# Recoil from a photon gun

Suppose you have a laser gun or a gun that shoots high frequency photons. Now according to Newton's laws there should be an equal and opposite reaction. So the question is - Will there be a recoil from a gun that shoots photons?

Note I just want a theoretical answer as I know that the recoil(if any) will be of a negligible magnitude and you might not feel it. But will there be a recoil?

Yes the gun will recoil but we need to look a special relativity rather then Newtonain-mechanics. According to special relativity a photon has momentum given by: $$p=\frac{E}{c}$$ Where $E$ is the energy of the photon and $c$ the speed of light. Linear momentum has to be conserved, and as such the gun (/ particles within the gun) must recoil when the photons are released.

Assuming the gun is made on one block of matter mass $m$ then its momentum is given by: $$p=\gamma mv$$ where $\gamma$ is the Lorentz factor, this is of cause realtivistic momentum, rather then classical. From the principle of the conservation of linear momentum the above two equations must be equal and thus: $$\gamma mv=\frac{E}{c}$$ assuming the recoil is much less then the speed of light $\gamma \approx 1$ then we have: $$v\approx \frac{E}{mc}$$ If we say the gun has mass of $4kg$ the energy of the photon of 10MeV then we get $$v=1.33\times10^{-21}ms^{-1}$$ Which is indeed small (for each photon released).

• But of course, if you shoot $10^{21}$ photons.... =) – Physicist137 Dec 1 '14 at 19:31
• If the photon gun is firing for some period with constant power (equal to the intensity of the beam at the mouth of the gun times the area of the mouth), then there will be a constant recoil force during that period, which can be most easily found by dividing p=E/c by t, giving F=P/c where F is the force and P is the power. If you use SI units where P is in Watts (joules/second) and c is 299792458 m/s, then F will be in units of Newtons. So even a very high-powered beam of, say, 1.21 Gigawatts would have relatively small recoil force, in this case about 4 Newtons = 0.9 pounds. – Hypnosifl Jan 24 '15 at 22:01

Good discussion of this question here. In short: because momentum p imparted by light with energy E is given by $E = pc$ then if we compare a photon "shot" to a bullet with the same energy the momentum generated by a photon gun is on the order of $10^{-6}$ the momentum of the traditional gun.

But felt recoil is a tricky subject, because it incorporates impulse (i.e., momentum over time), and the duration of a shot from a photon weapon would presumably be extremely short. Matt Springer uses a clever analysis to show that even a short photon burst (which would have the highest momentum) would create an impulse below the threshold of human hearing, and therefore "if it couldn't be heard it probably can't be felt."

So, yes, a photon gun creates recoil, but no, you probably won't be able to feel it.

No, the equal and opposite reaction in this case is handled by the electrons. As you may know photons do not exist by themselves in lasers and the like but are created when an electron is excited and later relaxes by releasing a photon, the opposite impulse of that photon is handled by the electron, so you have billions of billions of tiny electrons handling the of billions of billions of tiny "recoils".

• Yes but all the electrons are part of the gun, they must obtain an equal momentum to that of the photon in the opposite direction to it . This means that the gun 'system' as a whole gains a small momentum in the opposite direction to that of the photon. – user43487 Dec 1 '14 at 19:19
• @Joseph, yes, conservation of energy and all that but the momentum of the electrons is in turn handled by the atoms they are part of and in effect the human operating the gun does not feel any recoil at all. So if it is a question if there is any recoil AT ALL - yes, conservation of energy, if the queston is if the human will feel any recoil - no. – mathgenius Dec 1 '14 at 19:37
• I am now going to ask the obvious question, which is: what 'handles' the recoil of the atoms, (by the way I am not trying to argue with you, this is a genuine question)? – user43487 Dec 1 '14 at 19:41
• The question wasn't whether the recoil would be perceptible. – Rob Jeffries Dec 1 '14 at 21:48
• @Joseph, yeah i understand, don't worry, the recoil is not transferred at 100%, in effect the atoms go not give any recoil themselves. But Rob Jeffries is right, my mistake, my answer is wrong and Joseph's is right. Although, sorry, but your calculations are totally wrong. XD For one recoil is not measured in meters/second but in the units of force, sorry non-english guy here, don't know the english terminology and the amount you get in the end is WAAAAAAAAAY too high for nuclear/atomic physics. :D – mathgenius Dec 1 '14 at 23:30