Exploring Mass-Energy Equivalence and Nucleons

[quasar987]

I was thinking just a moment ago and fragments of random knowledge and ideas gathered to make this question...

If I remember my college physics class correctly, an evidence of the mass-energy equivalence is that in an atom, the sum of the rest masses of the nucleons is greater than the rest mass of the nucleus. The missing energy is being used by the field, i.e. it serves as a medium for the nuclear (strong?) force to act between the nucleons.

Is it true that the mass missing is precisely equal, via [itex]E=m_0c^2[/itex], to the nuclear potential energy of the system??


Side Q: Does "nucleon" has a plural? Ethimologically, where do the peculiar "plural endings" such as "1 nucleus, 2 nuclei", "1 radius, 2 radii",etc. come from? Greek?

 

[Rob Woodside]

2 nucleons; unless you are president of the US, then it is "nuculons"

 

[Chronos]

Momentum contributes inertial mass to any atom. Explaining it is harder. Higgs boson?

 

[quasar987]

What? What about Higgs bosons? How does your statement about momentum answers my question about potential?

 

[Andrew Mason]

Is it true that the mass missing is precisely equal, via [itex]E=m_0c^2[/itex], to the nuclear potential energy of the system??

Nucleons have less mass when they are bound together in nuclei than when separate. The binding energy (the energy required to separate them) is released when nucleons fuse. This energy release results in a loss of rest mass: For example the rest mass of the proton is 938.3 Mev (c^-2). and the rest mass of a neutron is 939.6 Mev. but the rest mass of a helium nucleus is 3727.3 Mev or about 28.3 Mev. less than the separate masses. (For large nuclei, this is still true on average, although the outer protons will release energy when they break apart from the nucleus because the nuclear binding energies of the outer protons are less than the energy required to overcome the electrical repulsion).

In theory the energy released is exactly loss of rest mass multiplied by c². How precisely this has been shown by experiment, I don't know but I am not aware of any serious discrepancies.

Side Q: Does "nucleon" has a plural? Ethimologically, where do the peculiar "plural endings" such as "1 nucleus, 2 nuclei", "1 radius, 2 radii",etc. come from? Greek?

The 'us' endings are latin but the 'eon' endings are greek. The plural of nucleon should be 'nuclea' since it is greek. But 'nucleons' is what is used. I don't think anyone uses nuclea. Kind of like "Physics Forums" really should be "Physics Fora".

AM

 

[Garth]

Perhaps the energy of the field can be located in the particles and all inertial mass is 'stored' potential energy? I know, I know, heresy, heresy!

Just a thought

Garth

 

[dextercioby]

I was thinking just a moment ago and fragments of random knowledge and ideas gathered to make this question...

If I remember my college physics class correctly, an evidence of the mass-energy equivalence is that in an atom, the sum of the rest masses of the nucleons is greater than the rest mass of the nucleus. The missing energy is being used by the field, i.e. it serves as a medium for the nuclear (strong?) force to act between the nucleons.

Is it true that the mass missing is precisely equal, via [itex]E=m_0c^2[/itex], to the nuclear potential energy of the system??


Side Q: Does "nucleon" has a plural? Ethimologically, where do the peculiar "plural endings" such as "1 nucleus, 2 nuclei", "1 radius, 2 radii",etc. come from? Greek?

It's pretty hard to make such computations:at quantum level (SM),fermions (the quarks from the nucleus) get mass because of the Higgs boson.But these calculations are very difficult since they imply a whole lotta Feynman diagrams,both for QCD and for electroweak interaction.Roughly speaking,the "mass defect" of nuclei can be put in connection with nuclear interaction potential energy,but learn that is this an incorrect picture,neglecting both internal structure of nuclei and worse,the quantum description...Nuclear physics is both quantum and relativistic,not only one of them.

From Latin.The part with "-us","-ei".The part with "-(e)on" comes from Ancient Greek.It's a mix-up of etymologies.

Daniel.

 

[quasar987]

In what sense can it be "put into connection"?

And what do we know about the nuclear force? Do we have a mathematical formulation for it?

