"Falling into the nucleus", as stated in that Stack Exchange question, is a classical (as in "wrong" :) ) way to look at it.
The 1s orbital of the electron is spherically symmetric, with non-zero probability of the electron being right in the center of the atom (so within the nucleus), and decreasing probability of it being farther away. So e.g. a good approximation of the He atom is of two neutrons, two protons, and two electrons, all in exactly the same position (with the electrons having "more spread").
At the end of the day, there are interactions that are seen in Nature and interactions that aren't. We codify the patterns as conservation of lepton number, baryon number, etc. If the numbers of what you have add up to zero, they can annihilate.
These conservation laws also accommodate other weird things, like beta decay, in which a neutron decays ("splitting") into a proton, an electron, and an anti-neutrino. It's not that the neutron is "composed" of those three things. But its total energy is higher than the sum of the energy at rest of those three particles: Whenever that's the case and the conservation laws allow it, we see it happen naturally.
As someone who hasn't studied this (yet) does that mean that the reason protons and electrons don't annihilate is because their Baryon Number wouldn't sum up to zero? (With Protons having 1 and Electrons 0 if I understood correctly)
That's what we currently observe, yes. The particles of matter in the Standard Model are quarks (that join to form protons and neutrons among other things) and leptons (electrons, muons, taus, and neutrinos). The number of {quarks - antiquarks}, as well as that of {leptons - antileptons}, is conserved.
If you start with a proton and an electron, you have 3 quarks and 1 lepton, so whatever the interaction you have to end up with 3 quarks and 1 lepton (plus any number of quark-antiquark and lepton-antilepton pairs). E.g. for beta decay:
Neutron has a baryon number of 1 and so it is conserved in your example. Even in normal matter, some elements undergo Electron Capture (p + e- -> n + ν).
But baryon number conservation is an asserted symmetry and there is no fundamental reason it holds. Finding proton decay would demonstrate that it does not but so far there is no evidence that protons (or bound neutrons) spontaneously decay.
> At the end of the day, there are interactions that are seen in Nature and interactions that aren't.
That's provably false. Every reaction occurs in nature, even the vanishingly improbable ones, just at an extremely low reaction coefficient. They're still there, just at a probability of 10^-14 or whatever.
What? There are interactions that can never occur because they're forbidden by the laws of physics - you'll never violate conservation of [energy, baryon number, momentum, etc.] even with probability 10^-14.
Sure, technically correct is the best kind of correct I suppose.
But if the reaction is the least bit reversible (and most are) then the reverse reaction is still proceeding even though the forward reaction is stronger. It's just doing so at an incredibly low rate, and the products are likely to be immediately converted by the forward reaction.
You are looking at averages and claiming they hold for every single event in a stochastic simulation. Taking the example of entropy - it's not impossible that entropy decreases in a system, it's just less likely than it increasing. On a stochastic level, entropy decreases all the time, it's just that on average it increases more than it decreases.
Reactions work the same way. You're not actually making chemicals react as a singular act, you're creating a forward reaction that occurs more rapidly than the reverse reaction.
If we had a hypothetical chemical Maxwell's Demon - you could "bottle" up the tiny bits of those outputs from the reverse reaction before they underwent the forward reaction again.
You're assuming one can expect the knowledge of chemical reactions to apply to particle interactions, and that is not the case.
For example particle accelerators can shoot particles against some target one by one, and so there's no need to look at averages. Some interactions never occur, to the best of our measuring ability (i.e. highest energies and number of repetitions). Some others are right away forbidden by laws much stronger than entropy in thermodynamics, in the sense that they're not averages, but mathematical derivations off the symmetries of the universe.
> The concentrations of reactants and products in an equilibrium mixture are determined by the analytical concentrations of the reagents (A and B or C and D) and the equilibrium constant, K. The magnitude of the equilibrium constant depends on the Gibbs free energy change for the reaction.[2] So, when the free energy change is large (more than about 30 kJ mol−1), then the equilibrium constant is large (log K > 3) and the concentrations of the reactants at equilibrium are very small. Such a reaction is sometimes considered to be an irreversible reaction, although in reality small amounts of the reactants are still expected to be present in the reacting system. A truly irreversible chemical reaction is usually achieved when one of the products exits the reacting system, for example, as does carbon dioxide (volatile) in the reaction
Assuming you do not outright lose some reactants from the system, the reverse reaction is still occurring. However, because the reaction constant is so small, the resulting product is highly probable to essentially immediately undergo the forward reaction. However, it will still be present in some equilibrium - just an incredibly low one, in the ratio of the reaction rate coefficients. You'll have 10^14 times as much of the forward reaction, or whatever.
Chemical reactions, ignoring those with nuclear interactions, are only bound by the law of conservation of energy and the decrease of entropy. A chemist looks at them in the macro scale, in which macroscopic properties like temperature and pressure are set, and thus each molecule's energy isn't a fixed value (instead being taken off a set, according to Maxwell's probability distribution). This, and the probabilistic nature of the law of entropy, leads to all allowed reactions happening somewhere at the micro scale, even if extremely rarely.
