Talking about both photons and electrons. Uncertainty principle is about position and momentum, but electron is considered wave?
We have mathematical model of light being EM Waves, what does it being particle even mean?
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A particle will appear to be in a single precise location when we go looking for it, but its possible “locations” when we’re not looking is a field of probabilities that move like a wave. Those probabilities represent how likely you are to find the particle at any given location when you go looking for it again*
This means we can get an idea of where we’re likeliest to find the particle next time we look by calculating how those waves move. They can do some weird stuff that you wouldn’t expect particles to be able to do
There are different competing *interpretations* of what this means: is the wave the actual particle? does the particle exist in between the times we’re looking for it? We can’t really say yet. It’s still an interesting open question
* when I say “look for” a particle, you can’t just continuously watch them move around. You have to do something to them to get a reaction, like wait for them to hit a barrier you’ve set up.
Obligatory excellent PBS Space Time video on the subject: https://youtu.be/p-MNSLsjjdo
Light and electrons are two good examples because they get at the problem from different directions.
Let’s start with light. It started out as obviously a wave based on the physics being developed by the big greats of electromagnetics, culminating in Maxwell’s equations that you might have heard of. The core math of light is definitely that of a wave, and that classical wave model predicts almost everything light does: propagation, refraction, reflection, polarization, interference, etc. It’s not important that we go into all those things, just that you understand that they’re inherently wave-based, and light does all of them.
Until light hits something and gets absorbed, that is. Absorption (and emission) is where the wave model fails completely, and where the particle side of the duality shows up. Energy from light can only get absorbed in discrete chunks, which we call photons. We’re good at detecting very low quantities of light, so we can actually build devices that see each individual chunk getting absorbed from very weak light sources hitting them. I mentioned interference above, and this is where it gets wonky. You can have interference by sending light through two narrow slits, and the pattern the light makes will end up with light bars with dark spaces between them. But, do this with the photon-counter, and you see each individual hit as it happens. Wait long enough, and the pattern still emerges, built up from each individual hit. So even though the energy is still in individual chunks, it follows the wave rules for how it should move through and past the slits. Weird.
Then we have electrons, which were very much thought of as particles. There’s a bunch of them around atoms, we can see them move around with electricity, they have mass, lots of the original EM work on electrons was very much that they are a particle.
Until someone tried putting them through that double-slit experiment like they did for light, *and the electrons behaved just like the light did*. They made the same interference pattern, showing that they, too, followed the wave rules. So now light is both wave-like and particle-like, and electrons are both particle-like and wave-like. Even weirder!
This was expanded to *all* particles, though doing the interference experiment with larger particles gets much harder, but the math checks out.
We know all of this very well by experimentation, as the quantum mechanics theories that predict it are the most verified theories in the history of science. But your guess is as good as anyone’s as to why, or how to answer the question of “is it a particle or a wave.” Both, neither, sometimes one or the other. I’m convinced we still don’t yet have the full story.
Everything we call a particle exhibits wave-particle duality at some scale. This is at the heart of quantum mechanics. For something like photons, the wave-particle duality is easily seen through the double slit experiment. If we let a few photons through at a time, we will see where those individual photons strike the screen in the end. If we let a lot of them through, we will see a wave-like interference pattern emerge. So it’s not that the electron “is considered a wave.” The electron is a particle, it’s just one that often prefers to behave like a wave, which is by no stretch unusual.
The degree to which the wave or particle nature is more/less noticeable depends on a lot of factors, such as the types of particles you’re working with (and their properties), and whether/how they’re entangled with other particles or the environment. In lighter particles–like massless photons or very light electrons–the wave-like properties tend to dominate at the relevant scales, and we usually only see particle-like behavior when we cause some kind of interaction/measurement that forces the particle to take a position. In the case of the double-slit experiment, the photon would continue to evolve probabilistically if we didn’t force it into a position by interposing the screen.
We have found through a lot of experimentation (old and new) that heavier particles also exhibit wave/particle duality, but there’s a limit past which the wavelike properties aren’t really detectable or relevant. A particle’s “de Broglie” wavelength is the wavelength scale at which a particle’s wavelike properties become important. But when you start to bind simple particles together into larger particles/systems/compounds, you very quickly reach a point where the size of your particle/system/compound is *larger* than the de Broglie wavelength, at which point the wavelike properties of the particles are no longer noticeable or particularly relevant.
If you want to ask “why” questions, you’re getting into foundations of QM which is probably outside the scope of ELI5.
A particle is just a very narrow wave!
When they say that something is a (probability) wave, this describes some chances, for example of the location of the thing. Chances are usually highest in the middle and then it falls of radially in some way. It turns out to form wave-like shape when done correctly, hence the name.
The area under the wave is kinda fixed, as the probability of being _anywhere_ is 100%. So you can either have a long-reaching and flat wave, or a very perky and narrow one. The former describes a large uncertainty about the location (or momentum or else), while the latter only leaves little options.
A particle is the latter, a very narrow wave. In theory, an ideal particle is an infinitely narrow wave of infinite height completely restricted to the center, but such a thing simply does not exist in nature.
In the end, the threshold for particle is always arbitrary and there is no natural cut-off for the required narrow-ness. This is often presented wrongly as if things change between a wave-like and a particle state, while in reality, all is a wave, some of them are just more narrow, or “particle-like”.
Quantum mechanics is tricky. One of the best ways to understand particle wave duality is through the classical double slit experiment.
On the experiment we have 3 things. First we have a source of light that fires one photon at a time. Next we have a barrier with 2 thin slits cut into it. On the opposite side of the barrier we have a surface that will detect where the single photon we fired lands. All we do then is fire photon after photon at the slits and see where it impacts on the sensor, then record that.
If a photon is purely a particle, the pattern of impacts on the detector surface will be 2 slits as the particles won’t be able to impact the sensor shaded by the barrier. However, this is not what we see. What we actually see is a series of vertical stripes of dense impact areas. This means a photon isn’t acting like a particle. It is acting like a wave. If you were to propel a water wave through those slits you’d find a similar pattern of peaks.
How is this possible? Well photons and electrons are so small and moving so fast they they act like waves. So that’s how we describe them mathematical. They are a single measurable amount of stuff, that acts like a wave when in motion until it impacts something or is measured. Once it is measured it resolves to a single packet of stuff.
That last part is where the Heisenberg uncertainty principle comes from. If we measure the location of the photon or electron we can’t know its motion or waveform. We forced it to resolve to a particle for that instant. However if we observe it’s wave form or motion we can’t know the exact location of the photon or electron because it is existing as a wave of probability.
Wave-particle duality doesn’t mean that a thing is both a wave and a particle at the same time, or that it’s sometimes a wave and sometimes a particle.
What it means is that photons and electrons and so on are actually a third type of thing, and at some times that thing is best represented by what we would classically call a particle, and at other times it’s best represented by the classical idea of a wave.
But in reality, it’s neither.
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