Can you provide a cite? (Not doubting you, just interested. Well, maybe a little bit doubting…)
Actually no. Perhaps that is the source of much of this confusion. The nit I was picking was with the OP, and only with the OP. He said “It seems that Energy, Momentum and Mass (three conserved quantities)…”. Given that he sounded like a layman, I wanted to make sure he understood that mass in not conserved in the way he might think.
I was responding with a direct counterexample to your post, which seemed to be making a point regardless of whether the situation was classical or not. Then, I followed up with an immediate BUT (because I wanted to discuss the classical situation), and proceeded to describe a clearly classical field and I said so explicitly…
ETA: looking at it again, I can see how it can be misinterpreted. Everything after the (response to your question) photon example is entirely separate.
Oh sorry, your original example did not mention photons, but rather involved the oh-so-classical case of muon decay. My bad.:rolleyes:
Anyway, it appears that you do not have any reply to the actual substance of my posts, just to this trivial aside. You need to stop further obfuscating the issues by making piddling debating points to defend your indefensible mistakes. You are wrong.
I do not claim to be competent to judge whether you are correct to assert that mass is not always conserved in “classical” systems, when “classical” is used in the technical sense in which modern physicists employ that term. Others seem to think you are wrong about that anyway, but even if you are right, it is a huge, stinky red-herring with respect to the OP’s question, which is clearly concerned with the historical emergence of the concept of mass (etc.). If you were to point out that in the 20th century, thanks to Einstein, the concept of mass, that had been stable for over two centuries, underwent fundamental changes, that would be true and relevant, but that is not what you have been doing.
Let me repeat. Your claims are blatantly historically false. In physics and chemistry before the emergence of relativity theory and QM, mass was believed to be conserved, it was, indeed, explicitly stated that it was a fundamental law of nature that mass was always and everywhere conserved, and even before this was stated and accepted by chemists as an explicit law, it was implicit in the very concept of mass, the concept that Newton introduced into science and that continued to hold sway until Einstein.
We all know that mass is not always conserved according to modern physics, but to project that understanding back onto the past, onto the original formation of the concept of mass and its stable use for over two centuries, is to falsify history and, in particular it turns the relatively clear, true answer that can be given to this aspect of the OP’s question into a confused and untrue mess.
John Archibald Wheeler on page 251 of Spacetime Physics says:
It would seem that a reasonable person, of some intelligence, would see that one of the biggest names in relativity, John Wheeler, is clearly saying that there is no difference between rest mass and invariant mass.
Mass is mass is mass, and it is defined as the magnitude of energy momentum four-vector. And therefore mass cannot be converted to energy, and is absolutely conserved.
What the hell is your problem njtt? I jumped into this thread to try to help make sure the OP understood a basic concept. Apparently some of you are more interested in just shitting on people.
If you are going to say that “my claims are blatantly historically false” you better at least tell me what exactly those claims are. I can guess all of your wrath is resulting from this one line:
I have not seen any cite from you that this is “blatantly historically false.” I would assume that it is false in the context of chemistry, but I am a physicist, and my interest is in physics. In physics, long before Einstein came along, for instance, there was Lagrangian mechanics, the framework that forms the bedrock of “classical physics” as it is known today. In Lagrangian mechanics momentum and energy are conserved because of Noether’s theorem – ie due to spatial and time translation symmetries of the Lagrangian. But mass conservation, though often invoked, is not a premise of the theory. Before Einstein, for instance, people like Heaviside, Thomson, Lorentz, even Maxwell, tried to describe mass as being partly composed of (massless) electromagnetic radiation, and indeed they even came up with mass-energy equivalence relations. And classical field theories are rich with non-mass conserving Lagrangians.
Frankly I do not understand – I should actually say that I am appalled and even somewhat disgusted – that this is the response I am getting form trying to make a simple concept clear for the OP. That concept is: in the real world mass is not conserved in the same sense that energy or momentum is conserved. If you invoke the relativistic construction called ‘invariant mass’ then yes, “mass is conserved” – but in the real world the concept of mass as it was classically understood is not conserved. And I only invoke(d) the term “classically understood” because I am working under the assumption that the OP is not intimately familiar with relativity, not because I am set on getting into a stupid argument about the history of mass conservation.
