By logic, matter is something that exists independently, and has mass (unspecialized meaning of mass) and net volume (subtracting the inner empty space).

And by logic, motion is a property of matter; motion is dependent on matter.

By logic, something that has mass (unspecialized meaning of mass) or net volume (i.e. independently exists) (e.g. matter) cannot be completely or partially converted to something that doesn't have mass (unspecialized meaning of mass) or net volume (i.e. doesn't independently exist) (e.g. motion), and vice versa.

Therefore I think by logic, either 'violation of logic' or magic is possible, or mass-energy conversion or equivalence is not true.

Does mass-energy conversion or equivalence violate the law of logic or mathematics?

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    $\begingroup$ Matter and mass are different things. Mass and energy are both properties of Matter. $\endgroup$ Dec 2 '20 at 22:49
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    $\begingroup$ This seems more like a philosophy question but the answer to the question in the title is obviously no: it definitely doesn't violate the laws of logic or mathematics. Saying matter is a substance that exists and energy is a property of matter is incorrect. Or else light/radiation doesn't exist, e.g. see physics.stackexchange.com/q/356637 $\endgroup$
    – Eletie
    Dec 2 '20 at 22:51
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    $\begingroup$ If I arbitrarily declare that wheat exists and bread doesn't, and then discover that wheat can be turned into bread, have I discovered a mathematical or logical paradox? $\endgroup$
    – WillO
    Dec 2 '20 at 23:37

This is actually a good question, because it involves a very common misperception held by many scientists, and that is:

Matter is substance

The idea predates the "atom", (the atom that was the smallest indivisible chunk of "substance"), with the 4 elements of Earth, Fire, etc....Surely "Earth" was substance. It seems like pure common sense.

Of course, foundations were rocked when

$$ E = mc^2 $$

was discovered, as it told us mass and energy were equivalent. Chemical and nuclear reactions converted binding energy to kinetic energy, which showed up as a mass difference in the initial and final states.

But that's binding energy, a few percent of the total mass. Certainly some mass was fundamental...it was stuff, like the electron, or the quarks that make up the nucleons.

Well, the Standard Model says: no. For simplicity, if we focus on the electron, it has a mass:

$$ m_e \approx 511\,{\rm KeV/c^2} $$

That mass is not substance, it is a coupling to the Higgs field. If the Higgs field is 0, then the electron is massless. If the Higgs takes its present value, then the electron has mass.

What that mass means is that to create an electron from the electron field, the lowest energy state, the one with zero momentum, it has an energy of 511 KeV. That is it. It is not substance, it's a minimum energy.

This is just the nature of quantum fields. The so-called particles aren't particles, they're excitations of a field. They look like particles because they come with conserved quantum numbers like "electron number", charge, and spin...it really looks like substance.

But its not. It's just like a photon, which is a quantum of the electromagnetic field. It is a particle, but we don't think of it as substance...mainly because it is its own antiparticle, so its number is not conserved.

If you bring an electron (not substance) near a positron (also: not substance), they annihilate into photons (not substance). You may say, well a positron is "anti-matter", but that just means it is an electron field excitation with conjugate quantum numbers..it is not "anti-substance".


I don’t know much about Einstein’s relativity, but as far as in classical mechanics, mass, or intertial mass to be exact, is a quantitative measure of the intertia of an object ( the resistance to change in velocity). classically, m=F/a.

What mass-energy equivalence says, basically, is that energy itself has mass. When you add energy to an object, its resistance to change in velocity increases, and when you remove it, it decreases. Now, coincidentally, it turns out that the gravitational mass (the “charge” of gravitation) is equal to inertial mass, so what you measure on a balance, ( normal contact force exerted/local gravitational field) also decreases.

I don’t think it’s correct to say that mass is converted into “energy”. What actually happens is, upon fission, the total nuclear potential energy of the atom decreases which is released as internal energy of the surrounding(erroneously called heat), energy of photons and k.e. Now, since the total energy of just the atom has decreased, the intertial/gravitational mass value associated with the atom has decreased too. And the decrease in the mass value is now associated the other energies.