If you look at the micro scale, though, and instead of having a soup of molecules you deal with single molecules, whether a reaction is possible or not isn't a probabilistic thing anymore. The energies your molecules have are actual numbers, and if they don't add up, you won't have a reaction.
And what if there is a micro-scale reversal of entropy, as I previously mentioned? Let's say a collision of two electrons, or an electron with a surrounding gas molecule, that results in a sudden increase in orbital energy of an electron (plus another particle losing all its energy of course). Vanishingly unlikely of course, but with an uncountable number of collisions occurring every instant it will occur somewhere, sometime.
You say that it's "observable" with single-particle experiments. Are you sure you've performed enough of those experiments to unconditionally guarantee that such situations will never under any circumstances occur?
As an example of how you can be wrong on this: since the 1940s, Bi-209 was believed to be a stable element. However, recent research has actually determined that it is very slightly unstable - with a half life of approximately 4.6 x 10^19 years. That's more than one billion times the current estimated age of the universe. It's not stable at all, it just had unmeasurably low amounts of instability.
If you sat around looking at a single-molecule sample of that reaction, you would see absolutely nothing - unless you had a few trillion years to sit around. That particular experiment doesn't exhibit the behavior you're trying to model. It's like saying that because Newton's Laws Of Motion adequately explain everything on Earth, they could never be superceded by General Relativity.
I don't accept that other physical reactions categorically cannot occur at similarly improbable rates. The decay of smaller "stable" atoms, for example, may occur with a half-life of 10^100 or 10^1000 years that is simply beyond our current ability to measure.
With a sufficient number of simulations you can come up all-heads any arbitrary number of times that you want to name. You can even roll a perfect 20 on a D20 any number of times. Even something like spontaneous fission is theoretically possible - it's just vanishingly unlikely.
> And what if there is a micro-scale reversal of entropy, as I previously mentioned? Let's say a collision of two electrons, or an electron with a surrounding gas molecule, that results in a sudden increase in orbital energy of an electron (plus another particle losing all its energy of course). Vanishingly unlikely of course, but with an uncountable number of collisions occurring every instant it will occur somewhere, sometime.
Sorry, I'm not sure what you mean by this.
> You say that it's "observable" with single-particle experiments. Are you sure you've performed enough of those experiments to unconditionally guarantee that such situations will never under any circumstances occur?
I said (in the other reply) it's observable "to the best of our measuring ability" (repetitions, and energy), precisely because we'll never reach 100% certainty.
But your wrong claim wasn't "things that we don't know yet might be happening", rather "all particle interactions imaginable are happening all the time, just with a small probability". The former is tautologically true. The latter is just pseudoscience, as it is:
1. Unfalsifiable: the more we keep measuring that only some interactions happen in Nature, the further you'd just push that small probability.
2. Without predictive power.
It's not like superseding Newton's laws of motion with GR. It's like saying "beyond the speeds and masses we've observed, objects are free from any laws of motion whatsoever". And furthermore adding that it can be proved.
And that's only for laws like conservation of quark and lepton numbers. For conservation of energy and momentum, the prohibition is much stronger: Noether proved mathematically that they're another way of saying the laws of Nature are the same today than yesterday, and the same here than a meter away. Claiming they're being broken all the time is the same as saying the laws of physics are different all over the place, and from one moment to the next. The slightest evidence or proof of something of the sort, and we pretty much start all physics from scratch :)
In no way have I ever claimed that conservation of momentum is violated. I've specifically disclaimed that fact - with the caveat that dice are played constantly on a galactic scale, and anything is stochastically possible will eventually occur - even if it's probable at 10^-100 like Bi-209. I also happen to think that smaller molecules may also decay, and that you just haven't happened to observe enough single-particle data to observe an event that occurs at 10^-1000. Sue me.
Yes you did, and that was the whole point of the thread?
>> At the end of the day, there are interactions that are seen in Nature and interactions that aren't.
> That's provably false. Every reaction occurs in nature, even the vanishingly improbable ones, just at an extremely low reaction coefficient. They're still there, just at a probability of 10^-14 or whatever.
To the best of our knowledge, not every reaction occurs in Nature, and chemical equilibrium has nothing to do with it. The patterns we observe as to which can occur and which can't, we call conservation laws. You might want to accept that or not; doesn't change what the experiments output. And of course if there was proof of the contrary you'd be onto something very very big.
The 1s orbital of the electron is spherically symmetric, with non-zero probability of the electron being right in the center of the atom (so within the nucleus), and decreasing probability of it being farther away. So e.g. a good approximation of the He atom is of two neutrons, two protons, and two electrons, all in exactly the same position (with the electrons having "more spread").
At the end of the day, there are interactions that are seen in Nature and interactions that aren't. We codify the patterns as conservation of lepton number, baryon number, etc. If the numbers of what you have add up to zero, they can annihilate.
These conservation laws also accommodate other weird things, like beta decay, in which a neutron decays ("splitting") into a proton, an electron, and an anti-neutrino. It's not that the neutron is "composed" of those three things. But its total energy is higher than the sum of the energy at rest of those three particles: Whenever that's the case and the conservation laws allow it, we see it happen naturally.