Special relativity does not seem to specifically exclude tachyons, so long as they do not cross the lightspeed barrier and do not interact with other particles to cause causality violations. Quantum mechanical analyses of tachyons indicate that even though they travel faster than light they would not be able to carry information faster than light, thus failing to violate causality. But in this case, if tachyons are by their very nature indetectable, it brings into question how real they might be.

See Occam's razor; compare tardon, luxon.

Although the above argument results in a curious conclusion, the meat of the tachyon paradox is this: In relativity, the transcendence of a tachyon is frame-dependent. That is, while a tachyon might appear to be transcendent in one frame, it would appear to others to still have a nonzero energy. But in this case we have a situation where in one frame it would have come to zero energy and would stop emitting Cherenov radiation, but in another frame it would still have energy left and should be emitting Cherenkov radiation on its way to transcendence. Since they cannot both be true, by relativistic arguments, tachyons cannot be charged.

This argument naturally does not make any account of quantum mechanical treatments of tachyons, which complicate the situation a great deal.

Compare tachyon, luxon.

First law of thermodynamics

The change in internal energy of a system is the sum of the heat transferred to or from the system and the work done on or by the system.

Second law of thermodynamics

The entropy -- a measure of the unavailability of a system's energy to do useful work -- of a closed system tends to increase with time.

Third law of thermodynamics

For changes involving only perfect crystalline solids at absolute zero, the change of the total entropy is zero.

Zeroth law of thermodynamics

If two bodies are each in thermal equilibrium with a third body, then all three bodies are in thermal equilibrium with each other.

That is actually not the paradox. The paradox stems from attempting to naively analyze the situation to figure out why. From Henrik's point of view (and from everyone else on Earth), Albert seems to speed off for a long time, linger around, and then return. Thus he should be the younger one, which is what we see. But from Albert's point of view, it's Henrik (and the whole of the Earth) that are travelling, not he. According to special relativity, if Henrik is moving relative to Albert, then Albert should measure his clock as ticking slower -- and thus Henrik is the one who should be younger. But this is not what happens.

So what's wrong with our analysis? The key point here is that the symmetry was broken. Albert did something that Henrik did not -- Albert accelerated in turning around. Henrik did no accelerating, as he and all the other people on the Earth can attest to (neglecting gravity). So Albert broke the symmetry, and when he returns, he is the younger one.