On Mar 4, 5:40 am, "harry" wrote:
"Eric Gisse" wrote in message

...



On Mar 4, 4:47 am, "
wrote:
On Mar 4, 2:17 pm, "Artful" wrote:

wrote in message

...

I'm not sure I know exactly how to use the Minkowski diagram. For
example, let's say you have a stationary observer and a moving
observer, and an event somewhere, for which the coordinates are x and
t in the stationary frame and x' and t' in the moving frame. How do
you get t', for example, from the Minkowski diagram?

Ram.

Seehttp://en.wikipedia.org/wiki/Minkowski_diagram
Look at the diagram in the section entitled "Minkowski diagram in
special
relativity" with the caption "In the theory of relativity both
observers
assign the event at A to different times."

Artful:

I considered it, but it seems to contradict the equations for Lorentz
transformation. I mean, when I tried to get x' and t' through the
diagram and through Lorentz transformation, I got different things. I
expressed x' and t' using trigonometry from the diagrams, and I got
some kind of ugly mess. Can you point out my mistake? Or maybe there
is an analysis of how Minkowski diagrams work somewhere on the web?

Thanks,
Ram.

Lorentz transformations have nothing to do with spacetime diagrams.
Lorentz transformations are a specific type of transformation between
inertial reference frames, and the Minkowski/space-time diagram is a
characterization of the geometry of a manifold [they generalize to
conformal diagrams] by using null paths [the paths light travel along]
which is unrelated to frame transformations.

That's wrong. Instead, I think that the intro of the above link is quite
right:

I looked at the image, saw the familiar cone, and figured it was just
another name for a space-time diagram.


"The Minkowski diagram [...] provides an illustration of the properties of
space and time in the special theory of relativity. It allows a quantitative
understanding of the corresponding phenomena like time dilation and length
contraction without mathematical equations."

Roughly, a rotation in a Minkowski diagram corresponds to a Lorentz
transformation. A different result is most likely due to either a wrong
rotation or a wrong projection. There are many detailed manuals on the web
that may be clearer and more detailed than Wikipedia, for example:http://www.physics.usyd.edu.au/super...ties/Mechanics...
(Found with Google, haven't checked it but it looks good)

Harald