On Mar 4, 8:46 pm, George Hammond wrote:
On Tue, 4 Mar 2008 04:08:59 -0800 (PST),

" 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.

[Hammond]
Only an amateur would try to use a Minkowski diagram
(rotation diagram) to study a Lorentz transformation.
The EXPERTS use OBLIQUE COORDINATE DIAGRAMS.... you've
probaly seen these in professional publications.
The Minkowski diagram does not show "true lengths" and as
someone pointed out you CANNOT use Euclidean Geometry in the
diagram.... and it does NOT give you ture picture of the
transformation.
The EXPERTS use the LOEDEL (oblique) diagram.
Understanding this diagram is equivalent to MASTERING SR,
and it can be done in a few minutes. It turns out that the
Lorentz Transformation is IDENTICAL to the coordinate
transformation between two OBLIQUE coordinate systems... one
obtuse and the other acute. Euclidean geometry applies, the
scales are true length,... the whole thing is a miracle!
The CLASSIC text on this is SHADOWITZ'S book, which only
costs $6.95 in the ppbk Dover edition....one of the all time
best book bargains ever! DON'T LEAVE HOME WITHOUT IT!!!

if so right a book, why tha fok is only 6.95?

and why 6.95 and not 7

definetly you are a gay


SPECIAL RELATIVITY, Albert Shadowitz, 1968, Dover ppbk,
ISBN 0-486-65743-4 only $6.95 a few years ago.

By the way, you can Google the Loedel diagram but all you
get is amateur crap explanations..... for chrissakes spend
the $6.95 and buy Shadowitz'a classic book and wrap up your
studies of SR in a couple of hours!

=====================================
SCIENTIFIC PROOF OF GOD WEBSITE
http://geocities.com/scientific_proof_of_god
mirror site:
http://proof-of-god.freewebsitehosting.com
GOD=G_uv (a folk song on mp3)
http://interrobang.jwgh.org/songs/hammond.mp3
=====================================

:
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?

You've got to be aware that the units of an xt frame have a different
"length" than those of any other x't' frame. All units are to be found along
a hyperbolic curve, one for space axes' units and another for time axes'
ones. This relationship corresponds to Lorentz-equations "singling out" a
space coordinate x' (t'=0) or a time coordinate t' (x'=0), ending up in
hyperbolic (x,t) correspondents.
Example in
http://home.scarlet.be/~pin12499/MyS...ntzObjects.PNG
at my SRT page
http://home.scarlet.be/~pin12499/paratwin.htm
with much more graphic stuff.

guido

" 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?

Through the given point, draw a line parallel to the x' axis. The
intersection of that line and the t' axis gives the value of t' for
the given point.

Mike Fontenot

On Mar 4, 9:46*pm, George Hammond wrote:
On Tue, 4 Mar 2008 04:08:59 -0800 (PST),

" 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.

[Hammond]
* Only an amateur would try to use a Minkowski diagram
(rotation diagram) to study a Lorentz transformation.
* *The EXPERTS use OBLIQUE COORDINATE DIAGRAMS.... you've
probaly seen these in professional publications.
* *The Minkowski diagram does not show "true lengths" and as
someone pointed out you CANNOT use Euclidean Geometry in the
diagram.... and it does NOT give you ture picture of the
transformation.
* *The EXPERTS use the LOEDEL (oblique) diagram.
Understanding this diagram is equivalent to MASTERING SR,
and it can be done in a few minutes. *It turns out that the
Lorentz Transformation is IDENTICAL to the coordinate
transformation between two OBLIQUE coordinate systems... one
obtuse and the other acute. *Euclidean geometry applies, the
scales are true length,... the whole thing is a miracle!
* *The CLASSIC text on this is SHADOWITZ'S book, which only
costs $6.95 in the ppbk Dover edition....one of the all time
best book bargains ever! *DON'T LEAVE HOME WITHOUT IT!!!

SPECIAL RELATIVITY, Albert Shadowitz, 1968, Dover ppbk,
* * ISBN 0-486-65743-4 * * *only $6.95 a few years ago.

By the way, you can Google the Loedel diagram but all you
get is amateur crap explanations..... for chrissakes spend
the $6.95 and buy Shadowitz'a classic book and wrap up your
studies of SR in a couple of hours!

=====================================
* * *SCIENTIFIC PROOF OF GOD WEBSITE
*http://geocities.com/scientific_proof_of_god
* *mirror site:
*http://proof-of-god.freewebsitehosting.com
* * * GOD=G_uv * (a folk song on mp3)
*http://interrobang.jwgh.org/songs/hammond.mp3
=====================================

I'll check out the book at the library, thanks.

Ram.

