## x' and t

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A Random Player
Posts: 523
Joined: Mon Jun 03, 2013 4:54 pm

### x' and t

If I know x' and t (in a Minkowski diagram), or x and t', how do I find x and t?
(Making a simple Minkowski diagram drawer.)
Edit: Without solving a system of equations.
\$1 = 100¢ = (10¢)^2 = (\$0.10)^2 = \$0.01 = 1¢ [1]
Always check your units or you will have no money!

testtubegames
Posts: 1078
Joined: Mon Nov 19, 2012 7:54 pm

### Re: x' and t

Without solving a system of equations, eh? Well, you'll need to deal with the Lorentz Transformations to be sure. But they aren't too tough (haha... I make myself laugh...). At least what you're looking to do shouldn't be too hard.

Lorentz Transformations

If you check out the equations, using the first one you come across (t' = ...), you'll see that three coordinates are represented. So if you want to find t, start with the equation for t', then rearrange it to find t as a function of t' and x.

Does this make sense / fit what you're trying to do?

A Random Player
Posts: 523
Joined: Mon Jun 03, 2013 4:54 pm

### Re: x' and t

testtubegames wrote:Without solving a system of equations, eh? Well, you'll need to deal with the Lorentz Transformations to be sure. But they aren't too tough (haha... I make myself laugh...). At least what you're looking to do shouldn't be too hard.

Lorentz Transformations

If you check out the equations, using the first one you come across (t' = ...), you'll see that three coordinates are represented. So if you want to find t, start with the equation for t', then rearrange it to find t as a function of t' and x.

Does this make sense / fit what you're trying to do?
Looks right!

It's been so long since I needed simple Algebra
\$1 = 100¢ = (10¢)^2 = (\$0.10)^2 = \$0.01 = 1¢ [1]
Always check your units or you will have no money!

testtubegames
Posts: 1078
Joined: Mon Nov 19, 2012 7:54 pm

### Re: x' and t

A Random Player wrote: Looks right!

It's been so long since I needed simple Algebra
Haha, sure. What exactly are you making with it? (you've got me intrigued)

A Random Player
Posts: 523
Joined: Mon Jun 03, 2013 4:54 pm

### Re: x' and t

testtubegames wrote:
A Random Player wrote: Looks right!

It's been so long since I needed simple Algebra
Haha, sure. What exactly are you making with it? (you've got me intrigued)
This:
Length contraction, as example.
Minkowski screenshot.png (40 KiB) Viewed 17838 times
I'm running into divide by 0 errors on x and x', and t and t', but that's to be expected.
\$1 = 100¢ = (10¢)^2 = (\$0.10)^2 = \$0.01 = 1¢ [1]
Always check your units or you will have no money!

testtubegames
Posts: 1078
Joined: Mon Nov 19, 2012 7:54 pm

### Re: x' and t

Neat! At first glance, it looks correct, too... The grid lines angle in like you'd expect.