Now, is this a generic property, reflecting a principle of nature? If we considered more general gravitational fields would a brachistochrone retain this property? The best way to describe this property is to forget about Newtonian kinematics altogheter and utilize semi-riemannian geometry.
However, to model a time-independent gravitational field we must restrict our attention to a stationary space-time, i.e. a smooth Lorentzian manifold (M,g) with a timelike Killing vector field W (defines the direction in space-time over which the metric doesn't change) . This will define such a thing as constant energy along a curve and will make the analogy with classical concepts possible. There are two possible brachistochrone problems in the context of stationary space-times:
- To minimize the travel time measured in terms of a global coordiante time defined by the timelike irrotational Killing field W. Irrotational means that the field perpendicular to W will be consistently tangent to spatial hypersurfaces. It foliates space-time with these constant time surfaces.
- Minimize the travel time in terms of the proper time
We are at the moment defining the conditions for isochronicity, and will give out the link for the results soon.
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A Brazilian friend of mine is convinced that UFOs [unidentified flying objects] exist and has sent me a link to a "report" produced by someone who allegedly worked on a secret project of backward engineering of an alien spacecraft. The link is:
http://www.zamandayolculuk.com/cetinbal/REACTOR.HTM
others are at
http://www.youtube.com/results?search_type=videos&search_query=bob%20lazar&search_sort=relevance&search_category=0&page=1
I do not know enough physics to be able to contradict what is written in the article, but you and your friends should.
I love the description of how an intense gravity wave produces a warp in space and this allows the spacecraft to take a shortcut and shorten a trip of a few light years. I would guess that this warp must be local and move with the spacecraft as I doubt that the gravity field and warp it generates would reach out a few light years. I would also think that they must have an efficient shielding on the spacecraft to avoid turning it into a black hole and avoid the time frame effects of traveling a few light years in distance.
I looked on the internet to see if I could find a rebuttal to this "report" that I could send to my friend and had no luck.
Is there a simple way to discredit this theory of alien spacecraft operation?
Even though this has nothing to do with what I posted...
There are just two things I would like to comment on right off the bat (I haven't seen the sites yet):
Gravitational radiation produces metric disturbances only on the plane orthogonal to the direction it is moving in.
Gravitational forces are immensely weaker than every other force, the energy output of a gravitational wave is weak, even if we are considering collapsing stars or neutron stars orbiting one another. That is the reason why, despite very intense efforts, none have been (directly) detected so far.
Another thing: producing a lot of electromagnetic energy through matter anti-matter collisions would not produce space-time distortions, we need a lot of energy-matter accelerating in a sort of non-uniform fashion for that (gravitational radiation arises from the time rate of change of the quadrupole moment of the system, and such a collision would have unchanging quadrupole moment). So, there are a lot of physical arguments that completely kill this scheme, and I haven't even looked at the particle physics stuff (which is not really my area).
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