Classical physics introduced two substances: matter and energy…in classical physics we had two conservation laws: one for matter, the other for energy. We have already asked whether modern physics still holds this view of two substabnces and the conservation laws. The answer is: “No.” According to the theory of relativity, there is no essential distinction between mass and energy…Instead of two conservation laws we have only one, that of mass-energy…How is it that this fact of energy having mass and mass representing energy remained for so long obscured?…The reason for this lack of immediate evidence is the very small rate of exchange between matter and energy…An example will make this clear. The quantity of heat able to convert thirty thousand tons of water into steam would weight about one gram! (Simon and Schuster, 1966; pp. 197-198)

The overall center of mass of the system doesn’t change, because all this happened internally, yet the box shifted ever so slightly to the left. In fact it shifted (E/Mc) times (L/c) or EL /M c*2).
To counter this leftward motion of the box, the energy of the light was moved a distance L, so if the overall center of mass didn’t change, we’d have

mass of box times distance it moved = mass associated with E times the distance it moved or

M times EL/(M c*2) = m L, where m is the mass associated with the energy of the light that moved. Solve for m and you get m = E/c*2.

The energy that went into making the light beam was originally stored as chemical energy in the battery and now it is thermal energy added to the opposite side of the box, but in-between it was the energy of the photons. But anyway, when in its chemical or thermal energy form, it added to the mass of the box by the amount E/c*2. That mass was transferred to the other side of the box.

I think the explanation goes something like this: chemical reaction 2H2 + O2 = 2H2O can be interpreted as electrons jumping from higher energy levels to lower ones to form a stable molecule of water.

Energy that these electrons lose is released as a bunch of zero-mass-moving-at-a-speed-of-light particles (photons?) with no change in mass for the whole thing.

IOW, in a very-very rough analogy: electrons in H2 and O2 are moving fast; they then slow themselves down by shooting out zero-mass particles which (slowing down that is) allows them to form an H2O molecule. In H2O electrons are moving slow; the total number of electrons, neutrons and protons is the same, the total mass is the same.

That’s my story anyway.

Of course, you yourself will weight a bit less after walking up the Empire State building, as you’ll be using energy. My friend was undecided on the point of a spaceship leaving orbit around the sun and travelling into clear space: he thought that maybe the loss of mass from the ship’s engines would cancel out any possible gain in mass. The problem is that it’s impossible to think of an isolated system in G.R. as you cannot remove everything, or you remove the gravity as well!

One can explain the spring more easily: ultimately, it’s a change in the atomic behaviour of the lattice of atoms which makes up the metal which makes the spring: if molecules can have less mass than their constituate atoms, then it doesn’t seem too surprising that stressing a spring can change its mass a small amount.

I think your collegue is wrong: mass most certainly is converted into energy in a chemical reaction. A water molecule literally has (a tiny tiny amount) less mass than 2 hydrogen atoms and an oxygen atom. If you read the Wikipedia on S.R. you’ll find that there is a difference between mass and momentum: a photon is massless but it has momentum; I have mass, and if I speed up, I gain momentum! An electron has mass though, so I’m not quite sure what you collegue meant.