Electrons themselves aren’t waves per se. Rather they are moving so fast that you can only describe their location, or their velocity at any one moment in time. You can never measure both, and it is only for that single moment in time. The next moment all those measurements will have changed. This is called the “Heisenberg Uncertainty Principle”. Because of this uncertainty, our best description of an electrons movement is not as single particle. Rather it is a wave of probabilities where certain areas are more likely to have the electron at any one moment. Due to this uncertainty it can be said that until we measure the electron in some way it is BOTH the probability wave and the particle at the same time.

It means it doesn’t have only definite, fixed characteristics. Instead many of its properties are random, with an average or expected value, and a probability distribution.

It also means that two electrons will interact in wave-like ways (adding together or even subtracting) rather than in particle-like ways (bouncing off each other).

When we get into quantum mechanics it is often easier to stop thinking about *things* doing stuff, and start thinking more about *systems* existing in *states*. In normal mechanics a chair is a thing. It can be moved around, it can be pushed or pulled. But a chair is made up of a huge number of different other things, all interacting in complicated ways; the chair is a *system*.

In QM, if you have a system that isn’t interacting with the outside world it behaves in a weird, probabilistic way. Rather than existing in a particular state, it has to be modelled as existing in *in a combination of all possible states*, with some complex (!) maths to explain how it all works. The system then collapses down to a specific state (with an associated probability) when you break open the system by interacting with it.

So if we have say an electron-in-a-box system, and we isolate it from the rest of the universe, there are a whole bunch of different states the system could be in (the electron could be on one side, or on the other, and moving left-to-right or right-to-left, moving faster, moving slower etc.). From the outside we have to model the system as being in a combination of all those possible states. And mathematically one of ways of doing that is with a probability wave.

Mostly it means that we don’t yet have an entirely clear picture of what a particle actually is.

When we try to measure them like particles we observe particle-like behavior (they have a discrete location or momentum, they ricochet off each other, etc) and when we try to measure them like waves they exhibit wave-like behavior (ex., create interference patterns with each other). They’re mostly likely something else entirely that exhibits these properties but we don’t know what that thing is.

I think the dominant model at the moment is Quantum Field Theory, which holds that every type of particle has a field and what we see as particles are points in that field where it has enough energy to be observed.

Short answer: particles are not waves. Rather, what we usually think of as particles (like electrons) are something different and altogether weird. So your confusion about wave-particle duality is not a sign of a lack of understanding. It is a sign of understanding that what we say about quantum theory doesn’t respect our intutions about either particles or waves.

One way that electrons show wave-like behavior is [interference patterns]

(https://en.wikipedia.org/wiki/Wave_interference). You can shoot one beam electrons at a detector, and where they hit looks somewhat random. But if you shoot *two* beams at a detector, you get a pattern. Electrons stop showing up where they used to, even though all you’ve done is shoot *more* electrons there.

Our only explanations for that involve waves. We need to fiddle a bit more with our understanding of waves to make it a *quantum* wave theory. But once we make those changes, we can describe electrons (and a bunch of other stuff) pretty well.

There are a certain set of behaviours which we group together and call a “particle”.

There are also a certain set of behaviours which we group together and call a “wave”.

Light does not fall into either one of those two groups of behaviours. It has some properties that would be found in one group, but also other properties which would be found in another group.

This is an issue of *language*, not *physics*. If we invented a word like “flurble” which described all of the properties of light, then light would be a flurble and not a particle or a wave.

First, explain Young’s Double Slit Experiment to a five-year-old, demonstrating wave-like characteristics of coherent light.

[https://courses.lumenlearning.com/suny-physics/chapter/27-3-youngs-double-slit-experiment/](https://courses.lumenlearning.com/suny-physics/chapter/27-3-youngs-double-slit-experiment/)

Then, explain Einstein’s Photoelectric Effect to a five-year-old, proving individual electrons travel as discrete particles.

Then, perform Young’s Double Slit Experiment together with individual electrons traveling as particles collected from Einstein’s Photoelectric Effect experiment, then passing though a double slit, collecting and locating the electrons on a collection plane behind the double slits.

