Electron-ness: Why Are All Electrons Identical? Part Three

INTRODUCTION: Individual members of the fundamental or elementary particles are absolutely identical with one another. In a police identification line-up, you couldn’t tell them apart. Why? Rather than go into an exhaustive review of the entire particle zoo, I’ll just hit on the electron and its antimatter mirror twin, the positron.

Continued from yesterday’s blog…

Perhaps in other parallel universes, ones that have different physics, all electrons (if they have electrons at all) might not be identical. That possibility is akin to asking about numbers of angels dancing on pinheads. There’s just no way of ever knowing since parallel universes are beyond the reach of science as we know it.

But say each member of the particle zoo weren’t identical to every other member in kind – sort of like the family of man (young/old; female/male; short/tall; fat/thin; black, white yellow and red). Say electrons came in a thousand variations of mass and electric charge; ditto the other elementary particles. You’d have a particle jungle. If that were the case, presumably it would prove to be very difficult to create identical atoms of the elements and identical molecular compounds and ultimately it would prove difficult to build up the structure of our Universe as we know it, including us. An analogy might be that it’s far easier to assemble a ten piece jigsaw puzzle and one with a billion pieces. Our particle zoo seems to be a Goldilocks zoo – not too many particles and variations thereof; not to few either (I mean a universe composed of just identical electrons is equally as bad for life as we know it). Of course if that – the Goldilocks particle zoo – weren’t so, we wouldn’t be here to ponder the issue.

Moving on up the chain, assuming all members of the particle zoo are identical then atoms of any particular element must be identical – if you’ve seen one gold atom, you’ve seen them all (though owning them all is quite a different matter). If elements come in different isotopes, then all the specific isotope atoms of that element are identical.

Further moving on up the chain, if identical atoms combine with other different identical atoms, then presumably the resulting molecules will be identical.  While that’s true, it’s only true up to a point, because eventually you can get molecules that while seemingly identical, have handedness. That is, your hands, while identical, aren’t identical because one has a left-handed orientation; the other has a right-handed orientation. That’s the point things start to fall apart or break down.

That apart, macro objects, like golf balls, are composed of millions of atoms and/or molecules. If a golf ball has one more, or one less molecule than another, well the two aren’t identical.

MATHS CONNECTION: Here, there and everywhere, on a flat surface, the shortest distance between two points is a straight line; triangles have a sum total 180 degrees; 2 + 2 = 4. In each case, it is so to as many decimal places as you care to calculate. Every 7 is identical to every other 7 – no more and no less. That’s true whether or not one is dealing with base ten, or in binary (base two).

So what’s the connection? All computer generated simulations, in whatever context, for whatever purpose, are ultimately software programs, which in turn are just mathematical constructions. All you see are ultimately expressions of maths, of binary bits, of 0’s and 1’s, something on or off. So if you simulate some object using binary software programming, and you create another object using the exact same binary software coding, then those two virtual objects are identical. Now, call what you have simulated, ‘electrons’. So if all electrons are identical, maybe it’s because they are mathematical constructions – the end products of computer software/programming.

In simulations, virtual objects can interact with other virtual objects (more mathematical wizardry). Change happens. Well, that’s what we observe in our reality too. The question is, is our reality really real reality, or simulated reality? Are our electrons identical because each is the product of an identical piece of binary software programming? That may not ultimately be the answer, but it’s an answer. Electrons are the same since they are all constructed from the same mathematical whole cloth of binary bits – of 0’s and 1’s. 

DISCUSSION: One may argue that there are indeed differences between electrons (and positrons), we just haven’t measured to enough decimal places yet. While that might be true, I personally wouldn’t want to bet on it.

CONCLUSION: I started out with the question of why all electrons are identical. The answer is, I don’t know and neither, I suspect does anyone else. However, the foundation of physics (itself the foundation for the other sciences) is grounded in maths, and maths, as noted above, has no problem with the concept. All identical equations yield identical results; the ‘equals’ sign itself demands identicalness. Perhaps maths has more fundamental ‘reality’ than anyone has given it credit for. That’s certainly the case if we should happen to be inhabiting a software generated, simulated Universe