Tachyons cause a lot of problems in movies with starships, but they also cause problems for people in real life. Specifically, they cause problems for students of relativity and string theorists. Learn about the ins and outs of tachyons, and why they need extra dimensions.
Whenever the Borg come jumping out of a wormhole in space, go ahead and blame tachyons. Whenever temporal distortions mean an older version of you has come back to scold the younger version of you, blame tachyons. Whenever an ancient vessel gets a boost across a galaxy, and re-starts an ancient war, blame tachyons. If you noticed that all of those things had a little something to do with time distortions, you are on to something.
Tachyons are particles that have mass, but travel faster than light. As most of us have heard from a fellow named Albert, nothing travels faster than light. In fact, only massless particles, like photons, travel at light speed at all. This is why tachyons are generally confined to episodes of Star Trek and thought experiments regarding whether, if you're late, you can use tachyons to send a signal back in time to warn yourself not to be late, and arrive on time, thereby never having sent the signal in the first place.
Before we dismiss tachyons as an annoyance to both philosophy students and Star Fleet captains, let's take a look at the problems they pose for string theorists. To travel at slower-than-light speeds, particles have to have a positive mass. To go at light speed, they need to have no mass. So when they go faster-than-light, they should have negative mass. That's a tough concept to picture, and it's about to get tougher.
The relationship between energy and mass is defined by Einstein as E = mc2. In string theory, all the particles in the universe are made up of strings that vibrate at different frequencies. The mass of a particle depends on the way the string is vibrating, but the energy level of the vibration doesn't just give us the mass of a particle, it gives us the squared mass of the particle. The vibrational energy of tachyons gives us a squared mass that is negative. Math students know this is impossible. There is no real number that anyone can square to make a negative number. Math students use the imaginary number i to signify the square root of negative one, but that's not something that can translate into the physical world.
In string theory, the lowest level fluctuations of a basic string – the kind that are unavoidable and present at all times because they are quantum fluctuations – add up to a negative squared mass. Strings can and do vibrate at frequencies beyond quantum fluctuations, and those vibrations pull the particle away from negative mass and towards positive mass, but the string would need to vibrate quite a lot to pull the string out of the red. We should be seeing a lot of tachyons. Why don't we?
While three dimensions don't provide enough wiggle room for strings, more dimensions give them quite a lot of room to vibrate. Anywhere between ten and twenty-six dimensions, depending on who you ask, gives them enough potential for vibration that even the slightest shimmy can pull them up from negative mass to zero mass, to become the massless particles we know and love. A bit more vibration and they can have a positive mass, and join the world of matter. Getting away from tachyons, and their squared negative mass is one of the reasons why string theory has so many dimensions.
So while tachyons are mostly seen on science fiction shows, they might one day be the basis for time travel, for faster-than-light travel, for travel to the furthest reaches of space, for understanding the many-dimensional universe, or for realizing that we've been on the completely wrong track when it comes to understanding the universe.