299,792,458 Metres per second. The Speed of Light, as well as all other particles with a mass of zero. Usually denoted as "c", the speed of light forms part of one of the most famous equations of all time; E=mc^2, which can be used to calculate the energy locked up in the mass of any object.
But what if a particle had negative mass?
Would it then be able to travel faster than the speed of light? It seems logical, as does the existence of a particle with negative mass; for each action there must be an equal and opposite reaction, if the Universe gave birth to particles with mass, would it not also have spat out particles of negative mass? After all, antimatter, a very real material is the precise opposite of matter. Note that antimatter does not have negative mass, but has opposite electrical charges, for example in "normal" matter, an electron has a negative charge, whilst an antimatter electron, or anti-electron has exactly the same magnitude (the value of the charge, ignoring if it is positive or negative) of charge, but a positive charge.
In fact, there are some physicists who believe that they have found a way of working the concept of negative mass into Special Relativity, one of the cornerstones of physics, without violating any of integral assumptions, without which the sound theory of Special Relativity would fall apart, a brief summary of which can be found here (article does require a greater knowledge of Physics than is assumed here). Interestingly, according to this way of thinking, gravity waves, predicted all the way back in 1916 by Einstein, and generally accepted to be a genuine phenomenon, would be almost impossible to detect. At the time of writing, despite our best efforts, nobody has been able to directly observe gravity waves, perhaps lending some credence to this way of thinking about negative mass.
Negative mass would also lead to some extremely odd scenarios; two negative mass objects would produce a pull, through gravity to each other, but would in fact end up repelling one another. The really weird bit comes when equal but opposite mass objects come close to each other; the positive mass would attract, whilst the negative mass would repel! This would lead to the two objects constantly accelerating, the positive mass away from the negative mass, the negative mass toward the positive mass, like a policeman chasing a thief, the policeman runs after the thief, who tries to escape the policeman, so he runs away, with the policeman in hot pursuit, both speeding up all the time to achieve their aim. There are numerous other strange phenomena that begin to occur once negative mass it taken to be real, which lead to all sorts of wondrous ideas, such as spaceships that could make interstellar travel possible and perpetual motion machines.
On the other hand, some argue that negative mass is simply an imaginary concept, that stems from the idea that it is impossible to square root a negative number, which creates an imaginary number. Also, if negative mass did exist, the odd interactions between it and positive mass objects would happen, and we have never observed anything resembling these counter intuitive motions. There are particles that do have negative mass, but, alas, they are strictly imaginary, called Tachyons, from the Greek for "swift", they do actually travel faster than the speed of light and are sometimes used, especially in Star Trek, as a mechanism for sci-fi time travel, despite the effects on causality that this would lead to.
Negative mass remains something of an imaginary concept right now, but in Physics, this is only a temporary state, if evidence can be found that shows it exists, then it must exist, regardless of what Einstein's theories show, which is something of the beauty of the Scientific method. But wouldn't it be good, if, just once, Star Trek had actually hit on to a profound and far reaching law of Nature...