x' and t

[A Random Player]

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.

[testtubegames]

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]

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

[testtubegames]

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]

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 29735 times

I'm running into divide by 0 errors on x and x', and t and t', but that's to be expected.

[testtubegames]

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