Physics of Irving Ezra Segal

Mark Loewe, Libertarian, for Congress, United States Representative, District 35, Texas
This list of publications of Irving Ezra Segal does not include unpublished manuscripts, such as "The Nature of Gravity", I. E. Segal (1998).

In 1989, Segal estimated the radius of the universe to be *R* = 160 ± 40 Mpc. In 2014, my attempt to use the same observed data to confirm Segal's estimate found *R* = 504.6 million lightyears = 154.7 million parsecs. The difference of 160 Mpc from 154.7 Mpc is well within Segal's estimated uncertainty of (at most) 40 Mpc.

Segal's chronometric redshift is given by *z* = tangent^{2}(*θ*/2) = tangent^{2}[*ct*/(2*R*)], where *R* is the radius of the universe, *c* is the speed of light, *t* is the Einstein time for light to travel from a source to an observer on a great circle of radius *R*, *ct* is the great circle distance from the source to the observer, and *θ* is the great circle angular separation of the source from the observer. Chronometric redshift does not require any assumption that the source moves with respect to the observer.

Light from galaxy GN-z11 is received with a redshift of *z* = 11.09. The chronometric estimate of the great circle distance of GN-z11 from us is roughly 1.29 billion lightyears. The chronometric estimate of the fraction of our spatial universe that is farther than GN-z11 from us is less than 4 percent.

This note currently lacks a helpful figure, which can be drawn by hand. The figure has a circle of radius *R* with horizontal tangent lines at the top and bottom, an arbitrary point on the circle (at, say, 3 hours and 30 minutes on a clock face), a line from the top tangent point that projects through the arbitrary point on the circle to a point on the bottom tangent line, and a line from the bottom tangent point that projects through the arbitrary point on the circle to a point on the top tangent line. The angle *θ* is measured (counter clockwise) from the bottom tangent point to the arbitrary point on the circle. The variable *x* is measured from the bottom tangent point to the projected point on the bottom tangent line (and increases from left to right). The variable *ξ* is measured negatively from the top tangent point to the projected point on the top tangent line (and increases from right to left).

This note confirms statements in "The Nature of Gravity", I. E. Segal (1998) (unpublished), that "The mean and variance of *m* would then be expected to be of the same order of magnitude. With the estimate of *R* in (54), *m*_{e} = 10^{37} in chronounits; this implies that the dispersion in *m* would be less than 1 part in 10^{17}, consistently with the observed sharp value."

This note is an attempt to confirm a statement in "The Nature of Gravity", I. E. Segal (1998) (unpublished), that "The two theoretical predictions are thus equally consistent with the presently accepted empirical value." One prediction is based on Schwarzschild's solution of general relativity and the other prediction seems to be based on Einstein's equivalence principle. General relativity and Segal's chronometric theory seem to be different extensions of Einstein's equivalence principle.

More to come ...

Mark Loewe, Libertarian, for Congress, United States Representative, District 35, Texas