On Mar 4, 11:29*pm, Mike Fontenot wrote:
" 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?

Through the given point, draw a line parallel to the x' axis. *The
intersection of that line and the t' axis gives the value of t' for
the given point.

* * * * Mike Fontenot

Mike --- This seems to contradict what Dirk was saying, which
according to my calculations works.

Ram.

Mike Fontenot wrote in message

" 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?

Through the given point, draw a line parallel to the x' axis. The
intersection of that line and the t' axis gives the value of t' for
the given point.

Yes, if you multiply with sqrt(1-v^2)/sqrt(1+v^2).
See my replies.

Dirk Vdm

On Mar 4, 8:35*pm, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-
SperM.hotmail.com wrote:
wrote in message

*



On Mar 4, 7:21 pm, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-
SperM.hotmail.com wrote:
PD wrote in message



On Mar 4, 10:52 am, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-
SperM.hotmail.com wrote:
PD wrote in message



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.

Of course you can.

OK, you can if you are VERY careful. For example, note the effect of
the a boost, which is called a "rotation" in Minkowski space. However,
this is not your garden-variety rotation, in that both axes get
rotated, say, clockwise, to do the transformation. In fact, the x-axis
rotates one way and the t-axis rotates the other way.

All sorts of mapping issues result from this shift from Euclidean to
hyperbolic geometry. For example, trig relations get replaced by
hyperbolic trig relations (sinh, cosh, tanh, rather than sin, cos,
tan). All of these are trackable if you are careful and understand
what is fundamentally different about the Minkowski diagram from the
usual pair of axes on a flat piece of paper.

Since in Euclidean terms we don't allow imaginary angles, we
shouldn't really call this a "real" rotation ("real" like in The Real
Numbers).
I made this thing some time ago. It just took some straightforward
standard high school level analytic geometry with lines, slopes,
and intersections, and as you can see, even if you're not careful,
once you have that scale factor, one can easilily "read" the
transformed coordinates from the Minkovski diagram :-)

Dirk Vdm

Dirk -- You are a godsend. That Java thing rocks. I tried some values,
and I checked it and it gives the same result as the Lorentz
Transformation. However, I tried to get x' and t' analytically from
the graph, but it didn't come out like the x' and t' that the app
said. Do I have a computation mistake, or did I not understand how x'
and t' are retirieved? I'll tell you how I retrieved them: For x', for
example I took the point x' on the graph and calculated its distance
from O. Is that what I'm supposed to do?

See my last message where I calculated the scale factor
for X' when X and T are known.
I'll leave the calculation of T' as an exercise. Let me know
if you get stuck :-)

Dirk Vdm

Ahoi sailor, it worked!
So my conclusion is, use Minkowski diagram but multiply it by the
magic factor sqrt(1-v^2)/sqrt(1+v^2). So that means that Minkowski
diagrams are only good for telling you which events happened on the
same time, but it's pretty hard to read from them what exactly that
time was.

Does this mean that this page:
http://www.physics.usyd.edu.au/super...i_Diagrams.pdf
Is rubbish? Because it doesn't mention the magic factor. Is that
factor mentioned in books about SR?

Curiously yours,
Ram.

wrote in message

On Mar 4, 8:35 pm, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-
SperM.hotmail.com wrote:
wrote in message





On Mar 4, 7:21 pm, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-
SperM.hotmail.com wrote:
PD wrote in message



On Mar 4, 10:52 am, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-
SperM.hotmail.com wrote:
PD wrote in message



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.

Of course you can.

OK, you can if you are VERY careful. For example, note the effect of
the a boost, which is called a "rotation" in Minkowski space. However,
this is not your garden-variety rotation, in that both axes get
rotated, say, clockwise, to do the transformation. In fact, the x-axis
rotates one way and the t-axis rotates the other way.

All sorts of mapping issues result from this shift from Euclidean to
hyperbolic geometry. For example, trig relations get replaced by
hyperbolic trig relations (sinh, cosh, tanh, rather than sin, cos,
tan). All of these are trackable if you are careful and understand
what is fundamentally different about the Minkowski diagram from the
usual pair of axes on a flat piece of paper.

Since in Euclidean terms we don't allow imaginary angles, we
shouldn't really call this a "real" rotation ("real" like in The Real
Numbers).
I made this thing some time ago. It just took some straightforward
standard high school level analytic geometry with lines, slopes,
and intersections, and as you can see, even if you're not careful,
once you have that scale factor, one can easilily "read" the
transformed coordinates from the Minkovski diagram :-)

Dirk Vdm

Dirk -- You are a godsend. That Java thing rocks. I tried some values,
and I checked it and it gives the same result as the Lorentz
Transformation. However, I tried to get x' and t' analytically from
the graph, but it didn't come out like the x' and t' that the app
said. Do I have a computation mistake, or did I not understand how x'
and t' are retirieved? I'll tell you how I retrieved them: For x', for
example I took the point x' on the graph and calculated its distance
from O. Is that what I'm supposed to do?

