We are stuck on the idea that 300,000 kilometres a second is a speed limit, because we intuitively believe that time runs at a constant universal rate. However, we have proven in many different experimental tests that time clearly does not run at a constant rate between different frames of reference. So with the right technology, you can sit in your star-drive spacecraft and make a quick cup of tea while eons pass by outside. It’s not about speed, it’s about reducing your personal travel time between two distant points. And that has a natural limit – of zero.

A decent little tutorial. One approach that can also be used is to note that the invariant speed, given by the velocity four-vector, has a constant length of c. The three spatial components are the velocity and the time component is \(gamma\)ct. If you are stationary, as we all are in our own rest frame, time ticks normally. But when one is moving — the spatial velocity vector is nonzero — the time component of the vector ~~shortens~~ compensates.

Update: Chad points out some sloppiness on my part. The vector is given by \({v_x}^2+{v_y}^2+{v_z}^2-gamma c^2\) so the components get bigger while the resultant stays constant.

Nitpick: Strictly speaking, since gamma is always greater than one, the time component of the 4-vector

increaseswhen the space component increases. The real difference is that the rule for adding them isn’t the usual Pythagorean theorem, but thedifferencebetween the squares of the space and time components.The overall point that the velocity through time changes as the velocity through space changes, though, is correct.Conservation of mass-energy arises from vacuum symmetry homogeneous time plus Noether’s theorems. If you can cheat the First Law of Thermodynamics, lightspeed is then negotiable. “Superluminal” phenomena are perceived projections that in fact break no rules. Terrell rotation physically rotates nothing. The relativistic broomstick fits within closed barn doors through footnotes. The universe does not tolerate contradiction (handy for priests, vexatious for theologians).

Theory fails for

discontinuity. Noether specifically excludes absolute discontinuous symmetries. Parity couples to translation and rotation. Physical theory cannot model parity. It manually inserts symmetry breakings to curve fit (Yang and Lee, Chern-Simons), then whines. SUSY is claimed. Proton decay and solar axions are absent. Km^3 of ice massing 920,000 kilotonnes IceCube versus Super-Kamiokande’s mere 50 kilotonnes of water, is proton decay’s assassin. Don’t take off your shoes!http://www.npl.washington.edu/AV/altvw43.html

Superluminal photons are OK, but it cannot be constructed.