Mass to Energy: how is momentum conserved?

[Cutter Ketch]

A nuclear bomb is in orbit. When it explodes some mass is converted to energy. Ok, in a real device not much mass, but some. Without breaking any laws of physics we can certainly imagine a case where there is less bulk and more fusing (or fissioning) material and the mass change is more significant. Let's say in the bomb's reference frame the explosion is spherically symmetric. With the change in mass, how is momentum conserved in the Earth reference frame?

I don't think the center of mass of the remaining material speeds up, so is the missing momentum all in the red shift / blue shift of the generated photons?

 

[Dale]

I don't think the center of mass of the remaining material speeds up, so is the missing momentum all in the red shift / blue shift of the generated photons?

Yes, exactly!

 

[Cutter Ketch]

Yes, exactly!

Hmmm ... well this may be the shortest thread ever. Thanks!

 

[anorlunda]

I think momentum is conserved. The radiation streaming out carries the momentum. The radiation pressure is enormous. In fact, the radiation pressure from an atomic explosion is used to implode the materials for a fusion explosion in a thermonuclear bomb. I don't see why red/blue shift needs to come into it.

The radiation pressure exerted by the large quantity of X-ray photons inside the closed casing might be enough to compress the secondary. Electromagnetic radiation such as X-rays or light carries momentum and exerts a force on any surface it strikes. The pressure of radiation at the intensities seen in everyday life, such as sunlight striking a surface, is usually imperceptible, but at the extreme intensities found in a thermonuclear bomb the pressure is enormous.

For two thermonuclear bombs for which the general size and primary characteristics are well understood, the Ivy Mike test bomb and the modern W-80 cruise missile warhead variant of the W-61 design, the radiation pressure was calculated to be 73 million bar (atmospheres) (7.3 T Pa) for the Ivy Mike design and 1,400 million bar (140 TPa) for the W-80.

 

[Cutter Ketch]

Momentum of a photon I E/c so for there

I think momentum is conserved. The radiation streaming out carries the momentum. The radiation pressure is enormous. In fact, the radiation pressure from an atomic explosion is used to implode the materials for a fusion explosion in a thermonuclear bomb. I don't see why red/blue shift needs to come into it.

Thanks for the wiki info. That's interesting.

Regarding red shift, radiation going in all directions in the bomb reference frame carries no momentum by symmetry. The speed of light is the same in all reference frames so the light is a symmetric sphere with a stationary center in the Earth frame too. If it were all the same light once again it would carry no net momentum by symmetry. However the symmetry is broken by the relative motion of the source. The forward light is blue shifted and the backward light is red shifted. The momentum of a photon is E/c. The red shift / blue shift is what gives the otherwise symmetric sphere of light net momentum.