I got it from your line, “If we’re not here, the questions don’t exist.” Talk about unwarranted assumptions!
It’s not science, though, and it’s a hijack to the OP. If you want to go debate philosophy in GD, feel free to start a thread there and I guarantee I won’t butt in.
Actually, the impression I got from Mathochist is that people who need analogies (of which I am one) sometimes end up arguing the validity of what are mathematical problems based on the limited accuracy of the analogy. The problem is, analogies are imperfect, and people with limited or no understanding of the mathematics involved will frequently end up citing the problems with the analogy as reasons for why the theory itself is flawed. This is extremely frustrating for everyone involved.
Analogies are a great way to derive understanding of an unfamiliar topic, but they are terrible for basing an argument on. If you get to the point where the analogy you’re using falls apart, it’s not necessarily a problem with the theory, it’s just time to stop using the analogy and move “up” and try to understand some of the fundamental concepts directly.
I completely understand. And you’re right, analogy is only there to illustrate or illuminate, and not to be used in substitute of the actual concept, otherwise it completely breaks down. But sometimes I don’t think that’s the issue. Sometimes it’s just a matter of patience until the layman can sort of work it out himself, or until analogy upon analogy can be used to further define the idea. When it came to the theory of relativity, it took me a while to really understand what was going on. In fact, it was the first facet of reality I encountered that I found to be very “unintuitive”, and I was rather dismayed by it. It took me a lot of reading and analogy for me to finally get to the point where I could say with confidence that I UNDERSTOOD what was happening there. Now, it almost seems second nature, and I don’t think of the universe the way I used to. All that without an ounce of math. But I GRASP it. And what I love about this place (at least idealistically) is that you are free to ask, and keep asking until you feel you got it, or that you just never will. Is it an exercise in futility? Maybe sometimes. But people like you and I understand the limitations of analogy, and know when to try another route. Until then, I say, keep asking, and let those with the patience, try to illuminate.
This is all I’ll say here, as this is not my thread, nor the forum. All you guys rock 
If the Universe were expanding into some vaguely-defined “emptiness”, there would be an edge to the Universe. But what if you were close to that edge, and looked at what was past it? If you can look past the “edge”, even if you don’t see anything there, then that beyond-the-edge region is part of the Universe, too, so it isn’t really the edge of the Universe.
The Universe has no edge. This may be because it’s infinite, or it may be in the same sense that the surface of the Earth has no edge: You can sail as far as you like on the Earth, but you’ll never sail off the edge.
Some theories of quantum gravity say that space is only defined relative to things - photons, quarks, matter or whatever. Therefore, if there are no things (before the Big Bang) there is no space.
If you think of the observable Universe as all the matter and energy in it then it makes sense to talk about an edge as the farthest reach of junk since the Big Bang and that if you were at the edge, you would be looking out into infinite blackness. As I understand it, you can’t think of the Universe this way. I am not saying that you guys are wrong, just that I don’t understand it.
BTW, I am perfectly willing to do a little math to understand this. However, it’s been a long time since I took Vector Calculus and Discrete Math and whenever I try to read more technical stuff about this, the author launches immediately into discussions about things like Hilbert space and Lorentz invariance without explaining things like that for the benefit of the novice. I looked that stuff up on Wikipedia once and those articles overloaded me with jargon and forgotten mathematical syntax in short order. Is there anything out there that bridges the gap between completely unintuitive statements like “the Big Bang created time and space which were entangled prior to Planck time” and the stuff aimed at the advanced physics student?
Thanks for your help,
Rob
sweeteviljesus, Penrose’s latest book may be of help.
[hijack]
Can someone explain the extrapolation that leads to the age of the universe i.e. what group of equations lead to the number 13.7 billion, so to speak?
[/hijack]
In a nutshell: The MAP satellite (yeah, yeah, WMAP, but I think it’s silly to rename an instrument after it’d been collecting data for a year) measured the apparent angular size of the fluctuations in the Cosmic Microwave Background. We already had a good theoretical understanding of how big those fluctuations should have been, so seeing how big they appear from our vantage point lets us determine how far away they were. Given how far away the light from the CMB is coming from, and knowing the redshift, we can very precisely determine Hubble’s constant. And the age of the Universe is inversely proportional to Hubble’s constant.
Of course, it’s actually more complicated than that. The standard-ruler distance calculation has to take into account the curvature of space and time between the standard ruler and the observer. Both the redshift and the theoretical size of the fluctuations depend on the age of the Universe at the time of decoupling. And the constant of proportionality between H and the age depends on the model one uses of the Universe’s expansion, which in turn depends on the composition of the Universe (how much is matter, how much radiant energy, and how much dark energy). But that’s the gist of it.
There are already numerous threads on this exact topic, and these same questions have been answered and these same objections have been raised. There’s nothing else to be said on this board but “start learning mathematics”.
That said, I’ll again restate what has already been said in this thread, but more explicitly. Consider a sphere (when mathematicians say “sphere” we mean the surface of a ball, not the whole solid interior). In fact, let’s be extremely explicit and consider the unit sphere in three-dimensional space – the collection of points exactly one unit from the origin.
Now, we can slice this sphere by planes parallel to the x-y plane, and at different heights z. For instance, z=0 gives a circle of radius 1. z=sqrt(3)/2 gives a circle of radius 1/2 because
x[sup]2[/sup] + y[sup]2[/sup] + z[sup]2[/sup] = 1[sup]2[/sup]
x[sup]2[/sup] + y[sup]2[/sup] + (sqrt(3)/2)[sup]2[/sup] = 1
x[sup]2[/sup] + y[sup]2[/sup] + 3/4 = 1
x[sup]2[/sup] + y[sup]2[/sup] = 1/4 = (1/2)^2
z=1 gives just the point (0,0) on the plane. z=3/2 gives no points (x,y) satisfying x[sup]2[/sup]+y[sup]2[/sup]+9/4=1.
So we can define a function on the sphere which takes a point and gives the z-value, and slice up the sphere by the different values. What we note is that there’s a “lowest point” on the sphere – below z=-1 there’s no sphere.
Now, in the universe we’ve got something like this sphere, but four-dimensional rather than two-dimensional (we’re thinking of a sphere in 3-space, but it is itself only two-dimensional). We slice it up by “time”, getting a bunch of slices we call “space”. The “big bang” is just the statement that there’s a “lowest point” for the universe like there was a lowest point on the sphere.
Now, this is slightly wrong because slicing up spacetime involves a lot of choice as to how we do it. If we chose a different method of slicing the sphere we could get a different “lowest point”, but in spacetime we always go back to the same lowest point.
Also, we should really have defined the function we used to slice the sphere by looking only at the sphere itself rather than the ambient space. Maybe the property we found of the sphere was dependant on how it was sitting in 3-space rather than anything inherent to the sphere itself.
A rougher hand-wavy explanation: Spacetime comes equipped with information at each point that says “these directions are forward in time, these are backward in time, and these are towards space”. Imagine two infinite cones placed tip-to-tip. Directions in one cone correspond to moving forward in time, in the other to backward in time. The further the direction is from the axis of the cones, the faster the path is moving. The boundary of the cone corresponds to a path moving at the speed of light.
Now, there’s one of these cones at each point in spacetime. If we draw a path through the point, either its tangent will point into the “forward” cone, into the “backward” cone, or out of the cones. We know that we can’t move faster than light, so every path describing the motion of a particle must point within the cones at every point along the path.
So, consider every possible path that always points into the backward cone at each point along itself. These will all eventually meet at one point in spacetime: the big bang.