# Faster than the speed of light but not at the speed of light

I was reading an article in a book and I don’t really get what they were saying.

Basically it said that nothing can go faster than the speed of light in a vacuum. Fine I understand that.

Then it went on to say that that wasn’t quite correct. It said that it is impossible to go AT the speed of light, but if you could cross the speed of light it would be possible.

In other words it bascially said you could travel at speeds faster than the speed of light if only you could CROSS the speed light travels at.

For instance if you’re going 50mph and you want to go 60mph you have to cross 55mph.

So if the speed of light is 186,282.397mps (miles per second) you can’t cross that but if you somehow could it would be possible to go 187,000.00mps.

If I’m saying this right is this so? If not maybe someone else has a clue about what this guy was writing about.

I hope this makes sense. I’ll see if does to anyone and if so then I’ll follow up

Thanks

It’s sort of a meaningless point, because to go from one speed to another without going the speeds in between, you’d need an infinite acceleration for an infinitesimal time. Infinite accleration requires infinite force, and thus infinite energy. You can see where this starts to become a problem. There’s no rational or intelligent way to even discuss the idea.

The issue is that mathematically, an object with positive mass traveling at lightspeed in free space effectively has infinite mass; the equations governing relativistic speeds trigger a division by zero error.

But an object with complex mass can travel faster than lightspeed, it just can never slow down. The equations now involve the square root of negative numbers. Mathematically, this is not a problem. In the real world, it’s a major problem.

I trust someone well versed in theoretical physics will stop by and give a more complete answer.

Not complex but purely imaginary rest mass – you don’t want a real part. You want to search for tachyons and read about them. They have imaginary rest mass, but that’s irrelevant since they can never be at rest. In fact they can’t be moving slower than the speed of light. Also their total energy decreases as they go faster. The basic relativistic relation between rest mass m_0 and mass m is

m = m_0 * SQRT(1 - v^2/c^2)

so if m_0 is imaginary, multiplying by the square root of a negative number (when v > c) gives a real “actual” mass.

One way I’ve seen it explained is that there are 3 types of speeds in the universe.

1. slower than c
2. c
3. faster than c.
Stuff that has mass is in category 1. Photons and anything with zero rest mass are in category 2. There might possibly exist things called tachyons that reside in category 3. The main thing to keep in mind is that once you’re in one category, it’s impossible to go into another one. Things with mass cannot go at or exceed c, massless particles cannot go any speed other than c, and should tachyons exist, they cannot go at or slower than c.

Umm… don’t we routinely see things going from 1 to 2? The sun generates photons, for instance.

Particles with mass can absorb and emit photons, but the particles themselves cannot travel at c.

So the photons are created/emitted at c? It goes:

No Photon --> Photon travelling away from source at c

with no intermediate acceleration?

Yup, photons are always traveling at c.

Thanks for the clarifications, OldGuy. I’d forgotten that tachyon physics involves pure imaginary mass, as well as the precise formulation of the relativity factor SQRT(1 - v^2/c^2).

So how would a particle with complex mass behave?

Certainly in a very complex fashion.

The standard equations of relativity cannot answer this question until we have an interpretation for what it means to have imaginary energy.

One idea you see from time to time in science fiction is that you can only travel at or above c for fractions of a second and in the right place. If you do it right, you get to where you’re going, generally through an interstellar fold. (Either you create the fold or it’s already there.) If you do it wrong, well, you’re gone as far as we’re concerned.

As I understand it, since matter gains mass the closer it gets to lightspeed, the more energy it takes to get closer and closer to c, and it would take an infinite amount of energy to actually reach c. Tachyons are the opposite, and take more and more energy to decelerate towards lightspeed, and would take an infinite amount of energy to reach c.

All of this is via acceleration, and the infinite energy cost can be avoided if you have another method to reach one of the previously mentioned “three speeds” that doesn’t involve acceleration. Most obviously, and quite commonly, as mentioned, by creating the particle already travelling at the desired speed. Two ideas you sometimes hear about in scientific speculation and ( more often ) sci fi are the idea of quantum jumping particles or objects over the “lightspeed barrier”, to tachyonic mode, as it were. The second, is to somehow transform or excite the particle or object into a new state that naturally travels at the desired speed. We haven’t the slightest idea how to do either, of course, or if they are even remotely possible. It’s good enough to handwave an FTL drive for a story, however.

I am trying to find another source with this. It also mentioned something about electrons and how they could do this because they can be in two places at once being both a particle and a wave, so they don’t have to acccelerate? Does this make sense? If not I’m completely misunderstanding.

No. Electrons are electrons, and it’s incorrect to say that they are a particle or wave-- that is just an analogy. We say that they sometimes behave like a wave and they sometimes behave like a particle but that doesn’t mean that they are either. Since they exist at a level below our ability to perceive them with our senses, we have to use an approximation if we want to describe them. That’s all it is.

However, electrons do have mass (9.11 × 10–31 kg), so they could not go from one velocity to another without accelerating.

Didn’t Einstein talk about the consequences of this in his twins paradox? Also, if it were possible to exceed c, wouldn’t you then be travelling back in time?