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Author Topic:   What is Time and Space
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 6 of 204 (227284)
07-29-2005 9:28 AM
Reply to: Message 1 by GDR
07-28-2005 7:11 PM


It's Hawking...
I'll come back to this later if I've got time (it's my 10th wedding aniversary) but PLEASE PLEASE PLEASE
It's HAWKING !!! Hawkins was the lad in Treasure Island... [ed for sp]
Which view represents reality?
Both are equally valid views. What you think of as reality (distance and time) is not a well defined concept. Space-time is four-dimensional and real distances are distances between 4d "events" not 3d "places". For example, I clap my hands at 10pm GMT here in the UK, and you clap your hands at 12pm GMT in Sidney. There is a 4d "distance" between the two events. It is "time-like" distance because I could manage to get from me to you between the two events (in my private space shuttle). However, if the events are such that I couldn't get between them, even at the speed of light, then the distance is "space-like". If the events are arranged so that light could just race from one event to the other, then the distance is "light-like" or "null". And that null distance is indeed zero.
To ask how far away something is, you have to specify in what 4d direction. Don't forget, a star is not a sphere sat in space, but a very long line stretching through space-time, as are we all (though not quite so long in our case!). The distance between the two lines depends totally on the direction you measure. The "minimum" distance is in a null-direction, and is always zero! But in 4d space-time what you are interested in not the shortest distance (which is always zero) but the furthest distance. The furthest distance is generally what we experience.
the only math I’m prepared for is distance = velocity X time
Oh dear...
This message has been edited by cavediver, 07-29-2005 09:51 AM

This message is a reply to:
 Message 1 by GDR, posted 07-28-2005 7:11 PM GDR has replied

Replies to this message:
 Message 10 by GDR, posted 07-29-2005 10:24 AM cavediver has replied
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 7 of 204 (227285)
07-29-2005 9:38 AM
Reply to: Message 3 by Percy
07-29-2005 7:45 AM


The amount of time that has passed between events, and the amount of space that exists between two points, is relative to the observer's reference frame. There is no one right answer.
This is only true for coordinate time and space, and these are not real concepts (as they depend upon your point of view). Real concepts do not depend upon a point of view. The proper time or proper distance along a chosen path between two events is invariant.

This message is a reply to:
 Message 3 by Percy, posted 07-29-2005 7:45 AM Percy has replied

Replies to this message:
 Message 8 by Percy, posted 07-29-2005 9:49 AM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 9 of 204 (227288)
07-29-2005 9:53 AM
Reply to: Message 8 by Percy
07-29-2005 9:49 AM


When I get back... dashing out. Ready for some maths?

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 14 of 204 (227339)
07-29-2005 12:05 PM
Reply to: Message 12 by Percy
07-29-2005 11:19 AM


Re: Uniform Time
Earth's gravity isn't strong enough to bend light around its circumference. For that you need to be at the event horizon of a black hole.
Not quite The photon orbit in Schwarzschild geometry is 50% further out than the event horizon. So you don't actually need a black hole to get the photon orbit, just a spherical mass M contained within r < 3M. It's so cool though. You build a tubular ring around the black hole at the photon orbit and once stood inside, it look straight! And you see lots of copies of yourself. If you build it between the photon orbit and the event horizon, it looks as if it is curving the wrong way! See, even the outside of black holes are fun

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 15 of 204 (227349)
07-29-2005 12:14 PM
Reply to: Message 13 by GDR
07-29-2005 12:03 PM


Re: Uniform Time
Hypothetically then, if the gravitational pull of the Earth bent my vision so that I could see beyond the horizon, (which I know doesn't happen in reality), and if I had strong enough vision, (which I don't), I could see my back.
In a closed universe (as described by Greene) yes you could, except you normally don't have time to! The universe collapses before your sight gets all the way around. If you prop up the universe from collapsing with a cosmological constant ("dark energy") then it's possible as long as the expansion doesn't always outpace light itself. In the Einstein Static Universe (ESU), where the universe stays the same size, then it is perfectly feasible.
You can consider other topologies too, like a torriodal universe. In that case you get to see multiple copies of yourself much more easily...

This message is a reply to:
 Message 13 by GDR, posted 07-29-2005 12:03 PM GDR has replied

Replies to this message:
 Message 20 by GDR, posted 07-29-2005 2:18 PM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 16 of 204 (227380)
07-29-2005 1:01 PM
Reply to: Message 3 by Percy
07-29-2005 7:45 AM


Another interesting question to ask is what an observer in a heavy gravtitational field would see. Let's say life somehow evolves on the surface of a neutron star, which has a very strong gravitational field, and let's assume this neutron star is relatively close to us within our own galaxy so that we know he sees pretty much the same thing we see when he peers up at the sky. How old a universe would this observer see?
I don't think I can answer this question. I know that when we turn our telescopes on this observer we would see time passing by more slowly for him, because he's in a strong gravitational field. But I'm not sure what he would see when he looks at us or the rest of the universe.
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...

