# Attempting to understand relativity and time dilation

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1. Dec 2, 2015

### Prierin

1. The problem statement, all variables and given/known data
t = t0/(1-v2/c2)1/2

2. Relevant equations
t = 10/(1-.95c^2/c^2)1/2

3. The attempt at a solution

The provided solutiojn to the example given above is:

t = 10/(1- (.95c)2/c2)1/2

t = 10/(1- .952)1/2

t = 10/ .312

t = 32

Unfortunately, no matter what I do the answer I continuously come up with is 51.28. I've tried four different approaches and come up with the same EXACT answer each time without fail. I am not so bold as to say the example above is incorrect as this level of math isn't my forte, so I am stuck. Can anyone explain to me WHY the answer would be 32 rather than 51.28?

I am not familiar with the 1/2 at the end of the formula and I suspect that may be what is throwing my numbers off. I am nto clever enough, it seems, to get my calculator to understand that portion correctly.

(On a side note, I have also seen this forumal written as t=t0/(1-v^2/c^2)^1/2. Not sure which is correct.)

2. Dec 2, 2015

### andrewkirk

That's what's correct, and your use of the other one is probably what's causing you problems.

3. Dec 2, 2015

### Prierin

OK, that's good to know, thanks. However. even with that I am still coming up with the same result of 51.28.

if c= 299792458 and .95c = 284802835.1

10/(1-284802835.1^2/299792458^2)^1/2 = 51.28205128205128205128

The example answer, however, is 32, so I am still confused as how they reached that conclusion.

EDIT: I just attempted to edit the formula somewhat and FINALLY gor 32 as an answer by using .5 rather than 1/2.

10/(1-284802835.1^2 / 299792458^2)^.5 = 32.02 I had a feeing the 1/2 was being interpreted incorrectly by the calculator as a division rather than a fraction... still, I'll need confirmation from someone who knows the math better than I before I celebrate

Last edited: Dec 2, 2015
4. Dec 2, 2015

### Ray Vickson

The correct formula is
$$t = \frac{t_0}{\sqrt{ 1 - v^2/c^2} }= \frac{t_0}{(1 - v^2/c^2)^{1/2} }$$
If you use that you will get 32.03. The "1/2" is not a fraction or anything like it; it is an exponent (= the "1/2"th power = square root).

5. Dec 2, 2015

### Prierin

BEAUTIFUL! I knew I was doing something wrong.

Now, I have calculated the formula both ways: 10/(sqrt(1-284802835.1^2/299792458^2)) & 10/(1-284802835.1^2/299792458^2)^.5 and have come up with the same EXACT answer of 32.02563076101742669665 (or 32.03) so now I am a happy chappie!

Thanks and kudos!

Now if I can just fogure out how to save values in the calculator LOL

6. Dec 2, 2015

### andrewkirk

It wasn't being interpreted incorrectly, it was being punched in incorrectly.
The standard rule for precedence of operators (ie which arithmetic operations get done before others) is that exponentiation is done before multiplication and division, which are done before addition and subtraction.
So if you punched in

10/(1-284802835.1^2/299792458^2)^1/2

then that means

10/((1-284802835.1^2/299792458^2)^1)/2

which is

$$\bigg[\frac{10}{(1-\frac{(284802835.1)^2}{(299792458)^2})^1}\bigg]\div 2$$

which is not what you want.

7. Dec 2, 2015

### Prierin

I meant to say, the calculator wasn't misinterpreting - I was. LOL

It makes sense now. As I pointed out, if I use ^.5 the answer comes out correctly so now I can breathe a little easier. I didn't *kneed* to know any of this math, but I have a curious mind and like to understand how things work...