Forces and their strengths

Forces and their strengths

In currently accepted physics, there are 4 forces and no more. They are of such varying strengths that this has amazed a number of great physicists [[i]].

Comparing their relative strengths is not easy because they don’t all act on the same particles, but only on particles susceptible to that force. We can, however, make a very rough comparison using their coupling constants, which are dimensionless numbers.

Nuclear strong force = 1
Electromagnetic force = 7.30 E-3
Nuclear weak force = 3.05 E-12
Gravitational force = 5.9 E-39

Using their inverse values, we can say that the electromagnetic force is 137 times weaker than the strong force, while the weak force is 3.28E11 times weaker still and gravitation trails them all, being 1.69E38 time weaker again.

Now what is so amazing about this number sequence?

3.28 E11
1.69 E38

If the sequence were

or even

then people would see a pattern and nobody would suggest that there are only 4 forces and no more. Is mathematics incapable of generating big numbers?

Let’s make some big numbers.

Note: The following section is just a demonstration of finding a function that grows at this rate and does not bear any significance to the theory in this blog.

Let us generalise the functions +,*,^ to hyper1, hyper2, hyper3 respectively and invent a new operation hyper4 which repeatedly exponentiates a number to itself. The hyper4 function is also referred to as a “Power Tower” [[ii]] or “tetration”.

So for example
x hyper4 4 = ((x ^ x) ^ x) ^ x

Here are the first few values for x:
1 hyper4 4 = 1
2 hyper4 4 = 256
3 hyper4 4 = 7.6E12
4 hyper4 4 = 3.4E38

Close enough? If this trend continues and there are in fact a larger number of forces, the next two forces would be at:
5 hyper4 4 = 2.35 E87
6 hyper4 4 = 1.20 E168

I contend that there are such forces and that they are simply be undetectably weak rather than non-existent. Maybe these forces become significant on the galactic scale and could explain why some astronomical observations disagree so much with current theories. Even if they are weaker, they can overpower gravity if their effects do not drop off as steeply with distance as gravity does, which decreases with the square of the distance.

A proton is a very small structure of around 1E-15m. It is made up of three quarks and is held together entirely by the strong force. A hydrogen atom is larger at around 1E-11m and is held together by the strong force and electromagnetism.

Adding the weak force to the mix gets us bigger atoms, for example a lead atom is around 1E-10m in size.

With a big jump in size we arrive at our solar system at 1E16m. This is held together by strong force, electromagnetism, weak force and gravity, but solar systems are by no means the largest structures we know. At the next level up there are galaxies (1E21m), groups of galaxies, clusters of galaxies, then super clusters and finally filaments, which are the largest structures known today.

It is already known that the gravity of visible objects is not strong enough even to hold our galaxy together. Current theories therefore attempt to explain astronomical observations by postulating “dark matter” which is an undetectable, unknown and so far unexplained substance, as well as super massive black holes at the centre of each galaxy.

[[i]] Richard Feynman, QED: The strange theory of light and matter


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