Tuesday, February 13, 2007

El Caracol

El Caracol (The Snake) at Chichen Itza was once thought to be just some kind of pavilion. Now we know that it was a sophisticated astronomical observatory. During solstice days, sunlight entering certain windows would produce a snake image on the inner walls. With its circular dome it even looks like an observatory.

Yesterday we saw the tallest structure, called Kukulkan's Pyramid. During Vernal and Autumnal equinox days, the stairway's shadow would appear as a snake descending the pyramid steps. This symbolised the serpent-god Kukulkan's descent to Earth. Arranging this display required advanced knowledge of astronomy and geometry.

The Mayans believed that Space and Time were a unity. More than 1000 years later Einstein would codify this idea into Special Relativity. Humans are hardwired to think this way. Few people know exactly how many kilometres are between work and home, but nearly everyone knows the time it takes to get to work, down to the minute. The conversion factor is the speed of your vehicle. Before accurate maps existed, the distances between towns was measured in days travel.

Special Relativity can be reduced to this simple principle: Space and Time are one phenomenon related by c. The light cone in 3 dimensions looks like the expanding spherical waves from a radio transmitter. If you are outside the light cone our separation is spacelike and you can't read this anyway. If you are within the sound of my voice, our separation is timelike. Our separation is then literally a matter of time.

The conversion factor between Space/Time is c. Factor c is more than just the speed of light, it is the speed of any massless particle. The effects of Special Relativity apply even in a dark room with the lights out. To convert Time into Space, just multiply by c.

Applied to our Universe, 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 the Big Bang, the Universe was a tiny volume. Scale R of the Universe is our timelike separation t from that centre, multiplied by today's conversion factor c. In equations, R = ct.

That is all you really need to understand the expanding Universe. The Universe can't expand at the same rate c forever, for gravity slows it down. From a simple principle come GM = tc^3 and predictions about expansion, redshift and structure formation. It also produces invitations to the most interesting places.


Blogger nige said...

Very interesting post with nice photos!

"The Universe can't expand at the same rate c forever, for gravity slows it down. From a simple principle come GM = tc^3 and predictions about expansion, redshift and structure formation."

Well, if gravity is a Yang-Mills quantum field theory, gravity can't slow down the expansion in the way predicted by Friedmann's solution to general relativity, because relativistic redshift of exchange radiation between masses at vast distances will weaken gravity between those masses.

The stress energy tensor T on the right hand side of G=8*Pi*T in general relativity needs to be corrected for this effect.

Nobody else seems to think about the consequences of this (see http://nige.wordpress.com/ for some results).

Best wishes,

3:01 AM  
Blogger L. Riofrio said...

HI Nige: Yours and other theories need to be explored too. Some form of modified gravity, as you have proposed, would be a natural idea to investigate.

12:15 PM  
Blogger Rae Ann said...

The snake imagery is very interesting! Lately I've been playing an idea about the imagery of Eve and the Serpent and the Tree of Knowledge. I haven't gotten it all together yet, and it's not 'scientific'. But I'll let you know if it gets worked out a little more.

5:04 AM  
Anonymous huxley said...

Nice photos and a great site.

Not to be a nitpicker, but Caracol actually means Snail, not Snake.

6:17 PM  
Blogger Toys Exporters said...

It is a very good habit to talk about interests and some people have a lot of interests on spaces and they always try to know about the phenomena of spaces like custom essay writing they also do a lot of study on spaces according to me it is just the matter of interest and if anybody have interest in any thing then he will definitely decide for how to know it.

8:21 PM  
Blogger Maria Owens said...

You always come with new ideas and thoughts. Your ideas are unique and can provide a base for further detailed studies, research articles and proofreading and editing services. Definitely if your ideas are modified and restructured into new version it can become a base for future research.

12:11 AM  

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