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Re: [Phys-l] three central misconceptions about relativity



On 10/17/2011 03:21 PM, Craft, Peter wrote:
What approach should I take with my students that will allow me to
cover the Syllabus

Teach them that special relativity is the geometry and trigonometry
of spacetime.

Teach them spacetime diagrams.

Teach them 4-vectors.

A great deal of what they know about the xy plane can be applied
to the xt plane directly. Even more can be applied with minor
modifications.

We trust special relativity because it is connected to -- and
consistent with -- a great many things that are already well
understood.

It unifies space and time.
It unifies momentum and energy.
It unifies low-speed kinematics with high-speed kinematics.
It unifies rest-energy with mass.
It unifies electricity and magnetism.
It explains why the speed of light is the same in all reference frames.
It lays the groundwork for further developments, including general
relativity and relativistic quantum mechanics.
Et cetera.

If somebody asks them a question with any real physical content,
they can answer using modern (post-1908) methods. They are more
likely to understand and remember these methods than anything
having to do with clocks that can't be trusted, rulers that can't
be trusted, velocity-dependent mass, or phlogiston.

Knowing the right answer is an advantage. For anything having
any real physics content, I see no scenario where knowing the
right answer puts the student (or teacher) at a disadvantage.

After they understand the physics, you can explain a little bit
of the history. That way if somebody asks them about phlogiston,
or about velocity-dependent mass, they can talk intelligently
about the history.

In particular, if they understand the physics, they will clearly
understand that for rotations in the xy plane, the x@lab component
will always be shorter than the proper length. This is just plain
old projective geometry. By the same token, for rotations in the
xt plane, the t@lab component will always be longer than the
proper time. There is nothing tricky about it. This is just
the geometry and trigonometry of spacetime. This specifically
allows you to check off the box on the almighty syllabus where
it refers to contraction and dilation. If this doesn't answer
the question that was asked, please explain in detail what the
problem is. I don't see a problem.

For details on all of this, see
http://www.av8n.com/physics/spacetime-welcome.htm