I Antimatter-matter annihilation: significance of opposite charge

[NothingsMatter]

TL;DR Summary

What is it about having the opposite charge and same mass that makes a particle and its antimatter partner annihilate each other?

I did a forum search and couldn't find this, so forgive me if my search skills were insufficient to find a previous explanation of this.

But, I'm a bit confused as to why merely having the same mass but opposite charge would cause, for example, an electron and positron to annihilate each other. Why couldn't they just bond to each other and be a happy little neutral particle with twice the mass, give or take a bit related to the energy change required for them to bond? What I have learned from the worst source (artificial intelligence) is that it creates an unstable situation, resulting in the two converting entirely to energy. But if so, why?

So, is there more to the picture than them just having the opposite charge but same mass? If not, what makes that so volatile? Why would opposite charges but different masses not cause the same thing?

Thanks.


Sidenote: My math background maximum is upper division undergrad level. but if your answer requires graduate level stuff, I'll figure it out enough to get a better understanding than I have now, regardless of the intermediate tag on this thread.

 

[DaveC426913]

But, I'm a bit confused as to why merely having the same mass but opposite charge would cause, for example, an electron and positron to annihilate each other. Why couldn't they just bond to each other and be a happy little neutral particle with twice the mass,

There is no such thing as a stable particle containing an electron and a positron.

The particles combine to form a new stable state. It just happens that the most common stable state is photons - usually gamma rays - that travel at the speed of light.

Wiki has a primer on annihilation, including an example of electron-positron collision. Give it a read and ask specific questions.

 

[PeroK]

TL;DR Summary: What is it about having the opposite charge and same mass that makes a particle and its antimatter partner annihilate each other?

But, I'm a bit confused as to why merely having the same mass but opposite charge would cause, for example, an electron and positron to annihilate each other.

One answer is because they can. When an electron and a positron interact, there are two main processes that are allowed by the laws of physics: scattering and annihilation. In the former case, the particles scatter off each other and go their separate ways. QED (Quantum Electrodynamics) gives you the probability that this happens and the distribution of scattering angles. These calculations are done using the so-called Feynman rules.

Note that at low energy, the scattering angles are closely approximated by Rutherford Scattering - which uses only classical electromagnetism.

QED also allows the two particles to annhihilate and produce two (or more) photons. And, again, the Feynman rules give you the probability for this, given the total energy of the interaction.

Why couldn't they just bond to each other and be a happy little neutral particle with twice the mass, give or take a bit related to the energy change required for them to bond?

This is possible in high-energy cases, where neutral mesons may be produced. See here, for example:

https://en.wikipedia.org/wiki/Electron–positron_annihilation#High-energy_case

Again, the probability of this can be calculated, given the energy of the interaction. These particles, like most elementary particles, are unstable and soon decay into smaller particles.

 

[fresh_42]

The German Wikipedia article about annihilation also mentions the possibility of building a positronium for about $0.1 \,\mathrm{ns}$ before annihilation.

 

[snorkack]

The German Wikipedia article about annihilation also mentions the possibility of building a positronium for about $0.1 \,\mathrm{ns}$ before annihilation.

Or 140 ns. And even 1100 ns.
The problem is that there is a lower lying more stable state. Electron and proton are unable to annihilate. So are electron and positive muon.
But same mass and opposite charges are not required for annihilation. Antineutron and proton also annihilate.

 

[Orodruin]

You have it backwards. Technically there could have existed particles of the same mass and energy that would not annihilate. However, being each other’s anti-particle implies that they must have the same mass and opposite charge - and that they can annihilate to photons since said charge is non-zero.

 

[snorkack]

However, being each other’s anti-particle implies that they must have the same mass and opposite charge - and that they can annihilate to photons since said charge is non-zero.

Proton and antiproton annihilate to mesons. Can a proton and antiproton annihilate to photons only, without any mesons?

 

[Orodruin]

Proton and antiproton annihilate to mesons. Can a proton and antiproton annihilate to photons only, without any mesons?

Sure they can. It is just not as likely to happen.

