BEGINNINGS: Go to your local store and buy several items of the same product – say a package of three golf balls. Though the golf balls appear identical, closer examination will reveal ever so slight differences. One ball maybe fractionally larger; another ever so slightly less spherical; perhaps the third is ever so slightly lighter. The generality that extends from this is that any two seemingly identical products will have nevertheless slight variations in their properties.

Now buy a packet of three electrons (or their antimatter equivalent, the positron). Each electron, or positron, will be identical in size, mass and electric charge to as many decimal places as you care to measure. All electrons (and positrons) are 100% absolutely identical clones.

Take one electron and one positron and bring them together. They annihilate releasing a fixed amount of energy. Take another electron and another positron and repeat the scenario. The pair will annihilate releasing an identical amount of energy in the process. The amount of energy released in each electron-positron annihilation case is the same, to as many decimal places as you can measure. That's quite unlike taking a match from a box of matches, striking same and releasing its stored chemical energy as heat energy. Another match from the same box wouldn't release, to as many decimal places as you care to measure, the absolutely identical amount of heat energy.

WHY IS THIS SO? #1: How come identical golf balls aren't but identical electrons (or positrons) are?

Electrons (or positrons), having mass, can be created from energy (just like mass can be converted to energy as in the case of the electron-positron annihilation process). You (human intelligence) can't create identical golf balls, but a seemingly non-intelligent natural process (Mother Nature by any other name) can create or produce copies of a fundamental particle, like an electron (or positron), that are clones of one another down to the nittiest-grittiest detail.

Even with quantum mechanics in force, you'd think energy could create or be converted into an electron with twice the standard electron mass or twice the electric charge, or thrice even. But no. You see one electron you've seen them all – every electron that is, was or will be, anywhere, everywhere, anytime, every time in our Universe.  Electrons, like Black Holes, have no hair. That means they have no individual personality. In fact Black Holes can be said to have some fuzz because they can and do differ in terms of size, mass and electric charge. Electrons have the exact same size, mass and electric charge, so absolutely no hair!  Relative to Black Holes, electrons (and positrons) are absolutely bald!

Invoking all things quantum is still a bit of a copout in that while quantum means things are this or that, one unit or two, one energy level or two energy levels, there's no explanation as to why it's only one or two, not one & a half. It just is, but why remains a mystery.

SO, WHY IS IT SO? #2: Why are all electrons (and positrons) identical?

1) Of course THE copout answer is that that's just the way God wanted it and no correspondence will be entered into regarding the matter.

Unfortunately, there is no real evidence for the existence of any deity past and/or present that stands up to any detailed scrutiny.

2) One could resort to an explanation via string theory merged with quantum physics. String theory just replaces elementary particles as little billiard balls for elementary little bits of string (albeit not string as we know it). Now maybe, as in all things quantum, these strings can be one unit in length, or two units, or three units, or four units, etc. Any positive whole number multiple of one string length is okay.  Now say that a two length unit of string is an electron. A two unit length of anti-string is therefore a positron.

Or, one can suggest that strings vibrate and can only vibrate at specific frequencies as any musician playing a stringed instrument knows. So, a string vibrating at one allowed frequency is an electron; if it vibrates at another allowable frequency maybe that's a proton or a neutron. Again, a vibrating anti-matter string would produce manifestations of the antimatter particles, a positron being dependent upon one of the allowable vibrating frequencies.

Of the two possibilities, it's the vibration rate theory that's preferred. All strings are of the same fundamental length – their rate of vibration can differ, but at precise intervals. What causes strings to vibrate at the rate they do, and how they can change rates of vibration (morph from one kind of particle into others) are questions better left for another time.

Unfortunately, string theory has no credibility in terms of any actual experimental evidence, and, to add insult to injury, it requires the postulation of ten to eleven dimensions in order to fit the pieces together. If string theory gets some experimental runs on the board then, and only then, will it be time to take strings seriously.

3) Well, one other possible explanation is that all electrons are absolutely identical because there is only one electron in actual existence. If you see the same object twice, thrice of a zillion times over, then it's the same object and the fact that it is consistently identical is not a great mystery. But how can the Universe contain only one electron? That seems to be the least obvious statement anyone could ever make – the statement of a total wacko.

Well, one explanation goes something like this. Our one electron has zipped back and forth between the Alpha and Omega points again, and again, and again. Now multiply ‘again' by zillions upon zillions upon zillions of times. When you take a cross section at any ‘now' point in time between the Alpha and the Omega, there will be zillions upon zillions upon zillions of electrons visible ‘now'. Simple, isn't it?

Unfortunately, while there is no violation of physical laws at the micro level in travelling through time (apart from going forward at a rate of one second per second which we do whether we like it or not), no exact causality mechanism has been proposed to explain how and why an elementary particle shifts gear into time reverse (or forward again). But, this is interesting, this time travel bit, so let's explore it in some greater detail.

