Specific FTL Questions

[Kuroneko]

We can percieve that gravity waves aren't compression waves?

Normally, when people talk of gravity waves, they mean gravitational radiation (by analogy with electromagnetic waves/radiation), which propagates as vacuum curvature. The analogy of electromagnetic radiation is actually quite powerful, although not perfect--gravity waves are transverse, not longitudinal (compression). In that sense, there are no gravity waves that are compression waves.

Regarding Ricci and Weyl curvature, I can read the words, get an impression of the math behind them but its beyond me, at least at 4 in the morning (again...).

The four-dimensional Riemann curvature tensor turns out to have twenty degrees of freedom, despite having 4^4 = 256 components. Ten of them are fixed by the Ricci curvature, which (by Einstein's field equation), represents local stress, energy, and momentum: spacetime that has "stuff" in it. What's left over is the Weyl curvature, which is vacuum and can be interepred as the tidal force of gravity. A good example of this is an isolated black hole, which has no stress-energy-momentum anywhere. It's pure vacuum, so it is "made of" Weyl curvature only. Note that it is still possible to refer to the black hole's energy (mass), just not locate any piece of it anywhere in spacetime. That's the reason for the qualifier 'local' previously--everywhere one cares to look, there is only vacuum.

Geodesics I get, but why so much matter and tidal effects, if, by this hypothesis, we can't entirely assume the conditions of the 'parent' Universe apply to this one in their entirety? I'm assuming by matter you mean density rather than raw quantity for some reason, and that tidal effects would come from the (almost garaunteed) rotation of the black hole in question?

A black hole universe should have convergence between galaxies, not the observed divergence. The observed quantity of matter isn't enough to close the oberved universe, which can be restated in terms of density. Both are problems, although, again, it is possible to artificially preserve the hypothesis by tweaking some parameters. That's not the point--the problem is that there is no reason to believe that the universe is a black hole, not that one can rationalize it to fit observations by some ad hoc means.

Didn't the WMAP data at least suggest that the Universe was bigger than what we could observe, since no patterns could be found?

Yes, in the sense that WMAP suggested that the universe is flat to measurement error, which would imply infinite. But a black hole interpetation doesn't need flatness; it needs the universe to have positive curvature. WMAP doesn't support your hypothesis. Again, it is possible to hold that there is positive curvature below WMAP's measurement error, but this ad hoc method is not science.

[Ariphaos]

Normally, when people talk of gravity waves, they mean gravitational radiation (by analogy with electromagnetic waves/radiation), which propagates as vacuum curvature. The analogy of electromagnetic radiation is actually quite powerful, although not perfect--gravity waves are transverse, not longitudinal (compression). In that sense, there are no gravity waves that are compression waves.

I have a feeling I only think I get this.

An EM wave increases in frequency with approaching velocity (of the source object), but not intensity. A gravity wave has increased intensity, but not frequency, with increased source velocity? Is this the difference between compression and transverse here?

The four-dimensional Riemann curvature tensor turns out to have twenty degrees of freedom, despite having 4^4 = 256 components. Ten of them are fixed by the Ricci curvature, which (by Einstein's field equation), represents local stress, energy, and momentum: spacetime that has "stuff" in it. What's left over is the Weyl curvature, which is vacuum and can be interepred as the tidal force of gravity. A good example of this is an isolated black hole, which has no stress-energy-momentum anywhere. It's pure vacuum, so it is "made of" Weyl curvature only. Note that it is still possible to refer to the black hole's energy (mass), just not locate any piece of it anywhere in spacetime. That's the reason for the qualifier 'local' previously--everywhere one cares to look, there is only vacuum.

Much better, thanks. I have more questions but it's pretty off-topic as is and I feel guilty for picking your brain so.

[McC]

Much better, thanks. I have more questions but it's pretty off-topic as is and I feel guilty for picking your brain so.

I don't mind, really. Watching you two go back and forth is educational, awe-inspiring, and highly confusing all at the same time. It's all interesting stuff, though, so feel free, so long as Kuroneko doesn't mind.

