This Space Intentionally Left Empty

[Old_Geezer]

Goes to show what nonsense my friends and I chat about at the pub. I really ought to start watching soaps or something so we have something sensible to chat about.

Anyway, last Saturday a friend of mine said words to the effect of, "You know how massive objects are supposed to warp space ? Well in that case what happens to the space nearby ? " And we discussed visual models such as the rubber sheet with the dip and the balls rolling in circles around it as it "orbited" The gist of the question was whether space nearer the object became denser as it was forced to curve around it and more rarefied further out. Which implies space is a "material" of some sort than can be crushed/stretched and what this space-time fabric is.

I could only ponder and say, "Well yes, I suppose it does", but the idea of dense of thin space seemed just weird.

Anyone got a simple explanation on whether one can get a variety of space density and what is meant by that ? Should I look for a dense part of space to live in, or am I better in a rarefied bit ?

[jomifl]

Density is a function of mass....

[jim360]

I think this question is probably similar in nature to those that could be asked about, say, magnetic field lines around a magnet. Any traditional diagram shows the lines being rather sparse where the field is weak, and all bunched up together in a region where the magnetic field is strong. But in reality this is an utter nonsense, because the magnetic field is continuous, not discrete, so that if you were really to draw field lines then you would have to draw an infinite number of them to reflect the true field. It's just that the picture of talking of "lines bunched together" provides a useful visual description of what is going on -- and indeed the iron filings do align themselves along these field lines.

Returning to your question, then, I think xkcd answered it best:

http://xkcd.com/895/

Hopefully not with the "boring" response at the end.

[Old_Geezer]

Not boring, but not really giving a lot of insight either. It's like what is often the case, one can follow what is said but is still left with a question afterwards.

BTW the iron filings know where the dense lines are ;-)

[jim360]

I suppose the gist of the point of that comic is that you can take these visual explanations too seriously. I love the "ball-on-netting" analogy for General Relativity, as it captures quite a lot of the basic ideas very effectively. But it's also horribly deficient. Firstly it only captures two out of four dimensions; secondly it can only ever really model something like a simplified Schwartzschild solution rather than, say, all of the really interesting ones; and thirdly it gives the illusion of space as actually being something, rather than what is closer to the truth of spacetime as "a set of coordinates for measuring where you are".

This last is the key problem with the question, really. Spacetime has no substance to it. So it can't be more, or less dense.* What can and does happen is that as you get closer to a model, the way in which you measure coordinates becomes more noticeably warped and distorted from a flat space. It's probably better then to view the sheet that you are placing your massive object on as a square netting, because then you can more easily see the effect you are interested in, which is geometry becoming distorted.

For this experiment you will need some oranges and the netting they came in. Carefully cut the netting and stretch it out reasonably tight over a bowl, taping it down to the sides. Now put an orange at the center of the netting. Look straight down from above the orange and see how the squares that make up the netting become more and more distorted from their shape. If your bowl is see-through you could try down the same from below. The distortion will be even more pronounced.

General Relativity is about how the geometry of space and time changes around a mass, which is turn tells you how to measure coordinates and determine where and when you are in the Universe. Making the sheet on which the ball rests looking more like square netting is, I think, the best link to the truth you can get.



*This is only true in classical General Relativity, and it's possible that future Quantum Gravity models might end up implying that Spacetime is a lattice of (presumably massless) stuff of some sort, like "foam", but at the moment this is nothing more than a cool idea and anyway it's something I don't understand in the slightest.

[heathfield]

I like the one about falling objects not actually accelerating - instead, they fall at a constant speed, but undergo a time shift.

[ToraToraTora]

as jim says the whole rubber sheet thing is often taken too literally. It is only designed to enable a concept to be demonstrated. So a heavy ball distorts the sheet so that is what is happenning, but in 4 dimensions, that cannot be visualised (not even in 3!) so you have to use the black box technique. ie accept that an effect is presen but that you cannot visualise it. Anyway you are really looking at strength of distortion rather than density in your original point.

[Old_Geezer]

Cheers Jim et al. I shall give it deeper thought this evening. Now all I need to do is sum it up so simply I can regurgitate it flawlessly after a few pints and yet still seem to make sense.

[mibn2cweus]

That's odd. I always thought of space as being stretched out (less dense) within a gravitational field . . . then I suppose it's all relative to the observer. :o/

[jim360]

Again, the concept of space being stretched out would imply that it has substance, which is not what's seen. As an aside, this is basically the same reason that Cosmic Inflation -- the idea that the Universe grew in size many billions of times in a tiny fraction of a second -- is possible. The required growth rate implies that inflation occurred at a speed many times faster than light, which would violate Special Relativity if spacetime was a thing with some substance to it. But it's not so it doesn't.

[scowie]

Just tell your mates that it's not worth pondering on since this whole warping of space-time malarkey doesn't fit with all the observations that show that gravity does not bend light, i.e. the lack of any deflection of the light from stars viewed close to the sun (but above it's plasma atmosphere), the lack of any gravitational lensing of the stars that orbit Sagitarrius A* at the centre of the Milky Way, or the lack of any real "Einstein rings" which should be visible wherever one star is viewed behind another.

Here's a lecture about this stuff:

if you can get passed the guy's southern drawl :)

[mibn2cweus]

Probably a waste of time pointing out that Newtonian gravity diminishes with the SQUARE of the radius.

[jim360]

Scowie's posts seen to all say the same thing. And it's not worth paying much attention to. Even Newton himself knew his theories weren't the end of the story. Insisting otherwise makes no sense at all.

[scowie]

@mibn2cweus: But light passing the sun at a greater distance has a more perpendicular vector with respect to the sun for a greater stretch of it's path so the total expected deviation as viewed from earth does not have an inverse square relationship with the minimum passing distance.

@jim360: So observational evidence isn't worth paying any attention to? If i'm wrong about such observations it shouldn't be too hard for you to come up with a link to an article showing a contrary observation. One that directly contradicts the specific observations I refered to that is — i'm well aware of the hubble deep field lensing effects (which may well be due to good old refraction rather than gravity) and Einstein's Cross (which probably isn't any kind of lensing).

[jim360]

I coudl come up with thousands of such articles, if I could be bothered. Instead I'll just refer you to the astrophysics and GR sections of the arXiv where 78 papers were released last week. I know that they've not undergone a full peer-review but it doesn't matter too much -- by this point the evidence for General Relativity is overwhelming; from the accurate determination of Mercury's orbit (which was indeed one of the early motivations for General Relativity in the first place) to the correct modelling of Black Holes, to early-Universe cosmology.

Since the Eddington observations of the "Einstein Cross" effect, similar observations have been recorded dozens of times. I'm vaguely aware of claims that some of the data were tweaked in this first measurement, but it's been performed too many times to be a fluke or a hoax.

Newtonian Gravity only allows for the bending of light to occur at all if you cheat and pretend that photons have some mass, and then take the limit that their mass goes to zero. And even then it's out by a factor of 2.