What is Time and Space

I wouldn't be to concerned with how "old" the universe.
That question basically translates into how many of my "spacelike" slices can fit between now and the big bang.Different observers will get wildly differing answers.

Yeah, but our proper time didn't truely exist before the formulation of the Solar System, so that integration is an idealisation.
To be accurate we'd have to sum the integrals of the proper time of different objects until we reach the big bang.
In other words our proper time path back to the big bang isn't actually our path from the big bang, so when we integrate proper time back to the big bang we're technically assuming Earth was in existence right up to (tau) = 0.There is a section on this in Gravitation.

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Sorry, I'm a theorist. The universe is a mathematical solution to Einstein's equation (or some possibly string inspired variant). It's (approximately) a 4d hausdorff manifold with pseudo-Riemannian metric and I can integrate "god-like" between any two events I feel like. I don't need the earth or any physical object. I just choose locally non-accelerating frames.

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Yes, but that can't give you the age of the universe from Earth's perspective.
You can choose any two events and integrate, but it won't mean anything with regards to the age of the universe.
Earth's proper time isn't defined before it's existence, when it was just an ensemble of gas and rock (roughly).
To get the age of the universe from Earth's point of view would require Earth existing at the Big Bang.

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I really don't understand your reliance on the Earth.

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I amn't relying on the Earth, just using it as an example that there is no object in the universe which can truely say the big bang happened "x" years ago.
All any object can do is extrapolate its proper time back to the big bang and call the integral of this "the age of the universe".
However the problem is no objects "current proper time" existed even 500,000 years after the big bang.

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The Galaxy has been here a lot longer than the Earth has... is that good enough?

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No, not really.
It was an issue in 70s cosmology and is now considered largely unimportant.

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Let me see if I have this right. Protons are neutral but they act as agents for the electro-static force by, for example, attracting a negatively charged particle to a positively charged one. Gravitons are capable of exercising either positive gravity or negative gravity on mass, which is gravitationally neutral. I'm experiencing positive gravity right now but when might I encounter negative gravity?

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Gravity is a little weird compared with the other forces*.
Mass is gravitational charge**, but unlike electromagnetism there is only one charge, no positive and negative and it always attracts.
Gravity is also gravitationally charged, which is what makes it especially weird. Gravity itself feels gravity.
In other words just as gravity can pull two objects together it can also pull gravity together.*Some people believe that gravity is so different from the other forces because it isn't truly a force.
**Technically it isn't only mass that is gravitational charge. Stress, angular momentum and electric charge can also cause gravity.

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Also it seems to me that the original singularity would be different than a singularity in a black hole.

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Definitely.
The Big Bang singularity was "special" where as singularities in black holes are "generic".
This is because any star can collapse into a black hole, but the beginning of the universe was obviously specific or balanced in some way.
(In truth it is to do with a thing called phase space but I won't go into that.)

I wouldn't get the road to reality if I were you.
If you aren't familiar with the maths, it is pretty hard to follow.It's basically a book for a mathematician who wants to learn physics or a physicist who has an interest in pure maths or maths methods.It certainly isn't for the lay reader.

I pretty much read the book as a physicist interested in seeing how a mathematician approached certain things.
It was also fairly good for seeing the development of certain avenues of physics, such as advanced Quantum Field Theory (I'm a relativistic astrophysicists in training, so although I'd know a good deal of QFT, I wouldn't have a detailed knowledge of QCD's finer points.) and unusual approaches to unification, outside the Loop Quantum Gravity and String Theory crowd.

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Is there a book that you know of that provides the concept, an explanation of the math and the formula?

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You said you don't know calculus, so would you like examples of good calculus books or something else.

Light exists in spacetime, it's just that from its point of view spacetime wouldn't be divided into space and time and would appear as static spacetime.*

There still isn't any evidence for the graviton, so I wouldn't really rely on it as an explanation of gravity for now.
(In fact the graviton might be just us attempting to give everything a particle, which mightn't apply to gravity.)The best way to think of gravity is still as curved spacetime.
Although most of the effect of gravity come from the curvature of time rather than space.This message has been edited by Son Goku, 08-04-2005 02:27 PM

Vanilla (as Einstein formulated it) General Relativity wouldn't allow it.
Extended General Relativity may allow for a bit of it, due to the possible existence of time machines.However, Quantum Physics may allow for all of it.
John G. Cramer, a professor at the university of Washington, has similar idea of communication between the future and past, resulting in a non-static past.
Or at least a more "involved" past. In a sense, the past doesn't sit there twiddling its thumbs.You can read about it here:
Alternate View Column AV-16

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geometradynamicist

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Haven't heard that word for a while.You are, of course, correct. General Relativity is the classical limit of some grander theory.I'm aware of what the graviton truely is, but I'm expressing the view of some that gravity mightn't be a quantum field, or that current QFT doesn't apply to it.I haven't read up much on current Quantum Gravity (outside the preliminaries), but I think the original problem was that direct quantisation caused the theory to diverge wildely after the first loop order.As it stands the quantum aspects of gravity (or if you ask some, the general relativistic aspects of QM) haven't been worked out, so for now I'm suggesting that the lay reader stick with General Relativity.As a side note, are you from the String theory camp or the Loop Quantum Gravity camp?

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Well, this is the part I want to get my brain around. This view of space-time has to be just as accurate as our perspective, correct?

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Yes, absolutely. The only difficulty is that photons don't really have a rest frame. In a sense, the universe from their point of view is a little bit odd.

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So if we were moving at that speed, we would see an object as a path of that object at all points on that path, at once. So we would be looking at it's past, present, and future all as one time, spread out in space.

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Since a photon is moving at the speed of light, it sees its whole life as a single instant, however because of length contraction it also sees everything compressed to one point.
This is what I meant by their view of the world being unusual. They basically have no point of view, everything to them is crushed into a single moment, in a single spot.
So when we talk about a photon, we have to do it from the point of view of something else.

Length contraction is one prediction of relativity.The faster I go, the shorter lengths appear.When I'm standing still, the distance between the Earth and the moon is 384,400 km.If I'm going at half the speed of light, the distance between the Earth and the Moon is 332, 900 km.If I'm going at 99% of the speed of light, the distance between the Earth and the Moon is 54, 226 kmHowever if I'm going at the speed of light the distance between the Earth and the Moon is zero.
In fact the distance between anything is zero.
And the time between any two events is zero.So to a photon everything happens all at once and in the same spot.
So there is no time or space for the changes to "fit" into.

Everything is only one place and time from a photon's point of view.Ordinary matter still experiences time and space.This doesn't mean that space or time are ilusions in any way, just that a photon doesn't really have a conventional point of view, in fact in essence it doesn't have one at all.The best way to phrase it is that space and time are very much real, but a photon has no consistent point of view from which to judge them.This is summed up by the fact that a photon has no reference frame.

Holographic principle - WikipediaThis is what the whole projection thing is about.