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.

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.

See http://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."

On Mar 4, 7:08*am, "
wrote:
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?

The answer in two short lines:
"Relativistic particle dynamics"
http://farside.ph.utexas.edu/teachin...s/node126.html


Ram.

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.

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.

On Mar 4, 6:08*am, "
wrote:
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.

No, you can't. The temptation is to use a Minkowski diagram like a 2D
Euclidean geometry, which would allow you to do all sorts of Euclidean
geometrical constructions (with a compass and a straight edge) and
trigonometric relations. But the relationship between x and t in a
Minkowski diagram is NOT Euclidean, and you will quickly run into
problems if you try to apply Euclidean rules to it.

PD

On Mar 4, 3:51*pm, Eric Gisse wrote:
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.

Your answer is somewhat confusing to me. Can Minkowski diagrams tell
you what x' and t' are? (When I say x' and t', I mean the coordinates
of an event from the frame of the moving observer)
This is from the Wikipedia page on Minkowski diagrams:
"Its main purpose is to allow for the space and time coordinates x and
t used by one observer to read off immediately the corresponding x'
and t' used by the other and vice versa."
Is this not correct?

And as I understand, the Lorentz transformation is supposed to tell
you x' and t' as well.

Shouldn't the two answers be the same, or am I missing something?


Thanks,

Ram.

On Mar 4, 4:23*pm, PD wrote:
On Mar 4, 6:08*am, "
wrote:

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.

No, you can't. The temptation is to use a Minkowski diagram like a 2D
Euclidean geometry, which would allow you to do all sorts of Euclidean
geometrical constructions (with a compass and a straight edge) and
trigonometric relations. But the relationship between x and t in a
Minkowski diagram is NOT Euclidean, and you will quickly run into
problems if you try to apply Euclidean rules to it.

PD

Are you saying that I cannot get x' and t' from the Minkowski diagram?
Because the page at Wikipedia says that this is its purpose. And if I
can get x' and t' from it, how do I do it? I tried the method that
they say in Wikipedia, but it didn't come out like the Lorentz
transformation. What am I missing?

Ram.

On Mar 4, 8:35*am, "
wrote:
On Mar 4, 4:23*pm, PD wrote:





On Mar 4, 6:08*am, "
wrote:

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.

No, you can't. The temptation is to use a Minkowski diagram like a 2D
Euclidean geometry, which would allow you to do all sorts of Euclidean
geometrical constructions (with a compass and a straight edge) and
trigonometric relations. But the relationship between x and t in a
Minkowski diagram is NOT Euclidean, and you will quickly run into
problems if you try to apply Euclidean rules to it.

PD

Are you saying that I cannot get x' and t' from the Minkowski diagram?
Because the page at Wikipedia says that this is its purpose. And if I
can get x' and t' from it, how do I do it? I tried the method that
they say in Wikipedia, but it didn't come out like the Lorentz
transformation. What am I missing?

I suggest you buy a book. Spacetime Physics, by Taylor and Wheeler.
Very affordable when bought used. Do not attempt to learn physics from
the internet or from Usenet.


Ram.- Hide quoted text -

- Show quoted text -

"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.

See http://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:

"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...i_Diagrams.pdf
(Found with Google, haven't checked it but it looks good)

Harald