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[Phys-l] 100 years of spacetime



Next year (2008) marks the 100th anniversary of Minkowski's
brilliant presentation ``Raum und Zeit".

I can't help thinking he had fun writing it. It's not every
day you get to write a line like this:

> From this moment on, space by itself and time by itself are doomed
> to sink into mere shadows, and only a kind of union of the two
> will preserve an independent reality.

He went on to present ideas such as spacetime diagram, world-line,
forward cone, past cone, proper time, and so forth.

It's not every day you get to start with something by Einstein
and make it simultaneously more elegant, more mathematically
sophisticated, more physical, more visualizable, and more
practical.



http://de.wikisource.org/wiki/Raum_und_Zeit_(Minkowski)


H. Minkowski, ``Raum und Zeit",
80. Versammlung Deutscher Naturforscher (Köln, 1908).
Published in Physikalische Zeitschrift _10_ 104-111 (1909)
and Jahresbericht der Deutschen Mathematiker-Vereinigung
_18_ 75-88 (1909).


=====
Pedagogical implications:

I am shocked and disappointed that introductory-level physics
texts continue to teach the contraction/dilation approach to
relativity. That has been passé for 99 years now, going on 100.
It is as if the introductory electronics discussion focussed
on Fleming valves.

I'm not saying that contraction and dilation are completely
wrong ideas; I'm just saying they are not the starting point
or the ending point of a modern (post-1908) discussion. They
are at best a one-star tourist attraction along the way; that
is: marginally interesting, but not worth a detour, especially
in an introductory course.

The contraction/dilation approach is not just passé, it's
masochistic. We could teach mechanics by emphasizing how
weird and paradoxical it is -- but we don't. Why should we
teach relativity that way?



As the saying goes, it is better to light a candle than to
curse the damn darkness.

My latest contribution in this direction is spacetime graph
paper. The ability to freehand an accurate spacetime diagram
is not a skill most folks were born with. So I have created
ready-made graph paper to describe a world with three observers:
The black observer sits at rest in the lab frame. The blue
observer is moving to the right with 0.5 radians of rapidity
(relative to the lab frame). The the red observer is moving
to the left. I have arranged that the event at the middle of
the paper has coordinates (0,0) in all three reference frames.

Here are the black grid and the blue grid together:
http://www.av8n.com/physics/spacetime005blue.pdf
Note that the light-blue shaded region is a /timelike unit square/.
In the blue coordinate system, it is aligned with the axes. That
is, it is a time-lapse shot (covering one unit of time) of a stick
(covering one unit of distance).
And here are the black grid and the red grid together
http://www.av8n.com/physics/spacetime005red.pdf
And similarly here are all three grids together:
http://www.av8n.com/physics/spacetime005redblue.pdf
I know this last one is a bit "busy" and is therefore not
a good starting place, but after you have built up some
expertise it comes in handy for multi-frame problems such
as the notorious "twins" problem.

More generally, I'm not saying you can learn relativity by
looking at a couple of pieces of funny graph paper, but rather
the converse: If you understand the principles of relativity,
there is a huuuge range of problems that you can understand
and explain by reference to a spacetime diagram.

Obviously I didn't freehand these graph papers. I threw
together a couple hundred lines of perl to do it. If
anybody wants the code (e.g. for making your own graph
paper with custom rapidity or custom spacing) let me know.

Other resources:
http://www.av8n.com/physics/twins.htm
http://www.av8n.com/physics/bevatron.htm
http://www.av8n.com/physics/odometer.pdf
http://www.av8n.com/physics/spacetime-trig.pdf