Let’s postulate that you have a muon in the brief time before it decays. At the same time, an electron is passing by with such high velocity that it’s relativistic mass equals that of the muon. Is the electron still fundamentally different from the muon as an elementary particle, or could one say that in a sense it has transformed into a muon? To what extent are muons (and taus) possibly just electrons that somehow have acquired a greater rest mass? What other than mass makes them definably different from each other?
That is an interesting question; in the Standard Model there should be something like lepton flavor conservation, so a decay like a muon turning into an electron plus a photon should occur less than 1 in 1050 times in the Standard Model. The main difference between electrons/muons is the mass; the spin, charge, hypercharge, etc. should be the same. IE it’s a kind of “heavy electron”. In fact, there are experimental tests of “lepton universality” to check that the different flavors have the same coupling to gauge bosons.
Mass is mass, and doesn’t change just because one thing is moving really fast. The electron’s mass is still much less than the muon’s mass.
Some textbooks talk about something that they call “relativistic mass”, but that’s just a superfluous and confusing word for “total energy”. When any physicist uses the word “mass”, we mean “rest mass”.
There was an interesting article about how to detect extra (compact) dimensions using something like what OP suggests.
A particle that is free to move in a compact extra dimension could in fact be moving quickly in that direction, basically “orbiting the universe” in that direction, and for us who are too big to resolve that compact dimension, it would look just like the original particle, but would have a different mass. For QM reasons, the extra energy would be quantized so it would look like a series of particles that are identical with a series of discrete masses.
I have been assured that this mechanism has been ruled out as the origin of the particle generations, but I couldn’t tell you specifically why.
I’d expect that such extradimensional excited states would have evenly-spaced masses, and also wouldn’t have any limit on the number of “generations”. Though there may well be ways around both of those, if you’re stubborn enough about making the hypothesis work.
Anyway, the different generations of charged leptons (appear to) (probably) have multiple differences between them, besides just mass. Each one corresponds to a (probably) different kind of neutrino, and those (probably) don’t even have a definite mass.
Do you think it’s possible to replace electrons with muons? That would make fusion power easier.
This reminds me of the particle physics class I took as an undergraduate in physics. The professor (Geoffery Chew IIRC) was working an illustrative problem on the board when one of the students asked, “Is that an electron or a proton?” Without turning around, he answered, “It doesn’t matter, all particles are the same.”
Everyone went dead silent, and he turned around, then we realized he meant for the purpose of the example. There was a bit of a relieved laugh among the students, and he continued with the lesson.
If you’re on a spaceship flying on 99.999% of the speed of light, do you turn into a planet?
Muon-induced fusion is actually a thing, but the short lifetimes of muons makes it impossible to use for practical fusion energy production.
This is often known as the Kaluza-Klein tower. Quantum mechanically, you can think of this as the particle in the direction of the extra dimension being confined in a box with length given by the radius R of the extra dimension. This leads to a ‘tower’ of excitations with energy ~n/R, where n counts the excitation level. If the extra dimension’s extension is on the order of the Planck length, then the first of these would have a mass of the order of the Planck mass, which is a pretty large quantity—several micrograms—and thus, much too big for any of the observed particles. Sizes on the order necessary to explain the generational structure of the known elementary particles have been ruled out by precision gravitational experiments, I believe.
(Incidentally, this is also the reason that the oft-repeated gloss of string theory as yielding particles as different vibrations of fundamental strings is somewhat misleading—the particles created even by the lowest such vibration would likewise be of Planck mass. So if the world according to string theory is compared to an orchestra, it’s just composed of instruments nobody plays.)
Don’t give up on it just yet… From the article you posted:
“By taking this factor into account, muon-catalyzed fusion can already exceed breakeven; however, the recirculated power is usually very large compared to power out to the electrical grid (about 3-5 times as large, according to estimates). Despite this rather high recirculated power, the overall cycle efficiency is comparable to conventional fission reactors; however the need for 4-6 MW electrical generating capacity for each megawatt out to the grid probably represents an unacceptably large capital investment. Pusch suggested using Bogdan Maglich’s “migma” self-colliding beam concept to significantly increase the muon production efficiency, by eliminating target losses, and using tritium nuclei as the driver beam, to optimize the number of negative muons.”
Two questions: is it the case that SM only predicts 3 flavors of leptons or is it that that’s all that’s been observed? I think it’s the former but am not sure. (Why 3 in that case?)
Also, does muon fusion create more energy than needed to create muons in the first place?
There are six lepton flavors, two per generation (electron, muon, tau, and the corresponding neutrinos). The three generations of the SM are not a prediction, and why there should be three, nobody knows. (It’s always seemed to me a bit like an out-of-ideas hollywood director remaking his greatest hit with action and everything dialed up…)
But it’s not exactly the case that it’s three just because we haven’t observed any more. The presence of extra generations would have observable effects on certain processes, such as the Z boson decay. The fact that those agree very well with the theoretical value obtained for three generations puts tight constraints on the existence of further ones.
That’s critically dependent on how many fusions a muon can catalyze before it decays, the answer being “maybe, it depends”. Which is why break-even muon fusion isn’t a thing at least yet.
I understand why they say this, but I don’t understand how it can be so sure.
If the fourth generation is a whole lot heavier, then it wouldn’t have an observable effect on the particles we know and love.
For instance, one of the reasons I see quoted as to why there are three generations is because there are three generations of neutrinos, and neutrino oscillation means that we should see all of them.
But the three generations are all extremely light, where virtually no energy is gained or lost when they change. If the fourth was quite heavy, then they wouldn’t be able to oscillate into it.
That sounds like the Sterile neutrino - Wikipedia hypothesis.
So Sterile Neutrinos could explain dark matter?
“They may, however, be responsible for a number of unexplained phenomena in physical cosmology and astrophysics, including dark matter, baryogenesis or hypothetical dark radiation.[4]”
We-ll… maybe. But they’re pretty speculative to put it mildly.
My understanding is that there are cosmological observations that also also put constraints on the number of neutrino families, including some early enough in the universe that you would expect there to be enough energy lying about for much more massive neutrinos to be created if they existed.
Yeah, the cosmological bounds put upper limits on the sum of the masses of all the neutrino varieties.