Why do electrons have mass?

Question

This really confuses me. I know that an electron is a single point of charge so is technically 0 dimensional (according to my physics teacher) unless you look at string theory i think. If an electron is a single point (existing as an uncertainty in an electron cloud if you look towards chemistry) then it must have no volume. If there is no volume how is there a mass? Please can somebody explain why?

Answer 1

The is is not a why answer, but all quantum objects with magnetic moment (the ability to store energy in a changing magnetic field), have a proportional mass. This applies also to electrons, since they have a non-zero magnetic moment.



"... unless you look at string theory i think."



Better guess again, since not all strings express in "space" as "volume" only in the Universe.



"If an electron is a single point"



It has a "classical electron radius", but it *is* a point particle.... it only ever interacts via its field...



"(existing as an uncertainty in an electron cloud if you look towards chemistry)"



This has *nothing* to do with the electron. The *system* of "atom" has this property. When the atom gives up photons to the Universe, the Universe no longer gets to know specifics about the internals of the atom.



"If there is no volume how is there a mass?"



It still has a magnetic moment, and it has no size, no volume. Learn to live with disappointment.

Answer 2

Electrons are not solid balls. If they were, then zero volume would indeed mean zero mass. Instead, electrons are quantum wave functions that in only limited ways act like particles. When you put an electron in a box (a quantum dot), it spreads out as a wave to fill the box and therefore cannot be said to have zero volume. When collapsed to a point, an electron indeed has a single location, but it is spread out in momentum space, so it can't be said to have absolutely zero volume.



All fundamental particles (electrons, photons, neutrinos. etc.) are in reality complex-valued quantum wave functions that can be collapsed to a single point in coordinate space, and are not solid little balls that permanently occupy a volume of space with solid matter. Just because they can be collapsed to a single point does not mean that they are actually infinitely small balls. They are actually waves and are typically not collapsed to a point until an interaction occurs.



Electrons have mass because they couple to the Higgs field.



I am sorry if this confusing. It is confusing to many people. But this is what the experiments tell us again and again.

Answer 3

The zero space point along with the untenable singularity issues that brings have been scrubbed several decades ago. In its place we have granular space with a minimum non-zero size and sub atomic particles with mass and non zero size. [See source.]



You mentioned strings. They are just one of several, non-zero models.



To pick a nit, the electron does not exist as a cloud, it exists within a cloud of uncertainty. We can quickly collapse that cloud by detecting the electron.



One more point. Mass is a measure of inertia. And even photons, without rest mass, have momenta and thus inertia. We can predict P = Mc = hF/c = E/c as the momentum of a mass-less photon. E = hF is the energy of a photon. That M...that's the relativisitc inertia and it has the same units, e.g., kg, as rest mass.

Answer 4

daryl has given a very good answer, to which I shall add only a few brief words. You will probably recall that in mechanics we often speak of a point mass, m. All this means is that the dimensions of the particle is small compared with the other distances involved, not that its volume is zero and its density infinite. The electron as a point charge is to be understood in the same spirit. Your physics teacher should stress the idea of orders of magnitude and approximations rather than fostering notions of zero dimensions in his/her students.

Answer 5

Electrons are matter, and since mass is the amount of matter in an entity electrons would have mass. Electrons are considered point charges, but that does not mean that they are literally point sources; charged, perfect metal spheres can be considered point charges beyond the surface of the metal. (see Gauss law). Also, we tend to treat electrons as particles with zero dimension as everything is so much larger than an electron, and the size of an electron would thus be so insignificant that it is not considered in most cases. Just because something is almost zero does not mean it is actually zero. Also, you might want to look at cases of special relativity where particles at relativistic speeds gain relativistic mass, such as photons which are thought to be particles without matter.

Answer 6

The idea that what has mass, has volume, and what has volume, has mass, is true in your common experience, but does not have to be true in everything. We talk about a "point mass" in physics all the time. Usually it is a convenient approximation, but a real object can exist in the same sense.

Answer 7

It is an observed fact that electrons have mass, there is no why to it. Same way as a photon has no mass still it has momentum. We have to build the pieces together consistent with observations and explain them.

Answer 8

a total mass of an atom is almost the sum of mass of protons and neutrons (because electrons are 1840 times lighter than protons)

Answer 9

It is partly related to the Higgs' boson