x' and t

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A Random Player
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x' and t

Post by 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.
$1 = 100¢ = (10¢)^2 = ($0.10)^2 = $0.01 = 1¢ [1]
Always check your units or you will have no money!
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testtubegames
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Re: x' and t

Post by 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
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Re: x' and t

Post by A Random Player »

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! :D

It's been so long since I needed simple Algebra :P
$1 = 100¢ = (10¢)^2 = ($0.10)^2 = $0.01 = 1¢ [1]
Always check your units or you will have no money!
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testtubegames
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Re: x' and t

Post by testtubegames »

A Random Player wrote: Looks right! :D

It's been so long since I needed simple Algebra :P
Haha, sure. What exactly are you making with it? (you've got me intrigued)
A Random Player
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Re: x' and t

Post by A Random Player »

testtubegames wrote:
A Random Player wrote: Looks right! :D

It's been so long since I needed simple Algebra :P
Haha, sure. What exactly are you making with it? (you've got me intrigued)
This:
Length contraction, as example.
Length contraction, as example.
Minkowski screenshot.png (40 KiB) Viewed 23381 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!
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testtubegames
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Re: x' and t

Post by testtubegames »

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