Re: [Phys-l] Re. Simultaneity

[Bob Sciamanda <treborsci@verizon.net>]

Using w = ict, the usual Lorentz xform can be written as:

x' = g(x+ivw/c),  and w' = g(w-ivx/c) where g =SQR(1/1-(v/c)^2)

This can be written as the explicitly orthogonal xform:

x' = xCOS(Q) + wSIN(Q) , and w'= wCOS(Q) - xSIN(Q),

where Q is the imaginary angle :
COS(Q) = g , and SIN(Q) = ivg/c


In my schooldays (many eons ago) this formalism was quite common,
eg., in texts by Joos, Panofsky/Phillips, Jackson, etc.
See Jackson, Classical Electrodynamics, paragraph ll.7 (first edition) for a good exposition and its use in electromagnetics.

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/

On May 22, 2009, John Denker <jsd@av8n.com> wrote: 

On 05/21/2009 01:05 PM, Bob Sciamanda wrote:
> If one uses the original Minkowski coordinates (x,y,z,w; where w =
> ict), one can maintain the orthogonality of x vs w and x' vs w' axis
> pairs in spacetime diagrams.

Please explain. I've never seen it done.

a) Presumably we all agree that within each set of axes, the actual
axes are orthogonal in actual spacetime, but
b) I don't know how to project that onto the page of the diagram in 
such a way that the projected axes are orthogonal on the page,
for more than one set of axes at a time, except in trivial cases.

c) Forsooth I don't even know how to do an orthogonal projection of 
ordinary Euclidean X,Y,Z axes onto the page in such a way that the 
three projections are orthogonal on the page.
http://www.phys.unt.edu/~klittler/demo_room/mech_demos/Vector%20Rods.jpg
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