Dirac's Large Numbers

He noted that the electric force between the proton and the electron is inversely proportional to the square of the distance, while the gravitational force is also inversely proportional to the square of the distance, but the ratio of those two forces, 10^39, does not depend on the distance. He resoned that the magnitude of the number makes other units of comparison inconsequential due to the largeness of the number, so it stands alone at the order of magnitude, unity.

If you express the age of the universe in atomic units of time, then you get a number of about 10^39, approximately the same as the previously mentioned number.

In 1937, Dirac proposed an explanation of the two large numbers in terms of a third one, which was the age of the universe t_U, (the epoch), measured in units of a typical atomic time e^2/mc^3. Using the present age of the universe, it turns out that...

e_3=t_U/(e^2/mc^3)=e_1

From this, Dirac postulated that the number of nucleons in the universe must increase with t_U^2, and the gravitational "constant" G must decrease by t_U-1.

Dirac also mentions the possibility that hc/e^2 and/or m_p/m_e might vary proportionally to the logarithm of t_U.

But gravity is cumulative, locally and so real particle pair production should increase the gravity of the universe, unless the creation of particles from vacuum energy leaves real holes in the vacuum that serve to counter-balance the increased gravitational effect, by increasing vacuum tension, via the increase in -rho that occurs with further rarefaction of the vacuum, where...

P is related to vacuum energy density, by P = -rho.

The number of nucleons in the universe must increase with t_U^2, as the universe ages, per the second law of thermodynamics in an expanding universe which requires that the breakdown of energy include the isolation of of high-energy photons that are known to interact with virtual particles in the quantum vacuum to create real particle pairs.

And so the number of nucleons in the universe increases, while G remains constant, since the decrease which occurse with t_U^-1 represents an increase in -rho, which is immediately offset by the increase in mass energy that comes about when you make a real massive particle from virtual particles in the vacuum.

I say, "further" rarefaction because real particle pair production should also increase with the increase in negative energy density, (DE), that comes about as a result of increasing tension between the vacuum and ordinary matter.

The square of the age of the universe equals the number of particles in it, because the size of the universe in astronamical units is proportional to the number of particles that have been created, meaning that vacuum expansion is inversely proportional to real and virtual particle pair production as the negative pressure component increases in proportion to the holes that get made in the vacuum by way of the condensation of its energy.

General Relativity can be accomidated to this idea fairly easily.

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