Lorentz Factor: Significance & Consequences

[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.

 

[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.

Somehow, I feel like I haven't answered your question.

 

[Naty1]

I wonder if there is a language 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

In physics, the Lorentz transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. ...It reflects the surprising fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events.

 

[bcrowell]

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.

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 -- 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.)

the factor and the transformation are the same:

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.

 

[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...

 

[elfmotat]

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...

\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

 

[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?

 

[DrGreg]

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?

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?

 

[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.

Is that what you are asking about?

 

[bodhi]

thanks for response guys