Eye in London
(Detainment has ended, though too late for the party at Imperial College. Though this week's events were disappointing, we must keep a stiff upper lip. Yesterday 4 times as many people read my talk online than would have seen it in Blackett Hall. My experience was a nuisance, but not that bad. It was nothing like the 3600 nights Galileo spent under house arrest, or the treatment given to Aung Suu Kyi and political prisoners worldwide. I am still more concerned about Faye Turney and the British servicemembers held in Iran.)
Here are Slides 2-3, with the accompanying text:
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.
(More coming soon.)