# Lorentz factor

1. Aug 20, 2011

### bodhi

please let me know what is a significance of lorentz factor,and what will happen if lorentz factor is not multiplied in the time equation of lorentz transformation.

2. Aug 20, 2011

### ghwellsjr

Then it won't work. You don't have to assign a special name (Lorentz factor) or symbolic notation (gamma) in the Lorentz transformation, just like you don't have to assign a symbolic notation (beta) to the velocity as a fraction of the speed of light, but if you don't do the calculations correctly, you won't get the correct answer.

Since the Lorentz factor is used twice in the Lorentz Transformation, it is given a special name and notation, just so that you don't have to repeat that same part of the formula, but you can't leave it out and not perform the multiplication or you will get the wrong answer.

3. Aug 20, 2011

### Naty1

I wonder if there is a langauge issue here...??
anyway,
the factor and the transformation are the same:

http://en.wikipedia.org/wiki/Lorentz_factor

http://en.wikipedia.org/wiki/Lorentz_transformation

4. Aug 20, 2011

### bcrowell

Staff Emeritus
If I'm understanding you correctly, then, e.g., you're asking what happens if you change the Lorentz transformation for time from $t'=\gamma t-\gamma vx$ (in units with c=1) to $t'=t-\gamma vx$. The answer is that it will violate the postulates of SR. (It doesn't really matter whether we're talking about Einstein's 1905 postulates, or some more modern system such as the one here http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html#Section7.2 [Broken] -- but to be concrete, in terms of the 1905 postulates it would cause the speed of light not to be the same in all frames.)

Huh? The WP articles you linked to show that they're different. The Lorentz factor is a number that occurs in the Lorentz transformation, which is an equation.

Last edited by a moderator: May 5, 2017
5. Aug 20, 2011

### Naty1

I was looking at c/(root[c2-v2] FACTOR

in the first referenc e

being equivalent to 1/(root[1-v2/c2] TRANSFORM

in the second.....

6. Aug 20, 2011

### elfmotat

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

They are both ways of writing the Lorentz FACTOR.

This is the Lorentz Transformation (where relative velocity between frames is only in x-direction):

$ct'=\gamma (ct-\beta x)$
$x'=\gamma (x-\beta ct)$
$y'=y$
$z'=z$

7. Aug 21, 2011

### bodhi

i didnt get a good enough solution to that,i mean 1/root(1-v^2/c^2) and its significance,if anyone knows it please share to me??????

8. Aug 21, 2011

### DrGreg

I don't really understand what you are asking. The significance of the Lorentz factor is that if you omit it, you get the wrong answer. If that doesn't answer your question, what sort of answer are you looking for?

9. Aug 21, 2011

### ghwellsjr

The value gamma, call the Lorentz Factor, is always a number greater than one for any speed greater than zero.

It is also the Time Dilation Factor. So two observers with a relative velocity will determine that time for the other one is stretched out by this amount. In other words, the other one's clock takes longer to tick by this amount.

The inverse or reciprocal of gamma is also the Length Contraction Factor. Those same two observers will determine that the lengths of everything along the direction of motion for the other one is shorter by this amount.