A Pauli game
Pauli's exclusion. Naievely put, two things cannot share the same state. Simple.
Let's tweak it a little, and see what happens in a given case. And yes, I do have an agenda with this. In no way do I suggest that any of this is correct, or relevent. It *will* be consistent relative to itself, however.
We're going to change Pauli to include the object in question - no two states the same, which includes the object itself. Once it is in a given state, it *must* change.
Now, let's make a 5-space. It'll be our typical XYZ, plus a B that we don't perceive (which is just a plain-old axis, just like X and Y and Z, and it is orthogonal to them), and a time (which is also just a plain old axis, orthogonal to the rest).
Let's stuff a singularity S at our origin. Our universe is born, we now have an object, and it has "state" as defined by our space. There's a problem - S has state, and our modified Pauli says it has to change. So, it moves. How far? How fast? Well, far and fast enough that it'll resolve the exclusion - per "tick" of the clock, it'll move its own radius from where it was. Also note it cannot go backwards - that "state" is already occupied.
Note that it doesn't matter what direction it goes - any will do. Just for yucks, let's say it initially started moving along B. We can easily have picked X or Y, but let's pick B.
Within the XYZ subspace, S isn't moving. Neat, huh? That's why we picked B.
So, let's give our little friend a kick in the pants. We induce a small velocity along X.
Question - it's been trucking along B in order to resolve the exclusion, at the rate of one radius per tick. Now that there's an X componant to it's velocity, does it need to travel along "B" a full radius?
Nope, it doesn't. "Speed" along B will decrease. In fact, if we "kick" up the speed along X to the point where S is now moving "one radius per tick", any speed along B will go to zero, won't it? After all, the displacement "per tick" along X is now adequate to fully resolve our exclusion.
So, we've created an interesting game which effectively has a similar rule to one in real life - there's no such thing as a standing wave.
We can expand our game a little bit - let's get rid of B.
Instead, let's say S initially "decided" to start travelling along T. How far, how fast? Again, one radius. (Yeah, I know there's a contradiction floating around here in regards to the definition of Time. If we're allowed to neglect friction, we can neglect this too. We're demonstrating a concept.)
So, S is cruising along T... and again, within our XYZ subspace, you and I would not perceive it as moving. We start our displacement along X - and S slows down along the T axis. How much? Well, Pythagoras solved that one - a^2 + b^2 = c^2. Keep pushing S faster along X, and displacement along T slows down even further. Finally reach the speed along X that resolves the exclusion? Displacement along T stops dead in its tracks. S is still moving, though, you'd better believe it.
Let's modify our game once again. By virtue of the exclusion, we've effectively asserted that S must move one radius per tick. The result, when XYZT is viewed as "flat" and "static" (unchanging) is that S is a long smear. There is no "time" in this view; all of the positions of S are kinda glued together to form a solid extrusion.
We're going to add a new assertion - when our space is viewed this way, S must be *continuous*. No gaps, breaks, cuts, jumps. Switching back to our "more normal" 3-space + time, this means that S *must* move one radius per tick, never slower, and *never faster*.
Moving faster, after all, would cause a break in the continuity we just defined.
So, let's replay our game one more time. Add speed along X, and T slows down etc. Keep going faster along X until displacement along T stops. Try to go even faster along X - and you can't, you'd "break" the smear (extrusion).
Do NOT try to apply this game to real life; the first thing you'll notice is that, if you *reduce* the speed along X, the exclusion must be resolved by a displacement along another axis - and no duh, that's the whole point of the game. But you'll notice that there is no rule for *which* axis that'll get picked - B, Y and Z are all just as likely. We don't observe that in real life, though - when I hit the brakes on my car, it doesn't usually start sliding sideways or flying. Usually.
Still, it's interesting to see the effect.
If you're *really* bored, (and I mean **really**), follow up on the a^2 + b^2 = c^2 thing. It'd be merely an exercise, but attempting to relate it to inertia / mass increases at relativistic speeds might be fun (even if futile).
Regarding space being a 3D thing or not - it's all about perception, and perception is why it's such a challenge.
Consider something, a game merely provided as a thought experiment.
Consider a creature who lives in a 2D world... that is, his perception is limited to exactly one single plane that is infinitely thin. Grab a stiff sheet of paper, neglect friction, and pretend it has no thickness. We're going to try to see what our creature sees, the same way he sees it, and eventually see how it scales as "dimensional perception" increases.
Take a round pen, and "intersect" the middle of it with our plane. ----|-----
Our creature will perceive the pen as a circular wall... remember, he has no concept of "up" and "down". Easy.
