### Exhibit 1: Hot Young Sun

(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

## 4 Comments:

Have you thought of editing the variable speed of light page on wikipedia to include your theory ?

http://en.wikipedia.org/wiki/Variable_speed_of_light

Good idea, Sam. Work on that is overdue.

Hi Louise,

Thanks for this very interesting post which clearly explains how you are getting the

GM = tc^3

relationship to give us less luminosity change from the sun in the past than the current (non-evolving c) theory gives.

You assume that the left hand side, GM, is constant, and that assumption tells you that tc^3 = constant, so c must be inversely proportional to the cube-root of time.

Then the famous relationship E=mc^2 means that the sun's radiant power, P = dE/dt, must have been higher in the past because c was higher.

The universe is around 13.7 billion years old, and Earth formed 4.54 billion years ago, so the absolute age of the universe when the Earth formed was 67% of its present age, so your relation c ~ t^(-1/3) suggests that c was 14% higher when Earth formed than it is now.

Since solar luminosity or power P = dE/dt = d(mc^2)/dt, it follows that where c is 14% higher, the solar luminosity have been 31% higher than current predictions of what it was 4.5 billion years ago.

Hence, instead of the sun emitting 70% of present luminosity when Earth formed, it was probably 1.31 * 70 = 92% of present luminosity, just as your graph shows.

So your figures make sense.

GM = tc^3

does however offer another simple possibility with changing constants, namely that G increases in direct proportion to the age of the universe, instead of c falling as the inverse cube root of time. It is useful perhaps to investigate this, if only to rule it out.

Dirac first investigated the possibility that G is inversely proportional to the age of the universe in 1938 (

Proceedings of the Royal Society of London A,vol. 165, page 199 and later papers), which was discredited by Teller in 1948 (Physical Reviewvol. 73, page 801) who showed that because the radiant power of the sun is a very strong function of G (Teller showed that solar luminosity is proportional to G^7).Hence Teller showed that the seas would have been boiling in the Cambrian period if Dirac's hypothesis (G ~ 1/t) was correct. Dirac was definitely wrong.

However, from your relationship

GM = tc^3

we see that G would be directly proportional to the age of the universe if G and not c is the variable.

So Teller's calculation would be inversed yet the conclusion would remain, since the seas would be frozen instead of boiling in the Cambrian: either way, there is disagreement between evolution and the notion that G varies.

However, there is a strong reason from quantum gravity why Teller's dismissal of G variations is as much bunk as von Neumann's famed 1932 "disproof" of hidden variables.

If G is varying and if the two long-range inverse-square law forces (gravity and electromagnetism) are related, their coupling constants will be related. Hence, any variation in G will be accompanied by a similar variation in the strength or coupling constant for electromagnetism. Fusion in the sun is a process dependent upon gravitational attraction producing a pressure in the sun which acts against the electromagnetic repulsion between protons (Coulomb's law).

If you make gravitation and Coulomb's law both stronger by the same factor, therefore, the increased Coulomb repulsion (acting to decrease the probability of protons approaching close enough for the strong force to fuse them) offsets the increased gravitation.

Hence, Teller's conclusion that luminosity is proportional to G^7 is completely false because it ignores the equally massive dependency on the electromagnetic force coupling constant, which varies the same was as G but has an opposite effect on the fusion rate in the sun.

So my argument is that it is a possibility that your relationship GM = tc^3 holds, with G varying but with no significant effect on solar luminosity (despite Teller's misunderstanding), simply because the variation in G is accompanied by a variation in electromagnetic force strength which cancels the effect of varying G out of the fusion rate model.

I think there is a mechanism for GM = tc^3 which suggests that G is proportional to t, instead of 1/c^(1/3) being proportional to t.

Hubble's v = HR implies cosmological acceleration a = dv/dt = d(HR)/dt = H(R/t) = Hv = H(HR) = RH^2, where H is Hubble's constant (shown to be a true constant by observations) and R = ct.

Hence cosmological acceleration would appear to be a = ctH^2, so if c is a constant then a is directly proportional to t.

Applying Newton's 2nd law F = Ma, we get outward force due to the mass in the universe M accelerating away from us radially,

F = Ma = MctH^2.

So that force appears directly proportional to the age of the universe. Newton's 3rd law suggests that there must be an equal and opposite (radially inward acting) reaction force.

Assuming that this is carried by gravitons being exchanged between all gravitational charges in the universe via a Yang-Mills quantum gravity, this inward force suggests a simple mechanism for gravity,

where G should be directly proportional to the age of the universe. As you know, I've worked this out in detail giving definite predictions at http://nige.wordpress.com/2007/05/25/quantum-gravity-mechanism-and-predictions/ such as predicting the value of G and comparing to measurements, and other tests.Because G and the electromagnetic coupling constant vary the same way as a function of time, gravitational compression variations offset Coulomb repulsion forces so fusion rates in stars and the big bang are practically unaffected by G being proportional to age of universe. However, the fact that G appears to have been smaller in the past than it currently is, implies the reason why the anisotropies in the CBR (emitted 400,000 years after the BB) turned out to be so much smaller than predicted in 1992, without requiring inflation theory.

The anisotropies are smaller than those predicted before COBE observations in 1992 (and more recently, WMAP) precisely because G was so much smaller when the CBR was emitted, than is assumed in current calculations.

I will get some detailed computer calculations done on this to make it more rigorous (I also want to see how this variation of G and other force coupling constants with time affects the very early time dynamics of the big bang).

It is just an alternative possibility...

Best wishes,

Nige

Hmmm. Didn't the geologists correct the physicsts back in the late 19th century when Kelvin determined the age of the universe based on thermodynamics (without E=mc2)?

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