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 17 of 204 (227382)
07-29-2005 1:03 PM
Reply to: Message 10 by GDR
07-29-2005 10:24 AM


Re: It's Hawking...
But it still says Hawkings!! No "s"

This message is a reply to:
 Message 10 by GDR, posted 07-29-2005 10:24 AM GDR has replied

Replies to this message:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 18 of 204 (227395)
07-29-2005 1:27 PM
Reply to: Message 8 by Percy
07-29-2005 9:49 AM


Okay, now I'm really confused. You'll have to explain the theory of invariantivity to me.
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.

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 21 of 204 (227471)
07-29-2005 3:53 PM
Reply to: Message 20 by GDR
07-29-2005 2:18 PM


Re: Uniform Time
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.
Exactly. Classical big bang theory (pre acceleration, pre inflationary ideas) has three possibilities: closed, flat and open. Only the closed collapses.
I had missed the connection between the cosmological constant and dark energy.
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!!!
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?
Essentially, yes. There is a future event horizon, through which galaxies will be passing, forever to be cut off from us.
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.
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...
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?
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...

This message is a reply to:
 Message 20 by GDR, posted 07-29-2005 2:18 PM GDR has replied

Replies to this message:
 Message 22 by GDR, posted 07-29-2005 7:07 PM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 23 of 204 (227585)
07-29-2005 7:54 PM
Reply to: Message 22 by GDR
07-29-2005 7:07 PM


Re: Uniform Time
First off, thanks for taking the time to advance my education.
You are more than welcome
Why don’t we subtract the rate of expansion from the speed of the light coming from closer galaxies?
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.
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?
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.

This message is a reply to:
 Message 22 by GDR, posted 07-29-2005 7:07 PM GDR has replied

Replies to this message:
 Message 24 by GDR, posted 07-29-2005 9:11 PM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 26 of 204 (227675)
07-30-2005 7:28 AM
Reply to: Message 25 by Son Goku
07-30-2005 7:15 AM


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.

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 28 of 204 (227679)
07-30-2005 7:56 AM
Reply to: Message 24 by GDR
07-29-2005 9:11 PM


Re: Uniform Time
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.
Yes
This would mean then that the actual time elapsed, (from our perspective of time) is greater than if there were no expansion?
Yes
If this is the case then doesn't it once again throw off our calculations of the size and age of the universe?
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.
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.
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.

This message is a reply to:
 Message 24 by GDR, posted 07-29-2005 9:11 PM GDR has replied

Replies to this message:
 Message 30 by GDR, posted 07-30-2005 10:23 AM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 29 of 204 (227681)
07-30-2005 8:02 AM
Reply to: Message 27 by Son Goku
07-30-2005 7:38 AM


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

This message is a reply to:
 Message 27 by Son Goku, posted 07-30-2005 7:38 AM Son Goku has replied

Replies to this message:
 Message 33 by Son Goku, posted 07-30-2005 12:13 PM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 34 of 204 (227811)
07-30-2005 1:34 PM
Reply to: Message 33 by Son Goku
07-30-2005 12:13 PM


I really don't understand your reliance on the Earth. The Galaxy has been here a lot longer than the Earth has... is that good enough? And it's been comoving the whole time. Our motion within the Galaxy is negligible. And before that, the density perturbation which caused the Galaxy to form was there. That takes us back to just after the last inflationary epoch. I'm happy with that. Actually, I'm happy to get back to last-scattering which as I said earlier is 300,000 years later than inflation.

This message is a reply to:
 Message 33 by Son Goku, posted 07-30-2005 12:13 PM Son Goku has replied

Replies to this message:
 Message 39 by Son Goku, posted 07-30-2005 6:26 PM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 35 of 204 (227814)
07-30-2005 1:41 PM
Reply to: Message 32 by GDR
07-30-2005 10:45 AM


Re: Unobserved Moon
It seems that as our universe was infinitely small prior to the BB is could be infinitely large beyond our event horizon. (Whatever that means. )
Common misconception... amongst those that have thought hard enough to have got this far If the universe is infinite, it was infinite at the big bang... Surprise! Or at least, it was infinite for any time t>0. At t=0 it's size is ill-defined. Does that help? I don't usualy get this far in conversations to make this point. Thank you.
If the universe is finite, so closed (possibly accelerating) then the big bang was a point. In this case, back to the balloon analogy, and the event horizon is a circle around us on the balloon. The circle is getting bigger, but the not as quickly as the space is expanding. So galaxies close to us eventually pass over the circle to "the other side" and we just become more and more isolated on this finite balloon. Okay?

This message is a reply to:
 Message 32 by GDR, posted 07-30-2005 10:45 AM GDR has replied

Replies to this message:
 Message 37 by GDR, posted 07-30-2005 5:08 PM cavediver has replied

  
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