# How does energy convert into mass?

I've been wondering this question for a long long time.
In my world view, all energy is vibration/frequency/waves etc. and it's quite easy for me to imagine.

But then there's mass. To me it's like a compressed form of energy, where loads of energy is inside an imaginary ball or inside a path of curved space-time that infinitely spirals inwards towards this weird singularity where it finally converts in to mass. :uhh: But I don't believe that theory holds itself together. There must be something I am missing here. You're probably laughing at me right now, but I have no idea what mass is. I mean I do know at general level what mass is, of course, but when I try to unify my world view of vibration and mass together or even think about the process visually when energy converts in to mass, I only get blown away with multiple theories. I believe that many of you has thought about this too and I'd LOVE to hear your theories/facts. Related Other Physics Topics News on Phys.org
jedishrfu
Mentor
Welcome to PF!

The current state of science has no answer for your questions at least the way you've posed them. However they are in the realm of Quantum Mechanics where we have a limit on what we can observe and the conversion of energy to matter or vice versa happens on the other side of that limit and is beyond our ability to observe its inner workings.

PF has a policy here to focus on helping students with their science and math questions and to not discuss speculative science as it often leads to confusion and distracts from the primary mission of helping students. So don't be surprised if your thread is closed.

UltrafastPED
Gold Member
Almost all of the mass of prtons/neutrons can be assigned the kinetic energy of the quarks from which they are made.

That leaves maybe 2% due to the mass of the quarks. Electrons also have mass, and they have no parts.

Dale
Mentor

Energy does not convert into mass. Energy has mass. In other words, if you have an isolated system with a certain amount of energy, E, a certain amount of mass, m, and a certain amount of momentum, p, then those values will all stay constant regardless of what goes on inside the system. Also those values are related by ##m^2 c^2 = E^2/c^2 - p^2##.

You can start with a system of an electron and a positron and have them annihilate into a system of two photons, but the system as a whole will still have the same energy and mass and momentum as always.

Energy has mass.

Dale
Mentor
You are right, I should have said that energy and momentum have mass according to the equation I posted earlier: ##m^2 c^2 = E^2/c^2-p^2##. For a photon E=p (in units where c=1), so m=0.

The point I was trying to make was that whatever energy, mass, and momentum a system has, it has it all together. It does not "convert" from energy to mass, they are both there all the time and in the same amount.

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The point I was trying to make was that whatever energy, mass, and momentum a system has, it has it all together. It does not "convert" from energy to mass, they are both there all the time and in the same amount.
Thank you for your answer DaleSpam This helps me quite a lot!

But when you said: "It does not "convert" from energy to mass, they are both there all the time and in the same amount."

I got blown away with the "same amount". As far as I've learned, some particles have more mass, some have more energy.
E.g. Electron is mainly energy and the top quark is mainly mass.

I think I misunderstood the whole picture there.

Oh wait now I get it! Nevermind :D

Dale
Mentor
Sorry, that was unclear. "Same amount" just meant that each was constant over time (conserved) not that they were equal to each other.

• 1 person
"mass" is a characteristic of an object or system of objects. When dealing with systems of objects, the constituents of mass consist of both mass and various other forms of energy. Speaking about energy as if it is a thing is a fundamental error. Energy is a category of 'things', it is an abstraction with which we can make sense of the world. In General Relativity, the concept fails and a broader concept which includes momentum and pressure (or stress) must be used in order to form a 'thing' which is conserved. The Conservation Laws are the most important laws in physics because they force our calculations/predictions into certain paths. While it is another common error to confuse the electromagnetic field (as well as its particle, the photon) with "energy", by the time a student has some understanding of photons, she has also learned a bit about neutrinos, neutrons, gravity, the weak force, the strong force, quarks, gluons, bosons, etc.; which have energy/mass but are only distantly related (if at all) to electromagnetism.
Lord Kelvin said:"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be." You have my respect if you understand the Spherical Harmonics well enough to base you 'world view' on them... There is beauty in Science, but the beauty is not the evanescence of poetry, it requires a mutually defined bases. Our current best understanding of the Universe is based on gauge fields, particles, waves, and the curvature (and expansion) of space-time. I wonder if your use of the term "wave" has any significant relevance to what the term means in Physics?

