Understanding Nuclear Fusion and Particle Interactions

[Thomas Rigby]

What is the precise mechanism by which matter is converted to energy?

 

[weirdoguy]

matter is converted to energy

Matter is NOT converted to energy. Energy is not a 'thing' by itself, it's a property of things - in particular it's a property of matter. Just like velocity, or momentum. No one talks about converting matter into velocity, because it doesn't make sense. What may be converted to some form of energy is mass (which is also a property, not a thing), but I don't think there is any mechanism involved (that might depend on what you mean by "mechanism"). It just follows from the definition of mass in special relativity.

 

[kith]

Maybe an example helps: an electron and a positron can annihilate to produce two photons, i.e. matter can be converted to radiation / electromagnetic quanta.

Sometimes popular physics sources call this "the conversion of matter to pure energy" or something similar. This is incorrect. As @weirdoguy has pointed out, energy is not a thing but a property of both electrons and photons (or the corresponding quantum fields). The energy of the electron and the positron before and the energy of the two photons afterwards is exactly equal because energy is conserved.

 

[Thomas Rigby]

Matter is NOT converted to energy. Energy is not a 'thing' by itself, it's a property of things - in particular it's a property of matter. Just like velocity, or momentum. No one talks about converting matter into velocity, because it doesn't make sense. What may be converted to some form of energy is mass (which is also a property, not a thing), but I don't think there is any mechanism involved (that might depend on what you mean by "mechanism"). It just follows from the definition of mass in special relativity.

In more advanced courses, you will learn about something called "annihilation" in which an electron and an "anti-electron" combine to form two photons. I was hoping someone knowledgeable about nuclear physics could point me to an analogous mechanism in nuclear fission or fusion.

 

[Vanadium 50]

Fission (or fusioin) is the process.
You seem, despite the good answers here, to want to believe energy is a "thing". This will slow rather than speed up your understanding.

 

[Thomas Rigby]

I was hoping someone could point me to a source where I could read about the actual QFT theory behind fission or fusion, not indulge in petty discussions about the definition of "rest mass".

 

[ergospherical]

It's a simple consequence of special relativity - you could start with a blob of matter at rest which has mass $m$, which then fissions into two equal pieces of mass $m'$ which shoot off in opposite directions with speed $v > 0$. By virtue of energy conservation you can see $m = 2m'/\sqrt{1-v^2} > 2m'$.

 

[weirdoguy]

In more advanced courses, you will learn about something called "annihilation" in which an electron and an "anti-electron" combine to form two photons.

I did learn that, and I learned that it's not "converting matter to energy", beacuse energy is not a thing. Energy is a property that both photons and electron/postitron pair has.

 

[PeroK]

I was hoping someone could point me to a source where I could read about the actual QFT theory behind fission or fusion, not indulge in petty discussions about the definition of "rest mass".

In any process, the invariant mass of the system is conserved. In that sense mass is always conserved, although rest mass is not.

In QFT, the annihilation of a particle and its antiparticle can be represented by the appropriate Feynman diagrams. This is not strictly speaking a mechanism, but a method of calculating the probability of its happening.

 

[mfb]

Systems that can fission or fusion are too complex to use QFT without any sort of effective models. The best effective models are the fusion or fission processes, e. g. D+T -> He-4 + n. Sum the (rest) masses on both sides and you'll see that the sum decreased. The difference corresponds to the energy released in the process. Generally as kinetic energy of He-4 and the neutron, but once in a while you can also have an extra photon carrying away some energy.

 

[vanhees71]

In any process, the invariant mass of the system is conserved. In that sense mass is always conserved, although rest mass is not.

In QFT, the annihilation of a particle and its antiparticle can be represented by the appropriate Feynman diagrams. This is not strictly speaking a mechanism, but a method of calculating the probability of its happening.

This is a bit misleading. The "rest mass" is by definition the "invariant mass", i.e., $p_{\mu} p^{\mu}=m^2 c^2$ holds for any particle. For about 110 years one does not use any other definition of mass in relativistic physics anymore, because "relativistic mass" is just unnecessarily confusing. It's always good to work with scalars, vectors, and tensors and their components rather than with non-covariant quantities.

Take the annihilation reaction $e^+ + e^- \rightarrow 2 \gamma$. While the sum of the invariant masses on the left-hand side is $2m_e>0$ the sum of the invariant masses on the right-hand side is $2 m_{\gamma}=0$. What's of course conserved is the total energy and momentum and thus the center-momentum energy, $\sqrt{s}$ defined by the Mandelstam variable $s=(p_{1}+p_2)^2=(p_1'+p_2')^2$, where $p_1$ and $p_2$ are the four-momenta of the electron and positron in the initial and $p_1'$ and $p_2'$ those of the two photons in the final state. In some sense $\sqrt{s}/c$ is the "invariant mass" of the closed composite system (which consists in the asymptotic free initial state of an electron and a positron and in the asymptotic free final state in two photons).

In general, what's conserved in SRT are energy, momentum, and angular momentum, and the center of momentum of a closed system moves with constant velocity. These are the 10 conservation laws following from the 10 one-parameter subgroups of the proper orthochronous Poincare group, i.e., the symmetries of spacetime of special relativity (Minkowski spacetime).

Only in non-relativistic physics there is an addition almass-conservation law, and it's pretty subtle how this comes into being. The reason is that the spacetime-symmetry group of Newtonian physics, the Galilei group, is more complicated as a Lie group. It's Lie algebra has a non-trivial central charge, which turns out to be the mass of a system represented by a unitary ray representation of the Galilei group in quantum mechanics.

