- #1

- 190

- 1

## Main Question or Discussion Point

I would like to know a simple way of understanding how to derive the Lorentz transformation equations. My book states them without proof and on websites I only see complicated proofs that Im not mathematically ready for yet. Ok so I think i understand x'=γ(x-vt), but let me say it in my own words and have it confirmed as right just in case:

Suppose a reference frame with origin O' is moving at velocity v with respect to frame origin O and lets say an event happens at some point in space. O' has left O a time t ago (according to O), and O sees the event a distance x away, and O' sees the event a distance x' away. However, x' is actually shorter due to length contraction than it would have been had O' been at rest with respect to O. Therefore, to relate x to x', x must be the distance from O to O' (which is vt) plus the distance that x' would have seen had it been at rest with O, so we lengthen x' by multiplying x' by γ, so x=vt+x'γ and rearrangement leads to the conventional form.

Am i interpreting this right?

Now what i really dont understand is t'=γ(t-vx/c^2)...So if x' is the distance for O' to the event, and x is the distance for O to the event, and since in the previous equation, t was the time according to O that it took for O' to get a distance vt away, then in this equation, t' should be the time it took for O' to get that same distance away from O. So according to O', it took him the time t' to get the contracted distance vt/γ away from O. So t' is just t/γ....which is right but i dont see how it leads to above Lorentz equation...i feel im maybe misinterpreting what t' is supposed to mean???

note: i am trying to follow the diagram my book has drawn...i am assuming the labels it uses are supposed to correspond to the variables of the equations..but it doesnt specify what t' is, which is causing me confusion! :

http://af10.mail.ru/cgi-bin/readmsg?id=13354810280000000090;0;1&mode=attachment

Suppose a reference frame with origin O' is moving at velocity v with respect to frame origin O and lets say an event happens at some point in space. O' has left O a time t ago (according to O), and O sees the event a distance x away, and O' sees the event a distance x' away. However, x' is actually shorter due to length contraction than it would have been had O' been at rest with respect to O. Therefore, to relate x to x', x must be the distance from O to O' (which is vt) plus the distance that x' would have seen had it been at rest with O, so we lengthen x' by multiplying x' by γ, so x=vt+x'γ and rearrangement leads to the conventional form.

Am i interpreting this right?

Now what i really dont understand is t'=γ(t-vx/c^2)...So if x' is the distance for O' to the event, and x is the distance for O to the event, and since in the previous equation, t was the time according to O that it took for O' to get a distance vt away, then in this equation, t' should be the time it took for O' to get that same distance away from O. So according to O', it took him the time t' to get the contracted distance vt/γ away from O. So t' is just t/γ....which is right but i dont see how it leads to above Lorentz equation...i feel im maybe misinterpreting what t' is supposed to mean???

note: i am trying to follow the diagram my book has drawn...i am assuming the labels it uses are supposed to correspond to the variables of the equations..but it doesnt specify what t' is, which is causing me confusion! :

http://af10.mail.ru/cgi-bin/readmsg?id=13354810280000000090;0;1&mode=attachment

Last edited: