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Post by Progenitor A on Sept 7, 2010 9:24:29 GMT 1
Your questions are very searching naymissus and I am no expert but I think we have to remember that Newton's ideas were just a very good approximation of the way S-T works and it would be more pertinent to ask the same question in regard to Einstein's ideas. Perhaps Speaker_To_Animals could comment on this as she is a professional physicist. In fact Newton's theories are remarkably accurate (they use them for space-shot ballistics). One thing that S-T curvture can predict that Newton cannot, is of course, the influence of 'gravity' on massless particles such as photons, and not forgetting, the influence of mass on time.
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Post by abacus9900 on Sept 7, 2010 9:57:45 GMT 1
Indeed.
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Post by speakertoanimals on Sept 7, 2010 13:07:25 GMT 1
What it adds is quite a lot. Amongst others:
1) light in curved space, different prediction to Newtonian gravity
2) Perihelion of Mercury, different prediction to Newton
3) Time dilation, frame-dragging -- basically the gravitational effect of a rotating mass is not quite the same as a non-rotating mass.
4) Time delay, since newtonian gravity is instantaneous
5) Cosmological solutions and expansion of the universe
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Post by speakertoanimals on Sept 7, 2010 13:12:46 GMT 1
I should just add spacetime can be curved in the absence of matter -- gravitational waves.
And as regards mass, in Newtonian gravity the gravitational force depends on the mass of both objects. whereas in GR, curvature depends on the mass of large object (like the sun). Small test mass creates additional little dimple around itself as well, but ignoring that effect, all objects move through the curved spacetime in the same way.
The difference between Newton and Einstein is very clear -- both make predictions, and experiment agrees with einstein, and disagree with Newton.
You could add gravitational lensing to the list as well..............
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Post by Progenitor A on Sept 7, 2010 14:21:32 GMT 1
I should just add spacetime can be curved in the absence of matter -- gravitational waves. And as regards mass, in Newtonian gravity the gravitational force depends on the mass of both objects. whereas in GR, curvature depends on the mass of large object (like the sun). Small test mass creates additional little dimple around itself as well, but ignoring that effect, all objects move through the curved spacetime in the same way. The difference between Newton and Einstein is very clear -- both make predictions, and experiment agrees with einstein, and disagree with Newton. You could add gravitational lensing to the list as well.............. Very interseting However gravitational waves have not yet been found and the question arises anyway, what generated them? Can gravity exist independent of mass?
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Post by speakertoanimals on Sept 7, 2010 15:26:16 GMT 1
Curved spacetime is MORE than just gravity. If you are asking, can we have a curved spacetime totally empty of matter and energy, that is rather like asking, what will the spacetime of an empty universe be?
In electromagnetism, we know about solutions to Maxwells equations whenwe have charges or currents as sources. In free space without sources, there are other solutions which are em waves. Yes, physically the existence of such waves implies a source, but mathematical existence of the solution in empty space is a mathematical solution without sources. Same for gravitational waves, they are a solution of einstein equations in empty space.
Have to be a bit careful here, since em alone (having an energy density and momentum) can generate a gravitational field.
So, no matter and no non-gravitational (i.e. em field) solutions are the vacuum solutions of the einstein equations, and correspond to gravitational waves. there are also slightly odd models, like the Milne empty universe model, which can be viewed as having negative spatial curvature, although zero spacetime curvature.
The point is that no matter solutions needn't be just flat, static spacetime, there are other choices which historically helped the development of ideas in relativity.
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Post by abacus9900 on Sept 7, 2010 20:13:04 GMT 1
I wonder what all that meant?
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Post by Progenitor A on Sept 7, 2010 21:02:07 GMT 1
Curved spacetime is MORE than just gravity. If you are asking, can we have a curved spacetime totally empty of matter and energy, that is rather like asking, what will the spacetime of an empty universe be? In electromagnetism, we know about solutions to Maxwells equations whenwe have charges or currents as sources. In free space without sources, there are other solutions which are em waves. Yes, physically the existence of such waves implies a source, but mathematical existence of the solution in empty space is a mathematical solution without sources. Same for gravitational waves, they are a solution of einstein equations in empty space. Have to be a bit careful here, since em alone (having an energy density and momentum) can generate a gravitational field. So, no matter and no non-gravitational (i.e. em field) solutions are the vacuum solutions of the einstein equations, and correspond to gravitational waves. there are also slightly odd models, like the Milne empty universe model, which can be viewed as having negative spatial curvature, although zero spacetime curvature. The point is that no matter solutions needn't be just flat, static spacetime, there are other choices which historically helped the development of ideas in relativity. Could you try to simplify things for someone like me please?
