Lorentz Transformation Question

[Kunhee]

Homework Statement

For an event occurring at (x,t),
consider the quantity I = x^2 - (ct)^2
Find a simple expression for this in the S' frame: I' = x'^2 - (ct')^2
How are I and I' related, and why is this noteworthy?

The Attempt at a Solution

So the question is under "Lorentz Transformation" and I must
simplify I' = x'^2 - (ct')^2.

I am not sure if this is the way to go about it, but should I find
the equation in the form of "c =" ?

 

[Lucas SV]

You should write x' and t' in terms of x and t by using Lorentz transformations (specifically, what is called a boost in the $x$ direction).

 

[Kunhee]

When I do, do I find the quantities equal?

 

[Kunhee]

I plugged into
I' = x'^2 - (ct')^2

x' = y(x - ct)
t' = y(t - cx/c^2)
* y is Lorentz Factor

and I get that I' = 0

 

[Lucas SV]

When I do, do I find the quantities equal?

Yes, you should find that they are equal, I=I'. You got 0 because you wrote c instead of v in the Lorentz transformations. They are:

x' = y(x - vt)
t' = y(t - vx/c^2).

 

[Kunhee]

I see, thank you!