From: masa@athena.mit.edu (Masahiro Arakawa)
Subject: Re:STVI:TUC
Organization: Massachusetts Institute of Technology
Distribution: usa
Date: Sun, 26 Jul 1992 07:37:31 GMT

In article <1992Jul25.172053.24591@umbc3.umbc.edu> cs106b16@umbc5.umbc.edu
(cs106b16) writes:

>3) When the Klingons were under 0 g and were shoot they were thrown backwards.
>Why should this be? A phaser beam has no mass, thus no momentum! By the law of
>momentum they should have stayed exactly where they were 0 g or not.

Now, I'm no physicist (I tried to be one, and have failed), but bear with me
here.

A photon has mass which is proportional to its frequency. That is to say, these
massless particles can impart momentum to objects. Perhaps you've seen at
science museums or in your science classes those radiometers (or whatever they
are called) which are these glass bulbs with four panes attached and set on
a sharp point so that they can revolve freely. These planes have one dark side
and one light side, so that they reflect and absorb light differently. The 
reason this device works is because the light side reflects light, while the
dark side absorbs light. Let's say that a photon has momemtum m. Well, if it
were absorbed (by the dark side of a pane), then that pane would receive
momentum m. But if it were reflected, then, the reversal in direction of the
photon's movement means that there was a change of 2m in the momentum of this
particle (one m to stop it, and another m to send it in the other direction).

Or perhaps you've heard about these spaceships which operate on solar sails.
Well, they're supposed to work in the absence of a propulsion system as you and
I know know (in 20th century earth, that is) - no rockets. They work by
reflecting the light which would impinge upon their sails. Only problem is that
they would work only in propelling this craft away from the sun (the only real
source of photons in our neighborhood).

I digress. Anyway, my freshman chemistry text states that the momentum of a
photon of wavelength lambda has the momentum of h divided by lambda, where h
is Planck's constant, and is equal to 6.6260755 x 10^-34 (ten to the minus 
thirty-fourth power) Js (joule seconds). Also, the frequency of a photon is
equal to c, the speed of light in m/s (meters per second), divided by the 
wavelength in m (meters). Substituting this back into the previous expression 
for momentum, we get that momentum is equal to frequency times h divided by c. 
Since h and c are universal constants, momentum is proportional to frequency, 
as I claimed above. Of course, the momentum of a single photon in the visible 
light range is not very great - for a photon of red light (wavelength = 700
nanometers), its momentum is 946.6x10^-30 Js/m. Considering that the momentum
of a thrown tomato (0.1 kg at 10 m/s) is 1 Js/m, the momentum of one photon is
not too great. However, you put enough of them together, and you can throw
someone back.

The problem is - all this applies only if the photon's path was changed in
some way - if it passes through something without being absorbed, reflected, or
deflected, then there is no change in its momentum, and nothing (or nobody) is
thrown anywhere. In a more precise physics sense, velocity is a vector quantity
in that velocity has a direction as well as magnitude. For matter, since 
momentum is equal to mass times velocity, momentum must also be a vector 
quantity. So, of the momentum of the photon is equal both in direction and
velocity both before and after coming in contact with a Klingon, then the
Klingon experiences no change in momentum.

Enough. If you want to pursue this in more detail (as if this weren't enough),
consult your chemistry/physics/quantum mechanics books, ask a physicist, or
(if you dare) email me at masa@athena.mit.edu. 

Masahiro Arakawa
masa@athena.mit.edu

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