# Impossibility of exceeding c

1. Feb 11, 2014

### Paul77

Have been reading the "Impossibility of exceeding c" notes in the Lorentz Transformation
physics forum page:

www.physicsforums.com/library.php?do=view_item&itemid=19

Where it states:

"It is often said that nothing can be accelerated to the speed of light because its mass increases as it gets faster.

However, the fundamental reason is simply that "adding" speeds only adds tanh-1(speed/c), and so no amount of adding can make (speed/c) equal to (or greater than) 1."

Is this right - I understood that one of the posits of the Lorentz Transformations was that:

Both frames, the transforms are applied to, agree on the speed that a light beam is travelling at, and this is c, as this is required by special relativity.

This restriction was introduced after the results of the Michaelson Moorley interferometer experiment. So when the transforms are derived for frames observing a light beam we have already restricted the transforms to this!

Is'nt the use of rapidities just a re-representation to make it easier to use the transforms?

2. Feb 11, 2014

### dauto

What difference does it make? You can, if you will, take the simple addition of rapidities as your fundamental principle, don't you think?

Last edited: Feb 11, 2014
3. Feb 11, 2014

### Staff: Mentor

I agree with dauto, I am not sure what you are asking Paul77. In general there are a lot of different ways that you can write the same thing, and some ways make it easier to see something than others. He is just pointing out a clever way of writing things that makes the conclusion pretty obvious.

4. Feb 12, 2014

### Ibix

I wonder if the article is obliquely referencing the broad consensus that "mass increases" is a deprecated explanation for anything. And rapidity is certainly one of the first things you encounter from a differential geometry/general relativity preserve-the-norm-of-the-four-vector appoach. That at least arguably makes it more fundamental than more-or-less anything else.

5. Feb 12, 2014

### Paul77

Rapidities are a clever way of representing this but when I first came across this article I made the assumption
that c could not be exceeded because of how the maths works but then I watched a derivation of the lorentz transforms and realised that the 'fundemental' reason is that c is assumed to be the same in all frames - as a novice it was worth separating these two things out.

6. Feb 12, 2014

### dauto

There is more than one way to derive the Lorentz transformations. It may be derived from the requirement that the norm of a four vector is an invariant of the transformations. From that point of view, the constancy of the speed of light is not any more fundamental than the fact that the length of an object doesn't change when you look at if from a different point of view.

7. Feb 12, 2014

### Staff: Mentor

That is true. In the traditional formulation, all relativistic effects are based on two postulates, or assumptions:
1) the laws of physics are the same in all inertial frames
2) the speed, c, is the same in all frames

From those assumptions you get the Lorentz transforms and from the Lorentz transforms you get rapidity and rapidity shows that c is the speed limit in an obvious way.

We could simply answer every question with the two postulates, but then the conversation would be boring