I read on an article that electrons are “all the same.” Why is that and what does that mean? How can electrons be identical? Does that apply to other elementary particles?
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All electrons have the exact same mass and charge. We know because we have measured, used, interacted with and experimented on them for a long time and havn’t found one that is different.
We don’t know that they are the same. But we haven’t found any that are different. And all measures of the size of the electron show that it is smaller than the minimum size that we can measure. So the model of all electrons being the same and being a point with no size and no substructure fits all the data we have.
electrons look same according to everything we can measure about them: size, weight, charge.
they can have different energy levels, but energy level can change, depending on how that is more about how fast they moving.
The question of “all the same” goes back to the [fundamental math](https://en.wikipedia.org/wiki/Dirac_equation) that describes how electrons behave.
The word “same” can mean a lot of things in the general English language. But in terms of the physics description linked above, the word “same” has more precise meanings.
In 1950, the physicist Schrodinger wrote his own ELI5 about that, using analogies:
The older defunct classical notion of a particle would allow you to make an analogy where 2 electrons are represented by 2 coins. Then you could say: ‘I’m putting the first coin in this first box, and the second coin in this second box.’ Or ‘I’m putting both coins in the first box’ That’d make perfect sense.
But it turns out that the [math description makes that analogy fail](https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics) when talking about electrons.
Instead, as Schrodinger wrote, the correct modern analogy for the behavior of electrons would say that two electrons are analogous to two vacancies in a group. That changes everything. Now it doesn’t make sense to say “the first vacancy” is somehow “filled twice” while the second vacancy is somehow unfilled. It also makes no sense to attach *objective* labels to two equivalent vacancies.
And that represents the aspect of “sameness” that people refer to when talking about electrons.
As Schrodinger further wrote:
> The implication, far from obvious, is that the unsuspected epithet ‘this’ is not quite properly applicable to, say, an electron, except with caution, in a restricted sense, and sometimes not at all
Well it really boils down to what you mean by “different”.
If we say that two things are different when they are made from different things or the same things arranged differently then electrons are identical. They are elementary particles they are the things that build things. Being different like this on this scale makes very little sense. For example every hydrogen atom is the same. One proton, one electron. Two hydrogen atoms are identical. Difference requires some level of complexity.
As far as quantum mechanics is concerned electrons are fermions. They must be different. No two electrons can have identical quantum information at a give time. Things like position, momentum, spin. Every electron is different from the others in at least one of their properties. But saying that two electrons are different because they aren’t on the same spot, I don’t know how I feel about that.
So maybe like this: We can confidently say that this electron is different from that electron but if we named one Bill and the other Bob and someone shuffled them around we would still be able to tell they aren’t the same electron but we’d have a hard time saying which one is Bill and which one is Bob. Like perfectly identical twins. We can tell they are different people and they can do different things but there aren’t any visible differences.
When you hear that they are “all the same” it means that there is no accepted theory, experimental observation or even speculative physics that suggests that one electron can be measured or used to interact differently than any other electron.
On the other hand there is no accepted theory that says all electrons *must* be identical. New physics can change this thinking.
All elementary particles in the standard model are identical in this way.
All electrons are not equal. Some electrons are more equal than others.
I know. I’m positive.
When people say this, they are often talking about a statistical fact in quantum mechanics. When you’re trying to figure out what an entire system of particles does, one way to do it is by looking at the distribution of energy levels. A distribution of energy levels can be thought of as a way to describe how much extra freedom a system gains if you give it some more energy. For example if my system is at its lowest energy, there might only be one way to arrange the particles, because they each have to be at their private lowest energy state. However if I give the system a bit of energy, any of the particles might have it. If I give it some more energy, now multiple particles might each have energy, or a single one can have a lot of energy – the things the system can do grow exponentially.
If you have a quantifiable relationship between the amount of energy and how much freedom the system has, you can use some statistics to figure out on average what state all of the particles will be in over time. This allows you to derive related things, like how your system responds to extra heat being given to it, or what kind of thermal radiation it will emit.
Now is the key point – if you have two electrons, and you give them a single quantum of energy, you might think there are two states the system can be in – “electron 1 has energy” and “electron 2 has energy”. However, this turns out to give false predictions. In fact, there is a single state – “an electron has energy”. Quantum statistics, on a very deep level, does not distinguish between different electrons. If it did, very basic things like the colors we see in hot objects would just appear different.
Quantum field theory takes this one step farther, and doesn’t even treat electrons like particles – they are excitations in a field, and they are identical not because of happenstance but because they are the result of the same dynamics happening within a single object, the quantum electron field.
Does all of this mean that electrons are truly identical? Technically, they are only identical in regards to the things stated – the dynamics described by quantum mechanics/QFT and our current measurement limits. Our measurement limits are somewhat arbitrarily set by our current technology, which will improve over time, and our understanding of the relationship between quantum theory and the underlying objects it describes is currently a matter of interpretation. There’s no reason to presume electrons are different, but there are models consistent with current physics that would allow such a thing.
It gets better. There is a theory that says every electron seems identical because there is just one electron in the universe which keeps going back and forth in time.
Sean Carroll talks about it but I couldn’t find the lecture video just now.
Keeping it vaguely ELI5 – This is the “Quantum” in Quantum Mechanics. Physicists kept trying to break matter down into smaller and smaller units. And eventually they got down to a **model** of Electrons, Neutrons and Protons. And separately to explain light you have the Photon. These are sub atomic particles that contain a discrete amount of energy and mass (or not) and a specific charge (or not). Now **model** is the important word because we can’t actually see these sub atomic particles and this is because light itself is a sub atomic particle.
Imagine having on a blindfold and earplugs at a pool table so that all you can do is feel the white ball. You roll it down the table and wait for it or another ball to come back to you or not. That’s pretty much where we are when it comes to looking at sub atomic particles. We’ve built very big, incredibly expensive machines to throw sub atomic particles around to try understand them better but we still don’t have an actual photo of the 8 ball and probably never will.
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