Yes, actually, the conservation of mass was not generally assumed before Einstein. I am not “bringing up issues deriving from relativity theory”, I am doing the opposite – I was trying to discard those issues because I think they are irrelevant to the question posed by the OP. I am NOT the one arguing for the assumption that the OP means relativistic “invariant mass” – I think the OP means mass as it is understood by laymen.
Classical mechanics says nothing about whether or whether not mass is conserved. And no, the non-conservation of mass (as it is classically understood) does not require non-Newtonian dynamics. Classically, for instance, mass is not conserved in electrodynamics – charged bodies radiate away energy through a massless field.
Where in this example is a classical, Newtonian mass changing?
The invariant mass of a proton can certainly be calculated by looking at its constituents. In particular, the invariant mass of the proton is exactly equal to the invariant mass of its constituents. Did you mean something else here?
You seem to think that somehow if the mass is changing it is not ‘classical’. Classical mechanics has no interest whatsoever in whether or not the mass is changing. I have described a perfectly classical system that conserves energy and momentum but has rest mass ‘disappearing’ as energy is radiated away by the EM field.
I could be wrong here, but it is my understanding that the invariant mass is calculated from the sum E^2 - sum P^2, where each Ei = mic^2 +pic. In other words, potential energy does not enter into the invariant mass calculation. It is a purely kinematical variable. Thus, the invariant mass is not equal to the rest mass. I did not say that the invariant mass of the proton is not exactly equal to the invariant mass of its constituents.
I don’t see any rest mass disappearing. Are you picturing something like a accelerating electron? If so, the electron loses energy in the radiation but not any rest mass.
I took the latter as a subset of the former. I suppose you meant something specific by “looking at” other than “calculate the invariant mass of”.
This is incorrect. One must tally the potential energies as well. Indeed, otherwise a system’s invariant mass would vary as kinetic and potential energy slosh back and forth during the system’s evolution.
An atom will lose rest mass when it radiates a photon. But I am just discussing classical mechanics at a theoretical level. I am simply making up an example that is fully allowed within classical mechanics of a classical field theory without a mass gap where a charged massive field loses mass continuously as it radiates electromagnetic radiation. This is fully classical. There is nothing in classical mechanics that says anything at all about conservation of mass.
I suppose you are right, although I’m a little baffled that not once in my entire life have I seen an invariant mass calculated taking the potential energy into account, or ever seen a term quantifying such an effect. In any case I still stand by my point.
I would call that a non-classical system. The discrete emission of a photon from a de-exciting atom requires quantum mechanics to describe.
That’s because systems that are both bound and relativistic are non-trivial to work with, and so they do not come up as examples of invariant mass calculations. (This is especially true of bound hadronic systems. Yet, lattice QCD calculations can predict the masses of baryons and mesons to 5-10%.)
Please do not mis-quote me. It almost looks as though you purposefully tried to make it look as though I was saying the atom emitting a photon was classical, which is not at all what I said (although it illustrates the principle perfectly well – any classical charged particle with a macroscopic orbit will emit radiation and the rest mass of the system will descrease – entirely classically)
This is just false history. There is a whole scientific discipline called Chemistry for which the conservation of mass was a very crucial and explicit assumption, way before Einstein.
Furthermore, the conservation of mass is implicit, even if not yet explicit, for Newton. Newton defined mass (which was never a lay term, it is a technical term introduced by Newton) as the quantity of matter in a body. Unless you took some stuff away from a body, such as by cutting a bit off it, its mass would be conserved. If it is true (and I do not concede that it is) that conservation of mass was not much discussed by physicists (as distinguished from chemists) before Einstein, that is simply because no-one before ever dreamed that it might not be conserved, because conservation was built right into the very (Newtonian) concept of mass. In the context of mechanics,* only relativistic considerations are ever likely to tempt anyone to imagine that mass might not be conserved.
*Chemistry was a bit different, because matter was clearly transformed during chemical reactions, and their nature long remained mysterious. Thus non-conservation of mass in chemical reactions was at least thinkable, and it had to be (and was) discovered, and then was explicitly stated as a law, that mass is in fact conserved during reactions. In mechanics, however, where matter is not transformed but simply moved about, the point was simply never in question before Einstein.
Missed edit window:
You seem to be using the word “classical” in a sense that it acquired only after the development of relativity theory and QM. “Classical physics”, in that sense, is not at all the same thing as physical theory as it actually was before Einstein and Plank, and to talk as if it were the same, as you seem to be doing, is to falsify history (and, in particular, the story of how the concept of mass was developed, which is what the OP asked).
