Re: coordinates and equations.

On Nov 28, 9:02 am, papa_r...@xxxxxxxxxxx wrote:
"We express the principle of the invariance of the velocity of light
in mathematical form. For this purpose we consider two reference
systems K and K' moving relative to each other with constant velocity.
We choose the coordinate axes so that the axes X and X' coincide,
while the Y and Z axes are parallel to Y' and Z'; we designate the
time in the systems K and K' by t and t'.
Let the first event consist of sending out a signal, propagating with
light velocity, from a point having coordinates (xl, yl, zl, t1) in
the K system. We observe the propagation of this signal in the K
system. Let the second event consist of the arrival of the signal at
point (x2, y2, z2, t2). The signal propagates with velocity c; the
distance covered by it is therefore c(tl - t2). On the other hand,
this same distance equals [(x2 - xl)^2 + (y2 - yl)^2 + (z2 - zl )^2]
^1/2. Thus we can write the following relation between the coordinates
of the two events in the K system:

(x2 - xl)^2 + (y2 - yl)^2 + (z2 - zl )^2 - c^2 (t2 - tl)^2 = 0    (1)

The same two events, i.e. the propagation of the signal, can be
observed from the K' system:
Let the coordinates of the first event in the K' system be (x’1, y’1,
z’1, t’1) and of the second: (x’2, y’2, z’2, t’2). Since the velocity
of light is the same in the K and K' systems, we have, similarly to
(1):

(x’2 – x’l)^2 + (y’2 – y’l)^2 + (z’2 – z’l )^2 - c^2 (t’2 – t’l)^2 =
0    (2)

If (xl, yl, zl, t1) and (x2, y2, z2, t2) are the coordinates of any
two events, then the quantity

sl2 = [c^2 (t2 - tl)^2 - (x2 - xl)^2 - (y2 - yl)^2 - (z2 - zl )^2]
^1/2     (3)

is called the interval between these two events.
Thus it follows from the principle of invariance of the velocity of
light that if the interval between two events is zero in one
coordinate system, then it is equal to zero in all other systems."

Miguel Rios

Miguel,
Well, the Galilean transformation equations have t'=t, so if, as
scientists say, there is a clock in S' that is running slower than a
clock in S that shows t, then that clock cannot be showing t'. So, as
I have shown, the time on that clock is n', where n'=t(1-v/c).

Then with regard to your intervals, if time in S is t, and time in
S' is n', then the velocity of light is c in both frames of reference.
Robert B. Winn
.

Relevant Pages

  • Re: coordinates and equations.
    ... systems K and K' moving relative to each other with constant velocity. ... We choose the coordinate axes so that the axes X and X' coincide, ... distance covered by it is therefore c. ... clock in S that shows t, then that clock cannot be showing t'. ...
    (sci.physics.relativity)
  • Re: coordinates and equations.
    ... systems K and K' moving relative to each other with constant velocity. ... We choose the coordinate axes so that the axes X and X' coincide, ... distance covered by it is therefore c. ... clock in S that shows t, then that clock cannot be showing t'. ...
    (sci.physics.relativity)
  • Re: coordinates and equations.
    ... systems K and K' moving relative to each other with constant velocity. ... We choose the coordinate axes so that the axes X and X' coincide, ... We observe the propagation of this signal in the K ... clock in S that shows t, then that clock cannot be showing t'. ...
    (sci.physics.relativity)
  • Re: Principle of equivalence
    ... reference and said the clock was in S. ... I did no flipping of frames of reference. ... state velocity. ...
    (sci.physics.relativity)
  • Re: ABOUT THE GALILEI PRINCIPLE OF RELATIVITY
    ... so what these equations say is that if a clock in a moving frame ... of reference ticks four times while a clock in a frame of reference at ... it will show a faster velocity than a clock in S which shows t. ...
    (sci.physics.relativity)
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