lew@ihuxr.UUCP (Lew Mammel, Jr.) (11/13/83)
This is about Barry Setterfield's suggestion in "The Velocity of Light and The Age of The Universe" that the value of the speed of light is given (prior to 1960) by: c = 299792.5 km/sec * cosec^2 (T) ; T = pi * t / 12000 yrs t = 0 at 4040 BC i.e. T = pi/2 at 1960 AD Passing over for the moment any criticism of his selection of data, I will address what I feel is an irredeemable sin in his curve fitting technique. He arrived at his formula by fitting data from 1675 thru 1960 to the formula: log C(T) = A + B* log sin(T) The thing to notice is that "T" has already been defined prior to the fit. He gets away with this because all his data points fall very close to T = pi/2; t = 5715 at 1675 AD gives T = .9525 * pi/2 . This means that to an excellent approximation: sin(T) = 1 - .5 * (pi/2 - T)^2 The next term is (pi/2 - T)^4 / 4!, and is less than 1/1000 of the included term at 1675 AD. Considering that log(1+x) ~= x for small x, what this amounts to is fitting to the formula: log C(t) = a + b * (k*t)^2 = a + b*k^2 * t^2 ... where t is "years before 1960". In other words, only the value of b*k^2 affects the fit. We can pick k at will and adjust b to get the same fit. To check this, let's try doubling and halving k. This gives the formulas: c1(t) = c0 * sec(pi/2 * t/6000) ^ 2 (Setterfield's) c2(t) = c0 * sec(pi/2 * t/3000) ^ .5 c3(t) = c0 * sec(pi/2 * t/12000) ^ 8 Here is a comparison of the resulting values: t c1/c0-1 c2/c0-1 c3/c0-1 10 6.85392e-6 6.85395e-6 6.85392e-6 100 6.85702e-4 6.85938e-4 6.85644e-4 200 2.74658e-3 2.75036e-3 2.74563e-3 285 5.5878e-3 5.6035e-3 5.5839e-3 In case anyone is inclined to quibble over the quality of the agreement here, I'll point out that the exponent of -2 in Setterfield's equation is an approximation to -1.94665385 which he obtained from the fit. This gave a value of c = 301423 km/sec in 1675 AD compared to 301468, 301472, and 301467 for each of the "approximate" formulas. Setterfield stated of his approximation that "It is simple and precise and has exactly the same features and values of c throughout" (compared to the exact formula.) To beat this to death, the simplest formula which has the log c = a + b*t^2 character which determines the fit is simply: c = c0 * exp( (t/2737.71)^2 ) This matches Setterfield's "exact" fit better than his approximation, but it doesn't go to infinity at any finite time in the past. At t=6000 it gives a mere 3.3e6 km/sec, only ten times the present value. To sum up then, even if you go along with Setterfield all the way through his data selection and curve fitting, the resultant speed of light as a function of time does not lead to the conclusion that it was infinite at any certain time in the past. Setterfield simply injected the figure of 6000 years into his formula and built around it. Lew Mammel, Jr. ihuxr!lew