Does the energy of the strong force have mass? [closed]

Question

The mass of a proton is said to predominantly be "comprised" of the mass of the strong force interactions within the proton. Logically, one could conclude that the energy (the strong force energy in this case) has a mass of its own. Why is it then strongly opposed that the electromagnetic energy can have a mass? Or is it accepted that the strong force energy does have a mass, but the other types of energy don´t?

Answer 1

I think a simpler example will help to make the point.

Suppose we have two balls, of rest masses $m_1$ and $m_2$. Suppose first of all that they are not moving relative to one another. In this case the total rest mass of the system is $m_1 + m_2$ and the total system energy, in its rest frame, is $(m_1 + m_2) c^2$.

Next suppose we have the same two balls but they are moving relative to one another. For the sake of argument, let's suppose they are approaching one another with equal and opposite momenta. In this case the speeds satisfy $$ \gamma_1 m_1 v_1 = \gamma_2 m_2 v_2 $$ where $\gamma$ is the Lorentz factor: $$ \gamma_1 = \frac{1}{\sqrt{1 - v_1^2/c^2}} $$ and $\gamma_2$ is related similarly to $v_2$. We now have a system whose total momentum is zero and whose total energy is $$ E_{\rm tot} = \gamma_1 m_1 c^2 + \gamma_2 m_2 c^2. $$ Hence $$ E_{\rm tot} = (\gamma_1 m_1 + \gamma_2 m_2) c^2. $$ The rest mass of the composite system is equal to this total energy, divided by $c^2$: $$ M = \gamma_1 m_1 + \gamma_2 m_2. $$ This statement should surprise you if you don't know relativity, but it is a standard part of the theory and I am not going to prove it. The main thing to note is that when the particles are moving in the reference frame with zero total momentum, then $$ M > m_1 + m_2. $$ One can notice that $$ M - (m_1 + m_2) = \frac{K_1 + K_2}{c^2} $$ where $K_1$ and $K_2$ are the kinetic energies. So you can say that the extra rest mass of the composite system is owing to the kinetic energy of the parts of the system (in the reference frame of zero total momentum).

It is similar with the rest mass of composite systems such as protons. Now it is the quarks and gluons which have kinetic energy, and it turns out that they have a lot of kinetic energy. For the gluons their entire energy can be called kinetic energy (since they have zero rest energy) and for the quarks inside a proton the Lorentz factors are large so their kinetic energy is large compared to their rest energy.

If you had a ball made entirely of photons moving in different directions then there would be plenty of kinetic energy and therefore a non-zero rest mass of the entire ball, even though each photon inside it has zero rest mass.

Answer 2

The point of your question is not so much "why does the strong force have mass" but why does EM force have no mass.

This is where you are wrong. Energy related to the EM force does have mass.

A proton, as anna v described, is a very tightly bound complicated object, a "soup" of many antiquarks, just as many quarks plus 2 $u$ quarks and one $d$ quark and many gluons. Difficult to understand exactly what goes on, there. So let us try something simpler.

Conversely, in a nucleus, the protons and neutrons are bound just by the strong force that "leaks" out of their tightly bound insides. And there is EM force trying to expel the protons, because the total charge is positive. But the mass of a nucleus is not the sum of the mass of the number of isolated protons and neutrons that compose it. The mass of a nucleus is less than this sum, because of the negative binding energy of the strong force. But it is more than it should be if only negative binding energy of the strong force is considered. One has to add the positive repulsive energy of the EM force, which is less than that of the strong force (otherwise, the nucleus would disintegrate) but not neglibible

An example : the nucleus of "nitrogen 13", $^{13}$N is composed of 7 protons and 6 neutrons. A neutron is heavier than a proton, so the components of $^{13}$N if separated, have less mass than the 6 protons and 7 neutrons of "carbon 13" $^{13}$C. Strong interaction is about the same for these two nuclei. But $^{13}$N is unstable, $\beta^+$ radioactive. It spontaneously transforms into $^{13}$C by emitting one positron, which means is mass is more than the mass of $^{13}$C plus one positron (the mass of which is the same as that of an electron).

Why is it so heavy when the sum of the masses of its components is less than in the case of $^{13}$C ? Because of the mass related to the repulsive energy of the EM force which is much larger for 7 protons than 6 protons in essentially the same strong force environment.

Also you are wrong about the EM wave. Of course it has energy, and thus mass. The quantity which is zero for the photon is not its mass, it is its rest mass. Because a photon always propagates at light speed, it can never be at rest. "Rest mass" of a particle, as explained in the other answers is it total mass in motion minus its kinetic energy divided by $c^2$. The total mass in motion of a photon is exactly kinetic energy divided by $c^2$, consistent with zero "rest mass".

