Apr 00

zero dimensions

okay, this one’s going to get a little weird (as if they haven’t in the past)

someone emailed me about a previous rant where i said i would be able to prove that the universe was zero-dimensional. i’m not sure this is what anyone would call a proof, even the most liberal of philosophers, but it’s a fun little exercise, nonetheless, and something i thought long and hard on at the time. i was in high school when i first had these ideas, and i think that says enough.

first of all, let’s look at the universe. more than the three dimensions we can experience, aspects of it can be expressed in any number of dimensions. that is, it is n-dimensional. defining a new dimension along which to look makes some aspects of the natural world that much easier to nail down and understand.

so, what’s this n-dimensional universe made of? it really boils down to two things. well, one thing, and one not-thing: matter and space. matter – that is, matter and energy, since we know the two can each be considered in terms of the other, and, indeed, converted between (thank Einstein) – is all the stuff that is in the universe, and space is the non-stuff that is in between. make sense so far?

let’s look at matter first – it will make space seem that much easier later. matter is quantifiable, in that every bit of it can be summed up as a collection of a certain number of elementary particles – constantly changing, incorporating, evaporating, but still quantifiable. at first, the definition of ‘atom’ was that it was the smallest indivisible piece of matter, but since we started doing things like splitting them, that definition has changed to say the smallest piece of an element that is still that element. atoms, we come to find out, are made up of smaller bits, and those bits are made up of even smaller bits, quarks and gluons and the like. eventually, we may discover that all these quarks are really just clumps of congealed energy, or collections of some other, smaller particle, but i’m rather certain that, at some point, there will be bits of matter that won’t be divisible.

in any event, no matter how large a chunk of matter is, at any moment, it consists of a quantifiable – if really, really, large – number of particles. and every chunk of matter, no matter how small, acts on every other chunk of matter in the universe, at a distance, and in some ways – and this is a really sticky point – instantaneously.*

*there has been some work recently on a theoretical link between certain particles that, in fact, is instantaneous over any distance. to readers of science fiction, it proves that communications at faster-than-light speeds are possible, something writers of science fiction have been writing about for some time, but have never really had any good proof for. so, to vindicate the science fiction writers, some experimental physicists took a particle and split it into two identical pieces (the details of which are more than i can remember at this point, it may have been a particle and its anti-particle. for this discussion, it makes no difference). they then separated the two pieces and moved one sufficiently distant from the other that there could be no doubt that they were no longer the same particle.

at this point they started to futz with the first half, changing its spin or charge or something (i think it was spin, since everything seems to have a distinctive spin) and lo and behold, when they measured the second half, it was found to be spinning in the same manner as the first. it had been effected at a distance, and seemingly instantaneously, without their intervention.

that last part poses a problem. read it again. gravity, for instance, is proportional to the size of the two bodies in question, and inversely proportional to the distance between them. some seem to think gravity is intantaneous, and others that it is limited to the speed of light, but it makes little difference at this point – you’ll find out when i tell you about time. gravity’s effects are proportional, but never zero, since the distances between things is never infinite.

or is it?

let’s look back at space again. the space we normally experience is three dimensional – nevermind time for the moment (inadvertent pun. sorry) – and those three dimensions define the position of everything, and the distance between any two things.

but is space quantifiable, as is matter? no. there is no smallest distance that cannot be divided in half. it’s not as if there is a simplest unit of distance that any other measure can be expressed in terms of. even the international standards organizations express standard distances (meters, kilometers, etc) in terms of matter, chunks of matter that are one meter in length, a kilometer one fraction of the circumference of the earth, etc). if there were a universal measure of space not dependent on matter, it would have to be infinitesimal, that is, infinitely small. let’s call them smidges. so two points in space, no matter how close (so long as they’re not the same point, that would get too complicated for now) would be an infinite number of.. smidges.. from one another.

for a particle to move from one point to another, it would have to cross infinite smidges of space. the same can be said of any force acting over a distance, that the distance must be infinite smidges.

and since a smidge is infinitely small, even an infinite number of them is still no distance at all. which is my point, really, that there is no such thing as distance. which makes things like gravity, and other forces that act over a distance, very simple indeed.

and how can something move from here to there? it would have to move an infinite distance, thus at an infinite speed. or else, no distance, and thus, no speed. and yet, we know that things do move from place to place, and that bits of matter are effected at a distance by other bits of matter. but, since the distances involved – since space cannot be quantified – are really zero, everything must be adjacent, and really be sitting still.

so there’s no such a thing as distance. or space, for that matter, in the three dimensions we normally think of. if there’s no space, and no distance between things, then every particle of the universe is adjacent* – which makes all the stickiness of gravity, magnetism, and the like, very simple indeed. if every particle is adjacent, and there’s no distance between them, it’s a simple matter of seeing how they can effect one another instantaneously.

that is not to say that every particle inhabits the same point in space. remember, in zero dimensions, there are no terms to define a point in space. suffice it to say that, when nothing has a size or distance, or space between, everything is simply adjacent to everything else.

by the same token, time, as it can’t be quantified – there is an infinite number of instants between any moment and the next – doesn’t exist either. any measure of time ends up being an infinity of instances (and all infinities, big or small, end up being the same size, relatively, and just as troublesome) and, as before, an infinity of infinitesimal measures is still zero, and so every point in time is the same as every other.

and as time collapses in the same way space did, any number of dimensions will collapse.

and thinking of the universe as zero dimensional, rather than n-dimensional, really makes things simpler to understand. to me anyway. and am i right? probably not. there are holes in this that even i could drive a truck through, but it makes some things easier to understand, in much the same way that thinking in terms of an n-dimensional universe makes some things easier to understand.