Spin the pen in various directions, and note what happens - and remember, we're only interested in that infinitely thin section that our creature can perceive. You can produce spin 0 (if the pen is a cyllander), spin 1, spin 1/2, spin 2... you can create all types of "spin" based on the direction you rotate it. Interesting. Note that this is not necessarily the same "spin" that the quark-heads talk about, but it demonstrates a fair part of the concept. It certainly demonstrates the concept of things "coming into view", and will probably make our poor creature pull his hair out. It's especially interesting because our creature sees the pen changing - shape, size, you name it - but you and I know that the damned pen isn't changing one bit.
Now for a really neat demo - tilt the pen, and hold it still. ------/-----
Without rotating the pen, move it straight up or down. What's our creature going to perceive? Yep... he'll see the "pen" (the big circular wall, which is now an oval due to the tilt) moving across his plane. That's neat, and a good concept demonstrator - but it isn't the really cool part. The really cool part is that he'll see the pen moving along the X-Y plane- despite the reality that it's really moving along the (unperceived) Z axis. You can see that the pen has no horizontal motion whatsoever - yet, horizontal motion is exactly (and only) what he perceives. Take a second to reenforce why he perceives it that way, and make the reasons work. Remember, we don't care what his perception is, there is no horizontal motion in reality. The motion is all in the unperceived vertical. Period. The only thing changing (not moving, but changing) is the point of intersection with his ability to perceive, the cross-section within his perception.
Finally, grab a more complex object. Something fun - a coffee mug perhaps, or a fork, or even a pair of scissors. I'll use scissors, because I enjoy cutting things... and when we're done, we can use them to wreck havoc on our creature's universe.
Open the scissors up a little, and hold them below the sheet of paper. What's our creature going to perceive? Nothing.
Now, lift the scissors and stick the points into our creature's plane of perception.
Our creature will perceive the scissors as intially one, then two completely separate objects as the points come into view, right? And what else... they will appear to spontaneously exist. Of course, you know that the scissors have always been there, just not within the creature's view.
Things get interesting, though - if our creature decides to kick one of those objects, he'll notice that the other object moves a little. It'll make no sense to him - the two objects have nothing to do with each other, yet they almost seem to be... I dunno... entangled somehow. (And no, I'm not suggesting that this is how entanglement or pair production works, this is just a method of showing how a limited perception can create the illusion of such a thing.)
Move the scissors up, and notice that our creature would see the two objects moving toward each other, and also get bigger (as each blade gets thicker). Keep moving up, and our creature will be astonished when they actually merge (at the hinge-point). Keep moving up more, and more, and the creature will become baffled as the merged object suddenly breaks back into two separate pieces, moving away from each other. Move it up some more, to the handles and beyond, and our creature will see the two chunks break into four (when the handles are intersecting) then back to two (and the end of the handles), then suddenly shrink away to nothing!
Wash, rinse and repeat the game with something incredibly complex, like a lawnmower. Our poor creature is going to need a good stiff drink after trying to explain this one to his friends, I tell ya...
The one very cool thing about this entire game (and it is merely a game, it is not reality by any stretch) is that we've beaten the 2D perception of a 3D object to death, so we can see how it scales up. What we can do now is repeat the game, using a 4D object - namely, let's introduce what we perceive to be time into our game. Do this any way you like - open and close the scissors, spin them as you move them up and down, let them rust, whatever. You will rapidly discover that our (now hopelessly confused) creature cannot differentiate the 3D game from 4... he won't be able to tell how many dimensions we're throwing at him. He'll perceive them all as one single "dimension" that he calls "time". Think about when we played the game the first time - what we call Z in our perception, would be "time" in his, right? We then replay the game with both our Z and our time, it's still just "time" in his. He cannot tell if there is only one unperceived dimension, or one hundred... these extra vectors are all summed together into one, for him.
Now, stick your head out the nearest window, and watch a car drive by. You should be able to see it in a whole new way - as if you were some poor (hopefully drunk, by now) creature, perceiving a shifting 3D cross-section of a god-knows-how-many dimensional *static* object. There's still motion, for sure - but it isn't necessarily the object that's "moving", is it :) The thing that's actually moving just might be the point of intersection between our... uh, perspective-space and the object, and the "object's motion" is merely a side-effect of us only seeing a limited cross-section of a larger-dimensional solid.
I'm not suggesting that this is the case, but suddenly a photon spontaneously changing into an electron/selectron pair that move away from each other suddenly takes on a whole new... view. Or, the right-hand-rule - an electron following a helical path in an E-field? What if we took our pen, and made it wobble as it moved along? Fun games, regardless of how wrong they are.
It's all about perception, or lack thereof.