unified field theory

 Bizarre New Theorem of Pythagoras!

Chris Vuille

January 25, 2020

Figure 1: Distance from A to B

“The Square of the Hypotenuse is Equal to the Sum of the Squares

of the Legs.”

The theorem of Pythagoras gives the distance between two points. In a plane,

it is given by

∆s

2 = ∆x

2 + ∆y

2

(1)

where ∆s is the length of the hypotenuse and also the distance between the two

points, and ∆x and ∆y are the displacements, also called the legs of the triangle.

In the figure, the distance from point A to point B is

∆s

2 = 42 + 32 = 25 → ∆s =

√

25 = 5 (2)

Of course this number has units, so if the units were meters, you would say the distance is 5 meters.

In my theory, the theorem of Pythagoras is given by

∆s

2 = ∆x

2 + ∆y

2 + ∆x + ∆y + ∆N (3)

where N is some number. It is not associated with a direction, it’s just there! The number can change from point to

point, but it is not a displacement, like ∆s, ∆x, or ∆y. Now we compute the distance between two points. In today’s

universe, N changes very little from point to point, so ∆N is a very small number, call it .

∆s

2 = 42 + 32 + 4 + 3 +  = 32 +  → ∆s =

√

32 +  (4)

So the distance is now a little bit larger than 5.657 meters. While ∆N is usually a very small quantity, it could play roles

at the beginning of the universe or in black holes, and other contexts. It can be considered an effect of quantum mechanics.

∆x and ∆y turn out to be related to electric and magnetic fields. ∆x

2 and ∆y

2 are related to gravity, especially Einstein’s

theory of general relativity.

The theory in reality doesn’t look that much different from this. The distance function is infinitesimal because it has to

change from point to point. For example, ∆x becomes dx and ∆s becomes ds. That just means a displacement becomes

very tiny, so you can do calculus on it. It also includes another space dimension, and a time dimension. It might take the

form:

ds2 = −c

2

e

ν

dt2 + e

λ

dx2 + dy2 + dz2

+ Adt + Bdx + Cdy + Ddz + N (5)

Here, the quantities e

ν

, e

λ

, A, B, C, D all change as you go from location to location. N is the number function that also

changes as you go from location to location. The first part, through the dz term, is general relativity. The Adt+....+DdZ

term is electromagnetism, and N is the quantum contribution. You end up getting all kinds of numbers for a “distance”

that seem warped and nutty.

See? Completely whacko! That’s what I think the universe is!