[Phys-L] Re: momentum-hiding (was: collision question...)

["John S. Denker" <jsd@AV8N.COM>]

I suggested:

> > For homework, find tx explicitly in terms of m,
> > M, and the size of the box.

On 02/26/05 23:20, Carl Mungan wrote:
> ...... In the above example, the box is
> stationary half the time *regardless* of the values of m and M.

Sure.  There's a particularly clear argument for that
in the CoM frame: the "to" and the "fro" half-cycles
are mirror images of each other.  And non-relativistically
speaking, timing in the CoM frame is good in the lab
frame also.  This is a nice example of qualitative
reasoning IMHO.

> Were
> you expecting me to consider a more general case now to get some kind
> of uncertainty principle? Please repeat the conditions for this last
> problem.

The question wasn't asking for anything very deep.
Yes, the two half-cycles are equal ... but how long
are they?

The point is that an object can in the *short* term
hide some momentum.  But it can't hide very much for
very long.

Of course we are talking about a black box, where some
unseen internal mechanism is shifting around, warehousing
some momentum.  (If the box is not black i.e. opaque, then
questions of hiding momentum, or anything else, are vacuous).

The point is, if you want to hide momentum for a time tx,
the mechanism can't have a mass greater than the total
mass of the system, and it can't have a velocity greater
than (box size)/tx, so there are serious bounds on how
much momentum can be hidden.  You can calculate this bound
without knowing anything about how the mechanism works.

This is in contrast with energy-hiding.  A battery can
store a huge amount of energy, in a way that doesn't
show up in (say) the heat capacity, with a shelf-life
of many years.  Other examples abound.  You can't
calculate the shelf-life without knowing something about
the mechanism.
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