See my last message where I calculated the scale factor
for X' when X and T are known.
I'll leave the calculation of T' as an exercise. Let me know
if you get stuck :-)

Dirk Vdm

Ahoi sailor, it worked!
So my conclusion is, use Minkowski diagram but multiply it by the
magic factor sqrt(1-v^2)/sqrt(1+v^2). So that means that Minkowski
diagrams are only good for telling you which events happened on the
same time, but it's pretty hard to read from them what exactly that
time was.

I don't agree. It is pretty easy to read. It is just a scaling factor.
You can put the x'=1 and t'=1 marks and then estimate by merely
looking.


Does this mean that this page:
http://www.physics.usyd.edu.au/super...i_Diagrams.pdf
Is rubbish? Because it doesn't mention the magic factor.

That's what I meant.
You will find that the factor (0.686 for v=0.6) is present in the
points (x',t') = (1,0) and (0,1).
Not rubbish at all - just not explicitly mentioned.

Is that
factor mentioned in books about SR?

No idea, I have never seen it in books.
I calculated it a while ago when I was playing with Geometer's
Skechpad.
Here's another screenshot I made a few days earlier:
http://users.telenet.be/vdmoortel/di...sformation.png
To bad that saving as html/java is very limited. Compare the
quality difference between my previous Lorentz.htm and
Lorentz.png :-)

Cheers,
Dirk Vdm

On Mar 4, 4:19*pm, "
wrote:
On Mar 4, 8:35*pm, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-





SperM.hotmail.com wrote:
wrote in message

*

On Mar 4, 7:21 pm, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-
SperM.hotmail.com wrote:
PD wrote in message



On Mar 4, 10:52 am, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-
SperM.hotmail.com wrote:
PD wrote in message



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.

Of course you can.

OK, you can if you are VERY careful. For example, note the effect of
the a boost, which is called a "rotation" in Minkowski space. However,
this is not your garden-variety rotation, in that both axes get
rotated, say, clockwise, to do the transformation. In fact, the x-axis
rotates one way and the t-axis rotates the other way.

All sorts of mapping issues result from this shift from Euclidean to
hyperbolic geometry. For example, trig relations get replaced by
hyperbolic trig relations (sinh, cosh, tanh, rather than sin, cos,
tan). All of these are trackable if you are careful and understand
what is fundamentally different about the Minkowski diagram from the
usual pair of axes on a flat piece of paper.

Since in Euclidean terms we don't allow imaginary angles, we
shouldn't really call this a "real" rotation ("real" like in The Real
Numbers).
I made this thing some time ago. It just took some straightforward
standard high school level analytic geometry with lines, slopes,
and intersections, and as you can see, even if you're not careful,
once you have that scale factor, one can easilily "read" the
transformed coordinates from the Minkovski diagram :-)

Dirk Vdm

Dirk -- You are a godsend. That Java thing rocks. I tried some values,
and I checked it and it gives the same result as the Lorentz
Transformation. However, I tried to get x' and t' analytically from
the graph, but it didn't come out like the x' and t' that the app
said. Do I have a computation mistake, or did I not understand how x'
and t' are retirieved? I'll tell you how I retrieved them: For x', for
example I took the point x' on the graph and calculated its distance
from O. Is that what I'm supposed to do?

See my last message where I calculated the scale factor
for X' when X and T are known.
I'll leave the calculation of T' as an exercise. Let me know
if you get stuck :-)

Dirk Vdm

Ahoi sailor, it worked!
So my conclusion is, use Minkowski diagram but multiply it by the
magic factor sqrt(1-v^2)/sqrt(1+v^2). So that means that Minkowski
diagrams are only good for telling you which events happened on the
same time, but it's pretty hard to read from them what exactly that
time was.

Does this mean that this page:http://www.physics.usyd.edu.au/super...ties/Mechanics...
Is rubbish? Because it doesn't mention the magic factor.

Notice that the scales in the drawing in that link are already
rescaled by the "magic factor". The distance from 0 to 1 is different
on the two sets of axes. You were using a ruler that doesn't take that
rescaling into account.

Is that
factor mentioned in books about SR?

Curiously yours,
Ram.- Hide quoted text -

- Show quoted text -

wrote in message
...
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.

Then read it again .. that article shows nicely how all the effects of LT
are illustrated.

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?

No .. as I cannot see what you did .. you'll have to work it out for
yourself by reading the article there (and other articles and text) that
explain how the diagrams work