Friday, April 06, 2007

Why It Slows

Many of you have seen bits of this lecture before, so thanks for your patience. I will conclude with a new way of visualising c change.

An important lesson from Relativity is that Space and Time are really the same phenomenon. Humans are already hardwired to think this way. Few people know exactly how many kilometres are between work and home, yet most know how long it takes to reach work, often down to the minute. We are used to saying "8 minute drive" or "30 minutes away." The conversion factor is the speed limit of your vehicle.

Intervals in Space/Time are either Spacelike or Timelike. The lightcone follows the metric dr = cdt. Outside this cone, the interval is Spacelike. An event at the lightcone's origin can not affect an event outside. Inside the lightcone, the interval is Timelike. The difference is literally a matter of Time. The conversion factor here is Nature's own speed limit, the speed of light.

The local conditions of Special Relativity, which does not allow for gravity, are part of the curved Space/Time of General Relativity. There is no centre in Space, for every bit resembles every other bit. There is a centre in Time, called a "Big Bang." Our timelike separation from this origin is age of our Universe t, about 13.7 billion years. Now we state a simple principle: The characteristic scale, or radius of curvature R = ct. This is why, as t increases, the Universe expands. That is what powered the Big Bang and continues to drive expansion today.

The Universe can't expand at the same rate forever, because mass and gravity slow it down. Gravity then requires that:

GM = tc^3

Where G is Newton's gravitational constant, M is mass of the Universe. When t was tiny c was enormous, and the Universe expanded like a Bang. As t increases, expansion slowed due to gravitation and continues slowing asymptotically to this day. The curvature radius R, the Schwarzhild radius of a Black Hole, photon wavelengths, and even the size of magnetic fields increase at exactly the same rate!

Here's another way to explain c change. Photons can be thought of as satellites orbiting around the "Big Bang" origin. If you were an astronaut in low Earth orbit, satellites whizzing by your altitude in circular orbits would all have the same velocity. As a satellite's altitude increases, velocity goes down. Every photon that passes by at that moment has the same velocity and timelike separation from the Big Bang. As the Universe expands, that separation grows. Velocity of photons thereby decreases at a very small rate.

As you see, these equations are simple enough for a child to understand. Yet it has taken humans centuries to figure this out. Most physicists still can't explain it, leading to "dark energy" and other epicycles. Is it not fun to discover something simple?

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Anonymous Anonymous said...


Now I am beginning to understand a little about the argument with the speed of light slowing down.

As you mentioned before, it may also help to explain the mysterious "dark energy" that I keep hearing about (sounds similar to the "dark side of the force" from Star Wars).

Perhaps this helps explain Einstein's cosmological constant, although I am not too sure if he would be happy knowing someone challenged his "c" theory.


12:18 PM  
Blogger L. Riofrio said...

Thank you, Darnell. I am very happy that you enjoyed the post. Who knew that someone would grow up to challenge the dark side? The name "dark energy" will never catch on outside a small group of disciples..

Einstein later admitted that the cosmic constant was a blunder, and I am not one to argue with Einstein. He later favoured models that expand as R ~ t^{2/3}. like this one.

Einstein also wrote that constant c was “neither a supposition nor a hypothesis about the physical nature of light but a stipulation which I can make at my own free discretion.” In other words, constant c is not required.

3:11 PM  
Anonymous Anonymous said...

Dark matter does seem rather suspicious. The way it is employed and justified reminds me quite a bit of Newton's use of God to fill in the gaps he found in his physics. As a general principle, I think it is wise to avoid postulating new entities to solve problems. So, I find your approach appealing because it nicely matches philosophical methodology-it is simple, economical and avoids the postulation of mysterious entities. Also, I like going against prevailing opinions...they tend to be wrong. :)

5:21 AM  

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