 

[NothingsMatter]

You have it backwards. Technically there could have existed particles of the same mass and energy that would not annihilate. However, being each other’s anti-particle implies that they must have the same mass and opposite charge - and that they can annihilate to photons since said charge is non-zero.

So, you are saying the mass and charge are merely consequences of them being anti-particle partners, and they annihilate because they are anti-particle partners, not the other way around. If I understand what you are saying, it is not that the opposite charge and same mass causes them to annihilate, but rather, they wouldn't have the necessary properties to annihilate if they didn't have the opposite charge and same mass. Is that an accurate or close to accurate understanding of what you said?


If so, it then makes me wonder what other thing about them makes them annihilate each other, but I expect the answer is the same answer for why water freezes at 0 degrees C: that's just how ("god", "nature" etc) made it.

However, my guess is that this happens simply because it's a lower energy state after the annihilation. That seems to be why most things happen in physics, as far as I can tell, so it makes sense to me here. But I know nothing so \_(0_0 )_/

 

[snorkack]

Consider, for example, neutrino and antineutrino.
Can they annihilate?
If yes, to what?

 

[NothingsMatter]

Consider, for example, neutrino and antineutrino.
Can they annihilate?
If yes, to what?

Given that they have no charge, this further elucidates what Orodruin said (if I understood it correctly). So, if I'm on the right track in understanding it, then again it would boil down to the annihilation being a lower (lowest possible?) energy state of the system. As for what they become, I cannot say, since I don't really know what neutrinos are. I don't want to cheat and look it up, so I'm going to guess ether photons or another particle that corresponds to the electromagnetic spectrum. :) Maybe it depends upon the energy of the particles when they collide.

 

[Orodruin]

So, you are saying the mass and charge are merely consequences of them being anti-particle partners, and they annihilate because they are anti-particle partners, not the other way around. If I understand what you are saying, it is not that the opposite charge and same mass causes them to annihilate, but rather, they wouldn't have the necessary properties to annihilate if they didn't have the opposite charge and same mass. Is that an accurate or close to accurate understanding of what you said?

Yes. For example, for all we know (although that may not be the whole story), the muon could have just as well had the same mass as the electron. There are a number of theoretical points to be made here about how such a world would look like or even if it would actually be possible, but I am not going to go further into that detail here as that would be an A+ level discussion. The positron would then not annihilate with the negative muon even if they had the same mass.

If so, it then makes me wonder what other thing about them makes them annihilate each other, but I expect the answer is the same answer for why water freezes at 0 degrees C: that's just how ("god", "nature" etc) made it.

That's not the reason. The reason is that Anders Celsius defined 100 °C as the freezing point of water and 0 °C as the boiling point and that this was later reversed so that the lower fixed point of the scale (0 °C) instead referred to the freezing point.

If your question is instead "Why 273 K?" apart from the choice of the numerical value of the Boltzmann constant, then it is ultimately due to the value of the fine-structure constant.

However, my guess is that this happens simply because it's a lower energy state after the annihilation. That seems to be why most things happen in physics, as far as I can tell, so it makes sense to me here. But I know nothing so \_(0_0 )_/

Things happen because they can happen - there is a non-zero amplitude for it to happen, so it happens.

Consider, for example, neutrino and antineutrino.
Can they annihilate?
If yes, to what?

Yes. Depends on the energy.

since I don't really know what neutrinos are

Me neither! That makes two of us!

I don't want to cheat and look it up, so I'm going to guess ether photons or another particle that corresponds to the electromagnetic spectrum. :)

No. Neutrinos are neutral (no electric charge) leptons. Essentially relatives to electrons, muons, and taus. They only interact through the weak interactions mediated by W and Z bosons, where the interactions with the charged W bosons turn them into charged leptons or create them from charged leptons. Neutrinos have extremely small masses, which allow them to exhibit the phenomenon known as neutrino oscillations, where a neutrino originally created in an interaction with a muon can later be detected interacting with an electron. (This would not be possible were they massless.)

Maybe it depends upon the energy of the particles when they collide.

