(Editor's Note: This is an excellent argument. It is presented as hard scientific fact which makes it hard to refute. However, as always, your game is your own. You are free to use this explanation or to ignore it. However, everyone should read it whether they want lasers to have recoil or not.)
Here is my attempt to come up with some sort of definative answer to the question of whether lasers have recoil or not.
Light does have momentum. As anyone who has a physics book handy can verify, the momentum (I will use p as the symbol for momentum from here on out) of a photon is equal to plank's constant (h) divided by the wavelength of the photon (l). Thus, we have:
1) p = h/l
The energy of a photon (E), as you guys can all verify for yourselves, is plank's constant times the frequency of the photon (f), giving us:
2) E = h*f
We also know that the frequency of a photon times it's wavelength is equal to the speed of light (c) for any and all photons, giving us:
3) f*l = c
Rearranging equation 3, we get:
4) f = c/l
And, by plugging this into equation 2, we get:
5) E = c*h/l
Replacing h/l with p (that's equation 1), we get:
6) E = c*p
Which can be rearranged to say:
7) p = E/c
The momentum of any photon, therefore, is equal to its energy divided by the speed of light. The momentum of any n photons would be:
8) ptotal = p1 + p2 + .... + pn = E1/c + E2/c + ... + En/c
or:
9) ptotal = [E1 + E2 + ... + En] / c = Etotal/c
The total momentum of the light therefore depends only on the total energy.
According to the conversion book, a character with energy absorbtion can absorb 1 gigawatt of energy per level of experience, which is equivalent to 10 e-clips (pg. 47, top of second column). The problem is, gigawatts are a measure of power, or the rate at which energy is expended (or absorbed, in this case), which does not seem to be what they are trying to say. It would appear that they are talking about the total amount of energy that can be absorbed. Giving this figure in gigawatts is roughly equivalent to saying that I am 2 miles per hour tall.
Three possibilities present themselves:
Possibility one:
They meant to say that 1 gigawatt hour of energy was equivalent to 10 e-clips. This is not so far fetched, as energy is commonly measured in kilowatt hours (just look on your electrical meter). A gigawatt hour is the amount of energy that would be expended over the course of an hour at 1 gigawatt. Thus, 10 e-clip would contain:
This would place 1 e-clip's worth of energy at:
360 gigajoules of energy (360*109 joules)
Assuming that no more than a million joules go into sound and heat (which would seem reasonable), it can be assumed that for every e-clip fired off, roughly 360 gigajoules of light leave the barrel of the laser. A wilk's laser rifle has (I seem to recall, the book isn't with me) 20 shots, putting the light energy per shot at:
18 gigajoules of energy (18*109 joules)
Using equation 9 from the first section, we can determine the momentum of each laser blast.
p = E/c = (18*109 joules) / (3*108 m/s) = 60 Newton seconds
A newton second is a measure of momentum. A newton is a measure of force. If the recoil from the shot lasted for a full second, it would push against the user's hand with a force of 60 newtons.
However, the recoil likely lasts a fraction of a second, meaning the force would be proportionally greater. Although the same amount of momentum would be imparted to the user no matter the recoil time, a shorter time leads to a "sharper" recoil.
Assume the recoil actually lasts for one-tenth (1 second / 10) of a second.
p = 60 Newton seconds * (10 / 1 second) = 600 Newtons.
This is roughy equivalent to 135 lb of force applied over a tenth of a second.
Possibility two:
They meant to say that 1 gigajoule was equivalent to 10 e-clips. Thus each e-clip should have: 100 megajoules (100*106 joules)
And the energy per shot from a wilk's laser rifle would be:
100 megajoules / 20 shots = 5 megajoules (5*106
joules) per shot
Which can be plugged into equation 9 from above, giving:
p = E/c = (5*106 joules) / (3*108 m/s) = .01667 Newton seconds
Possibilty three:
The people at palladium had no idea what they were talking about when they said that 1 gigawatt was equivalent to 10 e-clips. There is certainly precedent for them not knowing what they were talking about (no insult intended, Maryann). It would be quite possible that they just wanted to have a number that sounded good, and didn't bother to check about the physics of anything. In this case the whole argument kinda falls apart.
For the sake of comparison, I tried to figure out what the recoil for a colt .45 would be. I found a figure of 200 grams for the bullet weight somewhere on the net (I'm not sure how accurate that is, could someone verify this for me?). The Revised HU book lists the muzzle velocity of a colt .45 as 250 m/s (pg. 203, top of first column). Thus the momentum of the bullet is:
p = .2 kg * 250 m/s = 50 Newton seconds
Therefore, in the case of possibility one, the recoil from most laser weapons is appreciable. Specifically, that of a wilk's laser rifle is slightly more powerful than a colt .45, which has a fair bit of kick.
In the case of possibility two, the recoil from most laser weapons is minor. It should be noticable, but will likely foul no one's aim, nor knock anyone back.
In the case of possibility three, there should be some recoil of an undetermined magnitude. There will be recoil, nonetheless. Momentum is always conserved; light (which has momentum) is emitted from the front of the energy weapon, so there will be some kick in the opposite direction.
By No Beard Pete (pmf@cs.umbc.edu)
Edited slightly by Chris Curtis (c-curtis@tamu.edu)