I just watched a bit of the BBC Horizon documentary on black holes where the gravitational effects of black holes on space are likened to those of water falls on water. video section of the doc here, at about 4 minutes in. In other words, black holes pull space towards them.
If that analogy is correct, is it true that all matter pulls space in towards it - and not just stretch or compress it? If it is true, that would make those “planets on a rubber sheet” diagrams work for me, except those diagrams never show the sheet moving (my problem with the rubber sheet diagram is that if the sheet doesn’t move, they only work if you already assume a downwards force - i.e. gravity).
Thanks for your time.
SP.
ETA: To clarify: is it true according to current physics that space itself is actually flowing towards mass, like water in a bucket with holes in the bottom, or am I stretching [heh] the metaphor?
Follow up question, and forgive me for being possibly naive here: if all this is true, does that mean that the force of gravity that we feel is the space rushing past us into the earth?
It seems to make sense to me, but I’m pretty skeptical about anything that would “explain” what gravity is and still makes sense to me.
Gravity is just the attractive force between masses. The bigger the mass, the more gravity.
The rubber sheet is a really good expression of how space is affected by gravity, but needs to extrapolated in to three dimensions(and probably four to include time) - where the rubber sheet is only demonstrating two. The rubber sheet is bent - space is bent. The rubber sheet doesn’t really move so much as bend. Space doesn’t really move so much as bend. That’s why the demonstration is a good one.
The gravity pulling stuff down on the rubber sheet is irrelevant - its just part of the demonstration.
I would say that by the time your analogy gets to saying that space flows, you’ve stretched your analogy too far. Analogies can only take you so far before you have to actually do the math.
What you seem to be saying is: gravity is a force that does both
a) pull masses towards each other
b) distorts space at the same time.
Also, as far as I can see, space isn’t just bent, it’s can also be stretched (by gravity, I mean - I’ve gathered that space can expand by some other unkown means), or am I wrong here?
Bent/stretched - yes they are synonymous in this case.
Here’s the thing. Space is bent around us. We’re all in three pretty big gravity wells each bending space a bit. But it doesn’t really have a percievable effect at this scale. Get a few hundred thousand miles from a black hole and the effects are increased by the incredible gravity. You wouldn’t notice then, but mostly because you’d be stretched and compressed beyond the capability of your body to sustain life.
I’m not particularity good at math. I was just thinking that maybe space flowing was an accurate description. But maybe I should give the math a serious try. How hard can it be?
Seriously, can you recommend a good book or intro text that does have the relevant maths and can be understood by a reasonably intelligent person with some (1st year university CS-level) maths experience?
The best introduction is probably Schutz, A First Course in General Relativity (also called “Schutz’s green book”, since he has another one that’s gray). You’ll need calculus, and a course in matrix algebra would also come in very handy, but for the tensor analysis (the part you probably haven’t had if you haven’t had a relativity course), the hardest part is actually realizing how easy it is.
I agree that the analogies presented for general relativity are poor with respect to what’s actually going on. This is as compared with other scientific analogies–like, say, the kinetic theory of matter, which actually explains a lot in just a few sentences and leads naturally into the mathematical model. The popular analogies of relativity, on the other hand, aren’t as easily grasped; it’s a subject that cries out for actually doing the math if you really want to understand the implications of the model.
That said, I think most mathematical descriptions of relativity are aimed at a much deeper level, i.e. it’s meant mainly for folks who plan on using it every day, not educated laymen who are interested in more than the thumbnail sketch provided by an episode of Nova.
The point on tensors is a good one, but in my experience (I haven’t seen the book Chronos cites), mathematical relativity texts often treat them so abstractly that they seem an unnecessary frustration. Why, for example, can’t concepts be explained in terms of an underlying “flat” space in which the curved space is embedded (e.g. explain Christoffel symbols on a 2D surface with respect to 3D space first–they’re basically the derivative of the unit vectors in that space with respect to an underlying 3D Cartesian system–then extend the math to scale up to 4D inside 5D)? That approach–from the few mathematical texts I’ve seen–seems verboten…
Because that introduces unnecessary complication, and they’re making it as simple as possible. Physics (or indeed, any science) deals only with what can be observed and measured, and if there is some higher-dimensional flat space we’re embedded in, we can’t observe or measure it, so leave it out of the physics.
Let me try to explain that rubber sheet. What is confusing is that it is using gravity to create an analogy with gravity. Would that rubber sheet work in free fall? Not as it is constituted. The function of gravity in the rubber sheet is to confine the marble to the sheet and also to overcome friction of the ball on the sheet. The reason you need this in the rubber sheet display and not in the real world are two: the planets, etc., are constrained to stay in 3-dimensional space (by what? damned if I know); the friction in space is utterly negligeable. So if you could somehow set up your rubber sheet in free-fall and simultanously both confine the marble to the sheet while avoiding–or overcoming–friction, the ball would still follow the circular orbit. The orbit wouldn’t decay, however. That supplies the energy required to overcome friction in the earthly display. There is no way of getting gravitational energy in free fall.
There is an idea that perhaps gravity is the result of some higher dimensional random current and a mass blocks the current on one side so what is left looks like a force. The best analogy for this is the way a dock attracts a boat (see below). Unfortunately, they cannot get the equations to work properly.
Docks attract boats? Sure they do, how often do you see boats at docks? Seriously, though they do and it is a well known phenomenon that you could demonstrate with a toy boat in a bathtub. The reason is that a boat in open water is being bombarded constantly by water molecules but the effects cancel. (Ultimately it is the failure to cancel on a tiny scale and over a short time that results in Brownian motion, but that is another story.) Now imagine that same boat just one cm from the dock (pretend the water is very smooth). It will still be bombarded on the outside by water molecules, but much less on the side adjacent to the dock. The result is a slow motion towards the dock and it thus appears that a dock attracts boats. Too bad it doesn’t work; it is such a pretty idea.
The reason the warped space analogy doesn’t work for me is the issue of stillness. I can see that if an object otherwise moving in a straight line encounters distorted space, that what for it would seem to be a straight line would look from the outside like a curved line (remapping of sorts). However this wouldn’t cause attraction in the case of two bodies that started out motionless unless the ‘waterfall’ idea was in effect and there not only distortion of coordinates but also movement of them through time. So that’s something I can’t wrap my head around.
