1. Jan 29, 2012

### Grimstone

I was watching a vid with Mr Hawking talking about a train (fictional) that gets to 99.9 C.
and the little girl gets up and runs forward. "as time in the train has slowed down. her momentum is not added to that of the trains speed. So she never reaches C"

A. trains %99.9 of C
B. time inside the train slows down.
C. the girls speed IS added to the trains but because time slowed down Even more? she cant hit C?

Tomcat does mach2 fires a sidewinder that does mach2. for a short bit. that winder IS doing mach4.
so why is Suzie's speed not added to the trains and thus she is moving faster than the train.

2. Jan 29, 2012

### Markus Hanke

It' because not only does the girl's clock run slower, but also, for an outside observer, all distances within the train are contracted. Such she can never reach c.

3. Jan 29, 2012

### Grimstone

but from a insiders view?

4. Jan 29, 2012

### alexg

From the insiders view, everything is normal, everything is moving at appears to be normal speed, light is still measured to be moving at c, and the little girl is running at normal little girl running speed.

5. Jan 29, 2012

### Drakkith

Staff Emeritus
From an inside view the train is not moving at all, it is at rest. So the little girl would be running at 5-10 MPH.

6. Jan 30, 2012

### zhermes

Correct; her speed is added to the train's, but non-linearly. I.e. $v \neq v_\textrm{train} + v_\textrm{suzie}$

The sidewinder would actually be going very (very very) close to mach 4, but not quite. At very small velocities, the effects of relativity are very (very very) small, and thus $v \approx v_\textrm{tomcat} + v_\textrm{sidewinder}$

The closer the velocities get to the speed of light the less effectively they add together.