Re: correct equations


<rbwinn3@xxxxxxxx> wrote in message
news:1139931118.902967.225270@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Harald,
Thank you for your response. First, let's consider where we
agree.

dx'/dt=w-v The speed of the photon relative to the x'
axis as measured in K.

Note the lack of indices, which can lead to confusions!
As you defined everything Galilean, we have:
* In K the measurement of the photon is in t, relative to x:
(dx/dt)photon=w.
* In K' the measurement of the photon is in t', relative to x':
dx'/dt'(photon)=w-v.
* In K the measurement of the photon relative to the x'-axis of K' is:
(dx/dt)photon-(dx/dt)[x'-axis]=w-v=(dx'/dt)[photon relative to K'].

Actually it is the velocity of the photon.
According to our description, the photon could be going either way.
This is of little value because it is based on time in K, not on t'.

I already showed you that your t'=t...

We need an equation where time is measured in K'. As seen
from K', K' is stationary, K is moving with a velocity of v'=-v
relative to K', so the equation will be
x=x'-v't'
x=x'+vt'
dx/dt'=w+v

I already showed you that in your system, (dx/dt)photon=(dx/dt')photon=w
(not w+v!).

Here once again: dx/dt'=dx'/dt'+vdt'/dt'=(w-v)+v=w.

Thus your dt'=dt, as we knew already. And as people knew one century ago,
with such definitions you can't consistently measure the same speed of light
in K and K' -- as you seem to acknowledge below.

Harald

Possibly it would be better to say dx/dt'=w-v' when talking to
scientists. If we keep x the same in both sets of equations, then x'
and t' are different in the second equation than they are in the first
equation because t' will be less or greater than t depending on which
way the photon is going.
Now consider photon A if A is the photon going in the +x
direction. This photon has a velocity of c relative to either set of
coordinates. From K the photon will appear to have gone a distance of
x'=x-vt in K'. dx'/dt=w-v From K' if we keep the same distance for
x, less time has elapsed in K', so the distance between the origins of
K and K' is less. vt>vt' x' will be a longer distance than as seen
from K, and t' will be a longer time. These values are not the same
as in the first equation, although we defined x to be the same in both
equations.
dx/dt'=w-v' =w+v

So, as I said, if we are in K' watching a flashlight in K that
is beamed along the x axis in the +x direction as Einstein described,
then the length of the flashlight beam will appear to us to be (w-v')t'
or (w+v)t'. The beam will be longer than the beam of a flashlight
turned on by us in K' at the origin at t=t'=0 when the origins
coincide. This tells us that more time has elapsed for the photons in
K than for the photons from our flashlight.
But suppose that the observer in K shines his flashlight the
other way when the origins coincide. In this case, the velocity of the
photons is -c in both frames of reference. As seen from K the photons
travel a distance of (-c-v)t in K'. As seen from K', K' is stationary,
and K is moving with a velocity of v'=-v relative to K'. The
flashlight is turned on in K when the origins coincide. A photon in K'
from the flashlight travels from the origin of K' to x'. A photon in K
travels from the origin of K to x. As seen from K'

x=x'-v't' = x'+vt'
dx/dt' = w+v

If we shine a flashlight in the -x direction the same time the
observer in K shines his, our flashlight beam will be longer because
the observer in K is moving away from us, and in our frame of
reference, the photons from both flashlights are moving away from us at
a velocity of -c. This tells us that for these photons, less time has
transpired in K than in K', just the opposite of what we observed for
the A photons.
I hope this explanation will clear up any confusion. When we
go from one equation to the other, the variables are not interchangable
except that we can specify one variable is the same in both equations.
According to these equations, both observers would see the same events
happen, but their perspectives would be different.
Robert B. Winn



.

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