Re: Galilean transformation equations

On Jan 5, 4:35 pm, rbwinn <rbwi...@xxxxxxxx> wrote:
On Jan 5, 6:41 am, Alen <al...@xxxxxxxxxxxxxxx> wrote:





On Jan 5, 2:38 am, rbwinn <rbwi...@xxxxxxxx> wrote:

On Jan 4, 5:52 am, Alen <al...@xxxxxxxxxxxxxxx> wrote:

[...]

Alen,
The same situation. For three dimensions you could express it
with these equations:

(x^2 + y^2 + z^2) - w^2t^2 = 0
[(x')^2 + (y')^2 + (z')^2] -w^2(n')^2 = 0

If y'=y and z'=z, then

x^2 -(x')^2 - w^2t^2 + w^2(n')^2 = 0
x'=x-vt
x'=wn'
x=xt
x^2 -(x-vt)^2 -x^2 +(x')^2 = 0
x'=x-vt

What the equations are saying is that if light is emitted at the
origins of S and S' when they coincide, then in S the light is
propagating as a sphere with a radius of ct from the origin of S, and
in S' the light is propagating as a sphere with a radius of cn' from
the origin of S'. S' is moving with a velocity of v relative to S
while this is happening according to a clock in S.
Robert B. Winn

I see that you are specifying the light in the two
frames completely independently of one another.
But Einstein was comparing how light travelled to
a point Y', say, on the y' axis, in both frames.

Light starts at origin O' in S' and travels along the
y' axis to Y', say. You can say that light starting at
origin O in S also travels along the y axis to get to
a corresponding point Y, in S. But Einstein wanted to
compare light getting to Y' in both frames, so, in S,
light has to travel diagonally, and not along the y axis,
to get to Y', because Y' is moving with S'. So light
travels a distance ct' in S', along the y' axis, to get to Y',
and a diagonal distance ct in S, to get to Y', composed
of ct' in the y direction and vt in the x direction, giving
a right triangle ct, ct', and vt, from which you get
(ct)^2 = (ct')^2 + (vt)^2. I think you are simply comparing
light travelling along the y axis in both frames, without
trying to compare how light gets to the one point, Y',
in both frames.

Alen- Hide quoted text -

- Show quoted text -

Alen,
     Here is the problem with what Einstein did.  S and S' are two
separate frames of reference.  A point in S cannot be used to denote
the place where light was emitted in S'.  He has the same problem in
his explanation of the train and lightning problem.  If light is
emitted at the origins of S and S' when they coincide, then in S' the
light proceeds from the origin of S' to (x,y,z), a point on the light
sphere expanding with a radius of cn' from the origin of S', where n'
is the time on a clock in S'.  If the Galilian transformation
equations are to be used, t'=t, meaning that t' is the same as t, time
on a clock in S.  This time gives the correct positions for
coordinates (x,y,z) and (x',y',z') according to a clock in S.  The
clock in S' is running slower and has to be shown by a different
variable, n'.
     We can show the problem Einstein had with his analysis of the
train and lightning problem.  Lightning strikes both ends of a train
simultaneously, leaving marks on the front and rear of the train and
marks on the railroad track.  The marks on the train are obviously the
length of the train apart.  How far apart are the marks on the track.
Scientists claim that the marks on the track are closer together than
the length of the train because of the length contraction.
   However, what actually happens is that in the frame of reference of
the railroad track, the light proceeds from the two marks left by the
lightning on the track and meets at a point midway between the two
marks on the track.  In the frame of reference of the train, the light
proceeds from the two marks left at the front and rear of the train
and meets at the middle of the train.  There is a relativity of time
between the two frames of reference, but no length contraction. The
points where light was emitted in S' do not change because the train
is moving.  In S' the light was emitted where the light struck the
front and rear of the train.  The points where the light struck the
railroad track are the points where light was emitted in S.  The
movement of the train has no effect on where light was emitted in S.
In S the light waves meet midway between the marks on the track.  In
S' the light waves meet at the middle of the train.  There is no
length contraction.
Robert B. Winn- Hide quoted text -

- Show quoted text -

you wrote "Here is the problem with what Einstein did. S and S' are
two
separate frames of reference. A point in S cannot be used to denote
the place where light was emitted in S' " the conclusion is you dont
understand what transformation are and ho to use them. for someone who
writes about Galilean transformation its a real problem....go back to
read a good honest text book about classical physics.
.

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