Flatland Turned on Out

By Eric Eliason

This book seeks for straightforward, understandable common-sense explanations to the problems of science. We go from math and topology to Physics and Chemistry directly to biology and Psychology. Math is used to understand the concepts rigorously while imagination helps get rid of the mysticism and there are Layman's sections throughout the book.

• Language: English
• Publisher: BookBaby
• Release date: Sep 11, 2017
• ISBN: 9781543946291

Book preview

everything

A Brief Note about the 0th Dimension

If we have one point, it cannot be empty or it doesn’t exist and it cannot be full or it has no consistency. At the end of this book we will show that when we have the state jump back and forth without repeating or randomness at an infinitely fast pace, we not only cover the 0th dimension but it is equivalent (isomorphic) to other dimensions, thus explaining them.

The First Dimension

We shall cover how everything in general works up to be like our lives!

No time:

We will use Newtonian Mechanics, Special Relativity, Electromagnetism, and Quantum Mechanics but in a straightforward manner.

Starting with Newtonian Mechanics, well first of all what is gravity? We can’t use the equation to come up with it so we must use logic and some basic math.

Brownian Gravity

Suppose there is a lost man at point 1 trying to get to point 0 on a number line.

|----|--|---|

0      1   2   3

He flips a coin and if the odds are heads, he goes right and if the odds are tails he goes left. Will he eventually get to 0 and will he eventually get to 0 no matter how far away he starts? The answer to both questions is yes as we will show.

Say he is at 1 and he flips the coin once. Heads and he stays lost and tails he finds home: ½.

Say he is at 1 and he flips the coin twice. TT and TH both find home because once he moves Tails the next toss doesn’t matter. HT winds up at 1 again and HH at 3: ½.

Say he is at 1 and he flips the coin three times: 5/8.

Say he is at 1 and he flips the coin four times: 5/8 again.

Say he is at 1 and he flips the coin five times: 11/16.

The chance may not be approaching 1 but it is clearly getting bigger by an inductive proof. Since no matter how far away he is the odds are greater than ½ of finding home, he makes it eventually.

Now what happens if he is at two and flips the coin twice. ¼ of the time he finds home, ½ the time he stands still, and ¼ of the time he goes to 4.

Say he is at 2 and flips the coin three times. With disregard for 0 he moves to the left a distance as often as to the right, and since it is possible to move past 0 and yet still find home, the odds are as great of sometime reaching 0 as 4. Thus when we multiply the distance away by n and the coin tosses by n, the math works out similarly.

If the odds are always greater than ½ of reaching 0, no matter how far you go, then eventually you will find home. This is also true in the second dimension, but not the third. In the third dimension we will need to introduce gravitons/gravity waves.

Layman’s Terms:

Simple gravity can be explained by a man who gets lost and tries to find an object by walking randomly. In the 1st and 2nd dimension if he walks long enough he will always find home. That can be the start of gravitational attraction.

1-D Gravity Formulation

Now to find the equation of gravity we jump to a different argument:

In case 1 let two particles be next to each other at a distance r1. x1 and x2 are their coordinates In case 2 let 2 particles be next to each other at a distance of r2 = 2*r1.

The potential energy in case 2 is half as much as case 1 because if you zoom in by a factor of 2 the potential energy will be simply twice as much for being twice as close. The closeness tells the likelihood of the particles connecting which turns them into one particle and that is gravity from scratch. Thus potential energy is measured by a constant (G) and a division of the radius. How de get the masses to work out? Again, if an object is twice as big, the diagram is twice as close and the potential energy is twice as much for the same reason.

Again we will circle around to gravitons and gravity waves in the 3-D section of this book.

Note that as particles are set to collapse you will get more and more detail by zooming in, hence from a zooming perspective a particle is a big bang and a big bang is a particle because it is all collapsing with itself. With gravity, when things get very close they usually expel each other at a huge rate, but not in 1-D.

Kinetic energy e(k) = ½*m*v(t)²    (1)

where m is mass of the object moving and v is its velocity (speed with direction). The derivation of this equation can be seen in Wikipedia.

and as we have seen,

Potential energy e(p) = -Gm1m2/r    (2)

where G is the constant we referred to and it is negative because it is an attracting force.

If we are looking at celestial physics with a specific limited number of particles, we want to know their positions through time knowing their mass, location, velocity, and acceleration (and change in acceleration if there is one). We know that if we have two particles we can do this through time. Here’s how to do it with two:

Kinetic energy is the energy of momentum carried by a particle as it moves. Potential energy is the energy brought forth through gravity.

E(k)+E(p)=0    (3)

since kinetic energy from velocity and the force of gravity are the only things happening to our particles (we will generalize to electric charge later). Given their positions e(p) may be calculated from (2) and hence e(k) from (2) and (3). Then v may be found from e(k) by (1). v is a function of x which is a function of t. How about a (acceleration)? Force equals mass times acceleration. Well the force of gravity is

F = Gm1m2/r²    (4)

and F=m*a    (5)

so we divide e(p) (from 2) by r we get F (from 4) and then we divide by the mass of the particle into F (5) we are considering to get a. Once we have m, x, v, and a for both particles

x(t) = x0+v0*t+0.5*a0*t²    (6)

Newton’s famous equation that comes straight from Calculus. If we are missing one m, one x, one v, or one a we can solve for it. Also, when there is more than one dimension it turns out fine.

And yet, almost 300 years after Isaac Newton’s death, we still cannot solve the equation for three bodies. If we have x(1), x(2), x(3), m(1), m(2), and m(3) we cannot solve it.

X1 with m1 -------------x2 with m2 ----------------- x3 with m3

Yet there is a way.

It is called having no time!

Why no time?

Time is something that only applies to living things. An inanimate object cannot experience time or be. When a living thing experiences time, it is unearthing memory or visualizing the future. Both of these things, later on in this book, we will show can exist at an instant. In fact an entire life, possibly even a very long one, could be nothing more than reverberations.

Yet velocity works. Why?

Consider a walking stickman. His center of gravity is beyond where his foot on the ground is. He is in a middle of a step. He cannot be stationary. He will fall forward and complete the step if nothing happens. Therefore even without time we can see that he has velocity. Many things do not have time yet have velocity. It can be fun to look at objects and see whether you could tell they were moving at an instant based on what you saw.

Consider further special relativity.

The dilation factor is

Note that c can be a hypotenuse of a right triangle with v and c²-v² the two legs since v² + (c²-v²) = c², following the Pythagorean Theorem. If v is close to c, there will be huge dilation.