Hi. I’ve just spent quite awhile reading the wiki pages on these topics. (and a bunch of hyperlinks.) There were some things I didn’t understand or just wanted to know. Please forgive me if these questions are ignorant.
The wiki quotes are in italics, followed by my questions.
A point-like electron (zero radius) generates serious mathematical difficulties due to the self-energy of the electron tending to infinity.
*Is this self-energy mentioned here referring to the energy an electron emits when changing state? Do electrons have near-infinite energy to expend? **
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The experimental lower bound for the electron’s mean lifetime is 6.6×1028 years, at a 90% confidence level.
Why does an electron have a finite lifetime? Does it have to do with continually emitting energy?
In the case of antisymmetry, solutions of the wave equation for interacting electrons result in a zero probability that each pair will occupy the same location or state. This is responsible for the Pauli exclusion principle, which precludes any two electrons from occupying the same quantum state. This principle explains many of the properties of electrons. For example, it causes groups of bound electrons to occupy different orbitals in an atom, rather than all overlapping each other in the same orbit.
**Electrons have a negative charge. Don’t two negative charges repel each other? Why does this alone not prevent electrons from occupying the same orbital?
** An experiment done by C. S. Wu at Columbia University showed that neutrinos always have left-handed chirality. Because antineutrinos and neutrinos are neutral particles, it is possible that they are the same particle. Particles that have this property are known as Majorana particles. Majorana neutrinos have the property that the neutrino and antineutrino could be distinguished only by chirality; what experiments observe as a difference between the neutrino and antineutrino could simply be due to one particle with two possible chiralities.
Are there hypotheses for a mechanism that would determine neutrino/antineutrino chirality? In other words, how would a particle’s charge (matter/antimatter) engender a positional or directional orientation? Also, if neutrinos only interact with matter via the weak force and gravity, does that mean that they would collect up around a very large source of gravity?
The experimental lower bound for the electron’s mean lifetime is 6.6×1028 years, at a 90% confidence level.
Why does an electron have a finite lifetime? Does it have to do with continually emitting energy?
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If the electron is a fundamental elementary particle, as currently believed, it’s lifetime is ‘infinite’. But these things are worth checking. The experiment you reference gives a “lower bound” of a long, long time. They may last (significantly) longer. It would literally take forever to show they last forever.
Essentially, they are saying “electrons last forever (as far as we’ve checked)”. Which helps support the concept that they are fundamental.
No to both questions. The self-energy essentially is essentially an interaction between the electron’s charge and its own electric field. The usual conclusion is that getting an infinite answer here is an artefact of using a somewhat wrong model that gives a (very) good approximation under the conditions we can measure things. The corresponding usual hope is that some future fuller understanding of electrons would resolve the issue (for example, by making the electron some sort of extended object which just looks pointlike to us given current experiments).
That’s an experimental limit. The electron lifetime is infinite in the Standard Model and I can’t think of any reasonably mainstream alternative that’s been proposed to it in which it’s not. (Some variant of preons perhaps?)
Remember that they’re also both being attracted by a positive nucleus.
Double beta decays are the classic area to test whether neutrinos are Majorana particles or not.
To some extent yes. But they’re also very light and going very fast.
Quantum mechanics is weird, and electrons cannot be considered as planets circling a nucleus. We used to think that, so we get cartoon images of electrons in orbit, and we have a vestigial word ‘orbital’, which is supposed to convey that the electron (which we previously imagined in orbit) is not really orbiting at all.
The wave equations show a ‘smeared-out’ probability of finding a bound electron in various places around the nucleus. Although the negative charges of the electrons are indeed repulsive, there is a non-zero probability that 2 electrons could be quite close (maybe even in the same place, though that is beyond me). What quantum mechanics cares about is not so much how close or far apart the electrons may be, but that they not have the same quantum properties (quantum numbers).
So actually , many electron orbitals do ‘overlap’. But there are significant differences in energy and angular momentum and spin for each of the electrons, making it ‘okay’ for them to co-exist. It’s kind of like a business which does not allow more than one employee per job description. Some employees may have some places they prefer to hang out and other places they are not allowed to go, but employees may still frequently meet up in the hallways. They just can’t be indistinguishable from each other.
IIRC, free electrons can be essentially indistinguishable.
To get a rough intuitive idea of the issue here, consider the electrostatic force that a charged particle would “feel” if it were sitting at a distance D from an electron. Now move the particle closer, to D/2. By the inverse square law, the force it feels would increase by a factor of 4. Now move it closer again, to D/4. Now the force is 16 times the original force. Each time you half the distance to the electron, the force quadruples. Since the electron is a point particle, this can go on indefinitely. You can get closer and closer to the electron, and increase the electrostatic force without limit. (This would not be an issue for a non-point particle like a proton, because at some point you can’t get any closer to the center of the particle because you run into it.)
This is great. Thanks for all the very helpful answers. So many things are really interesting about physics.
Could point particles have spatial features which are expressed in one of the dimensions we can’t observe? (those postulated by string theory.)
markn+: Oh, I get it! Zeno’s Arrow of untouchability.
Blue Blistering Barnacle: You reminded me of another question I meant to ask: since matter seems to be constantly emitting electrons through all the inevitable processes of decay and change – where do they all go? Do they usually wind up attached to other atoms, or are we swimming in a sea of free electrons?
Oh, and what I’m asking about neutrino chirality is basically this: Whether or not neutrinos and antineutrinos are the same particle with two possible states – why right-handedness in antineutrinos? Just to carry on the theme of “opposite world?” I just wonder what inherent property a particle’s charge would confer that would result in one or the other.
For the neutrino question, you can rephrase it in terms of the properties of the weak interaction (the only one that’s really relevant for neutrinos). But then one can just as well ask, why does the weak interaction behave that way? And the best answer we can give to that is “that’s just the way it is”.
Chronos: You’re right. I’m probably making the mistake of still thinking of these things in three-dimensional macro terms. Honestly, it’s quite a trick even attempting to get a firm grip on the idea of things like zero-point particles.