SmurfButcher Bob's Journal: 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).