E^2 - p^2 = m^2

["John S. Denker" <jsd@MONMOUTH.COM>]

I wrote:
> > The law that you want to remember is E^2 - p^2 c^2 = m^2 c^4

Then Ludwik Kowalski wrote:
> I would not refer to a 4-vector in the 4th week of the first
> physics course.
...
> the E=m*c^2 formula
> (make p=0 above) is well known (but not well understood).

I stand by my suggestion!

Starting therefrom you can derive
 -- E = m c^2           in the zeroth-order approximation
 -- KE = p^2 / 2m       in the first-order approximation
 -- E = pc              in the opposite (relativistic) limit

thereby achieving a unified understanding of several things.
This illustrates the power and unity of physics.  Four-vectors.
Conservation laws.  Low-order expansions.  It's hard to imagine
anything more central to what "physics" means to me.

....
> Most of university physics courses in the
> US are not based of what students are expected to know from
> a high school physics course.

Well, yes and no.  Learning proceeds from the known to the
unknown.  Two of the three points itemized above make contact
with things I would expect students to remember from high
school.  The new makes contact with the old.  The profound
makes contact with the superficial.