Summarry of the momentum wars and idea.

[Steve VanDevender <stevev@efn.org>]

KellySt@aol.com writes:

 > Ok, I'm geting lost in all these cascading arguments and
 > equations.  So to try to make sure we have an agreement, I'll
 > try to sumarize.

If you can't stand the math get out of the physics.

 > A beam of microwave photons headed in the direction of the
 > ship hits a conical set of mesh sails.  Because of the shallow
 > angle of the sails, the photons bounce off the sail moving
 > inward.  Because of the shallow angle most of the resulting
 > thrust vector is pointing outward and is canceled out by the
 > oposite side of the sail (I.E. most of the thrust on the sail,
 > or momentum if you prefer is concerted to a thrust load on the
 > sail.  No velocity change to ship or sail.), the remaining
 > foward part of the thrust vector does push the ship forward,
 > but at reduced levels.
 >
 > At this point the photons are moving forward and inward toward
 > the ships axis.  (Some energy and/or momentum was lost in the
 > first reflection.)  This photon stream them hits a power
 > converter, or waveguide feed into the engines or something.
 > At the point of the interaction it still has most its velocity
 > in a forward vector, and about all we've done is cut this
 > amount down due to reflections and power loses as it attempted
 > to rip apart the sail.
 > 
 > Are we all agreed on this?

Something that I don't think everyone is grasping in these
so-called "momentum wars" is that momentum is a vector quantity,
not a scalar quantity.  That means that two momentum vectors with
identical magnitudes that point in different directions are
different quantities of momentum, and one momentum vector cannot
be converted to the other.

You can redirect a photon beam laterally by reflection.  By
changing the beam's direction, the reflector must develop
momentum to conserve the original quantity that the photon beam
had before the reflection.  I think even those of us who are
doing the right things with momentum conservation are confusing
others by erroneously saying that the reflected beam has the same
momentum as the original beam.  It does not, because the
reflected beam is traveling in a different direction.

You simply cannot change the total quantity of momentum in a
system, ever.  A piece of the system can change its momentum by
exchanging momentum with other pieces, but no matter what it does
it cannot change the sum of the momenta of all the pieces.  So
the simple physical constraint in the system consisting of the
photon beam and the spaceship is that the total momentum of the
beam and ship remains the same before, during, and after _any_
interaction between them.  If the ship is to absorb the photon
beam, it _must_ absorb the momentum too.

Besides not treating momentum as a vector quantity, people are
making the mistake of thinking that lateral loading of the sail
assembly is a magical sink for momentum or energy.  The error is
in thinking that stress on a static structure absorbs energy or
momentum continuously over time.  If the sail does not move
relative to the ship, then it cannot absorb or dissipate momentum
separately from the ship.  It cannot absorb momentum if it does
not move, because momentum means motion.  For just an instant,
once, when the beam first touches the sail, the beam does work on
the static structure to stretch the sail and support members,
which absorb a small quantity of energy.  From that point on, as
long as the sail does not fall apart or the support members do
not break, no more energy is dissipated into loading of the sail
structure.

The reality that static stress does not continue to dissipate
energy over time is not intuitive, because our muscles aren't
static structures like boards or rods or wires; they must
dissipate energy even to hold a weight motionless above your
head, while a table holding the same weight does not dissipate
energy.