“Hello” said the proton.
“Hello” said the other proton. I refer to the other proton as the other proton, although of course it is impossible to be sure that the two of them had not swapped position.
“We could have a conversation” continued the first proton “It’s not like there are any observers”
“Observers always complicate matters” agreed the second proton “Who are you?”
“I’m a proton,” said the first proton, descriptively “who are you?”
“Well fancy that!” said the second proton “I’m a proton too”
“We must have so much in common, let us discuss matters”
“I carry one fundamental unit of charge,” said the second proton brightly, “and have half integer spin”
“Me too!” exclaimed the second proton excitedly.
“Hey!” said the first proton “why are we still talking to each other? If we both carry one fundamental unit of charge, we should experience a repulsive Coulomb force, equivalent to eight point nine nine times ten to the nine times one point six oh nine times ten to the negative nineteen (that’s you) times one point six oh nine times ten to the negative nineteen all divided by the distance between us squared!”
“You’re right!” said the second proton. “and yet I find myself strangely attracted to you. Maybe it's gravity?”
“I hope not. That much gravity is always a bad sign. I was part of a neutron star once. It was very interesting I suppose, but I’m glad I left” The proton sounded somewhat prim, but also slightly proud of having had such an interesting past.
“I’ve never been in a neutron star what’s it like?”
“It was filthy. I never thought I’d see so many fermions being so degenerate.”
“You broke the Pauli exclusion principle?” The second proton was shocked, but clearly very impressed by the first proton’s daring “I could never do that” The second proton briefly thought of saying “I thought only bosons did things like that”, but because that sort of language was unpleasantly prejudiced, the second proton didn’t.
“Anyhow” continued the first proton, “There were thousands of neutrons around, and there aren’t any here, so it can’t be gravity.”
“I was never much good at gravity, but that makes sense.”
“None of us are; we only have a mass of one point six seven two times ten to the negative twenty-seven kilograms”
“Well then, it can’t be gravity” The second proton looked at the first proton oddly “we could both be here if one of us was a neutron.”
“But we’re not,” the first proton said, and because the second proton was paying careful attention, the second proton noticed that there was absolutely nothing evasive about the way that the first proton said this. Despite this reassurance, the second proton went on
“I heard that most subatomic particles in neutron stars were neutrons.”
“Yes, there were thousands of them, all over the place. I’ve never been so crowded.”
Satisfied by this, the second proton said, “So if it's not gravity, which I realize was a very silly idea, what else could it be? Are we constrained by an external electrostatic potential?”
“I hope not. They always make my wavefunction tails look fat.” The first proton wondered vaguely about its own momentum, thus puffing out its position slightly, to show it was joking.
“I’m sure you have lovely exponential tails, except in the case of infinite wells, of course,” said the second proton reassuringly. Then the second proton realized that the first proton had significant ∆x, and trailed off.
“Oh! You were joking.”
The second proton looked embarrassed for a moment, before continuing brightly “It was very funny, and there must be some sort observation we could make to see if we’re constrained by an electric field”
“Let's go this way, and see if we bounce off anything.” The first proton stopped. “I’ve never tried to point before. I can’t can I?”
“No, we lack the structure necessary to do that. Let's travel along the line defined as including both of our positions, I’ll lead” The second proton felt slightly odd taking the lead like this, and put it down to wanting to impress the first proton, who had had such an exciting life.
“But our positions can not be known accurately, so the line you describe is more a probability cone, and since delta ex times delta rho is always greater than aych bar upon two, we could well end up moving at vastly different speeds.” The proton didn’t want to lose the second proton, who the first proton thought was very cute when embarrassed.
“Or equal to atch bar. If we try to travel very slowly with root atch bar certainty, and pay equal attention to our position, we shouldn’t lose each other. We can stop after we’ve travelled a bit and check neither of us has got lost.” The second proton had a feeling that they wouldn’t lose each other, despite the first proton’s statement, and was eager to find out if it was right.
“Come on Mr. ‘I was in a neutron star, I broke the Pauli exclusion principle’ no hanging around” and with that, the second proton set off, leading the first proton. It is always possible that they swapped position without anyone noticing.
“See? Still here.” said the leading proton. “Also, movement has broken symmetry, so we can experiment with different designations”
“That’s convenient” agreed the following proton.
After a while, the following proton added: “Our motion does not appear to be impeded by an electrostatic potential, although it could be that we’re travelling perpendicular to the field.”
“but a well would have impeded our motion. If it didn’t, it wouldn’t have held us together.”
“Yes,” agreed the first proton, “we’re still no closer to working out why we haven’t both pinged off somewhere. Not that I’m complaining”
The first proton thought a bit more “Maybe it’s the weak nuclear force, I never really understood…”
“Maybe” interrupted the second proton, synchronizing wavefunctions, “it’s love”, and then the second proton kissed the first proton.