Understanding the Lorentz Transformation Equations

[stevmg]

$$x_2=v*t$$.

I was told that this is incorrect but I don't even know what it is.

The Lorentz equations are:

x' = $$\gamma$$(x - vt)
t' = $$\gamma$$(t - vx/c²)

How would you write that in matrix format?

 

[Mark44]

$$x_2=v*t$$.

I was told that this is incorrect but I don't even know what it is.

I don't either.

The Lorentz equations are:

x' = $$\gamma$$(x - vt)
t' = $$\gamma$$(t - vx/c²)

How would you write that in matrix format?

Edit: Fill in the question marks.
$$\left[\begin{array}{c} x' \\ t' \end{array}\right] = \left[ \begin{array} {cc} ? & ? \\ ? & ? \end{array} \right] \left[\begin{array}{c} x \\ t \end{array}\right]$$

 

[Doc Al]

How would you write that in matrix format?

$$\left(<br /> \begin{array}{cc}<br /> x'\\<br /> t'<br /> \end{array}<br /> \right) = \left( \begin{array}{cc} ? & ?\\? & ?\end{array}\right)<br /> \left(<br /> \begin{array}{cc}<br /> x\\<br /> t<br /> \end{array}<br /> \right)$$

Fill in the ? marks.

 

[HallsofIvy]

Too late! Mark44 already did!

 

[Doc Al]

Too late! Mark44 already did!

 

[Mark44]

I revised my answer, realizing I gave too much help.

 

[stevmg]

I tried I can't make the matrix work.

I am wasting my time...

I'll just read from now on as this array/matrix stuff is pure crap to me.

Thanks anyway

 

[Mark44]

$$x_2=v*t$$.

I was told that this is incorrect but I don't even know what it is.

The Lorentz equations are:

x' = $$\gamma$$(x - vt)
t' = $$\gamma$$(t - vx/c²)

How would you write that in matrix format?

It might be helpful to write the equations above as
$$x' = \gamma x - \gamma vt$$
$$t' = -\gamma \frac{v}{c^2}x + \gamma t$$

 

[stevmg]

It might be helpful to write the equations above as
$$x' = \gamma x - \gamma vt$$
$$t' = -\gamma \frac{v}{c^2}x + \gamma t$$

I do not know how to write a matrix in Latex format and no matter how hard I try I never get it.

If I could hand write it, I would but that's not possible here.

I am NOT wasting more time on this and I thank you for your time.

Steve G
Melbourne FL

 

[Doc Al]

I do not know how to write a matrix in Latex format and no matter how hard I try I never get it.

You can always just click on one of the ones we provided and copy the code, but no matter.

If the only issue is that you can't write it, that's not a problem. If I write the matrix as:

$$\left( \begin{array}{cc} a & b\\c & d\end{array}\right)$$

We can discuss your answers for the elements a, b, c, and d.

 

[stevmg]

a = $$\gamma$$
b = -$$\gamma$$v
c = -$$\gamma$$v/c²
d = $$\gamma$$

 

[cronxeh]

a = $$\gamma$$
b = -$$\gamma$$v
c = -$$\gamma$$v/c²
d = $$\gamma$$

Thats correct, do you have to solve this linear ODE, or just write it in matrix form?

 

[Doc Al]

a = $$\gamma$$
b = -$$\gamma$$v
c = -$$\gamma$$v/c²
d = $$\gamma$$

Perfect.