Talk submitted for March 29
We can illustrate Special Relativity if we keep time t vertical and compress dimensions x, y, and zed into this line. An interval outside this cone is spacelike —an event here cannot affect an event there. An interval inside the light cone is timelike, literally a matter of time. Space and Time are related by factor c, called the speed of light. From this principle can be derived the useful equations of the Lorentz transformation.
Just as this is just one capsule of the London Eye, these local conditions are part of the larger Universe of General Relativity. Again x, y and zed are compressed into the screen. There is no centre in space; every bit resembles every other bit. There is a centre in time, what we call a “Big Bang”. Near that initial singularity, mass M of the Universe was occupied a small volume. Though separated from the Big Bang by 13 thousand million years, we are within its cone and that huge mass influences even the propagation of light.
Space/Time can be Unified by a simple principle. Scale R of the Universe is distance from that origin, age t multiplied by c. That is why as t increases, Space expands. It can’t expand at a constant rate, for mass and gravity slow it down. We’ll skip some math here. GM=tc^3. (Gravitational constant, Mass of Universe, 1 dimension of Time and 3 of Space.) Both sides are constant. When t was tiny c was enormous and the Universe expanded like a Bang. As t increased that expansion slowed due to gravitation and continues asymptotically to this day. This equation made the heretical prediction that c slows at a rate too tiny to detect, until now. Today we can compare prediction with experiment.
First we can solve for c and R. This is the metric of Einstein-de Sitter expansion, tracitionally the cosmologists'favourite model. Any cosmology should solve the Einstein-Friedmann equations. These simple expressions form an exact solution of k = 0 and density (Omega = 1) . This so-called critical density of mass is in fact a stable density. Below this density, quantum mechanics predicts that matter will form via pair production.
Before formation of matter, initial density for a given mass M is just M/V. That number is less than this number, and the difference is 4.507034% precisely what the WMAP spacecraft has measured. Location of the first acoustic peak shows that density as predicted. You can also model proportions of the Universe’s other components. The CMB provides an indication of change in c. The average temperature is the same over large areas. Even at this time of recombination, 300,000 years after the Big Bang, c was much faster.
We can search the CMB for signatures of inflation. (Thank you Dr. Cline for the graph.) The old paradigm says that density fluctuations should be the same at all scales. Inflation’s predicted power spectrum is ruled out by both COBE and WMAP. Here is the prediction of Unified Space/Time. When predictions fit the data this closely, perhaps there is something to the theory. CMB data was initially interpreted to indicate that the universe is flat, like the Earth. When changing c is a factor, it is curved with radius R = ct as predicted.
Colleagues in Australia caused a bit of stir when they claimed to detect alpha changing. Since the evidence is still non-conclusive, we can stipulate that product hc is indeed constant, as are the photon energy and Chandrasekhar limit. This means that redshifts of distant objects are indeed caused by expansion. It also verifies Dr. Lieu and Dr. Hillman’s very important finding (ApJ 585, L77, 2003), that “Planck time” is an illusion.
Extraordinary claims require extraordinary evidence. The most surprising prediction may already have been seen. Dr. Krauss says that supernova data “naively implied that the Universe was accelerating.” Redshifts are the only direct evidence of cosmic acceleration. (What was overlooked a child could ask.) What if v/c increases not because v is accelerating, but because c slows down?
When light of redshift Zed was emitted, c was faster by sqrt(1 + Z). Apparent redshift is therefore decreased. This factor is negligible for low redshifts, where zed increases linearly. An object of redshift 1.0 recedes at 60% of our present speed of light. That is only 42% of c at the time its light was emitted. The apparent redshift is just .57. Supernovae produce that light according to E=mc^2. Energy output is here doubled, for a magnitude shift of -.75. Connect the dots, and the upward curve of Type Ia redshifts is precisely predicted.
As you know, it was possible to believe that the Universe is accelerating due to some inferred repulsive energy. Now there is corroborating evidence from a nearby star. According to astrophysics, life should not have evolved here at all because at Earth’s formation the Sun was only about 70% as bright. Our average temperature would have been 10° below zero centigrade, frozen solid. Prof. Allen at Imperial says this can’t be true, for geology tells us Earth’s temperature was suitable for liquid water. This is called the “Faint Young Sun” paradox.
Here’s a hot young solution. The Sun also turns fuel to energy according to E=mc^2. Adjusting for change in c at various epochs, solar luminosity becomes a nearly level line. Some things are nearly constant, and the “solar constant” has allowed life to evolve over thousands of millions of years. This distinguishes Theory from “accelerating universe” ideas and models where c was higher only during an inflationary period. If c had not changed in precisely the amounts predicted, we would not have evolved to argue about it. A 2ND PLANE HAS HIT THE TOWERS. There are now two lines of evidence from truly independent sources indicating that c has slowed according to GM=tc^3.
More supportive data comes from the Lunar Laser Ranging Experiment. The PLANCK spacecraft will determine whether baryons are indeed 4.5%. Another indication would be discovery of supermassive Black Holes at high redshift. Dr. Blandford also alluded to discovery of ultra-high energy cosmic rays. All these experiments contribute to an exciting “c change” in physics.
Thank you again for sharing such outstanding science this week. This is truly a thrilling time to ask questions. Someone nearly succeeded in preventing you from hearing this, thinks you cannot understand something so simple. You have many outstanding questions, so please bring it on.