# What is the difference between mass-energy equivalence theory/law and the conservation of energy?

Hi
What is the difference between the
mass-energy equivalence theory/law(e=mc2 and the conservation of energy law? I’m not quite sure about how they are related. I believe the latter is the first law of thermodynamics. How does e=mc2 support the law of conservation? I look forward to your feedback

I don’t see a conflict.

Mass is energy, energy has mass, and both quantities are conserved.

So if I described Einstein’s equation e=mc2 as the law of conservation of energy, would that be technically correct? I somehow thought that Einstein’s equation was an improvement over the 1st law of thermodynamics or was it proof of it? I’m not quite sure.

e=mc^2 simply tells you “if I take this kilogram of matter and somehow turn it into pure energy, how much energy do I get out.”

Convservation of energy is that if you add up the types of energy in a reaction (heat, kinetic, mass equivalent, atomic bonds, etc) the total can’t change from before to after.

If a neutron at rest decays to proton, electron, and antineutrino, there will be slightly less mass after the reaction. That lost mass uses e=mc^2 to convert to energy, and that energy gets parcelled out as kinetic energy in the particles, and photon energy if any photons are emitted. Eout = Ein.

mass is energy. And it is conserved. You can “convert” energy to mass and back, because it’s really the same thing. But you can’t destroy mass=energy, or create it out of thin air.

This is actually subtly misleading. If neutron decays, the sum of the mass of the proton, the mass of the electron, and the mass of the anti-neutrino will be less than the mass of the original neutron. But the mass of the system of the proton, electron, and anti-neutrino will be exactly the same as that of the neutron.

The trick is that in relativity mass is not additive unless the objects are at rest relative to each other. I.e. the mass of a system of two objects with masses m1 and m2 is not necessarily m1 + m2.

It was neither. It is another law entirely. In fact, the equation by itself isn’t all that influential, it’s more a succinct illustration of the sort of thing Einstein’s relativity implies.

That’s not really how it works. Mass has energy and energy has mass, but they don’t “convert” back and forth.

My understanding is E=MC^2 shows how matter is energy. I think of matter as frozen energy. Conservation of energy just states that you can’t create energy, or destroy it, just change its form. Kinetic to heat for example.

No. That just tells you the relationship between mass and energy, and how much energy is contained in a certain amount of mass. The conservation of energy law is not something we usually write mathematically, but it would go something like this:

Delta E (for a closed system) = 0.

That is, the amount of Energy in a closed system (a system no subject to outside forces) is constant. Same for momentum. But the key is that the system must be closed. If outside forces can act on it, then the total amount of energy can change.

More precisely, the Law of Conservation of Energy states that the change in the energy contained within any bounded region is equal to the sum of all of the flows of energy across the boundaries of the region. In other words, if the energy in a region increases, it’s because energy entered the region, and if it decreases, it’s because energy left the region.

Thank you John Mace. Thank you all. Perhaps someone would like to comment of the following:

Does E=MC2 disprove the first law of thermodynamics?
It will depend on how you define energy. If you define energy in a non-relativistic manner, the first law is wrong. The first law still holds if you accept the relativistic definition of energy, the one which includes the rest mass energy.

IANAP, but it is my understanding that E = mc[sup]2[/sup] simply says “Mass IS energy. If you have a mass of m (kg), it is E joules of energy.”

I think they are related, but draw from different wellsprings.

First law of thermodynamics is very fundamental, and tells you what to expect when you measure the energy in your system. I believe it relates to a fundamental symmetry we believe the universe has (with respect to time?).

E = mc*2 tells you how matter and energy are related in your system. (For most practical purposes, we ignore matter’s contribution to the system’s energy because it is (mostly) the same before and after, but this can sometimes become important, especially when nuclear processes are involved.)

Thanks Blue Blistering Barnacle

I’ve seen a lot of reference to non-relativistic versus relativistic interpretations of transfers of energy to distinguish the two and a lot of debate. I’d really like more clarification on that.

While we’re at it, the actual law isn’t even E = mc[sup]2[/sup]. It’s E[sup]2[/sup] = p[sup]2[/sup]c[sup]2[/sup] + m[sup]2[/sup]c[sup]4[/sup]. It’s only in the (relatively boring) case where p = 0 that it reduces to E = mc[sup]2[/sup].

A crude example:

Lord Kelvin was a really smart guy who did very important work in thermodynamics. He famously calculated the Earth’s age to be about 20-40 million years (too short to support evolution as envisioned by Darwin), based on the Earth’s interior temperatures and conductivity of rock. But he was unable to account for radioactivity (as it was not yet discovered). Radioactivity adds heat to the center of the earth (or to any very radioactive object- read ‘The Martian’ for creative application of this). But it’s not ‘adding’ energy to the earth’s interior- that energy is counterbalanced by small losses of mass during nuclear decays, where forces and velocities are such that relativistic effects become apparent. (Incidentally, there is a similar but far more miniscule loss of mass in exothermic chemical reactions, if everything is fully accounted for.)
https://en.wikipedia.org/wiki/William_Thomson,_1st_Baron_Kelvin#Age_of_the_Earth:_geology_and_theology

Thanks Dr. Cube. Why do I see the word convert used at all? What would be a better phrasing for what happens between mass and energy?

In special relativity the conservation of energy, momentum and mass are all linked together and they can all be seen as coming from the translational symmetry of spacetime in special relativity. The mass though that is specifically conserved is the rest mass of an isolated system, which may include, some, all or part of its kinetic energy (depending on the system and the frame).

Now, using the usual relativistic definitions, mass and energy are not synonyms in special relativity: mass is invariant (i.e. the same in all frames), whereas energy is frame-dependent (i.e. depends on the frame of the observer). However a portion of the energy of a massive system can always be identified as the mass, so it is not incorrect to see mass as a type of energy.

You can certainly say that energy is converted between different forms. Just like a battery converts chemical energy to electrical energy, or an engine converts heat energy to kinetic energy, so too can you convert between, say, nuclear binding energy (which is usually accounted as “mass”) to radiant energy (which usually isn’t).

Is this a distinction between mass conferred by Higg’s mechanism vs relativistic mass in bound particle systems? Or is this something different?