elfmotat

Quite the contrary my friend. You should look around the forums and learn some real science.

This isn't even vaguely science related. It's you babbling about nonsensical, nonphysical gibberish.

I don't think so, at least not to my knowledge. All of the solutions I've seen with CTC's involve some sort of rotation or cylindrical symmetry. For example: http://en.wikipedia.org/wiki/Kerr_metric (its interior contains CTC's) http://en.wikipedia.org/wiki/Van_Stockum_dust http://en.wikipedia.org/wiki/G%C3%B6del_metric http://en.wikipedia.org/wiki/Tipler_cylinder

This sounds vaguely like the twin paradox. Basically, the ship needs to accelerate to turn around, so both observers agree that the ship has aged less.

In the FLRW metric (which you seem to be speaking of), no, though you may find the Godel metric of interest: http://en.wikipedia.org/wiki/Gödel_metric.

pmb's question was about photons, not 4-momentum in general.

The four-velocity of a photon is undefined.

Well, typically [math]p_\mu p^\mu \equiv m^2[/math]. Since [math]p^\mu =(E,p^i)[/math] where [math]p^i[/math] is the three-momentum, it's easy to see for a particle with m=0 that [math]E^2=p_i p^i[/math]. So massless particles have momentum by virtue of their energy.

I've never seen the inverse square law applied to relativistic bodies before, since it's generally only accurate at low velocities. This is interesting though.

The Einstein field equations say that the stress-energy tensor (a mathematical object which contains the information about the energy and momentum distribution of spacetime) is proportional to the Einstein tensor (a mathematical object which contains the information about the curvature of spacetime). As for your second question: physics creates models that represent the physical world. The usual interpretation of General Relativity is a literal one - that spacetime is "really" curved. You can also model gravity as a spin-2 massless field (gravitons) on a flat (non-curved) spacetime background. The math and predictions are equivalent. What is different is how we interpret them.

Your conclusion is correct, but your logic is flawed. Newton's inverse square law is a statement about rest mass, not relativistic mass. The reason that an object with large kinetic energy would have a greater gravitational influence is because the components of the stress-energy tensor are larger.

You're taking it too seriously. You shouldn't look at it as anything more than a crude analogy. What do you mean? Mass is a property of matter. This is no more a meaningful question than "what is charge really(?)" or "what is spin really?" As a side note, it isn't just mass which affects gravitation: it's the entire energy-momentum distribution. Again, you're taking the analogy too seriously. There is no "depression." Objects follow "straight" lines in curved spacetime - this produces the effect of what is seemingly mass being "attracted" to other mass. Conservation of momentum/energy. Translational and time symmetry. This is just gravity being presented under two different models. In GR, gravity is a pseudo-force which appears because of curved spacetime. In Newtonian gravity, it's a force of attraction between two masses. I have no idea what you mean by this. What are "the realities of the laws of motion" ? I really hate it when people say stuff like this. The question "but what's really happening(?)" is not a physically meaningful one. Science does not answer such questions. This is just not true. If you do good research then you can always have it submitted to a journal for peer-review. No PhD required. Granted, it will probably be difficult to know what to research if you're not in the loop, academically. I'd be interested in giving it a glance-over, if possible. It depends on how deep you want to go. For example, "why does this spring have its particular spring-constant?" You could go into detail about materials it's made from, its dimensions etc. But then I could ask the next question, "why does such and such material have said properties?" Then you could go into detail about the chemistry of the material. I could then ask why chemistry works that way, to which you could explain the nature of atoms, the electromagnetic force, quantum mechanics, etc. Eventually you get to a point where you're forced to say "that's just the way things are." For fundamental constants like G, c and h, you just have to say "that's just what they are."

I've seen it used before, yes. Off the top of my head, Schutz's Gravity from the Ground Up comes to mind (if you consider it a GR text - it's not exactly rigorous). http://www.gravityfromthegroundup.org/pdf/timecurves.pdf

This seems like more of a problem of language than physics. "Curved time" usually refers to when |g00|≠1 in a diagonal metric (though this doesn't necessarily imply Rabcd=0).

Light isn't absorbed and re-emmited when it travels through a medium. This is a common misconception. If it were true, then absorption spectrum would be discrete because atoms only have discrete energy levels.

Velocity certainly isn't necesarily the result of a force, and I don't know if it's at all meaninful/useful to think of expansion as a result of a force.

When you're near the surface of the Earth [imath]g=GM/r[/imath] is approximately constant. (Small compared to the Earth) objects follow parabolic paths if g=constant. Over a global region, such as in planetary orbits, (small compared to the sun) objects follow ellipses.

Basically there's this thing called "action" (denoted with the symbol S) and things always follow a path that extremizes the action (makes it as small or large as possible*). The action is the integral of the Lagrangian density over spacetime: [math]S=\int \mathcal{L}d^4x[/math] So to find the path on which things move, you just extremize the action: [math]\delta S=0[/math] *Technically it doesn't need to be a minimum or maximum - it can also be a "saddle point," but this is just a technicality.

To an observer an infinite distance away from the BH, yes.

This is unrelated nonsense. I don't know whether or not you could model gravity as rarefaction & compression of spacetime. I also don't know whether or not it would be very useful to think about it in this way. For example, would you consider the surface of a sphere to be a rarefied/contracted flat 2-d space? Curvature in differential geometry is just a measure of how much a vector changes when you parallel transport it. Parallel transporting a vector v means moving it an infinitesimal distance ds so that the vector locally does not change, or dv/ds=0. When you do this over a global region of space the vector may change. This means that parallel lines, when continued in a curved space, do not remain parallel. Below is a picture of a vector being parallel transported around a closed loop on the surface of a sphere. Notice how the vector has changed from when it returns to its initial location. This means that the surface of a sphere is a curved space.

Please explain what you mean by "speed of time."

It's spacetime which is curved - the curvature of time is just as important. It doesn't actually curve "into" anything. The curvature of General Relativity is what is known as "intrinsic curvature," which means that it doesn't rely on being embedded in a higher dimensional space. Why do you think it appears flat? What would you expect spacetime curvature to "look" like?

I still don't know what you're asking. What about Newtonian dynamics do you see as being "non-unified?"

Yes, but it won't be of much use unless you're already somewhat familiar with GR. If you want a good intro without any complicated math, I think Taylor and Wheeler's Exploring Black Holes will probably be what you're looking for. It would help if you were familiar with special relativity, namely the invariant interval.