The Poincare group has no non-trivial central charges, and all unitary ray representations can be lifted to proper unitary representations of its covering group, which boils down to substitute the Lorentz subgroup (generated by boosts and rotations) $\mathrm{SO}(1,3)^{\uparrow}$ by its covering group, $\mathrm{SL}(3,\mathbb{C})$, leading to the notion of half-integer spin. Any irreducible representation is then characterized by the Casimir operators, one of which is also invariant mass, due to $p_{\mu} p^{\mu}=m^2 c^2$, where $p_{\mu}$ are the generators of space-time translations, i.e., energy and momentum forming the components of a four-vector. Then you get two big classes of physically relevant representations, i.e., those with $m^2>0$ ("massive fields/particles") and $m^2=0$ ("massless fields/particles"). The other characterization then is the spin of the particle, defined by the representations of the so-called little group. For details see App. B in

https://itp.uni-frankfurt.de/~hees/publ/lect.pdf

There is no additional "mass-conservation law" in relativistic physics.

In Newtonian physics the Galilei group's Lie algebra has a non-trivial central charge, the mass. An when analyzing the unitary ray representations it turns out that despite the fact that you have to use the covering group, which boils down to substitute the rotation group SO(3) by its covering group SU(2), you have to extend the "classical Galilei group" to its non-trivial central extension, and mass turns out to be the corresponding central charge. It turns out that the proper irreps. of the original Galilei group do not lead to physically interpretible dynamics, and that's why the idea of "massless particles" doesn't make any sense in Newtonian physics. Further the usual non-relativistic QM follows from the non-trivial extension of the Galilei group, and you need a "mass superselection rule", i.e., in non-relativistic quantum mechanics there must not be superpositions of state vectors belonging to representations with different mass, and that's why there is the additional mass-conservation law in non-relativistic physics.

 

[Meir Achuz]

I was hoping someone could point me to a source where I could read about the actual QFT theory behind fission or fusion,

Fission and fusion depend only on non-relativistic QM and do not convert mass into energy.
You need particle creation or annihilation for that.

 

[Vanadium 50]

I was hoping someone could point me to a source where I could read about the actual QFT theory behind fission or fusion,

That's not what you asked, and as pointed out, QFT is ill-suited to answer questions of this complexity.

not indulge in petty discussions about the definition of "rest mass".

You were the first person to use this term in this thread.

 

[Thomas Rigby]

Systems that can fission or fusion are too complex to use QFT without any sort of effective models. The best effective models are the fusion or fission processes, e. g. D+T -> He-4 + n. Sum the (rest) masses on both sides and you'll see that the sum decreased. The difference corresponds to the energy released in the process. Generally as kinetic energy of He-4 and the neutron, but once in a while you can also have an extra photon carrying away some energy.

Yes, this is what I am looking for. Nuclear physics is new to me; what are "D", "T", and "+"?

Sorry if my wording is awkward, I am not familiar with the terminology of nuclear physics.

 

[Thomas Rigby]

Fission and fusion depend only on non-relativistic QM and do not convert mass into energy.
You need particle creation or annihilation for that.

That was my gut feeling, but I wasn't sure. What, then, is the simplest process I can study involving nucleons? I keep reading about Deuterium, I feel like that might be a prototypical model for what you are describing. In addition, such a reaction seems to require inelasticity, otherwise it is just a scattering problem.

 

[WernerQH]

What is the precise mechanism by which matter is converted to energy?

There is no mechanism. It is extremely misleading to talk about "conversion" of mass (matter) to energy. People tend to think that after the conversion you have less mass and more energy. But mass and energy are basically the same thing. Energy is conserved; it only changes to different forms of energy. Yes, mass and energy are quite disparate -- like height and distance in aviation. One is measured in feet, the other in miles. Putting up a ladder could be described as a conversion of length into height, but it does sound silly.

Conversion of energy is very common. When the kilogram was defined, it was not known that the mass of the prototype depends on its temperature. The added heat causes its mass to increase by about a picogram for each degree centigrade.

 

[vanhees71]

I'd not say "mass and energy are the same thing" but that mass is a specific form of energy.

 

[Meir Achuz]

I would say $m^2=E^2-p^2$ defines mass as being different from energy.
It's like saying the height of a tree and the distance from you to the top of the tree are different things.
They will have the same magnitude when you stand at the foot of the tree, but that does not make them the same thing.

 

[jartsa]

What is the precise mechanism by which matter is converted to energy?

A bucket full of matter is lowered into a black hole using a winch, that is a such mechanism.

Well okay, a different kind of mechanism is being asked for.

So there is a uranium nucleus that consists of 92 positive charges. Photon field near the nucleus is exited, because of those charges. The exited field has extra mass, because it is exited. I have been told, here, that "the extra mass of charges pushed together is in the electric field". The so called "electric field" is an exited photon field, in quantum field theory.

So when the photon field relaxes its mass decreases. It relaxes when the nucleus breaks into two parts.

So it was not matter that released some mass-energy but rather it was exited vacuum that did so.

So now you know what to study: vacuum. : )

 

[PeroK]

A bucket full of matter is lowered into a black hole using a winch, that is a such mechanism.

Why not just lower an empty bucket?

 

[Meir Achuz]

Maybe it should just be dark matter.

 

[mfb]

Fission and fusion depend only on non-relativistic QM and do not convert mass into energy.
You need particle creation or annihilation for that.

Fission and fusion can release part of the energy of the rest mass of the involved particles.
Annihilation is just a more efficient process in that aspect.

Yes, this is what I am looking for. Nuclear physics is new to me; what are "D", "T", and "+"?

Sorry if my wording is awkward, I am not familiar with the terminology of nuclear physics.

Deuterium, tritium, and "+" is just a plus sign. It's the fusion of deuterium and tritium to helium-4 and a neutron, the most interesting fusion process for potential future power plants.