I'll poor water on this fire at the outset by stating that time is but an illusion. Time doesn't exist; therefore time travel isn't possible. Time is but a label and has no more reality than the label ‘Wednesday'. We just arbitrarily call every 7th ‘day' Wednesday, but you can no more hold Wednesday in your hands and you can time. Time has no independent reality. You can't assign any physical properties to the concept. I mean time isn't a solid, it isn't a liquid, and it isn't a gas. Time has no size, weight, colour, texture, density, it doesn't vibrate or have a wavelength, ditto no odour or flavour, it has no temperature or pressure, it doesn't consist of any known combination of known forces and/or elementary particles, it corresponds to no known element or compound. You can't pour time into a bottle and store it; you can't confine time in a force field or in a prison cell or trap it on a piece of sticky fly paper. Therefore, if time has no substance, one can not actually travel through time. Our sole electron (or positron) isn't going anywhere – in time at least.

What we perceive as ‘time' is nothing but change – change in our environment; in our natural world; in our mechanical devices; and even in ourselves and associated companions (animal and human). Repeat – time is but an illusion. Change is real since it involves forces and particles; energy and matter, the sorts of things that when you kick them, they kick back. We measure ‘time' by the rate things change; rate of change is what we call ‘time'. Repeat - it's the change (in something) that is real. 

Now on the macro scale, that is scales we interact with on a day-to-day basis, change appears to all intents and purposes to go one way (usually from a state or high order to a state of disorder) and so we view time as flowing from past to present to future – in one direction; order to disorder – past to present to future. But change in just one direction (order to disorder – past to present to future) is ultimately a function of numbers and probability. The simple illustration is to introduce a drop of ink into a bowl of water. That's a high order situation. Now left to itself, there will be a change. The ink will disperse throughout the bowl of water. That's a state of disorder. If a disordered uniform mix of ink and water separated all by itself into a drop of pure ink and a bowl of pure water (high order), that too is change, but we would interpret or view such an event as going backwards in time. If you viewed such a happening on film, you'd immediately conclude the film was being run backwards.

There's a far greater probability for individual ink particles to spread out throughout a large volume than to come together in a small space. There's lots of pathways to spread out; far fewer pathways to come together. But at the micro level, the level at which those individual ink particles do their thing, they don't care where in the bowl of water they are. They are just as ‘happy' to be all together as a drop of ink, as dispersed and diluted. If they do come together as a drop of ink from a dispersed/diluted state, that's statistically unlikely, but such an event violates no laws of physics. It would be going from a state of maximum disorder to a highly ordered state; or, from an apparent future to present to past ordering. Such a change would appear for all practical purposes as apparent time travel – going backwards in time.

The catch – there's always a catch – is while all those ink particles are defying statistical probability and undergoing apparent time-reversal, the rest of the cosmos is acting in a statistically normal way – going forward in ‘time'. So, perhaps we have a Universe where for 99.9999% of the time, 99.9999% of events within the Universe march to the beat of the standard past – present – future ordering of things. That is, in terms of change happening in a statistically probable way. While now and again tiny pockets of the Universe reverse direction, they do so at least just temporarily.  One can only defy statistically probability for only so long. So the ink particles come back together again as a drop of ink within a bowl of water – then what? They no doubt reverse direction again and proceed normally.

An analogy might be that while some individuals are winners while playing the slot machines (high order), the club still rakes in the profits from the vastly greater majority of (disordered) losers, and that no doubt the few highly ordered winners will eventually descend into a state of disorder and contribute ultimately to the club's profit margin! It's more statistically likely for a winner to become a loser than for a loser to become a winner.

Back to electrons, on average, any given electron has a very high probability of participating in a changing set of circumstances consistent with statistically probability. That is, the electron is moving forward in ‘time'. But if in those rare (loser to winner) occasions the changing set of circumstances goes against the grain of statistically probability, then we would view that electron as moving backwards in ‘time'. But there ultimately is no backwards or forwards in time, just change which statistically goes or moves in one general direction (order to disorder), but which can now and again, and briefly, go the reverse direction (disorder to order).

To belabour the point, what we call the past is change which has already happened; the present is change which is happening; the future is change that will happen.

The question remains, can you revisit and experience a past event? Can there be an instant (or not so instant) replay? Take the example of the now dispersed ink in the bowl of water. If all the ink bits (particles) were to exactly retrace their movements (that's just so highly improbable that you'd wait longer than the age of our Universe to actually see it), they would eventually come together as an ink drop. If they now retrace those retraced movements (ditto on the statistical improbability) you get back to the exact same configuration of dispersed ink bits in the bowl of water. You will have witnessed an instant (or not so instant) replay of a past event. You would have in a sense travelled back in time to record an event that had already happened. Of course you would have ‘time' travelled with respect to that specific event and only that event.

Ah, that word ‘record'. Of course you could have filmed the original ink drop to dispersed ink event then watched the film at a later date, but that's cheating a bit, don't you think?

Okay, all that was an aside – back to the original question, why are all electrons identical? Or not, as the case may be.

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