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

[John Denker <jsd@av8n.com>]

On 10/16/2011 05:44 PM, Craft, Peter wrote:

> Remembering that student are going to be asked question directly on
> this material, what is the *best* approach for giving my students a
> good intro level understanding of relativity while at the same time
> enabling them to answer questions in the state test?
>
> They are asked questions such as
>
> a) How has our understanding of time been influenced by the discovery
> of the constancy of the speed of light?
>
> b) piece of radioactive material of mass 2.5 kilogram undergoes
> radioactive decay. How much energy is released if 10 grams of this
> mass are converted to energy during the decay process?
>
> c) A mass is moving in an inertial frame of reference at a velocity v
> relative to a stationary observer. The observer measures an apparent
> mass increase of 0.37%.Calculate the value of v in m/s.

Dealing with those specific questions is the easy part.

a)  This must be interpreted as a history question.

 The speed of light played a pivotal role in the history of 
 special relativity ... much as peas and fruit flies played
 pivotal roles in the history of genetics.  However, nowadays
 relativity is understood to have a vast domain of applicability,
 and the invariance of c is not even the tip of the iceberg ...
 just as peas and fruit flies are not even the tip of the iceberg
 of what you can do with genetics.

 There are many misconceptions about the history of relativity,
 but I see no harm in giving the correct answer.

b) I don't see any misconceptions here.  I don't see any scope
 for misinterpretation.  The question doesn't measure anything
 of great importance, since it's basically a plug-and-chug
 application of the famous E=mc^2 formula.  The question has
 some slight power to detect the worst forms of plug-and-chug,
 because somebody could plug in the wrong mass, so I guess
 there is "some" reasoning involved ... but it is not a check 
 for any real understanding of relativity principles.

c) I expect students to understand the word "ain't" ... even
 though it is bad grammar.  I expect them to translate it on
 sight to something more appropriate.

 I expect students to know that "heat" is ambiguous.  I expect
 them to translate it on sight to temperature, TdS, enthalpy, 
 energy, and/or entropy, as context may require.

 In the same vein, I expect students to be aware of the standard
 misconceptions about relativity.  I expect them to translate
 misconceived statements on sight ... especially when the
 translation is as transparent as it is here.  Translate 137%
 mass to 137% energy and turn the crank.

 rapidity = arccosh(1.37)
 v = tanh(rapidity)
 multiply by c to express the answer in m/s.

======================

The foregoing describes some short-term tactics that can be used.

In the longer term, the best *strategy* is to fix the standards, 
so that they are no longer 100+ years out of date.  This may 
require organizing the villagers to march on headquarters with 
torches and pitchforks.
  http://www.av8n.com/physics/img48//vanhelsing-villagers.jpg

This is not a physics problem;  it is a political problem, and
it must be dealt with using political methods.

> In our state mandated Physics Syllabus, the document we base our
> teaching on and on which our state wide assessment material is based
> it says (in part)

I've always said that we should judge the program by the test,
not by the so-called standards.  That's because the test has 
teeth, whereas the standards usually don't.

That cuts both ways:  In California, the standards aren't too
bad, but the questions are astonishingly bad.  This is a big
problem.

Judging by the limited data presented here, the NSW situation
is just the reverse.  The questions don't seem too bad.  On 
the scale of things, this strikes me as a relatively survivable 
problem.

> 1. identify that if c is constant then space and time become
> relative

That is insane on many levels.  Even at the purely grammatical
level, it doesn't make sense.  How can you talk about what
happens "if" c is a constant?  The fact is, the laws of physics
are relativistically invariant, and always have been.  The speed
of light is the same in all frames, and always has been.  There
is no meaningful "if...then" relationship here.

If we very generously re-interpret this from a statement about
"physics implying other physics" to a history question about
our knowledge of one thing implying knowledge of another, it 
is still insane.  The principle of relativity was set forth 
in 1632 with magnificent clarity ... long before anybody knew
anything about the speed of light.

> 2. discuss the concept that length standards are defined in terms of
> time in contrast to the original metre standard

That seems harmless.  I don't see how it has anything to do
with relativity, but that's OK.  It's still true that the meter
is defined in terms of the second, and has been for more than
25 years, for good reason.

> 3. explain qualitatively and quantitatively the consequence of
> special relativity in relation to:
>
> – the relativity of simultaneity  – the equivalence between mass and
> energy  – length contraction  – time dilation – mass dilation

Jeepers!  
 a) Relativity does in fact explain the breakdown of simultaneity 
  at a distance.  However ...
 b) The idea of clocks that can't be trusted is a Bad Idea
 c) The idea of rulers that can't be trusted is a Bad Idea
 d) Mass is provably not equivalent to energy.  I assume you realize
  that if you go down that road, you wind up with a longitudinal mass
  and a transverse mass and who-knows-what-all else ... and they can't
  all be equivalent to the energy.
 e) More generally, the idea of velocity-dependent mass is a Bad Idea.

Ideas (b) through (e) are as dead as phlogiston.

For students who will actually use relativity, every minute spent
teaching them these wacky ideas is at least two minutes wasted,
because the ideas will have to be unlearned.

For students who will never use relativity, you might argue that it 
doesn't matter what you teach them, in which case every minute spent 
teaching them these wacky ideas is "only" one minute wasted ... 
but it's actually worse than that.  Here's why: lessons about vectors 
in the xt plane can be used to /reinforce/ what is already known 
about vectors in the xy plane.  Similarly, lessons about rotations 
in the xt plane can be used to /reinforce/ what is already known 
about rotations in the xy plane.  In contrast, the contraction and 
dilation formulas don't connect to anything.  They don't reinforce 
anything.  So in addition to the wasted time, there is an opportunity
cost that must be taken into account, even for students who will
never directly use relativity.