Wednesday, February 6, 2008

No Infinities Principle: Proof

  1. Physics can be described mathematically,
  2. Therefore every phenomenon corresponds to an equation.
  3. Equations with infinities in them are not meaningful
  4. No variable can ever be infinite.

QED

So yeah. That's how bad modern physicists are at thinking. The proof really is that short.

Remember, they already use this principle. They simply don't recognize its full implications.

For example, as I said before, space and time are considered to be infinite by some, and this is socially accepted.

Nevertheless it is not mathematically acceptable. If space is infinite, then consider the very simple equation of constant motion in a straight line.

x=Ct That is, every second, the particle goes C meters further away from the origin.

So at t=9, the particle is at 9C. Simple.

Because space is relative, we can redefine the origin.

x - 12=Ct.

So at t=0, the particle is already at x=12.

Because space is infinite, we can redefine the origin to be infinity.

So at t=0, the equation reads

∞-∞=0

The problem is that ∞ - ∞ is undefined.

To show this mathematically, consider t!=0.

x-∞=3

x=∞ +3

Infinity + 3 is infinity

x=∞

Ergo, the particle hasn't moved. This is inconsistent. If we take any infinity to be physically meaningful, any equation with the infinite constant becomes meaningless.

The physical interpretation of this is that if space is infinite, then a particle can't ever reach a local area through finite movements. Ergo, it doesn't actually exist.

Therefore, either space is not infinite, which means the universe must have some sort of edge, or it is infinite but all the infinite space doesn't exist.

These statements are exactly equivalent under physics.

Ergo, the universe isn't infinite. It has an edge. Well...it can also wrap around in the manner of a video game world, or indeed the Earth's surface.


The proof for every other relative physical variable follows similarly.

And, out of curiosity, do you think absolute variables can be infinite? Infinite charge? Infinite mass? Infinite density? Infinite force?

Incidentally, this inevitably means that infinitesimals also cannot exist.

Because of this, I can NIP string theory right here.
  1. No infinities or 1/∞ exist.
  2. Strings are one dimentional.
  3. One of their physical properties, such as width, is infinitesimal.
  4. Strings do not exist.
QED

Now that's sad. Pathetic and tragic. Twenty years of string theory and the proof that it was mostly a waste is four lines long.

Four lines.


Similarly, we know for a fact that particles are not point particles.

A point particle has infinitesimal length, width, and depth, and therefore doesn't exist. But, particles do exist. Ergo they are not point-like.

Now, I can hear one objection. What equation uses the width or whatever of a particle?

Luckily, there is a separate proof. Given these two proofs are consistent, I use Axiom Two, say self-consistency is sufficient evidence for truth.

Here it is.

Assume our world has three dimensions of space, just as it appears to.

Assume a two-dimensional object exists. A plane, much like the thinnest piece of paper ever.

Now, according to cartoons, if you view it from the front, you'll be able to see it. However, if you view it from the side it will disappear.

We can verify that from the side, it disappears. Without width, it will not impede the flow of information from one side to the other.

But this leads to a contradiction! If the object does not exist from one angle, then it cannot exist from ANY angle! This is the principle of relativity.

To check this, ask; 'as a three-dimensional object passes through the plane, what part of the object will the plane intersect?' None. The intersection will have a volume of zero.

Look at this another way. If you stick your finger into the edge of the plane, it won't exist. It forms no barrier to entry. What happens if you now move your finger sideways? Well, it still can't form a barrier! That's relativity.

As such, true zero-dimension particles cannot exist. Therefore, they must have at least infinitesimal volume. But they cannot have infinitesimal volume, by the NIP.

As such they must have a regular amount of volume. And indeed the uncertainty principle ensures that the exact position of the 'point' particle can never be known. It always has some spatial extent.

Similarly, two colliding electrons cannot ever actually touch and produce infinite force. Either there must be a limit on their velocity to prevent them from exceeding their limited ability to produce force, OR when their maximum repulsion force is exceeded, their interaction will change them into some non-electron.

Or, you know, something completely surprising.


NIP has at least one surprising consequence. Nothing is continuous, at least physically. Everything must be quantized. Space, time, energy, everything. This is because the definition of continuity is that infinitesimal changes are allowed. However, infinitesimal changes are physically meaningless, and therefore continuity is physically meaningless. Physically meaningless things do not exist.


Also of interest is that NIP is equivalent to causality because it's equivalent to the fact that we can describe physics mathematically.

Consider any physical variable. It can vary, and it can only vary in quantum jumps. If the universe can be described mathematically, then these jumps will follow a formula. Each jump will be directly dependent on the position reached by the previous jump.

This is causality. Each cause has a unique set of effects. I say set because there is some leeway in the quantum jumps, but these are described by fixed averages, so you can't really say that causality is weakened by randomness.

(There is just one tiny problem. Particles are actually conscious. We can tell because we have brains. More on this later.)


On a human note, would you like to know how I discovered the NIP? I was considering fundamental particles one day, and how quarks are more fundamental than protons. I was wondering if it were logically possible for quarks to be made up of yet more fundamental particles.

After all, we've already gone from atoms to protons to quarks. Could we keep going? Yes, we could keep going, in principle. However, we cannot keep going indefinitely. Eventually, there must be a most fundamental particle. Otherwise it's turtles all the way down. Infinite regression.

(Note that this isn't just logically repugnant, it also violates Godel's Incompleteness Theorem. An infinite regression, if true, would technically be able to prove its own consistency. For any particle you wanted to prove was consistent, you could go one level deeper and use those particles as proof.

Because you can make the level arbitrary, this proves it for all levels. (Infinity is weird.) Godel proved that any such theorem can only prove itself by being inconsistent, and thus false.)

In short, Zeno was right, in a sense. However, he wasn't applying his theory in the right domain.

Also, he didn't know space and time are quantized, and so at some point the arrow will be touching the soldier, and one Planck-time (approx 1/10^43 s) after that, it must be at least one Planck-length (approx 1/10^35 m) inside the soldier.

Mathematically you can do continuous calculations. However, physically, you cannot.


I just found out about Compton wavelengths. These are minimum uncertainties in particle locations. These cutoffs satisfy the NIP.

Also, reading about de Broglie wavelengths, I just realized that the wavelength of a person is smaller than the Planck-length. This is why people never display, say, quantum tunneling behavior, not even really really rarely. The wavelength of a person isn't really really close to zero, it's actually indistinguishable from zero.


Notice again that physics has already discovered many of the predictions of the NIP, and yet has somehow failed to discover the NIP itself. I really do find this boggling.


So yeah. Take that, government-funded physics. Accept your ignorance lest I have to do it for you.

1 comment:

Drew Zi said...

David Deutzsche solves a lot of these problems, in his "The beginning of infinity" He also comes to the same conclusion you do about space being discontinuous in "fabric of reality". Though he still believes infinities exists, and he gives a very convincing argument that different laws of physics, make different things infinite. You would have to read his argument, I found it convincing at the time, but can't remember the ins and outs (it has been awhile since I read it).