# Anybody know how far off relativity becomes at large velocities and small distances?

1. Aug 1, 2008

### devronious

Hi there,

I'm wondering if anybody knows how far off relativity becomes at large velocities and small distances? Quantitativly? I just need to know a specific example at a specific velocity near c or maybe a couple along the c scale. Has anyone ran tests?

-Devin

2. Aug 2, 2008

### James R

Re: Anybody know how far off relativity becomes at large velocities and small distanc

This kind of thing is determined by the Lorentz factor, which is:

$$\gamma = \frac{1}{\sqrt{1-(v/c)^2}}$$

This factor appears in formulae such as the time dilation and length contraction formulae of special relativity.

The Lorentz factor at speed $v = 0$ has the value 1, which means no time dilation and no length contraction of an object at rest.

At a speed of half the speed of light, for example (v = c/2), the Lorentz factor is 1.15, which means that time is dilated by 15% compared to the rest frame, and length is contracted by about 15%.

At 90% of the speed of light (v = 0.9c), the Lorentz factor is 2.29, which means that clocks on the moving object run at a little under 1/2 the speed of clocks that are at rest, and the length of a moving object is contracted by a factor of a little over 2.

You can try other values of v yourself to get a feel for things.

3. Aug 2, 2008

### George Jones

Staff Emeritus
Re: Anybody know how far off relativity becomes at large velocities and small distanc

Could you elaborate a bit on what you mean by