| MadSci Network: Physics |
Hi,
Arrrggh! What a question! I better make it clear right now that this is way too difficult for me. I'm just an astronomer - you need to be talking to someone who understands quantum mechanics and rather fancy general relativity.
However, I just talked to someone who does know about that kind of thing, and here is what I could follow...
This is very complicated and difficult - skip bits you don't understand and then try again later. I've probably not explained it very well either, so try looking at the book I mention. I'm sorry - but if I try and explain it more simply I just know that you'll find an error (because I've said something that, because it's simple, isn't completely right) and feel that physics is `wrong'. I'd rather you understood some bits and realised that it is complicated, than think that it is easy but wrong! (This happens all the time on sci.physics on usenet, for example).
Also, please don't think I'm talking to you like you are stupid. I don't understand this very well, so I'm talking to myself as I write this. This is just how I try to understand physics, it's nothing personal!
OK, this is a bit technical, but maybe you can get the drift (don't ask me for more details!) - if not, keep going because I'll try and make more sense of it later. At a mathematical level the fundamental equation in general relativity - the bit that relates the curvature of space to the mass/energy density - is:
8 Pi G
R - 1/2 g R = ------ T
ij ij 4 ij
c
Where i and j are to do with these things being tensors (matrices or arrays of numbers, not a single value); R is the Ricci tensor, which is connected to the curvature of space; g is the metric tensor, which describes how you measure lengths in space; T is the energy momentum tensor.
Now when you have to solve this question you find R and g, which describes the curvature of space-time, for a particular T. T is the thing which describes what kind of matter you have.
T is made up of several components: the mass/energy density E; the pressure p; the four-velocity (that's like the velocity, but includes the extra time dimension) of the particles, u:
i j ij
T = ( E + p ) u u - p g
ij
Don't worry about those i's and j's now being in the air, but look at how energy and pressure appear in that equation. Normally E and p are positive, but for what you are interested in, people think that
E + p = 0or
p = -E
That removes the first term, and leaves something which, when you work through the equations, makes space expand rapidly.
Now, what do all those letters mean? E is the energy density and is always positive. But that means that p, the pressure, must be negative(!).
Notice that we are using the same equations as normally, it is not a different theory of gravity, just the same theory giving strange results when we use some very strange matter (with negative pressure).
Right, so lets get down to some physical details. What is pressure? Well, for particles moving around we know that pressure increases if they are heavier and moving at the same speed, or if they have the same mass and move faster. So you can see that pressure goes up when energy goes up. And since energy and mass are the same, you can see that, in a way (and I know it's a bit complicated!) pressure is like mass. So pressure makes gravity stronger (it curves space).
Now, before we go any further, I want to stop using the word gravity. You see, when you talk about `negative gravity' it doesn't really make much sense. Gravity is the word we use for what we are used to on earth. But, as Einstein showed, that is a result of curved space-time. If space-time curves in a different way, and things start to fly apart, that means things aren't like on earth. But it doesn't mean gravity is negative.
I think was a particularly difficult paragraph. What I mean is that `gravity' is just an approximation to the `real thing'. It's fine for thinking about stuff on earth, but it's a bad picture for when space-time curves in different ways.
OK, so we know that pressure makes gravity stronger, but I've just said I don't like to use `gravity' any more. It's better to say that pressure makes space-time curve in a way that makes things move together.
Now, negative pressure makes things move in a way that moves them further apart! (And that's not the same as negative gravity. Like I said, negative gravity doesn't really mean anything).
Well, almost. Another difficult idea: they are not moving further apart, they are staying still in their own little bit of the universe. But the space in-between them is growing!!! (This is the real reason why I don't want to use gravity - these things really aren't moving, even though they are getting further apart!)
This idea about space growing is a very difficult one. Usually it doesn't matter and we can talk about it by saying `galaxies are moving apart'. But then sometimes this leads to contradictions, and people think `aha, relativity doesn't work'. That's not true - it's because the picture they are using isn't right. That's why I am trying to explain this in more detail, because I think it is better to know that it is complicated than to think it is simple and wrong.
You asked about clocks. There's nothing very special here. We know what would happen because our universe is expanding in a similar way. We see that distant galaxies are redshifted. That means that clocks on distant galaxies are running slower than ours (according to us). The same would happen with negative mass. There's no time flowing backwards.
Negative pressure makes space grow. So for space travel you need some negative pressure stuff behind you. And in front you need something that makes space shrink. Then things in front get closer and things behind get further away. It's like travelling without really moving - and so you can go anywhere while staying still! This means you can go places without worrying about going faster than the speed of light!
Is this possible? Well, negative pressure is something that is connected with quantum mechanics and particle physics. No-one has a bucket of stuff with negative pressure in their office here!
Even if we could make this stuff, then we would need to build some kind of machine. If you were reading carefully you probably noticed that I didn't describe what would be in front of the spaceship - the bit that makes space smaller - even though that would be built with `normal' matter. That's because even making something like that is too complicated for me to understand. So even if we had stuff with negative pressure, building a spacecraft that could use it is difficult.
I've been talking about negative pressure. But you'll probably read (I think that Kip Thorne has written a good book on all this called `Black Holes and Time Warps') about negative mass. That's another way of explaining this (when I asked my clever colleague about this he said `Oh, just use negative mass - it's not right but it's easy to explain!', but I thought I'd try and explain it properly!). You see then you could think about gravity as something negative that comes from negative mass and pushes things apart. But this is just a way of talking about things. The way I describe above is really closer to what we think would really happen. I hope!
But don't let that stop you thinking of this as negative mass. Just don't be surprised if something later doesn't make sense. Then come back here and see if thinking about space expanding, rather than gravity being negative, helps.
Maybe it's clear by now that this kind of matter isn't going to form black holes. If you have lots of normal matter it makes space curve until nothing can escape - a black hole. In a way, space is shrinking. In contrast, lots of this `stuff' will just expand space like crazy.
Actually, this is `Inflation' which you may have heard about in connection with modern theories of the `big bang'. It's not the bang itself, but a stage just afterwards, when the universe expands at an enormous rate.
It is needed to solve some sticky problems with the big bang, but what actually causes it still isn't clear. You'll hear people talking about a phase transition: in some way, it is connected with unified theories of physics - I believe that the transition is the point when gravity and the other forces become `separate', but don't quote me on that...
However, that does mean that this `negative pressure stuff' can be the same `stuff' we have now, but at such high temperatures and pressures that the physics is very different.
Hope that makes some sense,