Heck, you are talking about systems emitting photons! Nobody ever heard of photons before Einstein.
Maybe (I do not know) mass is not always conserved in “classical physics” in the post Einstein/Heisenberg sense of “classical”, but in physics as it actually existed before their work, it most certainly was believed to be conserved. (And mass was a perfectly coherent concept in that physics, even though that physics did not fit empirical reality quite perfectly.)
I apologize for butchering your quote. That’s what I get for trying to post while simultaneously watching TV.
Yes, the macroscopic condition can remove the quantum aspects, but it is still non-Newtonian. I repeat my original claim:
This mass that you speak of as being lost is the (relativistic) invariant mass. This mass couldn’t have been non-conserved in Newtonian physics because it wasn’t yet defined.
Conservation of Mass in the classical sense was first stated by Antoine Lavoisier back in 1789, although other scientists had similar ideas back to the 1740s.
This is the classical form of conservation of mass, without relativity or quantum effects, which I believe is what the OP is looking for.
That’s not classical physics. That’s relativistic physics. Only by including relativity can mass be converted into energy.
Jesus, this is what happens what you are mis-quoted. I am NOT, and I HAVE NOT, called anything involving a photon a classical system!!! This is pointless if you can’t even follow the very basics of my argument.
Simply false. Any classical composite system with moving charged objects radiates away energy via the classical electromagnetic field. The system’s rest mass decreases due to loss of stored electromagnetic binding energy.
Does anyone at least agree with my point, my only reason for entering this discussion, which is simply that the classical concept of mass is not conserved, when, for instance, a particle decays. You can get pedantic if you want (“a particle decaying is not a classical concept”), but I think that’s a distraction – in the real world particles decay and the classical concept of mass is not conserved. I merely wanted to make the OP aware of this simple fact. Yes, there is something called ‘invariant mass’ that is conserved, but that is a more advanced concept.
But speaking towards that more advanced concept, the fact is that conservation of momentum and energy are a result of spatial and time translation invariance of the classical theory’s lagrangian. There is no such symmetry for the masses in the system. In classical lagrangian field theory, mass is not conserved unless there is a posited relation ship between mass and the other conserved quantities. For example, in relativity, an invariant mass is possible because the momentum and energy is conserved, and there is a relationship given between mass, momentum, and energy. Since 2 of the 3 are conserved, and mass can be derived from the other two, an invariant mass can be constructed. But one can certainly construct classical lagrangian field theories for which there is no such simple relationship.
The nit you were trying to pick when you entered the thread was in an exchange between Pleonast and Bytegeist, in their mentioning of how Newton originally wrote down his law (in terms of impulse rather than mass and velocity). They noted that Newton assumed mass was constant (which he, and the next two centuries’ of scientists, did).
You immediately said:
Our point is that this is an anachronistic irrelevance. In Newton’s time, mass was conserved. Your examples of mass not being conserved come from relatively modern times and are distractions to the discussion that was trying its hardest to get going. (I look forward to the thread recovering its original purpose of exploring historical developments.)
Regarding the statement you asked us about explicitly:
I’ve bolded those concepts that did not exist in Newton’s day. (I gave you “charged objects”, even though in his time, people were basically just rubbing materials together and seeing what got all static-y. The concept of an electric charge was rudimentary at best.) No one was dreaming that mass was not conserved, and no one was assuming that the light coming out of their chemical reactions was reducing the mass of the test tube’s contents by 0.00000000001%.
This has nothing to do with how you are quoted. You said (and I’ll put the whole thing in here) –
I certainly read that as saying that photon emission is classical. I think njtt did, too. If your first sentence doesn’t have anything to do with the rest of the paragraph, then you perhaps that could have been made cleared.
But it doesn’t matter either way, as it still remains unrelated to the concept of mass as it existed before 1905-ish. (Even once Maxwell had fleshed out electromagnetic radiation, he still didn’t propose that mass was changing anywhere. Mass was matter; matter was mass; both were inviolate.)
…much like this clause, which was supposed to end up as “then perhaps that could have been made clearer”.
“Rest mass” is not a classical concept. It is a relativistic concept. In classical mechanics, mass does not change when a body is in motion.
Apparently the first person to recogize that mass changes under motion in an electric field was Thomson in 1881. So that was one of the earliest precursors to relativity theory. I would say that classical physics is anything that was known before then, and before then mass certainly was believed to be conserved.