity is a force, we don't necessarily mean that there is some kind of "rope" attached to the Earth and the Sun system, or when we say that Gravity is the curvature of the fabric of spacetime, we don't necessarily mean that there is some physical fabric that bends so that objects can fall into it, and create what we see as Gravity, either. Its all metaphorical and mathematical in nature, just a way for us to describe operations that will yield accurate predictions, in a yet consistent and rigorous mathematical way.

In that framework, the electron - we have made it - to be a propability cloud that extends EVERYWHERE in the universe. There is a small probability that we can measure the electron to be very far away (when we do measure it and its wave function collapses), but that propability is extremely low so it never happens...

So the electron IS its wavefunction, and that is not weird at all, because the electron is an abstract mathematical object so it can behave however it likes! Also for example, the electron can be a particle and a wave at the same time, because who cares? Its our model and we can have the electron be whatever we want it to be...

Will such a theory make accurate predictions about the Universe? If no, then we don't use it, if yes, then at the very least, we have proved that our theory is at least usefull.

So the only thing that we can say about the nature of electrons, is that in the framework of their models, they are helpfull mathematical objects, that constitute very helpfull theories, like Quantum Mechanics...

Answering "why" these theories are so helpfull, is outside of the scope of physics.