Is it an epistemic possibility that there is only one electron in the universe — and by implication, I suppose, only one photon?
Do you mean epistemically possible given what we know about physics, or epistemically possible given what we know about logic? (Or something else?)
If physics, I remember when I was a kid I read that some theory or other has it that anti-particles are particles travelling backward in time, and that this in turn makes it possible that all electrons and positrons are in fact the same object zigzagging back and forth through time.
If logic, then even if the above scenario is physically impossible, I’d bet it’s logically possible. (Though I’d like to know what makes the particle “bounce” from time-direction to time-direction. That kind of acceleration may be impossible for reasons that aren’t just physical but mathematical, and if so, it may actually turn out to be logically impossible. But hey, if we’re talking about “logico-epistemological” possibility, then who says instantaneous acceleration isn’t “logically” possible?)
Well, I bet you were hoping for an answer from someone who actually knows something.
-FrL-
I can’t speak to the scientific implications (which is why I ask the question here), but I do believe there would be several philosophical implications. For example, such things as the orbits of electrons, or the emission of photons by collapsing electron orbits, or even the whole idea of cardinality and ordinality of any kind associated with them would become merely attributes of the single electron.
And thanks for asking for the clarification. I do indeed mean epistemically possible given what we know of physics. I think that whether there is a metaphysical possibility might be undecidable.
The notion sort of works for electrons, or any other fermion, in some cases, but it doesn’t work at all for bosons like photons. And even for electrons, you could, for instance, produce an electron and positron via pair production from a couple of photons, separate them, observe both separately, and then re-annihilate them: This would then be an electron which is definitely not the same electron as any other electron in the Universe. It’s even simpler if you allow non-electromagnetic interactions: The beta particle produced in the decay of a neutron is an electron which has a definite endpoint: There’s no electron in the neutron before the decay, but one comes out of it. As long as you have two or more beta decays in the Universe, you have too many endpoints for just one electron.
It was a reasonable suggestion at one point, but I beleive subsquent observations made it unlikely. I seem to the remember the book Schrodingers Kittens and the Search for Reality discusses this theory, amoung others (it’s the sequel to the excellent In Search fo Schrodinger’s Cat),
I always love hearing about bad ideas throughout history, and would appreciate hearing what this “one electron” theory is. I am having a really hard time even guessing the postulate. Does this electron travel in time, passing through the universe countless times each in a different place, interacting with itself?
That would be awesome!
I kinda jumps out at you if you draw a “Feynmann Diagram” like this of sub-atomic interactions. The “x” dimension represents time, the “y” dimension space.
One way of looking at that diagram (the obvious, “sane” way) is this:
An electron in the top left of the diagram (represented by e with minus) is travelling through space, getting closer and closer to a positron in the bottom left (an e with a plus). The two colide, and are destroyed, causing a release of energy (the squiggly line) then some other stuff on the right hand side of the diagram (which I’ll leave to someone who acutally understands this crap to explain).
However you could equally look at this diagram like this:
There is only ONE electron in this diagram. It starts in the top left of the diagram travels for forward in space and TIME. Until it spontenaously releases some energy (not such a crazy idea in quantum theory) and rebounds in the oposite direction in space and TIME. What one interetation sees as a positron the other sees as an electron TRAVELLING BACKWARDS IN TIME!
Doesn’t motion through space imply motion through time since there is only space-time? The question raises another philosophical implication — namely, that the electron (if there is only one) would be everywhere at once.
Not for fermions (the class of particle that electrons belong) there is no “arrow of time” for fermions.
We observe a lot more electrons than positrons. If there’s only one particle shuttling back and forth in time, where are the rest of the positrons?
That’s a question that comes up regardless, whether there’s one electron or many. To date, nobody has more than a vague inkling of a guess as to why electrons are so much more common than positrons. It’s possible that all of the positrons are in a different portion of the Universe, but if so, they’re so far away that we can’t hope to ever see them.
Why is that, Chronos? Why isn’t it possible that you’re observing some aspect of the one electron — some sort of “bump” or spike or something? (Your other example I really didn’t understand.)
That’s not too far from the truth to a certain degree. An electron either free or confined in a potential well (say an atom) can be represented by a wavefunction which will extend to infinity.
Therefore any electron will have a small but non zero value of being able to be found anywhere in the universe. It is of course very unlikely that it would be found in Alpha Centuri if it were confined to the shell of a hydrogen atom, but it is possible.
Of course according to quantum mechanics there is a non zero probability that a ball bouncing off a wall could go through the wall, but it’s not really likely.
To answer your first question yes, motion through space implies motion through time, but in one direction. i.e. towards the future. According to Einstein in order to travel into the past you need to travel faster than light.
So IMHO it’s possible, but unlikely that positrons are electrons travelling backwards in time.
For either example, it’s important to realize that a particle isn’t just a single point. It’s got zero (or very close to it) length, width, and height, but it has a nonzero duration, so in four dimensions, an electron is like a piece of string (not particularly related to the String Model) extending through time. You could, if you liked, make a very complicated tangle of string, with it going back and forth across some region, with as many strands crossing the region as you like, but it’s still only one string, and all those strands you see are just part of the one string (think of Cat’s Cradle, say). This is the origin of the idea that there might really be just one electron.
But suppose that you found a complete loop of string in your tangle: You start at one point on the loop, follow the string all the way along its length, and end up back at the point you started with, without ever getting to any of the other strands in the tangle. In that case, you know that that loop of string isn’t the same string as all of the other string in your tangle. That’s analogous to the pair-production-and-annihilation example I gave.
Likewise, suppose you found, somewhere in your tangle of string, an end. If you find more than two ends to your tangle of string, then you know for sure that there’s more than one piece of string, total, in your tangle, since a single piece of string only has two ends. That’s analogous to the beta decay example I gave.
It was the late great John Wheeler who came up with this idea, but soon rejected it. I think his one-time grad student Richard Feynman wrote about it in one of his books.
Thanks, Chronos. That was a very informative analogy.
The original suggestion was far from a “bad idea”. Nobody took it that seriously in the first place, but it suggested something that was immensely useful to theoretical physicists.
As bibliophage has noted, it was thought up by John Wheeler, but I’m not aware that he ever did much with it in its original form and I don’t think he ever mentioned it in any of his technical papers. The person he did tell immediately was Feynman; from his Nobel lecture:
This latter realisation is now a standard part of how physicists think, but was new at the time.
And to give credit where it’s due, the idea that a positron is an electron travelling backwards in time was - like quite a lot else - independently thought up by Ernst Stückelberg at much the same date. But without the additional notion that this might allow there to be only one of them.
Huh, I hadn’t realized that the “one electron” idea was the origin of the “positron = electron backwards in time” idea. I had thought it was the other way around.
Well, in his autobiography Wheeler implies that the two ideas came to him that same evening, possibly simultaneously.
The idea that Feynman “stole” does now seem so obvious to us that it is perhaps difficult to realise how non-obvious it was in 1940-1. But have a look at his 1949 paper “The Theory of Positrons” (Phys.Rev., 76, 749) where he first discusses the idea in print. He has to spend quite a bit of the paper explaining the idea. (As Feynman acknowledges in a footnote, Stückelberg had got the idea into print in 1941, but without making much of an impression.)
What you have to remember is that any notion smacking of a “trajectory” for a quantum particle at the microscopic level was pretty taboo at the time.