# Question about rearranging formula in Brian Cox's Why Does E=MC2

1. Feb 8, 2012

### DPR

This has been driving me insane. I don't get how he went from s/c to t/y. If someone could explain step by step how you do it I would greatly appreciate it.

2. Feb 16, 2012

### DPR

could someone help me out with this or give me some tips on what to study to be able to figure this out?

3. Feb 16, 2012

### Matterwave

s is defined as $s=\sqrt{-(\Delta x)^2+c^2(\Delta t)^2}$

Now divide both sides by $c\Delta t$ and you get:

$$\frac{s}{c\Delta t}=\sqrt{\frac{-(\Delta x)^2}{c^2(\Delta t)^2}+1}$$

Now notice that $\frac{\Delta x}{\Delta t}=v$ to get:

$$\frac{s}{c\Delta t}=\sqrt{-\frac{v^2}{c^2}+1}$$

Move the t to the right hand side and use the definition of gamma to get:
$$\frac{s}{c}=\frac{\Delta t}{\gamma}$$

4. Feb 16, 2012

### DPR

hey thanks! I really need to brush up on my math!

5. Feb 16, 2012

### Matterwave

One additional point. We often call $\frac{s}{c}$ the proper time $\tau=\frac{s}{c}$. You may see this proper time pop up more often depending on which sources you're reading.

6. Feb 16, 2012

### DPR

Thanks. How exactly did you go do this step? Now divide both sides by $c\Delta t$ and you get:

$$\frac{s}{c\Delta t}=\sqrt{\frac{-(\Delta x)^2}{c^2(\Delta t)^2}+1}$$

I get everything after that.

7. Feb 16, 2012

### elfmotat

$$\frac{s}{c\Delta t}=\frac{\sqrt{-(\Delta x)^2+c^2(\Delta t)^2}}{\sqrt{(c\Delta t)^2}}=\sqrt{\frac{-(\Delta x)^2+c^2(\Delta t)^2}{c^2(\Delta t)^2}}=\sqrt{\frac{-(\Delta x)^2}{c^2(\Delta t)^2}+\frac{c^2(\Delta t)^2}{c^2(\Delta t)^2}}=\sqrt{\frac{-(\Delta x)^2}{c^2(\Delta t)^2}+1}$$

8. Feb 16, 2012

### Matterwave

Just divide both sides like I said. You have to move the $c\Delta t$ inside the squareroot and divide both sides by it.

EDIT: What elfmotat said.

9. Feb 16, 2012

thanks guys!