Darth Wong wrote:To the best of my knowledge tachyons have never been observed at all, and remain nothing more than a mathematical abstraction. But that still makes them more scientific than subspace, which is just a completely made-up Star Trek term.
Mathematicians versed in linear algebra and topology would beg to differ with you on this last point. Check it:
http://en.wikipedia.org/wiki/Linear_subspace
http://en.wikipedia.org/wiki/Topological_subspace
If one of those Theories-of-Everything that introduces lots of compact dimensions to the usual spacetime pans out, then there are likely to be (uncountably-many!) subspaces of those curled up dimensions.
I'm not even within spitting distance of speculating what phenomena these real subspaces might create, or if they could be use to build FTL drives. However, considering that every time someone sits down to work out the properties of tachyons, they either (a) show instabilities (such as experiencing exponeintially growing acceleration, or the de Broglie matter waves going exponential), or (b) are forced to lose their tachyonic properties (such as tachyon condensation that produces the Higgs bosons).
SirNitram wrote:...as they are nothing but normal particles with a velocity above c, they're not very objectionable; nothing in science says something can't have a velocity above c, just that you can't accelerate up to such speeds from below-lightspeed.
At first blush, tachyons look perfectly consistent. Indeed, the dispersion relation for their de Broglie waves, ω^2 = k^2 - (m/\bar{h})^2 (where m is the imaginary part of the tachyon's mass (a real number), k is the circular wave number of the de Broglie wave, and ω is the angular frequency) is both Lorentz invariant and has a group velocity greater than c, indicating that they act just like sublight particles, but with the time axis switched with an arbitrary axis in space. What could be wrong?
The problem lies not with the equations, but in the boundary conditions. One boundary condition is the initial condition, where we ask "given this initial arragement, what happens?" a statement that singles out time as the direction of predicition.
Suppose we have a matter field that interacts with tachyons, a periodic arrangment of the source at time zero. The source will couple to a pair of tachyons going in two directions. So far, so good. But suppose we increase the wavelength λ of the source such that 2π/λ = k < - (m/\bar{h})^2, which is easy enough to arrange. Solving for ω, you find that no real number solutions exists, the angular frequency is imaginary, and occilatory solutions turn into exponentials, one of which is a growing exponential. The tachyon wave is unstable if proturbed with long-wavelength perturbations.
No one has found a cure for this, except in
tachyon condensations of tachyon fields. But when this occurs, the tachyonic aspects of the field disappears, and the quanta become particles of positive mass, and subject to the usual SR restrictions of forbidding information transfer (including of spaceships) at FTL speeds. Either way, the known properties of tachyons indicate that they're useless for FTL travel.
This is just my opinion here, but I'd say this puts tachyons and subspace on equal footing as mechanisms of going FTL. Sure, the footing for subspace may not be firm, but FTL by tachyon is equally firm.
"
. The "jump" FTL I mentioned is different from the Jump Drive of Battletech, which allows jumps to ANY star within a specified range, so we're up to (effectively) 5 methods of traveling Faster Than Light within science fiction, although some are similar to each other.
. Try googling "Alcubierre Warp Drive" or variations thereof to find the papers on it. There is a newer, modified version, but I forget who wrote that paper.
"Parallel dimension"? Oh yeah. One TNG episode ("Night Terrors", was it?) established that subspace was actually an infitite set of manifolds. So much for that.
