Einstein constant

Subject: Fwd: Einstein constant
Date: Fri, 13 Jun 2008 04:40:33 EDT

I am not sure if it is possible to define an arbitrary factor of 4 pi or so since the units of the physical quantities appearing in the Poisson equation are fixed, acceleration in m/s^2 and mass density in kg/m^3. I saw a factor of 4 pi in an article on the Poisson equation of mechanics, but the Einstein constant contains 8 pi. I will look into a mechanics book tonight.

Horst

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These are interesting questions, a neat derivation by Horst:

 

                                       del dot g = 8 pi G rho sub m         ------------------------ (1)

 

We should look up the NIST site or google around to find how k is measured experimentally. Marion and Thornton mention that G is the least precisely known fundamental constant. In paper 85 some serious internal inconcistencies were found in the data from standards laboratories on the fundamental constants. I have assumed that k is the constant of proportionality between mass density and a well defined scalar curvature in paper 113, but this assumption really comes out of habit, because k is of course used in the now obsolete Einstein field equation. In a self consistent geometry eq. (1) now defines the Newtonian limit and so the older Newton constant G should be used instead of the Einstein consatnt as Horst points out. The 8 pi can I think be regarded as a convention. So we could write,

 

                                       del dot g = G rho sub m           ------------------------- (2)

 

If we regard the 4 pi in the Coulomb law as an S.I. convention it is

 

                                       del dot E = rho sub e / eps0           ------------------------- (3)

 

so G plays the role of 1 / eps0, the inverse vacuum SI permittivity. The acceleration due to gravity g (metres per second squared) is the analogue of the electric field strength E (volts per metre). Here rho sub m is mass density in kilograms per cubic metre, adn rho sub e is charge density in coulombs per cubic metre.   

     

Both laws are the result of the spherical symmetry of spacetime. I have a feeling that all laws of physics are due to the spherical symmetry of spacetime through a generalization of the orbital theorem to all physics.

 

 

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Einstein constant

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Thu, 12 Jun 2008 08:43:23 -0400

In eq. (22) of note 113(9) (analogue of the Coulomb law) the product c^2*k appears, being the analogue of the inverse of the permittivity.

The dimensions of the product c^2*k with k being the Einstein constant is

    [ c^2 * k ] = m^3 / ( kg*s^2).

This is the same as for the Newton gravitational constant G. Actually the Einstein constant is given in Wikipedia by

    k = 4 pi G / c^2.

Therefore eq.(22) could be written

    nabla * g = 8 pi G rho_m.

The appearance of G is natural here, but I wonder if the factor 8 pi is correct. I am not sure how the Poisson equation in mechanics reads.

As far as I know, the value of k is determined from Einstein’s equations in the Newtonian limit. Meanwhile we know that this equation is not correct, so the value of k should be re-evaluated. Are there other common methods how k is determined?

Horst

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OK thanks again. There is no problem with the 4 pi and 8 pi because all of ECE is developed entirely in SI units.