Mass isn’t converted into energy here; nuclear potential energy is. it’s just that the decrease in energy is accompanied by a decrease in resistance to change in velocity, or intertial mass. Due to its complicated nature, I don’t think there’s a general formula for nuclear potential energy that you can use to find the energy released. So what you do is you find the decrease in mass and find the quantity of energy associated with that value and thus the energy released.

Note; the conservation of energy holds perfectly on its own. This doesn’t affect the already established law in any way whatsoever. The total amount of energy in an isolated system always remains unchanged; you din’t need to account for energy somehow being “converted” to mass because that is simply a wrong concept. It’s just that mass, or a measure of resistance to change in velocity to be exact, is a property of energy has.

Mass energy equivalence isn’t unique to fission/fusion. If you heat up the air inside a baloon, its resistance to change in velocity will increase too; the added heat contributes to inertia. In an exothermic chemical reaction, the mass of all the reactants is greater than that of all the products because the heat evolved took along with it the interia/mass associated with it.

  • $\begingroup$ Mass can be directly converted to energy in matter-antimatter annihilations. Your answer doesn't seem to consider that, by only addressing the mass-due-to-energy lost in chemical and nuclear reactions $\endgroup$ Dec 3 '20 at 3:35
  • $\begingroup$ "converted", again, doesn't seem to be the right word. The energy of the photons was still energy before the annihilation, maybe in the form of electrostatic and/or nuclear p.e. Using the word converted makes it sound like mass is a form of energy, and can be converted to and from other forms, like k.e and p.e for example. Thats simply not true, energy is converted to energy. You could also argue that the total rest mass of the isolated system containing the anti-aprticles, and the photons thereafter is still same, cuz the energy is still same $\endgroup$ Dec 3 '20 at 6:46
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    $\begingroup$ @SagarPatil in matter-anti matter collisions, energy, not mass, is converted into energy. If you did deep, you will find that 91% of the mass of protons and neutrons is due to potential energy of the constituent quarks. sciencenewsforstudents.org/article/…. $\endgroup$ Dec 22 '20 at 20:04
  • $\begingroup$ What of the other 9% of mass? $\endgroup$ Dec 25 '20 at 0:12

Here is a simple explanation. $E = mc^2$ means mass is energy, and vice versa. Energy is not converted to mass, energy is mass.

Whenever you have a change in energy there is corresponding change in mass. For example, a hot cup of coffee has more mass than a cold cup of coffee. The m in the equation is the relativistic mass; for example, for an object with kinetic energy the mass is greater than for the object at rest.

Discussions of exothermic nuclear reactions in physics texts show how rest mass of reactants is converted to kinetic energy of products, but for reactants and products the total mass- the m in $E = mc^2$- is not changed, and the total energy E is not changed.

To be correct the statement you quoted "the mass of the atoms that come out of a nuclear reaction is less than the mass of the atoms that go in, and the difference in mass shows up as heat and light with the same equivalent energy as the difference." should be " the rest mass of the atoms that come out of a nuclear reaction is less than the rest mass of the atoms that go in, and the difference in rest mass shows up as heat and light with the same equivalent energy as the difference".

  • $\begingroup$ I think we can say that the mass can be identified with the energy of a system measured in a reference frame where the system is at rest (its 3momentum vanishes). But we cannot declare that mass and energy coincide in general, just because energy is conserved and mass is not conserved. $\endgroup$ Dec 3 '20 at 6:21
  • $\begingroup$ @Valter Moretti I did not know this. Thanks for the information. Can you provide a reference that explains this in relatively simple terms? $\endgroup$
    – John Darby
    Dec 3 '20 at 15:26
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    $\begingroup$ Consider a particle with mass $M$ at rest in our laboratory which decays into a pair of particles of identical masses $m$ with non-vanishing momenta $p$ and $-p$ (momentum is conserved!). Since energy is conserved $Mc^2 = 2\sqrt{c^2p^2 +mc^4}$. This is incompatible with $M=2m$ unless $p=0$ which is false. Here energy is conserved and mass is not conserved. Everything respecting all laws of physics. $\endgroup$ Dec 3 '20 at 16:01
  • $\begingroup$ Thanks for the example. $\endgroup$
    – John Darby
    Dec 3 '20 at 16:12

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