 

[dextercioby]

1.Well,at that supersimplified level in which quantum calculations are wrongly ruled out,it's the only explanation we find as to why free nucleons have an energy/relativistic mass greater than when they are bond into nucleus.
2.We do.First of all,the concept of force is highly classical."Interaction" is the appropriate word.And we have a pretty good theory called Quantum Chromodynamics.The mediators of this interaction are quantum massless spin 1 particles called "gluons" (apud "glue").

Daniel.

 

[quasar987]

1.Well,at that supersimplified level in which quantum calculations are wrongly ruled out,it's the only explanation we find as to why free nucleons have an energy/relativistic mass greater than when they are bond into nucleus.

2.We do.First of all,the concept of force is highly classical."Interaction" is the appropriate word.And we have a pretty good theory called Quantum Chromodynamics.The mediators of this interaction are quantum massless spin 1 particles called "gluons" (apud "glue").

Mmmh, I see... But does this notion of interaction allows for an expression of the potential energy? Or do we only talk about the "energy of the field", potential energy being too classical a notion?

 

[dextercioby]

Mmmh, I see... But does this notion of interaction allows for an expression of the potential energy? Or do we only talk about the "energy of the field", potential energy being to classical a notion?

There are QFT's in which one can speak of a "potential" (think about [itex] \lambda\phi^{4} [/itex]),but in the case of Yang Mills,nope.It's too complicated.It is a selfinteracting field,just like the gravitational is."Potential energy" is a classical concept,indeed.In QM we speak about the "potential energy operator":[itex] \hat{V} [/itex].
So to answer your first question:yes and no.Depends on the situation.We have classical interactions,purely relativistic interactions,purely quantum interactions and quantum relativistic interactions.The latter are the toughest to handle.

Daniel.

 

[quasar987]

What is a self-interacting field?

I was also wondering: Is the only reason why two electrically or gravitationally interacting bodies do not "give away" some of their rest mass to the field that their interaction particles are massless?

Also, do we have experimental/observationnal evidence that the gravitational field propagates at c in vacuum?

 

[dextercioby]

1.Without any formula,its Feynman diagrams comprise vertices in which 2 identical particles meet (the lines/propagators associated to them),in the sense that the propagators converge to the same vertex.
2.No.The rest mass is an intrinsic property of every particle and it cannot change,no matter what interactions the particle may suffer.Of course,i mean a fundamental particle,with no internal structure:electron,quark,neutrino,gluon,Z,W bosons,photons,graviton,...
3.I don't know.An experimentalist should know.Anyway,if someone has done it,i'm sure it must have been very difficult,just like "weighing" neutrinos.There was a Nobel Prize awarded for discovery of gravitational waves,but,since no one has gotten a Nobel Prize for measuring the speed of gravitons,it hasn't happened.

Daniel.

 

[Andrew Mason]

Is the only reason why two electrically or gravitationally interacting bodies do not "give away" some of their rest mass to the field that their interaction particles are massless?

Is there not energy in the field between two electrically charged bodies? If there is, then there is rest mass in the field between two charged bodies. Actually, one cannot specify where the energy is located. I think classical electrodynamics provides identical results whether you assume that the energy is in the field or in the charged body.

Also, do we have experimental/observationnal evidence that the gravitational field propagates at c in vacuum?

Gravitons have not been found to exist. I am not persuaded that their existence is required by any known laws of physics, but many who know much more about these things than I do seem to think otherwise.

AM

 

[Chronos]

Atoms are less massive than the sum of the masses of the individual particles from which they are composed [e.g., hydrogen atom]. The missing mass is exactly equal to the binding force. Energy conservancy thing.

 

[quasar987]

2.No.The rest mass is an intrinsic property of every particle and it cannot change,no matter what interactions the particle may suffer.Of course,i mean a fundamental particle,with no internal structure:electron,quark,neutrino,gluon,Z,W bosons,photons,graviton,...

Then what is it that happens in the nucleus? Whose mass is transferred to the field if it isn't the quark's?

Atoms are less massive than the sum of the masses of the individual particles from which they are composed [e.g., hydrogen atom]. The missing mass is exactly equal to the binding force. Energy conservancy thing.

