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With the development of relativity it became clear that mass and energy are the same, and therefore that they aren't separately conserved (or balanced). It seems that during the same period when these developments took place, the notion of "matter" also got more and more conceptually separated from mass-energy, and its separated conservation laws (baryon, lepton) were introduced.

The distinction between "mass" and "matter" (or whatever you want to call it), and the need of a conservation law for the latter, separate from Einstein's equations, is for example crystal-clear in a brilliant paper by Eckart from 1940: The thermodynamics of irreversible processes. III. Relativistic theory of the simple fluid.

Surprisingly I don't manage to find much historical information on this separation before Eckart's paper; yet from the way he writes it sounds like the understanding was already there.

On the other hand, a work by von Laue from 1949, Inertia and energy (in Schilpp: Albert Einstein: Philosopher-Scientist, chapter II.19 p. 503) still shows confusion between "mass" and "matter".

Can someone point out some early works where matter-conservation laws were introduced?

  • $\begingroup$ Particle number conservation laws are typically not referred to as "conservation of matter", which is still used in chemistry and physics for conservation of mass when relativistic effects are negligible. Particle number conservation came up later than mass-energy equivalence, in 1950-60s, when most particles of the Standard Model were discovered, see Schulte, The co-discovery of conservation laws and particle families. $\endgroup$
    – Conifold
    Commented Apr 28 at 7:29
  • $\begingroup$ @Conifold thank you. Yes I know that terminology varies, but what I'm interested in is not the terminology, but the understanding that an additional conservation law was needed besides Einstein's equation. This understanding is for example crystal-clear in a work by Eckart from 1940 <doi.org/10.1103/PhysRev.58.919>. So it seems the idea was already present. But I haven't managed to find references prior to Eckart's. $\endgroup$
    – pglpm
    Commented Apr 28 at 11:24
  • $\begingroup$ The sort of distinction Eckart is talking about ("matter is to be interpreted as number of molecules, therefore, and not as inertia") goes back to the 19th century, when mass was already distinguished from the "amount of substance" as measured in moles proportional to the number of molecules. Ostwald derived "mole" from "molecule" in 1894. Eckart explicitly says that he is adapting the classical distinction to special relativity. Conservation mechanism of quantum particle numbers is of a different nature because those particles transmute. $\endgroup$
    – Conifold
    Commented Apr 28 at 22:11
  • $\begingroup$ Eckart explicitly says "The conservation of matter is expressed by the equation [...]" and "At this place in the considerations, however, it becomes important that matter be conserved" and "One result has appeared clearly: It is necessary to introduce the current-density of matter separately from the energy-momentum tensor." I'm not asking what's the nature of the conservation mechanism, but which literature started to make a distinction between conservation of mass-energy vs matter. Eckart does. Maybe a separate conservation of matter was already discussed in the 19th century? @Conifold $\endgroup$
    – pglpm
    Commented Apr 28 at 22:52
  • $\begingroup$ Eckart might have been the only one to use "conservation of matter" in this sense, it did not take. Schmid, for example, has no such expression although he follows Eckart and has particle density distinct from mass density. He also gives references to earlier papers on relativistic fluid dynamics by Herglotz, Lamla and Synge. You can check if they had what you are looking for (probably without the name). $\endgroup$
    – Conifold
    Commented Apr 28 at 23:53


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