Re: bringin einstein and lorentz to justice
Dirk Van de moortel
dedanoe <ded...@gmail.com> wrote in message
2d2bc633-140c-4bf0...@k13g2000hse.googlegroups.com
> Under the leadership of Einstein's SRT:
>
> t'=(t-V/c x/c)/Sqrt(1-Sqr(V/c))
> t=(t'+V/c x'/c)/Sqrt(1-Sqr(V/c))
>
> x'=(x-Vt)/Sqrt(1-Sqr(V/c))
> x=(x'+Vt')/Sqrt(1-Sqr(V/c))
> ---------------------------------
> As cited from "General Physics I"
> SBN: 9989-43006-3
> =================================
> The hack:
> ---------------------------------
> x'/t = (x-Vt)/(t'+V/c x'/c) and
> x/t' = (x'+Vt')/(t-V/c x/c) ==>
> x't'+VSqr(x'/c) = xt-Vt^2 and
> xt-VSqr(x/c)=x't'+Vt'^2 ==>
>
> x't'-xt=-V(Sqr(x'/c)-t^2) and
> x't'-xt=-V(Sqr(x/c)-t'^2) ==>
Typo.
That should be +t^2 and +t'^2
x't'-xt=-V(Sqr(x'/c)+t^2)
x't'-xt=-V(Sqr(x/c)+t'^2)
>
> -(x't'-xt)/V=(t^2+Sqr(x'/c)) and
> -(x't'-xt)/V=(t'^2+Sqr(x/c)) ==>
This is correct again.
>
> t^2+Sqr(x'/c)=t'^2+Sqr(x/c) ==>
Yes, we normally write this as
(x/c)^ - t^2 = (x'/c)^2 - t'^2
It's called the invariance of the interval.
>
> (t-t')(t+t')=(x-x')/c (x+x')/c
sure.
>
> V=x/t=c and V'=x'/t'=c
Where do you get this from?
When you about the coordinates of a light signal sent
out from the origin, you can say, and derive from the
transformation that
if the signal has equation
x/t = c
in the in the unprimed system, then it has equation
x'/t' = c
in the in the primed system.
Do you understand this?
Dirk Vdm
[ removed silly newsgroups and followup to sci.physics.relativity ]
dedanoe
<dirkvandemoor...@nospAm.hotmail.com> wrote:
> dedanoe <deda...@gmail.com> wrote in message
>
> 2d2bc633-140c-4bf0-bf4c-f22036660...@k13g2000hse.googlegroups.com
>
> - Show quoted text -
(x, t) and (x', t') are the properties of the moving body that we
observe in K and K' coordinate systems thereby they cannot be
considered as property of the light signal at the same instance. the
light signal must have its own (X, T) and (X', T') properties in K and
K' reference frame.
Dirk Van de moortel
You see this much too narrow.
In the context of the Lorentz transformations (provided by you)
(x, t) and (x', t') are the coordinates of arbitrary events as
measured, observed or calculated in two coordinate systems.
Any event taking place at location x at time t, as observed in
system K, takes place at location x' at time t', as observed in
system K', whereby the four numbers x,t,x',t' are related by
the transformation equations.
When you write x/t = c and x'/t' = c, the numbers x,t,x',t'
are still related by the transformation equations, but this time
they are only valid for events taking place on the path of a
particular light signal.
Do you understand that?
Dirk Vdm
glird
> dedanoe <deda...@gmail.com> wrote
<<< When you speak about the coordinates of a light signal sent
out from the origin, you can say, and derive from the
transformation that if the signal has the equation
x/t = c
in the in the unprimed system, then it has the equation
x'/t' = c
in the primed system. >>>
>
<< (x, t) and (x', t') are the properties of the moving body that we
observe in K and K' coordinate systems
In the context of the Lorentz transformations (provided by you)
(x, t) and (x', t') are the coordinates of arbitrary events as
measured, observed or calculated in two coordinate systems. >>
>
One of the two is moving at a different velocity than the other,
as plotted by both of them.
< Any event taking place at location x at time t, as observed in
system K, takes place at location x' at time t', as observed in
system K', whereby the four numbers x,t,x',t' are related by
the transformation equations. >
>
in classical physics the relation was given by the Galilean
transformation equations. In relativistic physics it is given
by the Lorentz transformation equations.
< When you write x/t = c and x'/t' = c, the numbers
[denoted by the symbols] x,t,x',t'
are still related by the transformation equations, but this time
they are only valid for events taking place on the path of a
particular light signal.
Do you understand that?
Dirk Vdm >>
>
That's correct wrt the Lorentz transformations. It is also correct
for an infinity of cases in which the length and time deformations are
NOT those required by the LTE.
It is false wrt the Galilean transformations
glird