And what is the force that keeps the electron and the proton binded together in the hydrogen atom? It's the electrical force. So you are answering 'yes' to my second question?

 

[Andrew Mason]

Then what is it that happens in the nucleus? Whose mass is transferred to the field if it isn't the quark's?

The mass is added by the addition of energy. Energy and mass are equivalent: [itex]E = mc^2[/itex]. The rest masses of the quarks are only a few Mev each. The balance of the mass (99% of the proton) is due to the binding energy of the quarks (you can think of it as the work required to overcome the strong nuclear force and free the quarks).

And what is the force that keeps the electron and the proton binded together in the hydrogen atom? It's the electrical force. So you are answering 'yes' to my second question?

A hydrogen atom that gains energy (ie. electron absorbs a photon and moves up to a higher level) gains mass. How much: [itex]\Delta m = E/c^2[/itex] So the premise to your question, that particles which interact through electric fields do not gain mass when they increase their energy, is incorrect.

AM

 

[quasar987]

A hydrogen atom that gains energy (ie. electron absorbs a photon and moves up to a higher level) gains mass. How much: [itex]\Delta m = E/c^2[/itex] So the premise to your question, that particles which interact through electric fields do not gain mass when they increase their energy, is incorrect.

I don't remember asking about that.


I would like to point out an error from me however... When I wrote

And what is the force that keeps the electron and the proton binded together in the hydrogen atom? It's the electrical force. So you are answering 'yes' to my second question?

as an answer to Chronos' post, I had in mind that my question was "Do electrically and gravitationally interacting particles give away some of their mass to the field just like the nucleons do?", as I initially intended to ask it when I started the thread and was asking for a conformation that this was really what he was saying.

The mass is added by the addition of energy. Energy and mass are equivalent: . The rest masses of the quarks are only a few Mev each. The balance of the mass (99% of the proton) is due to the binding energy of the quarks (you can think of it as the work required to overcome the strong nuclear force and free the quarks).

A question (more of a confusion, really) arises... In a nucleus, you got protons and neutron binded together by a force. What is this force? I'm thinking it cannot be the strong force (the one binding the quarks within the proton and neutron together) because we can easily fission nucleus but we cannot fission protons even in the strongest accelerators, so if it were the strong force that keeps the necleons together, it would be just as difficult to fission nuclei as it is separating the quarks from the protons or neutrons.

 

[Garth]

Consider.

We have an atom with 'intrinsic' invariant 'rest' mass.

We split the atom and find that it is composed of electrons, neutrons, protons who’s bound mass is less than their sum total unbound masses. We attribute the difference to the mass equivalent of the energy in the fields binding the atom together. This of course has to be a 'negative' energy-mass equivalent.

We then find we can decompose the nucleons into more fundamental quarks. Again by definition we say their individual masses are invariant, their "bound mass are less than their sum total unbound masses" and the loss of mass is again attributed to the negative energy-mass equivalent of the field.

What are quarks 'made of'?

Is it "turtles all the way down"?

At a fundamental level may not everything be a form of energy, and that mass is a 'stored' form of potential energy?

Do not the 'de Broglie' wave and its wavelength, the relativistic energy-mass equivalence and wave-particle duality all hint at there being no real difference between energy and mass, except that mass has the property of inertia?

Just a line of thought.

Garth

 

[Andrew Mason]

A question (more of a confusion, really) arises... In a nucleus, you got protons and neutron binded together by a force. What is this force? I'm thinking it cannot be the strong force (the one binding the quarks within the proton and neutron together) because we can easily fission nucleus but we cannot fission protons even in the strongest accelerators, so if it were the strong force that keeps the necleons together, it would be just as difficult to fission nuclei as it is separating the quarks from the protons or neutrons.

You will probably get a better answer to that question on the Nuclei & Particles board. But my understanding of the force binding nucleons is that it is a 'residual' strong force that derives from the strong nuclear force between quarks. It is much like the covalent bonding of atoms where the nuclei of two atoms pull on each others outer electrons, resulting in an attractive force between the two nuclei. In the nucleus, a quark of one nucleon will tug on the quarks of adjacent nucleons as well as binding the other two quarks in its own nucleon (which are much closer). That is the theory, anyway.

AM