MadSci Network: Astronomy Query:

### Re: what is the meaning (exact defintion) of 'times come to an end'?

Date: Sat Dec 16 11:58:55 2000
Posted By: Dan Mayer, Post-doc/Fellow, Mathematics and Theoretical and Particle Physics, I am currently out of work.
Area of science: Astronomy
ID: 975832803.As
Message:
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Sorry, but I could not find this quote. I would guess it is areference to
the fact that space-time could be curved in on itself (if the universe is
denser than the critical density), so that the universe eventually comes
together in a 'big crunch' which would end time.
Here is my answer to another question on general relativity, which gives a
(very) brief outline of the subject.

Space-time can be curved. It is curved by mass (or energy) - this being
the source of gravity. To warp it very much, a huge amount of mass would
be required - this is what happens in a Black Hole.

If you drew a circle on a flat piece of paper, and measured the radius and
the circumference, you would hope to find that
radius = circumference / 2*pi.
What if you were not aware of height, but lived on the Earth. You could
draw the equator - a circle. The radius should be measured from the centre
of the Earth. But being unaware of the direction 'down', you would
measure the radius from the North Pole. This would be much larger than the
actual radius. When you divided the equator (your circumference) by 2*pi,
you would find that your measured radius was much bigger than your
expected radius. There is an excess radius because the Earth's surface -
your space - is bent.

The surface area of a sphere is A=4*pi*(r^2). If you measured the surface
Area, you would expect to predict the radius, r=sqrt(A/(4pi)).
...unless, that is, our space-time is warped. In this case, there may be
= GM/(3c^2),
where G is Newton's Gravitational Constant, c is the speed of light, and M
is the mass inside the sphere (assumed to be evenly distributed).
G/3c^2 has a value of about 2.5*10^-29 cetimetres per gram, so for each
gram, there is an excess radius of about 2.5*10^-29 cm.
As you can see, a lot of energy is needed to warp space-time by a large
amount.

I suggest you read 'Hyperspace' by Michio Kaku for a good account of this
area, or 'A Brief History of Time' by Hawking, or perhaps 'Six Not-So-Easy
Pieces' by Feynman, whose explanation of General Relativity I have just
given you.

[Moderator's note:  Dan gives a great explanation of the basics of curved
space.  When we apply general relativity to the whole universe, it turns out
that it's possible that space can be like a sphere - this is called a "closed
universe".  In this case, it turns out that such a universe will collapse in a
"Big Crunch," exactly the opposite of a "Big Bang."  This would mean that time,
at least as we know it, would end.  However, recent observations suggest that
the universe will expand forever and that time will never end.  You can find
more information by searching our site under "Big Crunch."]

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