Thank you for your answer DaleSpam This helps me quite a lot!

But when you said: "It does not "convert" from energy to mass, they are both there all the time and in the same amount."

I got blown away with the "same amount". As far as I've learned, some particles have more mass, some have more energy.
E.g. Electron is mainly energy and the top quark is mainly mass.

I think I misunderstood the whole picture there.
specifically, the quote

"some particles have more mass, some have more energy.
E.g. Electron is mainly energy and the top quark is mainly mass."

makes no sense.

An electron at rest has as much mass as energy.
An electron in motion has more energy than mass according with E2 = (mc2)2 + (cp)2.

same thing is true for all other particles including the top.

Confusion can arise due to the conflation of “mass” and “rest mass”. All energy exhibits inertial mass, that is the point Einstein made in 1905, but that does not mean that the objects in the system which have this energy have rest mass ie would still have mass if they were brought to a state of rest. For example an electron and positron pair at rest and completely separated do have rest mass = 2x electron rest mass m’. The energy of this arrangement E= 2m’ c*c. If the pair are brought together and annihilate, two photons of gamma radiation are produced with the same total energy E= 2m’ c*c = 2 hv where v is the frequency of the gamma radiation and h is planck’s const. The photon has no rest mass. So we say “mass has been converted into energy” but we mean that the energy content of the rest mass of the e-e+ pair has been converted into electromagnetic energy. Both forms of energy still have inertial mass. Imagine an isolated box containing the electron-positron pair; the measured mass of this box and contents will be the same before the annihilation as it is after when the box contains two photons instead of the e-e+ pair because the total “mass-energy” of the system is unchanged.

we might say mass is a form of energy and energy is a form of mass.

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All energy exhibits inertial mass, that is the point Einstein made in 1905
Not all energy but only the rest energy of a system contribute to its mass. That's what Einsteins paper "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?" refers to. There is a similar relationship between total energy and relativistic mass but that's not what Einstein was talking about.

Does a box of photons exhibit inertial mass?

(the photons have zero rest mass but doesn't the energy density of the electromagnetic fields lead to the box of photons having greater inertia than an empty box?)

Does a box of photons exhibit inertial mass?
Even though the single photons have no mass a system consisting of more than one photon may have mass.

surely if the box had only one photon in it the inertia would be greater than an empty box?

jtbell
Mentor
Yes, the system of box+photon (or box+photons, if there is more than one photon) has more mass than an empty box.

This does not mean that photons have mass. In relativity, mass is not an additive quantity. The mass of a system does not, in general, equal the sum of the masses of its components.

(By "mass" I mean what most physicists today mean by "mass", namely what is also called "invariant mass" or "rest mass", not the "relativistic mass" which appears in popular-level introductions to relativity and even in some introductory textbooks.)

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jbriggs444
Homework Helper
2019 Award
Not all energy but only the rest energy of a system contribute to its mass. That's what Einsteins paper "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?" refers to. There is a similar relationship between total energy and relativistic mass but that's not what Einstein was talking about.
The rest energy of a system is not neccessarily equal to the sum of the rest energies of its component parts. The kinetic energy of the parts relative to a frame in which the system has zero total momentum contributes to the rest mass of the system.

Rest mass is not an additive property.

[Edit, beaten by jtbell]

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Dale
Mentor
Confusion can arise due to the conflation of “mass” and “rest mass”....
we might say mass is a form of energy and energy is a form of mass
This is a bit out of date (not wrong per se, just out of date). The modern convention is that the unqualified term "mass" refers to the "invariant mass", aka "rest mass". If you want to talk about the kind of mass that is just another name for energy then the modern convention is to use the term "relativistic mass".

By this modern convention mass is NOT a form of energy and energy is NOT a form of mass. The two are related by ##m^2 c^2 = E^2/c^2 - p^2##.

Imagine an isolated box containing the electron-positron pair; the measured mass of this box and contents will be the same before the annihilation as it is after when the box contains two photons instead of the e-e+ pair because the total “mass-energy” of the system is unchanged.
This is an excellent example

The rest energy of a system is not neccessarily equal to the sum of the rest energies of its component parts.
That's why I spoke about energy and mass of the system and not of its sub-systems.