[Ariphaos]

I don't mind, really. ;) Watching you two go back and forth is educational, awe-inspiring, and highly confusing all at the same time. It's all interesting stuff, though, so feel free, so long as Kuroneko doesn't mind.

It's not just the questions themselves, it's the math behind them and the answers. Tensors, Partial Differential Equations and Topology are all massive doses of mathness, of which I have very limited familiarity. Unlike Kuroneko explaining Ordinals in the Infinitier thread, these are not topics that can be so easily introduced.

Well, tensors don't look that bad, but I can't rightly say since I've only done linear algebra.

Partial differential equations takes what you learn in ordinary differential equations and applies that to partial derivatives instead of normal derivatives. Normal derivatives are easy, partial derivatives are hard. Ordinary diffeqs are hard. Three professors have spent much red ink telling me that I found those hard, and you don't do much with them but solve the most basic of equations. So not only is it hard, the fruits of your labor are such wonderful topics as how fast a rock cools, population growth equations, and spring tension. Equations many people have long since derived and provided for algebra and calculus students long ago.

So if your professor can't add their own flair to the topic, a year of your studies is very hard and very painful. Then you combine these two ideas. I believe there are reasons early mathematicians are sometimes considered to have questionable sanity.

Topology... I have a rough idea of what it is, I had a friend give me a brief introduction, but I don't even know where to begin learning how to apply math to them. Another two years of math, probably. To begin. At least a Master's in math before I could try talking about alternate spacetime metrics.

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My main point is, a good introduction to any of these is a valuable resource, I'd hate to see a thread with them get buried like the introduction to ordinals above is.

An introduction to PDEs would be a major project, and would probably have to start with the calculus. Covering two years of math.

I suspect Kuroneko is the only person here with a solid familiarity with topology, looking at the other math threads. At least with PDEs there are several other people here who ought to be familiar with the math leading up to them, or can even do them.

Oil may make the world go round, but math drives it forward.

[Kuroneko]

I have a feeling I only think I get this. An EM wave increases in frequency with approaching velocity (of the source object), but not intensity. A gravity wave has increased intensity, but not frequency, with increased source velocity? Is this the difference between compression and transverse here?

Nothing so difficult. A longitudinal (compression) wave exerts force in the direction it propagates--just think of sound. A transverse wave, on the other hand, exerts force in a direction perpendicular to its direction of propagation. The reason that electromagnetic waves are transverse is not obvious, but it can be explained in terms of electrostatic lines of force and the speed of light limit of information transfer; see my post on magnetism here. Now, if you think of gravity under the old Newtonian model for the moment, it is no mystery that gravitational waves are also transverse--gravitational lines of force are directly analogous to those of an electric charge. Obviously, relativistic gravity isn't really like that of the Newtonian model, but the basic picture remains the same, although still with some important differences.

[Ariphaos]

Nothing so difficult. A longitudinal (compression) wave exerts force in the direction it propagates--just think of sound. A transverse wave, on the other hand, exerts force in a direction perpendicular to its direction of propagation. The reason that electromagnetic waves are transverse is not obvious, but it can be explained in terms of electrostatic lines of force and the speed of light limit of information transfer; see my post on magnetism here. Now, if you think of gravity under the old Newtonian model for the moment, it is no mystery that gravitational waves are also transverse--gravitational lines of force are directly analogous to those of an electric charge. Obviously, relativistic gravity isn't really like that of the Newtonian model, but the basic picture remains the same, although still with some important differences.

That took me awhile to get :-p Danke.

Even still though, aren't gravity waves like this mostly theory? I've heard of the search for them, anyway.

[Kuroneko]

Even still though, aren't gravity waves like this mostly theory? I've heard of the search for them, anyway.

Well, yes; they are theoretical in the sense that they have not been experimentally confirmed. However, considering the success of GTR, there is no particular reason to doubt their existence either.