### A Brief History of c Change

In response to multiple requests, here is how humans began to suspect that c slows down. A changing speed of light is an old idea that somehow is not taught in schools. For much of history humans did not know whether light had a finite speed at all. Philosophers from Aristotle to Kepler thought the speed of light was infinite. Kepler's friend Galileo performed many experiments with nature, including an attempt to measure the speed of light.

Galileo described stationing observers on distant hilltops with covered lanterns. The first observer would uncover his lantern, and upon seeing a light the second observer would uncover his. In this way Galileo hoped to detect any time delay. Unfortunately, a good watch had not yet been invented. Galileo could not detect any finite speed.

In 1676 Dutch astronomer Ole Roemer finally measured the speed of light. He did so using another Galileo discovery, the moons of Jupiter. By measuring the times when the moons passed in and out of Jupiterâ€™s shadow, he finally found that light has a measurable speed. Since Roemerâ€™s time, many other experiments have been devised to more accurately measure c. Roemer visited Isaac Newton in 1679; this discovery is mentioned in Newton's Principia.

Isaac Newton could imagine cannonballs fired at orbital speed, and calculate that a satellite in a circular orbit would have a certain velocity at a given altitude. Since Newton knew that Moons and apples are both guided by one law, might he have suspected that light is also affected by gravity? Centuries later, Einstein would show that light is indeed affected by gravitation. Light is far too fast to be drawn into orbit around the Earth, but the mass of a Universe would indeed pull light into a circular path.

There has long been speculation of whether the speed of light has always been constant. In 1874, the year after Maxwell published his equations, William Thomson and P.G. Tait claimed to have found a decrease in the speed of light. (W. Thomson, and P.G. Tait, Natural Philosophy, V. 1, p. 403, 1874) Thomson was the 1st Lord Kelvin and a very prominent scientist of the time. J.Q. Stewart in 1931, H.E. Buc in 1932, and P.I. Wold in 1935 also suggested that c changes.

Change in c has been put forward as a cause of cosmological redshifts. This "tired light" explanation has been disfavoured by experiments, but we will see that c does have an affect on redshifts. Barry Setterfield has written an exhaustive study using statistical analysis to claim change in c. More recently John Moffat, Joao Maguiejo and Andreas Albrecht have independently suggested a change in c as a solution to cosmological puzzles. Many, many scientists have speculated that c changes.

In conclusion, anyone can speculate that the speed of light changes, and many people have. For this to be more than the story of a speculation, we need the theory behind c. Why does light travel at 299.792.5 kilometres per second, not faster or slower? What is the principle behind c? NEXT: A Theory that a child could understand.

Galileo described stationing observers on distant hilltops with covered lanterns. The first observer would uncover his lantern, and upon seeing a light the second observer would uncover his. In this way Galileo hoped to detect any time delay. Unfortunately, a good watch had not yet been invented. Galileo could not detect any finite speed.

In 1676 Dutch astronomer Ole Roemer finally measured the speed of light. He did so using another Galileo discovery, the moons of Jupiter. By measuring the times when the moons passed in and out of Jupiterâ€™s shadow, he finally found that light has a measurable speed. Since Roemerâ€™s time, many other experiments have been devised to more accurately measure c. Roemer visited Isaac Newton in 1679; this discovery is mentioned in Newton's Principia.

Isaac Newton could imagine cannonballs fired at orbital speed, and calculate that a satellite in a circular orbit would have a certain velocity at a given altitude. Since Newton knew that Moons and apples are both guided by one law, might he have suspected that light is also affected by gravity? Centuries later, Einstein would show that light is indeed affected by gravitation. Light is far too fast to be drawn into orbit around the Earth, but the mass of a Universe would indeed pull light into a circular path.

There has long been speculation of whether the speed of light has always been constant. In 1874, the year after Maxwell published his equations, William Thomson and P.G. Tait claimed to have found a decrease in the speed of light. (W. Thomson, and P.G. Tait, Natural Philosophy, V. 1, p. 403, 1874) Thomson was the 1st Lord Kelvin and a very prominent scientist of the time. J.Q. Stewart in 1931, H.E. Buc in 1932, and P.I. Wold in 1935 also suggested that c changes.

Change in c has been put forward as a cause of cosmological redshifts. This "tired light" explanation has been disfavoured by experiments, but we will see that c does have an affect on redshifts. Barry Setterfield has written an exhaustive study using statistical analysis to claim change in c. More recently John Moffat, Joao Maguiejo and Andreas Albrecht have independently suggested a change in c as a solution to cosmological puzzles. Many, many scientists have speculated that c changes.

