
(Solar luminosity vs. solar system age. L/Lo is luminosity as a fraction of present value. Lower line is standard solar model. Upper line indicates luminosity when c change is a factor. If speed of light c is precisely related to Universe age t by GM = tc^3, luminosity remains within a comfortable range for life to evolve.)
Over at Quantum Diaries, Tommaso has introduced discussion of whether fundamental values like the speed of light are really constant. This has led to a question by
Carl Brannen about the Sun. It is impossible to "prove" experimentally that c is constant, because a more accurate measurement could always prove that foolish. It is possible to measure c change over billions of years, if a scientist knows what to look for. One of these measurements involves the Sun and life on Earth.
The “Faint Young Sun” has been a paradox of astrophysics. Over decades physicists have developed a standard model for the Sun’s evolution. This model predicts that at about 4 Ga ago Earth was too cold to support life. The sedimentologic and fossil records contradict this prediction. The very appearance of life on Earth conflicts with the model. An answer may be deduced from Relativity and Space/Time.
The standard solar model predicts that about 4 Ga ago the Sun shone with scarcely 70 percent of its present power. Because power P is related to temperature T by the Stefan-Boltzmann law, P = $\delta$ T^4, Earth’s temperature would have been only 91 percent of present value. Today’s average temperature is about 283K, so in the past it would have been only 258K, 15K below freezing. An Earth frozen solid would reflect most sunlight into Space, maintaining even colder temperatures. The appearance of life and its evolution would have been very unlikely.
Geology shows evidence of extensive sedimentation 4 Ga ago, indicating the presence of rivers and seas. Other geologic markers corroborate presence of liquid water on Earth during this period. The earliest organisms are at least 3.4 Ga and possibly over 4 Ga old. Clearly liquid water and life both existed when the model predicts Earth was frozen solid. The fact that life exists today is in conflict with the standard solar model. This conflict with observations is the Faint Young Sun paradox.
A much higher concentration of carbon dioxide in Earth’s atmosphere has been suggested to maintain a proper temperature. This is an inferrence supported by no geological evidence whatsoever. Studies of iron carbonates by Rye et al. conclusively show that Earth had at most 20 percent the required amount of CO2. We have evidence that Mars also had temperatures suitable for liquid in its distant past. It is unlikely that CO2 would custom-heat both planets.
Fortunately, Relativity and new physics may help save the standard solar model. The Sun converts its fuel to energy according to E = mc^2. One theory of Space/Time predicts that c is related to t by:
GM = tc^3
Where t is age of the Universe, GM combines its mass and gravitational constant . Solving, we have c(t) ~ t^{-1/3}. Billions of years ago, solar output and temperature were therefore higher than originally predicted.
Earth is estimated to be 4.6 Ga and the Universe 13.7 Ga, 1.5 times its age at the time of Earth’s formation. Energy mc^2 is adjusted by 1.5^{2/3} = 1.31 times the initial estimate. Multiplying by an estimate of 70 percent, the Sun’s actual output was 0.917 of the present value. Temperature was then 98 percent of the value we enjoy today. If we start with an estimate of 76 percent, solar luminosity was exactly the present value. The “paradox” leads to an extraordinary test of Theory. If c had not changed in precisely the amounts predicted, life would not have evolved on Earth.
A PLANE HAS STRUCK THE TOWERS
Labels: physics, speed of light, sun