Small step to Unified Field Theory or Gravity and electromagnetism relation with JavaScript Distributed Computing

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Many scientists try to find so called Unified Field Theory. The term was coined by Einstein. The goal of this theory is finding relation between all known fields like gravity, electromagnetism etc. Let’s start from something small, for example, find relation between gravitational constant G and electromagnetic constants ε₀ (Vacuum permittivity), μ₀ (Vacuum permeability) and some other constants like π number, Planck's constant, Elementary charge (electron charge), Boltzmann constant. Here full random brute force method is suggested in order to find this relation.

Why there is a chance to find something interesting

Many times in the history scientists just guessed correct equation or found something accidentally. Some people tells that even Einstein just guessed his famous formula E=mc². In this sense why not to try again, especially now with modern technology new approaches can be used. There is no Einstein now a days, but there are computers, which can partially replace his very smart brain.

How it is implemented or technical details

For brute force Javascript language is used, because it can be run on almost any device from Browser without any additional software installation. Contributor just need to open website and click start button. It even works on iPhone, Android devices or tablet. Javascript implementation calculates some equation like G = {combination of different constants} and if this equation is true with some precision, program will save equation and result on the server. There is no any synchronization between different browsers and computers. Theory of probability will be used to cover all possible combinations and it is explained later. There were many talks about javascript distributed computing and it is one of the first real implementation of it.

How it will be calculated or mathematical details

This javascript program tries to generate and validate following generic equation

 (1)

From first glance, there are too many symbols :). Let's explain them. All numeric values are in SI units.

G – Gravitational constant (6.67408×10^-11)

exp – Euler's number (2.7182818). exp is used instead of standard e to avoid collision with Elementary charge (electron charge)

ε₀ – Vacuum permittivity (8.85418781762×10^-12)

μ₀ – Vacuum permeability (1.2566370614359×10^-6)

h – Planck constant (6.626070040×10^-34)

e – Elementary charge (electron charge) (1.6021766208×10^-19)

m, n – integer number, which can be 2, 3, 4, 5. It is needed to cover some cases like 3/2*Something and etc, which often appears in physical equations

π – Pi number (3.14159265…)

k – Boltzmann constant (1.38064852×10⁻²³). Well from units point of view it should not be here, because only this constant has Kelvin, but who knows, maybe we will find something very new here, like relation between thermodynamics and gravitation

a, b, c, d, f, g, I, j – exponents which can be -3, -2, -3/2, -1, -2/3, -1/2, -1/3, 0, 1/3, 1/2, 2/3, 1, 3/2, 2, 3, π, 2.7182818.  These are commonly used in physics exponents and cover most of the cases like 

etc. If it equals 0, then constant will be eliminated. For example,

that means ε₀ is not used here.

exp^x – will be randomly included or excluded during the calculations. A few examples:

Depends on random numbers generator these equations can be generated:

or something simpler if all exp is not chosen

Which can be rewritten in traditional way like this

How long it takes

It normal modern computer with default settings in Google Chrome browser this program can perform around 3000 validation of equation (1). Total number of possible combinations is 5.7×10¹³ or 57000000000000 which is 57000000 million or 57000 billion or just 57 trillion. Possibility to find needed combination out of all of them is 1.75×10^-14. Because it is pure random algorithm and there is no any synchronization between different computers, some overhead will be needed. For example, if this validation will be performed 57 trillion times, exactly as how many combinations, probability to find needed combination equals to 63%. Which is not very good, but if this validation will be performed 5 times more times (285 trillion), probability to find good result will be 99.9%. If only one computer will be used, it will take 3000 years, but if 1 million contributors will join, it will take only 26 hours.

Reasons why people should do it

• Help to make new step in science
• Help to prove new distributed javascript calculation technic
• Get some money! If there will be any cash prize for finding this relation (Nobel Prize or whatever), person who will find it will get 10% of this amount.

Update 1 or iteration 1 (09 November 2016)

First day of calculation showed, that there are some issues in main formula (1). There was some findings like this

and after units analysis it became clear, that Exp function can have inside only dimensionless constant like π or integer numbers. New generic equation is this

     (2)

Now program is updated and put Exp only to correct places. Also after consideration of many existing physical equations list of possible exponents was extended to -5, -14/3, -9/2, -13/3, -4, -11/3, -7/2, -10/3, -3, -8/3, -5/2, -7/3, -2, -5/3, -3/2, -4/3, -1, -2/3, -1/2, -1/3, 0, 1/3, 1/2, 2/3, 1, 4/3, 3/2, 5/3, 2, 7/3, 5/2, 8/3, 3, 10/3, 7/2, 11/3, 4, 13/3, 9/2, 14/3, 5, π, 2.7182818.
Time and number of possible combinations has been changed as well. Number of all combinations is 4.6×10¹⁵ or 4600 trillion. Time for 1 computer 240 000 years. Time for 1 million contributors 2000 hours (83 days).

Update 2 (11 November 2016)

After sometime it became clear, that exponents 1/3, 2/3, 5/3 and etc are not very common and they give too many findings, which does not look good. Some of these wrong findings:

as a result new list of exponents is this -5, -9/2, -4, -7/2, -3, -5/2, -2, -3/2, -1, -1/2, -1/3, 0, 1/3, 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, 5 and m, n will be from 2 to 15.
Time and number of possible combinations has been changed as well. Number of all combinations is 2.4×10¹⁴ or 240 trillion. Time for 1 computer 12 600 years. Time for 1 million contributors 111 hours.

Update 3 (26 November 2016)

Several new findings were found. Most interesting of them:

but they failed units test. Number of calculation reached 1 billion (1000 000 000)! But still many strange findings means that formula 2 as well as list of exponents have to be adjusted.

After some thinking it was decided: Let's start from something simple! Let's exclude most of the things, which looks strange and reduce number of combinations. Physics law should not be over-complicated. New adjusted simplified equation:

     (3)

Here Exp function, exponents 1/3, Boltzmann constant were excluded at all. Euler's Number and π number were excluded from exponents list.
Number of combinations now 3.5×10¹¹ or 350 billions. Total calculation time for one computer will be 18 years and for 10000 computers it is just 16 hours.

Update 4 (04 December 2016)

Still programs returns too many findings and all of them failed units test. Now auto units test has been added. Units test means that we do not get speed with units kg/s, but program check that if we get speed, units will be m/s. The same for gravitational constant G.
Also number of checked combinations reached 1.5 billion!

Update 5 (07 December 2016)

Just some interesting findings, but all failed units test. Last one looks very nice.

Update 6 (17 February 2017)

New task "Disproof of Riemann hypothesis from Millennium Prize Problems list" has been added. All details and explanation will be added soon in separate post.

P.S. all explanations and estimation above give a good justification that it is possible in the limited amount of time.