azizlwl said:
The universe is expanding as the cosmologists say and the analogy given as in the expanding balloon. But the balloon still has a center. The expanding universe after the big bang is also said taking place at nowhere and nowhen. Couldn't figure out how is something is expanding without referring to a point.
Thank You.
Ah, so the analogy is a good one but you have to be really careful (and wherever you read it from has to be even more careful!) The key point is that we liken the expansion of our universe to the SURFACE of the balloon, not the physical 3-dimensional balloon, only its two-dimensional surface (Don't think the surface is two-dimensional? Ask yourself how many coordinates you need to describe (uniquely) a point on the surface. The answer is of course two, which we usually use to be latitude and longitude). Now, as the physical balloon blows up, its surface expands in a manner similar to the expansion of our own universe -- points recede from each other with velocity proportional to their distance. Imagine putting yourself in the position of a dot on the surface of the balloon -- everyone else is running away! No point on the SURFACE can claim to be the center of the expansion. Furthermore, if we run the clock back and suck air out of the physical balloon, this is equivalent to contracting the universe, or running the clock back in time for our physical universe. Things get closer together. You can make the physical balloon as small as you like, and the points on the surface of the balloon get arbitrarily close together -- this is the big bang.
OK so hopefully the above discussion makes sense, now some caveats. Of course, our own universe is 3-dimensional, not 2, so the surface of a balloon cannot be a real analog of our expanding universe. Indeed, the mathematical object would be the 3-dimensional surface of a 4-dimensional sphere! Don't try too hard to picture this, it's likely impossible. The other big caveat is that in the balloon analogy, there still exists a PHYSICAL balloon, which has of course a center in the usual 3-dimensional space. The abstract jump you need to make is that the geometry embodied by the SURFACE of that balloon can exist independently of the physical object we know as the balloon. Specifically, if you imagine yourself living on the surface of the balloon, you can run experiments by drawing triangles and summing their angles. If your results show that the sum of the angles is always greater than 180 degrees, you have shown that you are living on a curved surface like the surface of the balloon -- But these properties (sum of angles > 180) are INTRINSIC too the world you're living in, you don't need to mention any larger 'balloon' that you're sitting on the surface of. This is the abstract step that trips a lot of people up, and it's quite a tough one. The take-away message here is that although when we visualize a 2-D surface of a balloon, we necessarily also picture the 3-D balloon object, this is only a limitation of our imagination as human beings, not a mathematical necessity. The conclusion, then, is that the universe, as a 3-D object, does NOT imply the existence of some 4-D object it is sitting on the surface of.
(Note: Everywhere I've been speaking strictly of the dimension of SPACE.)