Those individual electrons, traveling as particles, show up at the collection points behind the double slits as if they’re traveling as waves through the double slits, then hit specific points on the collector as particles. The pattern on the collection points, diffused in one direction by the narrow slits, has periodic spots where electrons frequently hit (bright) and never hit (dark) corresponding to the wavelength of the electron as calculated by the energy of the electron.

Cover one of the double slits, and the pattern changes so the bright and dark spots disappear, becoming only a wide smear caused by diffusion due to the narrow slit.

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Take Young’s experiment and dim the light so much that the light is traveling as identifiably separate photons, and you’ll still find the “bright” and “dark” points on the collection plane. Similarly, covering one of the double slits changes the pattern to the wide smear caused by diffusion of light through the narrow slit.

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Both the diffusion of these particles (photons or electrons) from passing through the narrow slits and the interference pattern created by the double narrow slits are evidence both photons (light packet) and electrons acting as waves.

Ok so a lot of these answers talking about the differences between particles and waves… are just wrong.

All matter has a waveform. Everything from subatomic particles to baseballs. That wavelength is mathematically defined.

Wavelength = Planck value / (mass * velocity)

(Planck value is very small constant value)

Now let’s talk about what wavelength is…. Imagine we see something – let’s use a baseball – if it had a wavelength of three feet… even though we can “see it” the baseball could actually be 3 feet from where we think it is. If we wanted to interact with the baseball, we’d be guessing where it actually is in that 3 foot long area. We can know where that 3 foot long stretch is, but we aren’t sure where the baseball is in that 3 feet.

Turns out, You can calculate the wavelength of a baseball! The only issue is that the wavelength will be absurdly small because the mass of the baseball is so relatively large.

So for a baseball the wavelength is so tiny that it doesn’t mean anything relative to the size of the baseball. It’s not a 3 feet search zone, it’s actually like 10^-35 feet. So in this case we’ll never be able to “see” the baseball but not interact with it.

For a sub atomic particle, the wavelength will be larger than the particle itself. In this case you have a very real chance of “seeing the particle” but not being able to know exactly where it is, because the wavelength (search zone) is so big relative to the particle.

This is a key concept. Everything is a wave. For subatomic particles, their wavelengths are larger than the particles themselves. This is where they get all of their unique properties. There is a lot more on that. But for an eli5 I’ll leave it there.

It’s a simplified way to describe what a photon is doing. A photon’s motion can be approximated as a straight line in a signal direction, but that really isn’t it true. The photon is actually vibrating around that line of motion, which means that in many cases it will behave like a way when interacting with other things.

For example, if we fire a photon through a tiny slit that is smaller than the amplitude of it’s vibrations, instead of just shooting straight through following the line of motion a particle would, it’s going to hit the sides of the slit and bounce off, creating an interference pattern the same way a wave would.

The problem for scientists is that there really isn’t any way to direction at what point in the vibration a photon is without destructively changing it’s motion. This means that they have to use probabilistic methods to describe the motion and behaviour of photons, especially as they interact with other things. A bunch of the weird confusing language & theories in quantum mechanics exist to deal with this problem.

It’s all probability.

Imagine a pool. You stand with your back towards it. You throw a ping pong ball over your head, behind you. The closer you guess where the ping pong ball lands the more money you win. Let’s say a million dollars if you’re within an inch. And a penny if you’re 10 feet off.

Now you have no idea where the ping pong ball will land. But you can take a pretty good guess that it’s slightly to the left about half way (the middle) of the pool. Now this is a fair guess. Now the odds of it landing “about the middle” might be 80%. But the ball could really be anywhere. And this is mathematically calculable. For example the odds of it being it the very absolute corner of the far left side might be .01% let’s say.

Okay! So when we add up all the possible locations, this is the “wave”. The ping pong is most likely in x locations, and less likely in y locations. It’s weird to imagine a single ping pong ball as many locations but essentially that’s what we’re talking about.

The particle isn’t a single electron just sitting there. It’s the totality of everywhere it could possibly be. And this is why it behaves weird. (See double slit experiment)

To add on. The “wave function” collapses when we know the location. So the ping pong goes from 80% possible location to 100% once you turn around and see it.

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