When a nucleus unstable by $\gamma$-decay emits a photon, its mass decreases by the total mass in motion of the emitted photon. In fact it is the total mass in motion of the nucleus that decreases by this amounts. Its rest mass decreases just a little a bit more, because the nucleus if initially at rest, it recoils because of the momentum of the emitted photon, which is its total mass in motion multiplied by $c$ (or equivalently, its energy divided by $c$). But the kinetic energy related to this recoil is, in practice, negligible, the squared of the energy of the photon divided by twice the mass of the nucleus times $c^2$. Or equivalently, $c^2$ times the square of the total mass in motion of the emitted photon divided by twice the mass of the nucleus.

Answer 3

A proton is formed of three quarks: uud. It has a rest mass of around 1000 $MeV/c^2$.

A up quark has a rest mass of 2 $MeV/c^2$.

Whilst a down quark has a rest mass of 5 $MeV/c^2$.

This means the total rest mass of uud is roughly 10 $MeV/c^2$. This is just 1% of the mass of the proton. The only other particles in the proton are gluons and these have zero rest mass. Thus they don't contribute. Hence the other 99% of the mass of a proton comes from the binding energy of the quarks, that is from the strong force.

Answer 4

Does the energy of the strong force have mass?

The short answer: Energy is an attribute of the invariant mass, energy is the first component of the four vector describing the particle or the system of particles.

At the level of protons and elementary particles, present day physics theory models have to use the four dimensional Lorentz representation, i.e. special relativity, which has simplified the mathematics and clarified the concepts.

Instead of using the variables "energy" and "momentum" as vaguely related variables through kinematic considerations, classical mechanics, one has the relativistic mechanics of special relativity and four vectors.

E is the total energy an p the momentum

Every particle is described by such a vector and the mass of the particle is the "length" of this vector, called the invariant mass.

When more than one elementary particles are involved, there is the addition of their four vectors and a new invariant mass using the algebra of four vectors, which also uniquely characterizes the composite particle.

For simple modeling of particles as $π^0$ to $γγ$ as an example , algebraically the invariant mass of the $π^0$ fits perfectly in the measurements with the invariant mass of the fourvectors of the two gamma.

In the case of the proton life is complicated

Snapshot of a proton -- and imagine all of the quarks (up,down,and strange -- u,d,s), antiquarks (u,d,s with a bar on top), and gluons (g) zipping around near the speed of light, banging into each other, and appearing and disappearing. (M.Strassler 2010)

The four vectors involved in building up the invariant mass of the proton are innumerable. QCD on the lattice, a quantum mechanical model is used in order to model such bound states.

So it is not energy that has mass , but the four vector describing a particle system that has a definite mass to be compared with measurements.

You state:

Logically, one could conclude that the energy (the strong force energy in this case) has a mass of its own.

Logic, though necessary is not sufficient to model particle physics, one needs the fourvector algebra. Two gammas (electromagnetic wave photons) have an invariant mass, all particles and composites of particles have the invariant mass of the four vector sum of the four vectors describing the individual particles (in the mainstream particle physics theories). The photon has zero invariant mass . Within the Feynman diagram calculations the four vectors used can have varying invariant mass ,but that is another story.

Answer 5

Why is it then strongly opposed that the electromagnetic energy can have a mass?

It is not at all true that electromagnetic energy cannot have mass. Mass is given by $m^2 c^2 = E^2/c^2 -p^2$. For a real photon, the momentum $p$ is large enough that $m=0$. However, in a nucleus most of the EM interaction will not consist of real photons but of virtual photons which can have a different “off shell” momentum. Also, when you add multiple photons, whether real or virtual, their energies and momenta add directly, and then their total mass is calculated from their total energy and momentum as above. This can result in a non-zero total mass even if all of the individual photons are real and each have zero mass.

Answer 6

You can associate it with a mass with electromagnetic energy. In fact, I think that's the context in which Einstein came up with $E^2=m^2c^4+p^2c^2$. The proton is composed of 2 up quarks and 1 down quark with the up quarks having charge $(2/3)e$ and the down quark having charge $(-1/3)e$.

So:

$E_{em}<3\cdot\frac{e^2}{4\pi\epsilon_0d}(\frac{4}{9})$. Energy of 3 charges of (2/3)e confined to a distance of $d$.Essentially, a maximum estimate of the energy contributions by E&M.

$\frac{e^2}{4\pi\epsilon_0}=1.44 \ eVnm$

$d\approx10^{-15}m=10^{-6}nm$

So $E_{em}<1.92MeV$.

$m_p\approx 938.28 MeV/c^2$

$E_p=m_pc^2$

$\frac{E_{em}}{E_p}=0.0246\%$

Correction:There's another contribution from quark mass coming to about 10MeV.

The only interactions in a stable proton are electromagnetic and strong. Even over estimating the E&M mass contribution, we get a very tiny contribution.