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Post by speakertoanimals on Sept 8, 2010 13:18:52 GMT 1
'Fraid not. The point being people are asking detailed question about spacetime can look like in the absence of matter. Which is not as simple as it sounds.
So, just empty in the region we are interested in (i.e., a gravitating mass outside that region)?
What do we mean by empty -- since radiation can create gravitational effects as well, hence whether or not we have em fields also matters.
And even when we have answered those questions, we have gravitational waves, and the slightly odd Milne universe, where space is curved, but spacetime is flat................
The answers aren't simple, because the questions aren't.
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Post by abacus9900 on Sept 8, 2010 17:08:03 GMT 1
How?
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Post by speakertoanimals on Sept 8, 2010 18:11:09 GMT 1
In general relativity, what generates the spacetime curvature is not just mass, but energy and momentum.
Mass is just another way of measuring energy content, hence energy generates a gravitationalo effect.
Radiation, such as just light, possesses energy (and momentum), so photons alone can change the shape of spacetime. The reason we don't notice this is because to produce a measurable gravitational field, you need a big chunk of mass (like a planet, although you can measure the mutual gravitational effect of a couple of lead balls given a very sensitive device).
So there just isn't enough energy density around in light nowadays to have a measurable effect, but the same wasn't always true, such as in the first few instants after the Big Bang.
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Post by abacus9900 on Sept 8, 2010 19:03:56 GMT 1
In general relativity, what generates the spacetime curvature is not just mass, but energy and momentum. Mass is just another way of measuring energy content, hence energy generates a gravitationalo effect. Ok, but a universe with nothing else in it but radiation would be much flatter than one like ours that contains planets, stars, etc, right?
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Post by Progenitor A on Sept 8, 2010 19:50:26 GMT 1
In general relativity, what generates the spacetime curvature is not just mass, but energy and momentum. Mass is just another way of measuring energy content, hence energy generates a gravitationalo effect. Are you sure? Has the missing link been found - that between gravity and em? How can we have momnetum without mass? Has the gravitational effect of energy been measured?
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Post by Progenitor A on Sept 9, 2010 7:57:16 GMT 1
Curved spacetime is MORE than just gravity. If you are asking, can we have a curved spacetime totally empty of matter and energy, that is rather like asking, what will the spacetime of an empty universe be? Good question In electromagnetism, we know about solutions to Maxwells equations when we have charges or currents as sources. In free space without sources, there are other solutions which are em waves. Yes, physically the existence of such waves implies a source, but mathematical existence of the solution in empty space is a mathematical solution without sources. Same for gravitational waves, they are a solution of einstein equations in empty space. Mathematics is tautological and can tell us anything as long as its rules are obeyed! Some of the stuff of mathematics is astonishing and extremely useful; other stuff can be a bucket of ordure. I would suggest that the mathematical existence of em waves without a source is such a bucket, interesting but quite useless. But then! em sources are invariably sourced from matter in some form, and the em waves are simply energy radiated by that matter, and the mass of that matter reduces as the waves propagate outwards. So the existence of em waves is just as 'concrete' as matter (it is simply another manifestation of matter). And indeed the universe could have been created by the interaction of em waves. OK , not such a bucket of ordure. But the mystery remains - where the hell did em waves come from? Have to be a bit careful here, since em alone (having an energy density and momentum) can generate a gravitational field. Yes, but surely only if they 'condense' into matter? em waves creating gravity has not been observed unless that em energy is converted into matter and the search for a direct correlation between em and gravity is the Holy Grail of physics So, no matter and no non-gravitational (i.e. em field) solutions are the vacuum solutions of the einstein equations, and correspond to gravitational waves. I can understand that em fields are a vacuum solution of equations, but the correspondence to gravitational waves is a bit of a leap I feel. But that is an hypothesis and scientists are looking for gravitational-em waves. No luck yet The point is that no matter solutions needn't be just flat, static spacetime, there are other choices which historically helped the development of ideas in relativity. Needn't perhaps but it has yet to shown that that is the case.
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Post by abacus9900 on Sept 9, 2010 10:05:51 GMT 1
I was going to make that point too but I am no expert whereas Speaker is. Perhaps Speaker would like to respond?
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