# Energy conservation in particle decay

• nolanp2
In summary, photons are affected by the gravitational potential of the other particle after decay, but the other particle's energy is not regained.
nolanp2
two massive particles a finite distance from each other are bound to each other gravitationally, so if one disappeared the other one would have its energy altered, and the conservation of mass-energy would be broken.

so what happens when a massive particle decays to a less massive particle with the emission of say a gamma ray? how would the energy of another particle in the vicinity be altered?

nolanp2 said:
two massive particles a finite distance from each other are bound to each other gravitationally, so if one disappeared the other one would have its energy altered, and the conservation of mass-energy would be broken.

so what happens when a massive particle decays to a less massive particle with the emission of say a gamma ray? how would the energy of another particle in the vicinity be altered?

Consider two heavenly bodies, say the Earth and the moon. Now, consider that the moon breaks up into two pieces in an explosion. What do you think would happen gravitationally ?

eh the center of mass would still be at the same point so not much i would guess? but there's still the same amount of mass, it's just been seperated. I'm tsalking about when the net mass of the system is reduced after the event, i don't see how the two relate.

nolanp2 said:
eh the center of mass would still be at the same point so not much i would guess? but there's still the same amount of mass, it's just been seperated. I'm tsalking about when the net mass of the system is reduced after the event, i don't see how the two relate.

Well, the center of mass, even in the decay of a particle, will still remain the same, and the total energy also. That is to say, if you add the 4-vectors (E,px,py,pz) of the decay products, you will obtain the original (E,px,py,pz) of the original particle before decay. Now, what counts gravitationally is the E (in fact, the energy-momentum tensor, but we can do with the E here).

So imagine that you have a pi-0, gravitationally bound to, say, a proton (quite hypothetic, I know). If the pi-0 decays into two photons (each initially of energy about the mass of the pi-0 divided by 2), then those two photons will have to "climb out of the gravitational potential well" of the proton, and loose energy (shift to red). In the end, the two photons will have a total energy which is less than the energy of the pi-0, with exactly the amount of gravitational energy they needed to overcome the gravitational potential energy.

Of course, in practice this is ridiculous, because the gravitational energy of a proton and a pion are so terribly tiny as compared to the mass-energy of a pion, that you will never be able to measure this.

nolanp2 said:
two massive particles a finite distance from each other are bound to each other gravitationally, so if one disappeared the other one would have its energy altered, and the conservation of mass-energy would be broken.

so what happens when a massive particle decays to a less massive particle with the emission of say a gamma ray? how would the energy of another particle in the vicinity be altered?
If photons could travel against the gravitational field without loosing energy, then energy conservation would be violated. We can use this to calculate the effect of gravity on the energy (frequency) of photons.
Imagine this experiment:

A particle with mass m decays into two photons, which travel upwards for a hight z in gravitational field g. Then they assemble back to original particle, which travels back to the original location. If gravity did not affect photons, then this (cyclical) proces would be a perpetuum mobile, since we would get out work done by gravitational force on every cycle.
For energy to be conserved, a photon traveling in gravitational field must loose exactly as much energy as a massive particle with m=E/c^2=h*f/c^2 (f=photon frequency).

This must also be true for infinitezimal hight dz:

m*g*dz=h*df
E*g*dz/c^2=h*df
f*g*dz/c^2=h*df

Consequence:

df/dz=f*g/c^2

ok so the photons are still affected by the gravitational potential of the other particle after decay, but what happens to the other particle after this? is the energy lost by the photons making up for the energy gained by the other particle by losing its original graitational well?

## 1. What is energy conservation in particle decay?

Energy conservation in particle decay is a fundamental principle in physics that states that the total energy of a closed system remains constant over time. This means that in any process, such as particle decay, the total amount of energy before and after the process must be the same.

## 2. How does energy conservation apply to particle decay?

In particle decay, a particle or system of particles undergoes a transformation into different particles. According to energy conservation, the total energy before the decay must be equal to the total energy after the decay. This means that the energy of the initial particles must be conserved and distributed among the new particles created in the decay.

## 3. Why is energy conservation important in particle decay?

Energy conservation is important in particle decay because it allows us to understand and predict the outcome of the decay process. By knowing the total energy before and after the decay, we can determine the types and properties of the particles that are created in the process.

## 4. How is energy conserved in different types of particle decay?

The conservation of energy in particle decay is demonstrated through different conservation laws that apply to different types of decay. For example, in beta decay, energy is conserved through the conservation of electric charge, lepton number, and baryon number. In gamma decay, energy is conserved through the conservation of momentum and energy.

## 5. What are the implications of violating energy conservation in particle decay?

If energy conservation is violated in particle decay, it would mean that the laws of physics are not consistent and predictable. This would contradict our current understanding of the universe and the fundamental principles of conservation of energy. Therefore, it is crucial to ensure that energy conservation holds true in all processes, including particle decay.

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