Mass to Energy: how is momentum conserved?

• Cutter Ketch
In summary, the conversation discusses the conservation of momentum in the Earth reference frame when a nuclear bomb explodes in orbit. It is suggested that the missing momentum is carried by the red shift and blue shift of the generated photons. The radiation pressure from the explosion is also mentioned, which is used to implode materials for a fusion explosion in a thermonuclear bomb. It is also noted that the speed of light is the same in all reference frames, but the symmetry is broken by the relative motion of the source, resulting in a net momentum due to red shift and blue shift.
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?

Cutter Ketch said:
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!

Dale said:
Yes, exactly!
Hmmm ... well this may be the shortest thread ever. Thanks!

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.

Momentum of a photon I E/c so for there
anorlunda said:
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.

Dale

1. What is the concept of mass to energy conversion?

The concept of mass to energy conversion is based on Albert Einstein's famous equation, E=mc^2, which states that mass and energy are two forms of the same thing. This means that mass can be converted into energy and vice versa.

2. How is momentum conserved in the process of mass to energy conversion?

In the process of mass to energy conversion, the total momentum of the system remains constant. This is because momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant in the absence of external forces.

3. Why is momentum conservation important in the context of mass to energy conversion?

Momentum conservation is important in the context of mass to energy conversion because it helps us understand and predict the behavior of particles during this process. It also ensures that the laws of physics are obeyed and that energy is conserved throughout the conversion process.

4. Can mass be converted into energy without violating the law of conservation of momentum?

Yes, mass can be converted into energy without violating the law of conservation of momentum. This is because, in the process of mass to energy conversion, the total momentum remains constant even though the mass is transformed into energy.

5. How does the conversion of mass to energy affect the momentum of the system?

The conversion of mass to energy affects the momentum of the system by changing the velocity of the particles involved. This means that the total momentum of the system may remain constant, but the individual momentums of the particles may change as a result of the conversion process.

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