# Traveling .999999 reapeating the speed of light .

1. Jul 25, 2009

### cragar

Is it possible to travel .999999999 repeating the speed of light , because that would be a 1 in math .

2. Jul 25, 2009

### maverick_starstrider

Sure. if you've got infinite enegy, or zero mass. If you are curious about the energy requirements the Kinetic energy required to reach a given velocity is given by:

$\gamma m c^2 - m c^2 = \frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}} - m c^2$ where m is the rest mass. Play around with it and you can get a sense of how the energy requirements increase to infinity as one approaches c.

3. Jul 25, 2009

### HallsofIvy

Is this a math problem or a physics problem?

In any case, your question is really "Is it possible to travel at velocity c" and the answer is "yes, for light but not for any massive object".

4. Jul 25, 2009

Staff Emeritus
And .999999999 doesn't equal 1, "in math". Those numbers differ by .00000001.

5. Jul 25, 2009

### negitron

No, but ".999999 repeating" does. It seems clear that what he really means is the more conventional ".999999..."

6. Jul 25, 2009

### Hootenanny

Staff Emeritus
More precisely, the limit of the series 0.99, 0.99, 0.999, ... equals one.

7. Jul 25, 2009

### Staff: Mentor

And the limit of the series $$\frac{10}{\sqrt{19}},\frac{100}{\sqrt{199}},\frac{1000}{\sqrt{19 99}},...$$ (the time dilation factor for v = .9 c, .99 c, .999 c, ...) is infinite.

8. Jul 25, 2009

### Janus

Staff Emeritus
You can't travel at 0.999999999... c, but you can travel at 0.99999999...9c, where in the first case the ... means an unending string of 9s, and the in the second it means a finite but undetermined number of 9s.

9. Jul 25, 2009

### Hurkyl

Staff Emeritus
Of course, that's exactly what "0.999 repeating" means.

10. Jul 25, 2009

Staff Emeritus
Well, since 0.999... and 1 are different representations of the same number (like 2-1 or 4/4), since a massive body can't travel at c, it can't travel at (0.999...)c either.

11. Jul 25, 2009

### cragar

i guess i should have said can something with mass travel at .99999 reapeating c and i guess it would be no , cause it is 1

12. Jul 25, 2009

### Staff: Mentor

Correct. And just fyi, you can write that like this: .999...

The thre periods at the end (an ellipsis) indicates they repeat forever.

13. Jul 26, 2009

### cragar

so then what could be that fastest you could travel if you had mass .

14. Jul 26, 2009

### Staff: Mentor

You can get arbitrarily close to C. Every time a new, bigger particle accelerator is built, they add a couple of more 9's to that.

15. Jul 26, 2009

### cragar

interesting

16. Jul 26, 2009

### maverick_starstrider

Theoretically? Well I guess if one could estimate all the energy in the universe and if all that went into the kinetic energy of a single things of mass m. Which I imagine woud be a great many 9's