Hypermatter Thoughts and Questions

[Surlethe]

Here are a few thoughts and questions I had on hypermatter. If we define hypermatter as matter traveling faster than c relative to the universe, then we can consider for a given object of mass m the function E(v) = mc^2γ, where γ = (1-(v/c)^2)^(-1/2). v is taken to be the speed of the object.

So, E(v) is a function from the positive reals to the complex plane. Essentially, it snaps the real line at c, stretches the first half out (0,c) along the positive real axis in the complex plane starting at mc^2, and deposits the second half (c,inf) along the negative real axis, with c+ε mapping to the neighborhood at infinity and the neighborhood at infinity along the real line mapping to the neighborhood of 0 on the negative real axis. The magnitude function |E(v)| looks like the graph portrayed on Dr Saxton's page.

Since the energy released upon acceleration of a superluminal object is going to be complex-valued (the values will lie on the positive imaginary axis -- e.g., (-3i) - (-5i) = 2i), there must be some way of converting the released energy to real energy.

Assuming that this conversion of imaginary to real energy is perfect, there are some thoughts on the limits of the efficiency of the process of accelerating hypermatter to nothing. If it costs some constant energy e to accelerate the hypermatter a small increment of velocity, call it dv, then as v increases and E(v) blows up, there will be a point where the e>dE/dv. This is where the marginal cost becomes greater than the marginal return, and beyond it, it's no longer economical to obtain energy from the hypermatter.

Finally, a hyperdrive seems to convert the ship's mass-energy to be fully complex-valued. Its effects seem analogous to a complex mapping of the ship's energy: perhaps a dilation of the plane followed by a reflection across the line -t + it, t real. Interestingly, if one considers the compactification of the plane into the Riemann sphere, the "end" of the positive real axis and the "end" of the negative imaginary axis both lie in the same neighborhood. Perhaps in order to transition into hyperspace, the ship's energy must be within a particular neighborhood of infinity, ensuring that it is "close" to the negative real axis for the hyperdrive's reflection to take effect.

Questions: does hypermatter of mass m lose rest energy from its own rest frame if the magnitude of its energy is less than mc^2 in another reference frame? For example, would 1 kg traveling at 100c relative to the generator it's in realize that it's got energy equivalent to about a tenth of a kilogram at rest relative to the generator? Another way to ask this is, what is it like to ride on a tachyon going through acceleration?

The lightspeed barrier essentially partitions all possible reference frames into three equivalence classes: tachyonic, bradyonic, and luxonic. When one frame jumps from superluminal to subluminal and vice-versa, it follows that the tachyonic frames become bradyonic, and the bradyonic become tachyonic. Is this legal in terms of relativity and equivalence of frames? It seems to be equivalent to a reflection across y = -x, as stated above.