I’m greatly enjoying this discussion. Thank you to CatSci in particular. I’m learning a lot. The analogy of the earth’s surface to try to understand the concept of a finite unbounded universe is really useful. I can feel that my mind, that has struggled with these mind-bending concepts, just became slightly less bent out of shape.
An exercise in dimension reduction may help:
Consider a cube. It has 3 dimensions. If you reduce if by one dimension, you get a plane, which is 2D.
If you reduce a plane by one dimension, you get a line, which is 1D. Reduce a line by one dimension and you get a point, which is zero-D.
Now, that zero dimension point can represent an object that has another dimension.
Consider a pencil, lets call it a line (forget that it has a width). If you look down the shaft of the pencil, it will look like a point. (point it directly at your eye and you only see the tip)
Consider a point on a page, that could represent a pencil that is pointing into the page (that you are looking down the shaft of).
That zero dimensional point can represent a one dimensional line, we just can’t see the dimension because it is going into the page and the page does not visually represent that dimension to us.
To go up a dimention, consider that a line can represent a plane that we are looking at on edge. The plane goes into the page and we are looking down its edge so then visually, that gets represented as a line. A line can represent a plane that is going into the page.
Still with me?
Now, consider the
surface of the Earth. Just the 2 dimensional surface, there is no up and down, just north/south and east/west (two dimensions)
Let those 2 dimensions of just the surface of the Earth represent all three spatial dimension (just like a plane can represent the edge of a cube).
Let the north-south direction represent the timeline.
While you are in the northern hemisphere, as you travel southward, the Earth gets bigger as you approach the equator.
That represents that three spatial dimension of the Universe expanding through time. As we go forward in time, the Universe gets bigger. As we go southwards, the
surface of the Earth gets bigger. Remember to keep this to just the surface, there is no interior and there is no exterior, as those would be additional spatial dimension beyond the three that we are talking about.
Now, let’s go back in time, or northwards on the surface of the Earth.
The surface gets smaller and smaller as you approach the north pole. That’s just like the Universe getting smaller and smaller as we approach the singularity.
So, what happens when you get to the north pole? That represents the singularity at time T=0.
Well, the surface of the Earth wraps back around on itself. That is, you can’t go any farther north than the north pole. At the north pole, any and every direction you look towards will be “south”. You cannot leave the
surface of the Earth and point upwards, because that dimension does not exist within this analogy.
Asking what is before the Big Bang is just like asking what is north of the North Pole. The question just does not make sense. You cannot go any farther north than that and there is no such thing as time before the Big Bang. Time, itself, along with space (i.e spacetime), emerged at the Big Bang. Since time started there, you can’t go back further than that.
At the north pole, all direction are south. At the Big Bang, all time is forward. The singularity is like the north pole, its a point where everything comes together and from it there is only one direction you can face, as all directions are the same: “south” or “forward”.
Make sense?
Any questions?