On Mar 5, 1:25*pm, "
wrote:
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 checked the book out at the library--It looks pretty nice. I read
the explanation about the Loedel diagram: It's simply a Minkowski
diagram, but instead of the stationary frame having a right angle
between its axis, you have an obtuse angle between them. This is like
the picture here shows:http://en.wikipedia.org/wiki/Minkowski_diagram
Not quite as complicated as to require a book, in my opinion.
However, George is right: This kind of space-time diagram does abolish
the need for the "magic factor". I checked it trigonometrically and
it's identical to the Lorentz transformation without using a factor.
There's no distortion. I'm very pleased with this kind of diagram,
I've already used it to confirm the formulas for length-contraction
and time-dilation. Thanks!

Best Wishes,
Ram Rachum.

And let me add an interesting question: Can one draw a Loedel diagram
for a system with three observers?

BW,
Ram.

On Wed, 5 Mar 2008 03:25:22 -0800 (PST),
" wrote:

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 checked the book out at the library--It looks pretty nice. I read
the explanation about the Loedel diagram: It's simply a Minkowski
diagram, but instead of the stationary frame having a right angle
between its axis, you have an obtuse angle between them. This is like
the picture here shows:
http://en.wikipedia.org/wiki/Minkowski_diagram
Not quite as complicated as to require a book,



[Hammond]
I knew you'd love it. All you really need is Chapter 2.
Look at Figure 19 on page 54 however... can you believe how
SIMPLY and dramatically this diagram explains the Lorentz
Contraction....wow... the whole of SR in a single picture!
And check out the Twins Paradox diagram on page 44...


However, George is right: This kind of space-time diagram does abolish
the need for the "magic factor".


[Hammond]
Right... no 'scale factors' needed... all lengths in the
diagram appear as "true lengths".



I checked it trigonometrically and
it's identical to the Lorentz transformation without using a factor.
There's no distortion. I'm very pleased with this kind of diagram,
I've already used it to confirm the formulas for length-contraction
and time-dilation. Thanks!

[Hammoond]
Yeah.... I really never could visualize SR until I came
across this book and discovered the "oblique axis"
method.... and discovered that the 'experts' use it all the
time!

Best Wishes,
Ram Rachum.

On Wed, 5 Mar 2008 08:59:48 -0800 (PST),
" wrote:

On Mar 5, 1:25*pm, "
wrote:
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 checked the book out at the library--It looks pretty nice. I read
the explanation about the Loedel diagram: It's simply a Minkowski
diagram, but instead of the stationary frame having a right angle
between its axis, you have an obtuse angle between them. This is like
the picture here shows:http://en.wikipedia.org/wiki/Minkowski_diagram
Not quite as complicated as to require a book, in my opinion.
However, George is right: This kind of space-time diagram does abolish
the need for the "magic factor". I checked it trigonometrically and
it's identical to the Lorentz transformation without using a factor.
There's no distortion. I'm very pleased with this kind of diagram,
I've already used it to confirm the formulas for length-contraction
and time-dilation. Thanks!

Best Wishes,
Ram Rachum.

And let me add an interesting question: Can one draw a Loedel diagram
for a system with three observers?

[Hammond]
You'd need 3 diagrams.


BW,
Ram.