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Axiom Verge

Submitted by Thomas on Sat, 2012-04-21 05:43.

I've finally announced my new game, Axiom Verge.  You should probably head over to that site for the foreseeable future, as it is where my attention is focused.  

The new site uses Squarespace, so it shouldn't have the issues this one had where modules become out of date and spam takes over.

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Big O and Pythagoream Theorem

Submitted by Thomas on Tue, 2012-01-10 20:46.

Earlier I mentioned the issue of representing space as a 3-dimensional array and light as a propogation of data from each cell in the array to its neighbors - namely that in such a representation, the number of steps between any two points is X + Y, whereas in the real world we have measured this distance to be C^2 = A^2 + B^2.

Here is a picture I drew of that representation, to refresh your memory:

 

The simplicity of this arrangement appeals to me - I see it as a kind of 3-dimensional lambda calculus -  so I'm hoping there is some kind of transformation by which a 3d array could be the underlying representation of our universe, even though, when measuring distances, we still end up with A^2 + B^2 = C^2.

At the forefront of my thoughts is algorithmic complexity - or Big O; basically the measuring of the number of steps to complete a task.

Beware:  Gross oversimplifications incoming! 

In the diamond diagram above,  it takes 4 steps for the light to iterate a distance of 4 pixels horizontally or overtically, and 8 steps for it to iterate a distance of on the diagonal.  So in the worst case it would be something like O(N).

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Interference Conundrum

Submitted by Thomas on Fri, 2011-12-30 13:33.
Earlier I was thinking that each frame, a random pixel of an advancing wavefront would be selected, and if it happened to 1) not interfere with itself and 2) run into a solid object (whatever *that* means), the entire wave is removed and the light is reflected from the new point. But the notion of "advancing wavefront" is a bit debatable, since the troughs also form their own wavefront. So they would need to have the same randomly selected pixel chosen in order for interference to occur. But by extension, this means that each emitting electron must pick the same random pixel for the duration of emission (which I thought to be constant for the life of the electron).

Is it just that each electron is assigned a random id at birth, and this somehow indexes the emitted points of the wave (maybe with a modulo over the number of points at a given distance)?
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More Musing on Electric Fields

Submitted by Thomas on Wed, 2011-12-21 20:47.

So, if the electric field propogates like light - where each point on the field is like a new point source - how is that different than saying that all of space is filled with electrons?  Is it just that there's enough positively charge fields that the two cancel out?

Also mind bending is the thought that the field is radiatiating out from the electron each frame, but the electron itself can also move.

And when it does so, it leaves a gap behind it, in a shape of an expanding half-shell.

I know that magnetism is supposed to be created by moving electric charges, so it would have been good for this explanding half-shell to explain this, but my understanding is that the magnetic field travels in a circle around the direction of movement, while this gap is moving in the opposite direction.

There is also the problem that if electrons are forced to move in discrete increments of planck length, then when it moves, it's running into its own electric field.  Why doesn't the field repel it?  Is there some notion that fields ignore the source they came from?

Or, perhaps, the field is repelling it.  Could it be that "mass" or at least "inertia" is just a measure of how much objects are pushed back by their own electric fields?

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More Conjecture On The Electric Field and Light Propogation

Submitted by Thomas on Wed, 2011-12-21 03:51.

While I was trying to come up with a way to represent the electron's field in a way that could be proportional to the surface area, I imagined that each pixel (voxel?) along the surface contained a fraction of the charge/field/force/whatever, thus explaining why the force decreases as the surface area increases.  But how is each pixel informed of how much force it has?  Does it divide evenly every update?  Is there some limit past which it can no longer divide, being reduced to the smallest integral number?

So instead, suppose it's something like the way I thought light could behave - for each update, a random point is chosen along the advancing diamond, and if this point intersects with an object, the force is applied.  Then it would be the same force no matter where the intersection happened, just that your probability of being hit by that force increases as you get closer.  Though I'm not sure if that section of the the field is now absorbed or if it continues onwards.  Do electric fields become weaker as more things get pushed around by them?

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Coulomb's Law in Array World

Submitted by Thomas on Tue, 2011-12-20 21:07.

In an effort to better understand what an electric field is - and thus gain some notion of what an oscillating electric field could be - I decided to start with the the force exerted by static charges.

In our world, this is represented by

F = q1 * q2 / (4 * pi * r^2 * E0)

Where F is the force, q1 and q1 are the charges, and E0 is some ridiculously complicated constant called the permitivity of free space.  Since I'm pretty far from understanding what E0 is under than "some unchanging number", I thought I would look at the others.

The "4 * pi * r^2" refers to the surface area of a sphere.  So basically this means that the force is divded up evenly around the sphere defined by your radius.  But in Array World, there are no spheres, just diamonds, so we'll need to find the surface area of a diamond for this.

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More On The Double Slit

Submitted by Thomas on Tue, 2011-12-20 05:41.

I did another rendition because the wavelength I chose earlier was too small to really see the geometry of the pattern.  As you can see, it's argyle.

What really confuses me - both in my made-up Array World and in real-world examples - is what is actually meant by "cancelling out"?  Experimentally, it signifies that the probability of a photon appearing at that point is 0, but how does this happen?

What it boils down to is that I'm really baffled by the notion of electrons emitting photons when they change state.  Experiments show that the amount of potential energy the electron lost in the drop in orbital is proportional to the frequency of the light emitted when it does so (Freqency = Energy / Planck's constant).  This same frequency is what determines the diffraction pattern you see - a single photon interfering with itself.

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Double Slit Diffraction in Array World

Submitted by Thomas on Mon, 2011-12-19 21:09.

Here's an approximation of how it would look.

It took all lunch break for me to figure out how to make this in Photoshop, so no description for now.  I think I'll post one more update on the subject, but after that, I think the math is starting to go over my head (especially once I tried to look at the equation for an electron orbital, and remembered why I switched majors back in college). 

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Faster than light possible in Array Land?

Submitted by Thomas on Sun, 2011-12-18 13:16.
It occurs to me that, considering the lack of a square root in time dilation and length contraction, speeds faster than light may be entirely possible in Array Land. And we've just started accelerating neutrinos faster than light. Hmm.
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On the other hand . . .

Submitted by Thomas on Sun, 2011-12-18 01:08.

. . . Maybe I'm not as wrong as I thought.

It turns out that the time dilation derivation I found on the web is based on light moving perpendicular to the direction of motion.  In the direction parallel, these don't work because the person on earth thinks the person in the rocket has measured it as squished, which is in keeping with the light reaching the back of the rocket earlier than the sides.

So for the sake of time dilation, we only need be concerned with the sensors on the left and right.  The guy in the rocket sees the leading edge hit on frame 4, the guy on the ground sees it hit on frame 8.  This fits with the Array Land version of relativity, where T' = T * (1 - v/c), because 8 * 0.5 is 4.

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