No, I am concerned with the truth, and in avoiding needless obfuscation. You appear to be concerned with avoiding admitting that you were wrong.
Yes that. All the rest of your postings have been essentially devoted to defending that false claim from multiple objections from various people. I have explained how mass conservation is implicit in Newton’s original definition of mass. If you really want a cite on the Law of Conservation of Mass, here is Wikipedia. (But I think you knew about that really, didn’t you.)
Not being a premise of some theory does not equate to not being considered true (especially when “often invoked,” which clearly implies that it was considered true).
It is beyond my competence to comment on the details of that, but I would be very surprised if, at the time, anybody involved in that work (excepting perhaps the odd crank) understood it to imply that mass might not be conserved. If I am wrong about that, so be it, but it is still an obscure footnote on the concept of mass that obscures rather than clarifies what the OP is trying to understand.
Because your intervention was both false and (even if it had been technically true) obfuscatory rather than clarificatory. Your ‘appalling and somewhat disgusting’ defensiveness after being called on it by multiple people, and now your attempt to make things personal, has just made things worse. Get over yourself.
If your point had been that since the acceptance of relativity theory mass has not been understood to be conserved, then that would have been true and helpful, but that is not what you said.
I know Wikipedia isn’t the best source, but it’s the fastest thing I can find right now:
“It was recognized by J. J. Thomson in 1881 that a charged body—due to its electromagnetic Self-energy—is harder to set in motion than an uncharged body, which was worked out on more detail by Heaviside (1889) and George Frederick Charles Searle (1896). So the electrostatic energy behaves as having some sort of electromagnetic mass, which can increase the normal mechanical mass of the bodies.”
You obviously need to go back and actually look at my posts njtt, where it is obviously you who seems interested in being a jerk and being obfuscatory. Very early on, before you started attacking me, I said:
Is this wrong? Is this obfuscatory? Is this deserving of derailing a thread in order to completely obnoxiously attack someone with an odd vehemence? You say you are concerned with the truth… you don’t seem concerned with the truth, or with helping the OP. If you were, you would respond to the above quote with: “yes, I too hope the OP understands that the sum of the masses of the particles in a system is not conserved.” Instead you seem incredibly interested in discrediting me for some bizarre reason.
As you yourself admit, you are not qualified to comment on the very question you seem so adamant about. You state that mass conservation is implicit in Newton’s definition of mass (wrong) while at the same time cite a wikipedia article that states that “The principle of conservation of mass was first outlined clearly by Antoine Lavoisier” (who was born after Newton Died). The very article you cite does not do credit to your point. Also, I see that someone else put up a link already about how previous to Einstein the non-conservation of mass was very much a mainstream concept that was worked on by some of the leaders in the field.
These are my thoughts from reading the thread:
In special relativity the Minkowski norm of the vector sum of the four momentum of the constituent particles is the conserved mass, whereas the sum of the Minkowski norm of the four momentum (i.e. the individual masses) of the constituent particles is not conserved (this is just a rehash of what’s been said before).
I don’t think anyonhe disagrees with ther above and for good reason the former quantity is usually described as the mass of a system i.e. it’s a measure of the inertia of the centre of mass of the system. This contrasts to Newtonian physics where the sum of the masses of the consituent particles/systems is equal to the mass of the system.
That said the latter quantity has it’s uses, plus it’s Lorentz invariant too. For those who like to see relatvity geometrically like me, the fact that the former is always greater than or equal to the latter is a result of the Minkowskian version of the triangle inequality.
Also with the former definition your actually adding equivalnce classes of four momentum vectors which is fine in speical relativity where parallel transport creates natural equivalent classes of four vectors on the Minkwski manifold, but it means that in general you cannot apply this definition of mass to systems in general relativity.