Indeed. Neutrino collisions are, however, extremely rare due to neutrinos only interacting through the weak interaction.

 

[berkeman]

The reason is that Anders Celsius defined 100 °C as the freezing point of water and 0 °C as the boiling point and that this was later reversed so that the lower fixed point of the scale (0 °C) instead referred to the freezing point.

I'm getting dizzy.

(not your fault, you're just presenting facts)

Me neither! That makes two of us!

Your PhD thesis and many peer-reviewed journal articles notwithstanding.

 

[Orodruin]

Your PhD thesis and many peer-reviewed journal articles notwithstanding.

I don’t even know if they are Dirac or Majorana fermions!

 

[Orodruin]

I don’t even know if they are Dirac or Majorana fermions!

… although when a I think about it, nobody else knows either …

 

[fresh_42]

… although when a I think about it, nobody else knows either …

Kind of reminds me of an event long ago. A fellow student entered our lounge, constantly shaking his head and mumbling: "Zero divisors, zero divisors! There are no zero divisors at all."

 

[ohwilleke]

At a very big picture level, every interaction that conserves various quantum numbers like electromagnetic charge, QCD color charge, CPT, mass-energy, momentum, baryon number, lepton number, and (with some very specific and narrow exceptions) fermion generation (and possibly others that I'm forgetting at the moment) can and do happen.

You can draw Feynman diagrams of all of the possibilities and each diagram implies a formula for calculating the probability of a particular Feynman diagram interaction occurring.

Annihilation interactions are governed by an annihilation operator, and there is a counterpart called a creation operator. But, ultimately, there is really nothing special about annihilation and creation interactions, they are just one subset of all possible Feynman diagrams that seem notable because the particles that exist at the beginning aren't the same as the particles that exist at the end when viewed along the time dimension. There aren't particularly special rules that apply to how annihilation and creation interactions work relative to other interactions of particles that conserve the proper quantities and can be represented by Feynman diagrams. (And, all Feynman diagrams worth in both directions of time.)

Consider, for example, neutrino and antineutrino.
Can they annihilate?
If yes, to what?

Neutrinos and antineutrinos can't annihilate directly to photons, because photons only interact at the "tree level" (i.e. directly) with particles that have electromagnetic charge (like quarks, charged leptons, and W bosons, but unlike neutrinos, Z bosons, gluons and Higgs bosons - Higgs boson decays to photons are actually multi-step processes). Neutrinos and anti-neutrinos don't interact directly with either photons or gluons.

Neutrinos and anti-neutrinos do interact directly with W and Z bosons, but since W and Z bosons are quite massive (ca. 80 and 90 GeV respectively to one significant digit), a neutrino/antineutrino pair have to have lots of momentum to give rise to an "on shell" real W or Z bosons (you'd need a W+ and W- boson pair to net out to zero electromagnetic charge), as opposed to a mere "off shell" or "virtual" W boson pair or Z boson that is constrained to decay only to end particles with mass-energy and momentum no greater than the original neutrino/antineutrino pair. The high mass of the W and Z boson also make the probability of even virtual neutrino/antineutrino annihilation to some other produce end products that have mass-energy identical to the original particles (which implies a sum of rest masses for those produced particles that is equal to or greater than that amount) low.

We don't know for sure whether or not neutrinos can interact directly with Higgs bosons (this is part of the Dirac v. Majorana debate with some additional twists to it, because the left handed nature of neutrinos suggests that they should not interact with Higgs bosons the way other fermions do), because particles that do interact directly with Higgs bosons do so as a function of their rest masses, and neutrino rest masses are so tiny that even if they did interact directly with Higgs bosons, Higgs boson decays to neutrinos would be vanishingly rare and would also be extremely difficult to detect (because neutrinos interact so weakly with other particles). As it is, we still haven't even detected Higgs boson decays to electron-positron pairs and electrons have rest masses that are probably at least a million times greater than the greatest neutrino mass, in addition to being vastly more difficult to observe when neutrinos are produced. Even if it does happen (which is very much in doubt), direct detection of this is easily 40-100 years in the future, in terms of the experimental instrumentation and scale that would be necessary.

