# Not So Fast

In Physics by Brian Koberlein1 Comment

One of the fundamental principles of modern physics is that nothing can travel faster than light. Of course when this is mentioned, someone usually suggests a way to get around that limit. What about warp drive, for example. Or what about tachyons? These are hypothetical particles that can never go slower than the speed of light. What I like about tachyons is that it’s a good example of how what seems like a simple and obvious solution turns out to be deeply complex when you take it seriously.

The basic idea of tachyons comes from special relativity. One of the things we know is that the observed speed of light is the same no matter what frame of reference you are in. Two observers could be moving away from each other at nearly the speed of light, and they would each measure the same light speed. In order for this to work, some strange physics has to occur.  As you approach the speed of light (as seen from another observer), your time would appear to slow down, and your mass would appear to increase. Both of these conspire to ensure that you can never reach the speed of light. It would take an infinite amount of energy to do so, which simply isn’t possible.

But many people have pointed out that technically special relativity prevents you from crossing light speed, not moving faster than light. In principle you could start with a speed faster than light, and special relativity would require that you never move slower than light. These hypothetical objects are often called tachyons.  It seems light a clear solution to light’s speed limit, but it turns out things are not so simple.

A tachyon (gray) passing by would be observed as two subluminal particles. Credit: Wikipedia

To begin with, any faster-than-light object would still be viewed by the light coming from the object. Since light is governed by the cosmic speed limit, we wouldn’t actually observe something moving faster than light. Instead, as a tachyon raced past us, we would observe two particles racing away from each other. One as an echo of the object as it speeds away from us, the other as a “past” echo from when the object was speeding toward us. Both of these echo particles would appear to move slower than light.

Then there is the problem with special relativity itself. If you presume a particle is always moving faster than light, but obeys special relativity, then the math requires that the mass of tachyons be imaginary. As far as we know, all particles have positive mass. Some have speculated that antiparticles might have negative mass, but there is no evidence to support that idea. Still, you might argue, photons have zero mass, so perhaps imaginary mass is possible. We shouldn’t discard an idea just because of imaginary mass.

Fair enough, but even if we allow for imaginary mass tachyons, they should still conform to quantum theory. In quantum theory, objects are described as quantum fields, from which we can observe non-local “wave-like” effects and local “particle-like” effects. The mathematics of quantum theory is very clear, so it is relatively straightforward to plug an imaginary mass into the equations to see what happens. When you do that, it looks like a description of a faster-than-light particle, but when you look closely what you find is that the “particle” aspect of the quantum field actually travels slower than light. So what started as a simply solution to move faster than light turns out to be something that moves slower than light.

Interestingly, imaginary mass does appear in certain areas of physics. In superconductivity, for example, quantum fields can have an “effective” imaginary mass through the superconductor. Particles don’t really have imaginary mass, but the interaction between materials and currents makes it easy to describe in that way.

Often in “alternative” physics you will see simple answers proposed to difficult problems. Just break a basic physical law or propose a radically different interpretation to standard science, and the solution is “obviously” clear.  But as we can see, even a small tweak of known physical theories has a kind of cascade effect, which only appear when you look at things closely. Even then, the effect can be radically different than you initially thought.

So the next time you hear of a revolutionary new theory that “changes everything,” you might reply with “not so fast.”