Another Mass Question

Going back to the famous E=MC^2 equation, “I was once told” (no cite) that every action involving energy meant some small conversion of energy to/from mass was going on.

I took this to mean ; If I light a match, the light/heat energy comes from a chemical reaction (burning) but that involves a small amount of mass in the match being converted to energy.

Or, if I compress a spring (adding potential energy) somewhere (in the spring? or muscles in my body?) a small amount of mass was being converted to energy.

Is that so?

FWIW - I always had the simplistic view that if, say, a ball rolled down a hill it was merely converting one form of energy (potential) to another (kinetic). Is far more going on?

Yes, it’s so. The c in E=mc^2 is however so very large, that for everyday energies in the units we operate with, it’s an infinitesimal amount of mass (also in everyday units).

I don’t really like the phrasing “mass is converted to energy” as it implies some distinction between energy and mass. It’s more like “energy that was once entirely contained in the mass of the mass is now contained in the mass and motion of the resulting products”.

Energy has mass. It’s incorrect to say that one is converted into the other. It is true that if you light a match, the mass that was in the chemical bonds “escapes” in the form of light and heat, but that light and heat still have mass. Mass is conserved, energy is conserved, nothing is “converted”.

I once calculated the mass gained from rest mass if a body is moving (relative to me) at a speed v. It turned out, to a very high approximation, assuming v << c, to be (1/2)mv^2, what we generally call the kinetic energy.

But if the mass in the chemical bonds escapes as light and heat, that is conversion; that’s exactly the conversion the OP asks about.

When a Uranium atom decays into daughter elements, some of the mass that was in the form of binding energy is released as “loose” energy – light and heat. I think it is valid to view bound energy – the kind that can be weighed – and radiant energy as “different,” for engineering purposes anyway.

Otherwise, why even bother having two words?

It all depends on how you define your system. If you had a super-strong radiation-proof box, and put it on a scale, and then set off an antimatter bomb inside of it, the reading on the scale would not change even though the atoms and anti-atoms were converted to gamma rays and neutrinos.

Or to look at a simpler example, with just a positron and an electron: After they annihilate, the resulting pair of gamma rays has exactly the same mass as the original electron and positron… but each gamma ray by itself has zero mass.

Or even an insulated box containing H2 and O2 molecules. Ignite it and some of the mass is put into photons and the kinetic energy of the resulting water molecules. As you say, it will weigh exactly the same before and after.

Sure, the grand total is conserved. But there is still speed-of-light radiant energy and non-zero-rest-mass matter, as two observed classes of “thing.” In some cases, they turn into each other.

The OP wondered if this is true in merely chemical reactions, and the answer seems to be, yes, it is. Striking a match converts a tiny amount of non-zero-rest-mass matter into speed-of-light radiant energy (as well as converting a whole lot of chemical bonds into radiant energy…)

(Should I be worried about the latter here? Are chemical bonds to candle-light an example in any way of E=mc^2?)

Yes, all conversion of “bound” energy into “free” is E=mc^2.

What you are converting in these reactions is energy. Energy from chemical bonds is released as energy in the form of light and heat. The energy had the same mass before as it did after. Nothing is converted from energy to mass or vice versa. There’s a certain amount of mass associated with the matter, and a certain amount associated with the energy. And that is the same both before and after the reaction. Mass isn’t converted to energy, energy isn’t converted into mass, energy is just converted from one type to another.

Like I said, it works better if, instead of thinking about mass being converted into energy, you think about the energy itself having mass. The energy is converted from one form to another, and it may be dispersed, making it hard to measure where it went, but it still has the same amount of mass before and after the reaction. The equation might be better expressed in this case as M = E/C^2. Which basically just means “energy has a small amount of mass, too”.

Yes, but some of that energy is confined in what we generally consider matter, and some of it isn’t. If you weigh a specific number of hydrogen and oxygen molecules at room temperature, let them react and cool back down to room temperature, they will weigh less in a way they wouldn’t if you just let them sit around for forever.

Right, and if you combine matter and antimatter it all turns into energetic photons. The energy after still has the same mass as it did before. Mass is still conserved, and energy is still conserved. I see what you’re saying though, and at that point I think it’s just a matter of perspective.

This is the singular most important aspect of mass in relativity: The mass of a system of objects is not necessarily the same as the sum of the masses of its components. If you can only remember one statement about relativity and mass, it’s not “mass is energy”, it’s that one.

By my math, the space shuttle main engines converted 0.142 grams of mass to energy during ascent (the hydrogen and oxygen going into the engines weighed that much more than the steam that came out of the engines).

Photons have energy. Energy has mass. The mass of the energy of the resulting photons is the same as the mass of the matter and antimatter that combined to create those photons with that energy. Mass is conserved.

A photon doesn’t have mass. A system of more that one photon almost certainly does (unless they all happen to be going in exactly the same direction).

The system is what we’re talking about. It has the same mass before and after the reaction. If you’re calculating rest mass from the perspective of the photon itself, you’ve changed the coordinate system and of course you’re going to get different answers.