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Re: [Phys-L] another DIY relativity experiment



On 05/19/2016 09:17 PM, I wrote:
IMHO it is a tremendous pedagogical blunder to tell students
that relativity is weird and paradoxical. It's not. Most of
what relativity has to say is completely reasonable, prosaic,
and familiar.

Here's an example: Suppose we write a particle's energy and
momentum as
E = m cosh v [1]
p = m sinh v

which is just what we would get by considering [E,p] as a
four-vector and rotating it by an angle v in the xt plane
(in units where c=1). You can't have the cosh contribution
without the sinh contribution, so equation [1] is one idea,
not two. It's just trigonometry.

We can expand the trig functions using Taylor series in
the neighborhood of v=0:

E = m + 1/2 m v^2 + 1/24 m v^4 ....
p = m v + 1/6 m v^3 ....

I have to ask, why are the terms in v^1 and v^2 sometimes
considered "non-relativistic" while all the lower and higher
terms are considered "relativistic"?

Relativity only seems weird when people refuse to look at the
familiar non-weird terms.

I mention this in the context of DIY relativity, because it
seems to me that measuring the ordinary momentum (m v) and
the ordinary kinetic energy (1/2 m v^2) should count as a
relativity experiment. In the low-speed limit, these are the
only possible values that are consistent with the rest energy
(m c^2) and consistent with the idea that [E,p] is a four-vector.

As a separate matter, let's consider a wider range of speeds.
In the low-speed limit KE = 1/2 p•v while in the high-speed
limit KE = p•v (with no factor of 1/2). You can measure the
latter using a Nichols radiometer (not to be confused with
a Crookes radiometer). So this is another DIY relativity
experiment.

Without relativity, the two limiting cases are hard to explain
and hard to reconcile with each other ... but relativity explains
the low-speed case, the high-speed case, and everything in between.

In the same spirit, every measurement of the magnetic field
of an electric current is a DIY relativity experiment. There
/must/ be a magnetic field; otherwise the electric field would
be inconsistent with relativity. This is yet another non-weird
prediction that relativity makes.

You can do lots of DIY Eötvös experiments. If you didn't
believe in relativity, the fact that everything has the same
inertia-to-gravitation ratio would be a very, very weird and
implausible coincidence. Relativity makes the observed result
much less weird.

Relativity is great for providing a /unified/ view of things
that would otherwise have to be learned separately. Among
other things:
-- it unifies space and time
-- it unifies the ideas of slope and velocity:
slope = tan θ in the xy plane
velocity = tanh θ in the xt plane
-- it unifies electricity and magnetism
-- it unifies mass, energy, and momentum
-- it unifies the low-speed behavior, the high-speed behavior
and (!) everything in between
-- et cetera

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