# A thought experiment about the speed of light and breaking it

#### Zebobez

If you were to actually break the speed of light under relativistic conditions, what would happen exactly? Would you go back in time? Would you cause a "light boom" like a sonic boom but bigger? I've been running some thought experiments in my head (with almost no formal physics training) and I think it's a possibility that by breaking the speed of light one would create a new speed of light that travels as fast as the fastest speed achieved by the speed limit breaker. Thus, when one starship breaks the speed of light, the speed of light for the whole of the universe changes. Is this mathematically possible? If not, what would happen if the speed of light is broken? I'm not asking if it's possible. I'm asking what would happen if someone--specifically an observer, not a tachyon--broke the speed of light under Einstien's rules.

#### studiot

We have no evidence whatsoever as to what might happen beyond the speed of light, ie that sublight laws hold.
We do know that the maths becomes asymptotic to infinity for some properties as light speed is approached from below.
But have nothing to base what might happen beyond that, i.e. how or whether the function might recover finiteness.

We also know that there are some physically observed functions that do the same thing at other lower critical speeds so we can actually observe what happens to them, and yes a new regime is established.
For instance the specific energy curve of a liquid flowing down a slope becomes asymptotic to infinity at a critical slope, beyond which a phenomenon known as a hydraulic jump occurs. This has two regimes the flow switches between for above and below the ciritcal speed but no maths for flow at the critical speed.

However we have never observed anything slowing down from a superluminal speed, just as we have never observed anything or anyone travelling back in time.

#### Zebobez

Aw man, I was hoping for some math or stuff. Oh well! I'll just keep thinking! Thanks a bunch for your answer! Perhaps light does have a phenomenon comparable to hydraulic jump!

#### studiot

You want maths?
What does the tangent function look like approaching and at 90 degrees?

topsquark

Infinity.

#### studiot

Does it ?

I think it does much more than that it exemplifies the issue I am talking about.

#### Zebobez

Ah I see where you're going with this! Haha. I was just wondering if anyone had done the legwork and written a mathematical proof of what happens when the tangent function approaches infinity. I suppose that would be a good rephrasing of my question!

#### studiot

The question is
Hw does the tangent get from plus infinity to minus infinity as the angle passes through 90 ?

Does the relativistic mass etc start reducing as the velocity passes through c or what?

#### Zebobez

I would imagine, in this case, that at +infinity the tangent reverses direction in some sort of code switch and becomes -infinity. But I don't know! Maybe there's something cool there! I suppose this means I can take liberties!

#### studiot

All it means is that we don't have enough theory or observational evidence to predict what the form of the curves are beyond c.

In the hydraulic jump the energy curve has two finite values at the critical point, which is forbidden in the mathematical theory, but we can observe the water surfaces in reality.

topsquark