## Tuesday, September 12, 2006

### Beauty in the Equations

Today's image is much more pleasant. History shows that our achievements last longer than the obstacles. That is reason to spend years working on something that may not be recognised in this lifetime. I hope you all enjoy the graphics.

The "Big Bang" can be drawn as a point. Cosmologists agree that the baby Universe had a finite volume and therefore a finite mass M. All points of this Universe were very close to one another. Our separation from the Big Bang is a matter of Time, not Space. That interval is simply age t of the Universe. Astronomers have estimated that age at about 14 billion years.

The light cone represents the local conditions of Special Relativity. Our mass, even the mass of our galaxy, is negligible compared to mass M of the Universe. We are within the light cone of that enormous mass, and its gravity is affecting us. Fortunately there was only one Big Bang to pull us back. As Newton showed, the gravitational force from a spherical mass distribution is the same as if all that mass were concentrated in a point.

Einstein theorised that this Universe is of spherical shape. Our three dimensions x, y and z are now confined to a circle. Any direction that we can travel in Space keeps us within that circle. The Universe might appear infinite and flat to our experience, but can still be curved in the fourth dimension.

In this spherical Universe, the combined gravitational attraction would be the same as if everything was in a point. There is no centre in Space, for every bit resembles every other bit. There is a centre in the Time dimension, which we call a "Big Bang." As time passes, our Universe expands away from the Big Bang.

Newton's Law of Gravitation insists that mass affects us at a distance. It is meaningless to express this attraction over Time, so we must add the conversion factor c. Here we can expand on one principle of Special Relativity. Since Space and Time are one phenomenon related by c:

Scale R of the Universe is its age t multiplied by c.

This astonishingly simple relation tells why we live in a growing Universe. As time t increases, scale R expands. Most laws of physics are time-symnetrical; they do not favour any direction forward or backward in Time. Expansion does not share this symnetry, it is called an Arrow of Time.

At a distant beginning time of zero, the Universe would have had zero dimension. Everything that we know resembled a single point. Since that time our Universe has been expanding. It can't expand at the same rate c continuously, for gravity slows it down. Conversion factor c must be further related to t. This leads to an astonishing but testable prediction.

paul valletta said...

"Our separation from the Big Bang is a matter of Time, not Space."

But let me give another Quote:
"Between Two points in Space, there is One Time, between Two points in Time there is but One Space."

The Future lay's between two points in Spacetime. One Time = Now.
Now lays between the Future and the Past.

The "two" points in Time are always Future and Past ?

Now is always ONE space, THEN is always "two" times?

According to your passage quoted above, our separation from the Big Bang is a question of Time, so thus we are detached from the Big Bang in Time but not Space?...thus the Big Bang is continueous for all spacetime co-ordinates?

Question:How can a Big Bang event be singular in time (one-off), and be continueous in Space? ;)

12:30 AM
L. Riofrio said...

Hello Paul: Near the Big Bang, all points in Space were very close together. Our distance, R = ct from one point near the BB, is virtually the same as our distance from any other point in the BB. Imagine all points in the Universe, including our location, crammed in a very small Universe.

You are correct: Expansion and slowing of the BB is continuous for all Space/Time coordinates. The Big Bang ain't over, we are still in it.

There is an inner boundary in Time, an initial singularity when t = 0 and R = 0. We can consider this a boundary condition.

7:18 AM
paul valletta said...

Hello l.riofrio, so let me see if I have the correct image of your statement,"There is an inner boundary in Time, an initial singularity when t = 0 and R = 0. We can consider this a boundary condition."

Would you agree that this image can be representative:

http://eskesthai.blogspot.com/2006/09/coxeter-and-platos-cave.html

where the inner "white_void" is the location of a singularity, and the outer "End_points" form a structured boundary?

All points on the "outer_boundary" are self similar, as all points in the "inner_singularity" are self similar ?

At the core singularity there is no Time, thus no structure, at the outer edge, there is structure, thus there is time. One can assimilate the outer boundary with discrete, exact time_lengths, from point to point.

Looking from any outer structured location, would project that all
locations are infact identical, it is only when one glances into the past core, does one observe change?

Surely the inner 'initial' boundary does not equal the outer 'structured' boundary?

12:23 PM
Anonymous said...

You claim that R=ct, and that therefore because the age of the universe is increasing, the "radius of the universe" (which is poorly defined in your definition) is increasing linearly.

However you claim that the speed of light is decreasing as 1/t.

Under your own maths, this would give R=(1/t)*t = constant.

Note that I do not agree with this R=ct definition.

1:03 PM

As Newton showed, the gravitational force from
a spherical mass distribution is the same as if
all that mass were concentrated in a point.

12:17 AM
qraal said...

Hi Louise,
How does that work? If R=ct, but c is a function of t, then why does that equation imply constant expansion? What am I missing??? I need to sit down and integrate this one out...

1:13 AM
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