What was after the big bang?

Question

There are two stars A and B in two remote galaxies.
We measured angle S between these stars in
the sky, and asked their hypothetical inghabitants
to do the same, ie angles between A&S from B,
and B&S from A. Is the sum of angles
A + B + S greater, equal to, or smaller than π?

Answer 1

You can sort of do this experiment, not by going to distant galaxies, but by making a large number of observations of galaxy radius vs. distance. If you assume that galaxies are the same size (or if you think you can assume some particular *kind* of galaxies is always roughly the same size), then the angular size of that kind of galaxy should be inversely proportional to its distance.

So you do the experiment, and if very distant galaxies are bigger than they should be, it's because triangles have more than 180 degrees in them, and vice versa.

Such experiments have been done, but they show that large triangles have about 180 degrees in them.

There are other experiments that are done as well, such as counting the number of galaxies within a sphere of radius r for various values of r. If space is flat, the volume of the sphere (proportional to number of galaxies in the count) should be proportional to r^3. If the volume is more than r^3, space is closed and vice versa. Again, these experiments show that space is flat, but the experimental errors are huge.

Answer 2

If we can make all three measurements simultaneously, and ignore gravity, you will get exactly π radians for the sum of the three angles. If you take into account the curvature of the path of light by gravity, we have three points:

____S


A________B

The light that goes from S to B actually starts out heading further to the right of B, but the gravity of A and B curve it so it hits B. However, this means it's hitting B from a direction different than the actual direction in which S lies (from B's perspective).

Therefore, B sees S as being further to its "right" than S actually is. Likewise, B sees A as being further to its "left" than A actually is. Therefore, if it was an equilateral triangle, all three civilizations would measure their angles as being greater than 60 degrees, despite the true angles being exactly 60 degrees. They would all communicate and come up with a total greater than 180 degrees, i.e., greater than π radians.

However, if the remoteness of the galaxies makes fast communication impossible, and the galaxies are drifting large distances relative to each other in unknown directions, then the measurements might be made millions of years apart. If this is the case, there is no way to know what the sum of the angles will be, since each person will be measuring a different-shaped triangle.

Answer 3

I don't think we know the answer to that question for sure yet.

It appears that the angle is pretty close to pi though (space-time pretty close to flat).

Get back to me in another 10 billion years and the answer should be more obvious.

Answer 4

Big pregnancy.

Thanks for asking!