How Do Minkowski Diagrams Illustrate Lorentz Transformations?

[stevmg]

kev -

From your prior post you brought in this URL: http://hubpages.com/hub/Minkowski-Diagram
which has this diagram (figure 3)

Using his v = 0.6c, how do you prove that the (1,1) is the same as the (2,2)

I can't make it happen.

Also, his Lorentz and Inverse Lorentz transformations are wrong. With the t and t' equations, he has his + and - inverted which will really mess one up if one tries to follow his logic.

Below is what he wrote:
Lorentz transformations* ...Inverse Lorentz transformations*
x' = (x-vt)/(1-v2/c2)1/2 ......x = (x'+vt')/(1-v2/c2)1/2
y' = y .........y = y'
z' = z......... z = z'
t' = (t + vx/c2)/ (1-v2/c2)1/2 ...t = (t' - vx'/c2)/ (1-v2/c2)1/2

This is what it should be:
Lorentz transformations* ...Inverse Lorentz transformations*
x' = (x-vt)/(1-v2/c2)1/2 ......x = (x'+vt')/(1-v2/c2)1/2
y' = y .........y = y'
z' = z......... z = z'
t' = (t - vx/c2)/ (1-v2/c2)1/2 ...t = (t' + vx'/c2)/ (1-v2/c2)1/2

How do we get to him and inform him of this?

stevmg

 

[yossell]

What's going wrong stevemg? As far as I can see, plugging x = 2, t = 2 and v = 0.6c into those equations for the Lorentz transformation gives you x' = 1 and t' = 1.

x' = (2 - 0.6 x 2)/sqrt(1 - 0.36) = (2 - 1.2)/0.8) = 1.

etc.

 

[stevmg]

Hey, thanks, yossell...

Needed a kickstart as I was drawing a blank. Remember, this is still relatively new to me.

Sometimes the answer lies right in front of you and you don't see it. Surely glad that Fleming saw it when he saw that the Penicillium mold blocked the growth of staphylococcal aureus bacteria (1928.)

stevmg