Realistically, if neutrinos did interact with Higgs bosons, we'd determine that not by directly detecting decays, but by calculating how much the probability of some much more common and easier to measure process would be tweaked if virtual Higgs boson interactions with neutrinos were possible and then measuring that process to extreme precision and comparing the results to the theoretical prediction.

 

[Orodruin]

because the left handed nature of neutrinos suggests that they should interact with Higgs bosons the way other fermions do)

This I do not really agree with. Left-handedness is not a prerequisite for interactions with the Higgs for charged particles either. In fact, the terms in the Lagrangian with two fermions and a Higgs connect the left-handed fields to the right-handed ones (as scalar interactions must!). The question of whether the neutrinos interact with the Higgs or not is rather a question of the existence of the corresponding right-handed fermion field with the appropriate quantum numbers to insert such a term into the Lagrangian - i.e., the existence of a right-handed neutrino.

The above of course assumes we are treating the standard model (possibly augmented by right-handed neutrinos) as a renormalisable theory. If we instead start looking at the standard model as an effective field theory, we know that the neutrino interactions with the Higgs field in the form of the Weinberg operator is the only possible operator at dimension 5.

 

[ohwilleke]

This I do not really agree with. Left-handedness is not a prerequisite for interactions with the Higgs for charged particles either. In fact, the terms in the Lagrangian with two fermions and a Higgs connect the left-handed fields to the right-handed ones (as scalar interactions must!). The question of whether the neutrinos interact with the Higgs or not is rather a question of the existence of the corresponding right-handed fermion field with the appropriate quantum numbers to insert such a term into the Lagrangian - i.e., the existence of a right-handed neutrino.

The above of course assumes we are treating the standard model (possibly augmented by right-handed neutrinos) as a renormalisable theory. If we instead start looking at the standard model as an effective field theory, we know that the neutrino interactions with the Higgs field in the form of the Weinberg operator is the only possible operator at dimension 5.

UPDATE: I think that the issue may be much simpler. I wrote "should" when I meant to write "should not"

FIRST RESPONSE:

I think we agree about more than we disagree over.

I agree with you that if there are right-handed neutrinos, then neutrinos can interact with the Higgs field, while if there are not, it cannot, as least as the Lagrangian equations for the Higgs field are conventionally formulated.

It is conventional to say that in the Standard Model there are not right-handed neutrinos, and hence there is a mathematical problem with having neutrinos interact with the Higgs field (which is why I made the statement that I did).

But, certainly, in an extension of the Standard Model that introduced right-handed neutrinos, this problem would not exist. (And, of course, it is not truly left-handedness per se that it the problem, it is having a left-handed but not a right handed version of the neutrino that is the problem. The same problem would be present if neutrinos were exclusively right-handed, and there were no left-handed neutrinos.)

 

[BVirtual]

The history of the positron is important for understanding 'anti-particles.' The positron was theorized to exist by a scientist who looked at the QM math equation for the electron. He saw there was a squared variable term involved, and the number squared could therefore be positive, for the electron, or the number to be squared could be negative. Both cases would result in a positive number. So, he wanted to be famous and get in line for a Nobel Prize, and he went out on a limb, and wrote a paper to a journal that theorized there existed a type of particle that is the opposite of the electron, and would have positive charge, and if the two were ever to meet in a collision, then they would annihilate, or combine together, and being unstable, would decay into two Gamma Ray photons. Experimentalists went looking, and found the positron.

So in answer to the original posted question, how are they different, it is in the math equations. The math predicted an anti-particle of opposite charge, and all other properties would be identical (thus the same mass). He found a symmetry in the QM math for the electron, and made a prediction, a good call.

 

[renormalize]

The positron was theorized to exist by a scientist who looked at the QM math equation for the electron.

Please give credit where due: the 'scientist' was Paul Adrien Maurice Dirac, who shared with Erwin Schrödinger the 1933 Nobel prize in physics for "the discovery of new productive forms of atomic theory."

 

[BVirtual]

Thank you @berkeman for doing the look up and post.