Understanding Time Dilation Formula: Exploring the Concept of Time Dilation

[cd27]

i had initially posted this thread a whle back andi t's been so long since it has been replied to that it's been placed in the archives (lol!). i am still however, having problems with it. i do not undertstand what this individual was talking about when they said i had a problem with the factor of time dilation.

https://www.physicsforums.com/showthread.php?t=67782

cd

(p.s. i am only in teh beginning class of geometry)

 

[Doc Al]

What exactly is the issue that you are having with the time dilation formula? Is it a problem with the physics or with the math?

 

[jtbell]

cd27, after a quick read of your original thread, it seems to me you're confused about "difference" versus "factor". All this is, is that whereas you calculated the difference $\Delta t - \Delta t^\prime$, people generally use the ratio $\Delta t / \Delta t^\prime$ when talking about time dilation:

$$\Delta t = \frac {\Delta t^\prime}{\sqrt{1 - v^2 / c^2}}$$

$$\frac {\Delta t}{\Delta t^\prime} = \frac {1}{\sqrt{1 - v^2 / c^2}}$$

This quantity comes up over and over again in relativity (not just in time dilation), so we call it $\gamma$ for short:

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

so that

$$\frac {\Delta t}{\Delta t^\prime} = \gamma$$

or

$$\Delta t = \gamma \Delta t^\prime$$

We call $\gamma$ a factor because a factor is what you multiply something by, in order to get something else.

 

[cd27]

interseting...now can ask "why" they use ratio rather than difference?

cd

 

[cd27]

$$\frac {\Delta t}{\Delta t^\prime} = \gamma$$

does this mean divide? so i divide my originl time by the T' to get this "factor"?

also, so i get a factor (the purpose of the factor) is so that i can multiply it to something else-what other formulas (for some reason or another) would i multiply this to and why use a factor to do it?

sorry if i ask so many questions, i just hate mathematics, and it's not b/c it's a hard subject (it's actually rather simple-but like i said in my other thread, you don't know what you haven't learned), i just can't stand it when my teacher tells me to "do this" or gives me some type of formula without telling me why i am supposed to do it or why the person who came up with the formula did what they did.

i understand things much better when i understand why they are done. plus, I'm fascinated with understanding things. eh...it's just something i like to do.

cd

 

[jtbell]

Right, it means divide.

In relativity, $\gamma$ turns up in formulas for length contraction, time dilation, relativistic momentum and energy, the Lorentz transformation, etc. As for why this is so, it comes out of the derivation of those formulas from the fundamental postulates of relativity. If you want to get into that stuff, ask the folks over in the relativity forum here for suggestions for books to get you started. You're getting into physics now, not math.

 

[cd27]

lol, i know a bit about physics as well.

cd