I got a book out from my university library a while ago on the recommendation of an acquaintance, Faster than the Speed of Light, by Joao Magueijo. I've since read the book and returned it, and I have some questions related to the content of the book. Unfortunately I can't ask this acquaintance, as he's currently quite busy, so I thought I'd put these questions out here.
1) There is one passage in the book that says:
So basically, instead of gravity being a force, its influence upon objects' movement can be explained by its topology. On the opposite page it gives a diagram showing this where there is an object orbiting a gravity well, where the object is still traveling in a straight line, but because of the orientation of the space it is traveling through, it orbits the well; it is apparently experiencing no force.
This seems intuitively fine for objects already in an orbit, but what if you just put an object into the influence of the gravity well? It would accelerate towards the well, so it should be experiencing a force. But if gravity is not providing the force, then where does it come from?
2) On a related note, with the 'gravity is not a force' model, how do you explain the effects of gravity on objects themselves; i.e. tidal forces?
3) How fast does gravity travel?
4) If you had a two-body system, with the two bodies initially separated by a vast but finite distance and initially still relative to each other, how fast would the bodies get before they collided? From my limited knowledge of relativity the mass of the bodies would increase as their velocity increases; but I also seem to recall that in a gravitational field this would be offset by the fact that gravity acts more strongly on more massive objects (so, for example, a feather and an anvil in a vacuum would fall at exactly the same acceleration). How does this work?
5) There was quite a vague statement of how general relativity predicts that the universe must have been constantly expanding since 1 second after the Big Bang; could someone expand on that?
6) What evidence is there for the constancy of the speed of light? I remember reading of an article giving observational evidence for a varying fine structure constant, alpha; what evidence is there to suggest that the speed of light in vacuum is constant across all space and has been constant for the entire history of the universe? Or is it just an assumption?
7) On a related note to the two-body question, if you had two objects individually accelerated to, say, 0.6c, and moving directly towards each other, the velocities of body A relative to body B would not be 1.2c; it would be something below c. What's the equation that you would use to calculate this? I thought maybe you used relativistic momentum; in which case the relative speed would be 0.832c; can someone verify this?
I'm starting at the OP, mostly because there has been a lot of nay saying and misleading info so far. Most of this information is easily attainable on wikipedia and is largely correct.
1.
This is a fundamental thing about GR, that what we perceive gravity is due to the warping of space-time by an energy density. There is a very good thought experiment involving flat landers that I suggest you look up, but remember that it is an analogy and you have to use your own melon to link it back to our 3+1 dimensional universe.
The short version is that objects travel in straight lines along geodesics in a curved spacetime.
2.
Tidal forces work fine in GR. To go back to the rubber sheet analogy, the far side of your object will be "higher" than the near side and is where the whole tidal interaction will arise.
3.
The current theory is that gravity should travel at c. The reason for this is that the standard model predicts that massless particles should travel at c, and gravity is thought to be mediated by the graviton.
There are theories where it travels at higher or lower than c but they are mostly fringe.
The large gravity wave detectors should be able to pin this down once they are actually able to detect one.
4.
This should be calculable, but tedious using SR. Unless the objects are very big, the answer should be very close to the work done since that is pretty much the definition.
5.
Our most direct evidence of this is the CMB (Cosmic Microwave Background) and the Hubble flow of galaxies. We can measure the recessional velocity of galaxies as a function of redshift to get at this number.
Look up the CMB, big bang and hubble's law for more info.
6.
Our evidence for the speed of light being a constant is mainly that, observations. There are some math proofs which show that the wave speed given Maxwell's equations must be a constant. Again wiki has an interesting article on this, turns out that you can change the value of c all you want, but the dimensionless quantity alpha has to stay the same or physics might break.
The measurement of alpha that you mentioned being different is largely disputed since the same measurement with higher sensitivity gave results consistent with the current alpha. The measurement was done a quasar.
7.
I think this has been answered correctlly using the lorentz equations.