What is Time and Space

He's going to see the universe in fast forward. In Newtonian speak, the incoming photons are getting blue-shifted as they fall down the gravity well. That's why it's a bad idea hanging around outside a black hole... you run out of universe pretty quickly if you're not careful! I'm not saying that falling inside the black hole is going to be any better...

But it still says Hawkings!! No "s"

Well, we call it the Principle of Covariance. Which is really what all of modern mathematical physics is about... things don't change just becasue you look at them differently... if they do, then you're looking at the wrong thing.That's why we use tensors... they're the language of covariance. The simplest tensor is the scalar... just a number. E.g. a number of apples, say 4. Our universe appears to obey conservation of apple number, in the sense that it doesn't matter how you look at the apples, there are always 4.Another scalar is the infinitessimal 4-distance between two points in space-time, ds. If we integrate ds along a chosen path through 4-space, we obtain another scalar... the 4-distance along the path. This has to be agreed upon by all observers no matter their coordinate system, as the number is a scalar.Our problem is that what we call time and distance are not 4-scalars. They are components of 4-vectors. We integrate them naively to obtain our results. And this is fine as long as we don't change coordinate system too much... i.e. stay well away from relativistic speeds and gravity wells. If we don't, we find these components break down.The scalars transform invariantly between coordinate systems. The vector components transform covariantly (or contravariantly) so that scalars constructed from these vectors transform invariantly.

Well, I was trying to make the point in that sentence that I'm not the brightest light in the chandelier.I rest my case. This message has been edited by GDR, 07-29-2005 11:18 AM

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Everybody is entitled to my opinion.

I assume what you mean by collasping is the concept of the universe that was going to eventually pull back to its original singularity prior to finding out that the expansion was accelerating. I had missed the connection between the cosmological constant and dark energy. I'll have to read up on that again.Another thing in this that I don't understand is this. As I understand it, the expansion of the universe is accelerating, and at some point it will mean that galaxies will be moving away from us at greater than the speed of light. At that point in time when the rate of expansion exceeds the speed of light relative to us, the light that the galaxy is emitting will never reach us, not that we will notice it for billions of years. Is this correct?If that is true it brings up 2 questions for me.1. As light is always moving at the same speed relative to the observer why does it matter that the galaxy in question is moving away from us faster than the speed of light? I don't understand why the light won't reach us.2. As we say that the world is about 16 billion years old how would we know that there aren't already galaxies that are beyond 16 billion light years away that are moving away from us at a rate that exceeds light speed?

Exactly. Classical big bang theory (pre acceleration, pre inflationary ideas) has three possibilities: closed, flat and open. Only the closed collapses. The cosmological constant is a constant (in time and space) energy density that can be positive or negative, and is part of General Relativity. It is the obvious choice for dark energy, assuming that dark energy is constant, and you're thinking only of GR. String theory can produce a number of fields that look like a CC but which can vary. We call these fields quintessence. Supergravity (SUGRA) is famous for predicting a cosmological constant that was 10^30 times bigger than that observed... SUGRA became known as the most unsuccessful theory in physics ever!!! Essentially, yes. There is a future event horizon, through which galaxies will be passing, forever to be cut off from us. Don't think of the galaxies moving. Nothing is really moving. It is simply the space between the galaxies that is expanding. Now over a far enough seperation, the expansion of space will be quicker than the light crossing that space. Think of an ant crawling on the balloon while the balloon is inflated... There are Or at least there had better be! This is all a bit backwards, because we never used to deal with stuff like this except for in de-Sitter space (another story). When the expansion was slowing down, more galaxies were appearing as time went on, as we'd allowed more time for their light to reach us. We said our past particle horizon was growing. But if the universe is accelerating, it all changes, and we get a future event horizon. Oh well...

First off, thanks for taking the time to advance my education. I was writing out what I didn't understand when the penny dropped. As I now understand it, the photons from the galaxy are still moving at the speed of light (relative to us) towards us, but the ballon has grown to such a size that the points on the far side of the ballon are expanding away from us at a rate greater than the speed of light. However, if the expansion of the universe is not the same as relative motion, then why isn't the distance affected when the expansion on the balloon is less than the speed of light? Why don’t we subtract the rate of expansion from the speed of the light coming from closer galaxies?It also raises another question. If we can no longer observe or measure the furthest galaxies do they cease to exist? But aren't we basing our estimate of the age of the universe on the distance of the furthest galaxies. If there are galaxies that we can no longer observe couldn't it mean that the universe is a lot older than we think?This message has been edited by GDR, 07-29-2005 04:08 PM

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Everybody is entitled to my opinion.

