### Laser recoil, relativistic momentum and whether mass counts

Posted:

**Sun Sep 09, 2018 6:29 pm UTC**Kyle of Because Science did a video about "The Death Star's OTHER Fatal Flaw," which you can see here:

https://www.youtube.com/watch?v=K6-q2edmiGk

His argument was that the recoil of a laser with that much power would have shot the weapon out of the far side of the station, or launched the whole station off into space, or something like that. I think he went with solid metal ball of incredible strength and said it would be launched into the distance.

Here's the calculation for the recoil: https://www.youtube.com/watch?v=K6-q2edmiGk&t=260s

His answer was 7.5 * 10

We know it has energy, therefore it must have momentum, but to have momentum it must have mass and he crossed out part of the equation because it doesn't have mass. Well, we know its velocity, so

E

E

E = sqr(2) m c

Right, so 2.2 x 10

which means its momentum is 5.189 x 10

Right?

We disagree by a factor of sqr(2) because he crossed out the rest mass mc

Does that part count, or was he right to cross it out? Does light have mass in the sense of momentum but no mass in the sense of mc

https://www.youtube.com/watch?v=K6-q2edmiGk

His argument was that the recoil of a laser with that much power would have shot the weapon out of the far side of the station, or launched the whole station off into space, or something like that. I think he went with solid metal ball of incredible strength and said it would be launched into the distance.

Here's the calculation for the recoil: https://www.youtube.com/watch?v=K6-q2edmiGk&t=260s

His answer was 7.5 * 10

^{23}We know it has energy, therefore it must have momentum, but to have momentum it must have mass and he crossed out part of the equation because it doesn't have mass. Well, we know its velocity, so

E

^{2}= (m v)^{2}c^{2}+ m^{2}c^{4}becomesE

^{2}= m^{2}c^{4}+ m^{2}c^{4}= 2 m^{2}c^{4}soE = sqr(2) m c

^{2}..... Oh, hello there, mutant version of simplified kinetic energy equation.Right, so 2.2 x 10

^{32}J / 1271031076302266264 = m = 1730877279390832 kg,which means its momentum is 5.189 x 10

^{23}kg m/s.Right?

We disagree by a factor of sqr(2) because he crossed out the rest mass mc

^{2}part and I left it in and calculated it using the mass derived from the other part.Does that part count, or was he right to cross it out? Does light have mass in the sense of momentum but no mass in the sense of mc

^{2}, both at the same time?