Growing the Universe

RANT#16: Back in Rant #12 we noted that the space around the Sun seems to be stretching at the rate of 20 cm/year/AU which converts to 0.13 kn/sec/Mpc or about 0.17% of the Hubble constant of 74.2 km/sec/Mpc. I had given 0.34 instead of 0.13 in my paper and can't find the discrepancy - either way we have a ball park figure. Now about growth rates here comes the tricky math part. If a quantity, say X, increases with time by a certain amount, say dX/dt, that does not depend on how big X is then we have an absolute growth of X+dx in the time interval dt. But if the growth amount depends on the how big X is then we have a relative growth of dx/X/dt = (1/X)dX/dt. This is a per centage growth if you muliply by 100. By itself, the ratio dX/X is a logarithmic change noted as d(log X). The log of a quantity (number) is given as the power (exponent) that a selected base number must be raised to to give that number. If we select our base as 10 then the log of 100 is 2. That is 10 to the power of 2 (squared) is 100. As odd as it may seem the log can be fractional not just whole numbers. To add to the confusion there turns out to be a "natural" base equal to 2.71828... which is also irrational like PI = 3.1415928.... The natural logarithms are written dX/X = d(ln X). We won't but it's easy to convert between ln X and log X, e.g. ln(10)=2.303 while log(10)=1. The point of all this is that the Hubble constant can be expressed in terms of a distance scaling factor that only depends on what interval of time you choose. Layzer (cited in Rant #12) using this (Friedman) constant "a" gives the Hubble constant as H = (1/a)(da/dt) and as we've seen then H = d ln(a)/dt where a = a(@t)= R(@t)/R(t=0). what we want to know is what contribution to the intergalactic Hubble constant of 74.2 would an expansion of 20 cm/year/Au contribute in our region of space. All this leads to calculating the change with H dt = d(ln a) = d ln(R/Ro) = dln R for dt = 1 year and the change in R to be from 1AU (where the rate is 20 cm/year/AU) to R the distance in AUs that light travels in one year 1. Finally we get that H = ln (R=6.35e4 AU) = 11.06! This result differs from my original paper where I had introduced a variable N that four years later has me baffled. Snce this is a Blog and not a Scientific paper I can admit mistakes. So the upshot of all this that our Sun is contributing 11.06 km/sec/Mpc to the expansion of the universe in our regions of the galaxy. And my assertion is that this is due to the radiation emanating from the Sun whose lengthening photons are causing the expansion of space about the star. I'll go further and maintain that radiation is not waves in space but waves of space.