My late friend Vic Stenger pointed out that there's a different way of
looking at this. Most people say gravity is the weakest force because
they compare the gravitational force between two elementary charged
particles, e.g. two electrons, two protons, or an electron and a proton,
to the EM force between them and gravity is weaker by a large factor on
the order of 1e-36. But while there is a natural unit of electric
charge, there are no particles with a natural unit of gravitational
charge, i.e. mass. But there is a natural unit of mass; it’s just not
one that any particle has (at least not any particle we could produce).
It’s the Planck mass. The Planck mass is derived just from the
fundamental constants:
m_P = \sqrt{\frac{\hbar c}{G}} = 2.18e-18 Kg
So we should calculate the ratio of the gravitational to EM force of two
Planck masses each with unit charge
\frac{F_G}{F_{EM}} = G m_P^2/Ke^2 = 137
where K is Coulomb’s constant and G is Newton’s constant. And behold,
the gravity is stronger by the inverse of the fine-structure constant.
Why this great discrepancy in the two ways of looking at the question?
Well, first in quantum field theory the particles are all massless. Few
get a little mass from interaction with the Higgs field which has (for
no particular reason) a non-zero vacuum energy. All the rest of the
particle masses come from the binding energy of fields. So they have
very little gravitational mass. The Planck mass is the mass of the
smallest possible black hole, one whose de Broglie wave length equals
its diameter. And it is huge by particle standards. It’s the mass of a
bacterium. So in this way of looking at it gravity is strong, but the
fundamental particles are almost massless.
Brent
On 12/27/2022 3:46 AM, John Clark wrote:
On Tue, Dec 27, 2022 at 5:59 AM Jason Resch <jasonre...@gmail.com> wrote:
/> There's an interesting relationship between the strength of the
electrostatic repulsion between two protons, and the gravitational
attraction of protons. It works out such that it takes ~10^54
protons gathered together in one place before the gravitational
attraction can overwhelm the electrostatic repulsion. In other
words, stars as as big and long-lived as they are because gravity
is so weak./
That's true, and one of the biggest mysteries in physics is why
gravity is so weak, after all the strong nuclear force can keep 100 or
even 2 protons in one place. The only explanation I've heard is the
hypothesis that there are other spatial dimensions besides the 3 that
we're familiar with, string theory claims there are at least 9, but
that all the forces of nature EXCEPT for gravity are confined to just
3 dimensions so they generally follow the law that says they decrease
with distance according to the well known 1/r^2 rule, but gravity is
free to radiate into all 9 dimensions so it decreases with distance
according to a 1/r^8 rule; and the reason we don't see gravity behave
this way in our everyday life is it the other 6 dimensions are curled
up very tightly so the effect becomes apparent only at the ultra
microscopic scale. It's a nice theory but there's not a scrap of
experimental evidence to support it.
John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>
hfl
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