Re: [Phys-L] speed of light .. foundational issues

["Derek McKenzie" <derek@physicsfootnotes.com>]

Sorry for my ambiguous grammar, but when I said: "Students already think
that strange things happen to you as you approach the speed of light, as
if *that* were any different to any other speed.", my *that* referred to
the sub-luminar speed *approaching* that of light; not to the speed of
light itself, which of course is geometrically special.

And by that I meant, of course, that students already think that their
personal experience on a spaceship traveling at .9995c would be
different to one traveling at 50 km/h (relative to a given inertial
frame), and describing neutrinos as if they have an objective
'close-to-light' speed perpetuates this misconception.

I agree with you completely on your geometric and trigonometric emphasis
in teaching relativity, and have done for some years, but this
neutrino-speak erks me because it flies in the face of that framework.

Having said all that, the paper you recommended is very interesting, and
I am much clearer now on how this incorrect language has come to be so
deeply entrenched; rather ironically, it turns out, as there are (if
mainstream cosmological models are correct) many times more 'slow'
cosmic neutrinos around us than relativistic neutrinos emanating from
the sun!

Derek McKenzie
PhysicsFootnotes.com



-------- Original Message --------
Subject: Re: [Phys-L] speed of light .. foundational issues
From: John Denker <jsd@av8n.com>
Date: Sat, July 09, 2016 12:49 am
To: Phys-L@Phys-L.org

On 07/08/2016 03:42 PM, Derek McKenzie wrote:

> Meanwhile though, I still have a serious pedagogical issues with the
> language, and I don't believe I'm just being pedantic.

Fair enough.

> the speed of light, as if that were any different to any other speed.

The speed of light *is* in some ways different from any other speed.

At the very least, you can say that the speed of light is special
for rotations in the xt plane, in the same way that a radian is
special for rotations in the xy plane.

 -- trig functions like sin() and tan() are nice and linear when
 the rotation angle is small compared to 1 radian, but they
 exhibit significant nonlinearity for larger angles.

 -- trig functions like sinh() and tanh() are nice and linear
 when the rotation angle (i.e. the rapidity) is small compared
 to 1, but they exhibit significant nonlinearity for larger
 rapidities.

Actually the speed of light is even more special than that,
because anything moving at the speed of light in one frame
is moving at the speed of light in any other frame. In 1905
Einstein showed that you can more-or-less derive all of special
relativity starting from this one observation (although that
is IMHO more of a show-off stunt than a reasonable pedagogical
derivation).

> Students already think that strange things happen to you as you approach
> the speed of light,

Well, that's because they've been taught to think about it in a
clumsy, archaic way. The modern (post-1908) way is much simpler,
namely:
 *) Special relativity is the geometry and trigonometry of
 spacetime ... nothing more and nothing less.
 *) *THE* length of a ruler is its proper length, defined in
 the frame comoving with the ruler.
 *) *THE* timing of a clock is its proper time, defined in 
 the frame comoving with the clock.
 *) *THE* mass is the invariant mass.
 *) The physics does not care what frame (if any) is chosen
 by whatever observers (if any) are involved.
 *) The /projection/ onto this-or-that frame will depend on
 the choice of frame, but that's just the projection; that's
 not the real physics. The shadow of a ruler changes if I
 rotate the ruler, but that's just the shadow; *THE* length
 of the ruler is invariant. This is not entirely a new idea;
 it has been understood for 2300 years that the thing that is
 most easily observed is not necessarily the best representation
 of the underlying reality.
 https://faculty.washington.edu/smcohen/320/cave.htm

 *) If special relativity seems weird and paradoxical,
 you're doing it wrong. Most of the predictions of special
 relativity are prosaic and well known. Mostly special 
 relativity serves to give a unified view of things that
 otherwise would have to be learned separately.
 -- unification of space and time
 -- unification of rotations and boosts
 -- unification of mass, momentum, and energy
 -- unification of electricity and magnetism
 -- et cetera

These ideas are developed in more detail, with diagrams, at
 https://www.av8n.com/physics/spacetime-welcome.htm

Special relativity is the geometry and trigonometry of spacetime
... nothing more and nothing less.

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