In conclusion, anyone can speculate that the speed of light changes, and many people have. For this to be more than the story of a speculation, we need the theory behind c. Why does light travel at 299.792.5 kilometres per second, not faster or slower? What is the principle behind c? NEXT: A Theory that a child could understand.

## 4 Comments:

A wonderful post. Now I get a better idea of what your papers / book will look like.

This is extremely interesting, and well worth investigation. In order to cover all possibilities, I wonder if maybe, if you write a longer paper, you might include some discussion of the possibility of alternative variables in GM = tc^3?

c = (GM/t)^{1/3} is a major solution, and you have investigated it and found that it explains interesting features in the experimental data, but I'm aiming to write a detailed paper analysing and comparing the possibility that c varies with the possibility that something else varies.

The idea - which may be wrong - is that as you look to larger distances, you're looking back in time. This means that the normal Hubble law v = Hr (there's no observable gravitational retardation on the expansion, which either doesn't exist at all at great distances, unless long-range gravity is being cancelled out by outward acceleration due to "dark energy" which seems too much of an ad hoc, convenient epicycle-type invention) can be written:

v = Hr = Hct

where t is the time past you are looking back to, and H is Hubble's parameter. The key thing here is that from our frame of reference, in which we always see things further back in time when we see greater distances (due to travel time of light and long range fields), there is a variation of velocity with time as seen in our frame of reference. This is equivalent to an acceleration.

v = dr/dt hence dt = dr/v

hence

a = dv/dt = dv/(dr/v) = v*dv/dr

now substituting v = Hr

a = v*dv/dr = Hr*d(Hr)/dr

= Hr*H = (H^2)r.

So the mass of the universe M around us at an effective average radial distance from us r has outward force

F = Ma = M(H^2)r.

By Newton's 3rd law of motion, there should be an inward reaction force. From a look at the particles in that could be giving that force, the gauge boson radiation which causes curvature and gravity looks the most likely.

Conjecture: curvature is due to an inward force of F = Ma = M(H^2)r in our spacetime due to the outward motion of matter around us.

But notice that if this is correct, G is caused by an inward force which is proportional to some scale of the universe, r. If this is correct, the gravitational coupling constant G will be increasing in proportion to r, which in turn is proportional to age of universe t.

The result from a full theory is G = (3/4)(H^2)/(Pi*Rho*e^3), which is your equation with a factor of e^3 included theoretically from other effects (the redshift of exchange radiation and the increasing density of the universe with greater distance/time past).

Since H^2 = 1/t^2 and Rho is proportional to r^{-3} or t^{-3}, G here is proportional in this equation to (1/t^2)/(t^{-3}) = t, agreeing with the simplified argument above that G is directly proportional to age of universe t.

Dirac investigated the a different idea, whereby G is inversely proportional to t.

Dirac's idea was derided by Teller in 1948 who claimed it would affect fusion rates in the sun, making the sea boil in the Cambrian when life was evolving! It's true that fusion rates in stars and indeed the first few minutes of the big bang itself, depend in an extremely sensitive way on G (actually G to quite a large power) due to gravitational compression being the basis for fusion, but if the electromagnetism force is unified with and thus varies the same way with time as gravity (Coulomb's law is also a long range inverse square law, like gravity), the variation in

repulsionbetween protons will offset the variation in gravitationalattraction. In addition the G proportional to t idea has a few good experimental agreements already, like your theory. For instance, the weaker G at the time of emission of the CBR means that the smaller than expected ripples in the CBR spectrum from galaxy seeding is due to weaker gravity.This does seem to offer an alternative variation possibility in case c change is not the right solution. I hope to fully investigate both models.

This is very interesting indeed!

Although it is a bit scary (as that would change a whole lot of theories which I suspect is the real reason for resistance).

My question is if light is slowing down, and if light is radiation, does that mean that in the future radio communications will slow down as well?

And if it continues to decelerate, will that mean faster than light travel will be possible in the next million years via rockets?

Also, if light was faster in the past, what would cause it to slow down? The second law of Thermodynamics?

Sorry for all of the questions, but this is the first time I've heard this theory presented in a rational form (at least that I can somewhat grasp it).

Looking forward to the next post.

:-)HI all. Nigel, I do think that what you are describing need investigating too. I do believe in cultivating alternative theories, and a varying G would be a good counterpoint to varying c.

Not to worry, Darnell. Change in c is so small that it will not affect our lives even in a million years.

However, a changing c opens the possibility of primordial Black Holes, which would be a great aid to future Space travel. Friday's post explains why it slows.

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