You are more than welcome Because it doesn't make any sense to do that. Think of a photon entering the solar system from Andromeda. If you measure it's speed from Pluto to us, it will be pretty much c. It has just taken longer because it has travelled through expanding space. It hasn't slowed down "locally". However, as the space has expanded, its wavelength must have increased with that expansion, which we observe as the redshift. No, that's not what we do. The age is given by running the expansion backwards. But you have a point. If the expansion is accelerating, then we will have underestimated the age of the universe. But I think the acceleration is sufficiently small to make only a slight change necessary.

Are you saying then that from the perspective of Earth, expansion is causing the photon from another galaxy to have to travel a greater distance to get here, (until it reaches our galaxy), than if there were no expansion. (After it hits our galaxy there is no further expansion and the speed is c.) This would mean then that the actual time elapsed, (from our perspective of time) is greater than if there were no expansion? If this is the case then doesn't it once again throw off our calculations of the size and age of the universe?edited to addThis is rather esoteric science but somewhere in the Greene book, (darned if I can find it) he refers back to the old axiom "if a tree falls in the forest and there is no one there to hear it does it make a sound". He related it to the moon and said something to the affect that if there was no one observing or measuring the moon it might not exist. This is what crossed my mind when we lose the ability to measure or observe whole galaxies because of expansion. Do they cease to exist?At this point there is no answer, but it seems to me that if that is considered as a possiblity it could certainly give a whole new slant to what is happening to our universe.Like I said, a little knowledge is a dangerous thing. This message has been edited by GDR, 07-29-2005 06:36 PMThis message has been edited by GDR, 07-29-2005 06:38 PM

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.

I'm not sure I understand you. The proper time from the big bang to now measured in a comoving frame (near as damn-it us, ignoring peculiar motion) is what we call the age of the universe, and this is a maximum. Any integration of proper time over a different path will give a shorter time, all the way down to zero for a null path.

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.

Yes Yes No, because we don't measure the age of the universe this way. We measure the age by extrapolating the expansion backwards.I should point out that by "age of the universe" I'm really talking about time since around recombination, which was about 300,000 years after the big bang. It is entirely possible that with quantum gravity we will find that the universe continues beyond the "big-bang" at t=0 into a negative t region which could be finite or infinite. The universe is very possibly infinite in extent in time. It's like asking how old is a person. We measure from birth, but we could from conception, or the creation of the egg (not long after conception of the mother), or from the nucleosynthesis of the heavy elements from which that person is made. Well, you have almost left physics (and most definitely the topic ), but think about the things that the moon affects. Can you ever be truely disconnected from it? You can still feel its gravitational influence (if you are supersensitive enough). How would you ever be free of its existence?Now if the moon disappeared across a horzion, there would still be some observers closer to it, who would still be in causal contact with it and with you. If it dropped into a black hole, then it really would have gone, but you'd see evidence of it in the Hawking radiation emitted.

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.Where in Gravitation? My copy is 3 meters away but my lunch is ready

Good morning caregiver from my version of spacetime which of course is good afternoon in your universe. I have just re-read this entire thread. It has been extremely helpful and thank you very much.One question about the expansion and its acceleration. I don't think there is a point in asking how we measure the expansion because I don't imagine there is any hope in me understanding the answer, but does science have confidence in the calculations used to ascertain both the expansion and the acceleration?Another question then. I'm wondering how the motion of bodies through 3 dimensional space affects the perception of time. The planets orbit at different rates of speed around the sun. As we actually have a point in space to use as a reference, (the sun), we can say that they are moving at a different velocity than us. Would an observer on Neptune have a totally different estimate of the age of the universe as us? Another way of asking would be; if I were to relocate to Neptune and live there for a year would my watch still read the same as if I hadn't moved?

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Everybody is entitled to my opinion.