Historically speaking, the conservation of energy has been deduced from the quantitive physical theories from the Renaissance onwards. Gradually the importance of this law was recognised and eventually placed at the pinnacle of physical science. It was the quantitative nature that allowed for the empirical discovery that something was being conserved. This is the empirical & scientific view.

But when we look at energy as a substance, that is something that remains conserved through accidental change, we see in fact that the conservation of energy is a law that characterises the meaning and the substance of energy. This is a philosophical view - we have here an invention of a concept.

Certainly, I feel the first paragraph is correct. I'm unsure of the second. It seems very likely that this must be true. But I've never seen this argument made before. Has this indeed been done (or disputed) by someone?


Given that there are several conservation laws in physics - angular momentum, linear momentum etc. One needs to modify the above observation; and simply say are there substances in physics? Is there only one substance or many substances. If there are many then one cannot convert (part of) one to another as that would violate its identity as a substance.

Historically, the conservation of mass is the first discovered and probably dates from antiquity although I have no plausible reference for it.

The angle I'm trying to aim for is that conservation is important from 'purely' philosophical aims in the idea of substance; in the same way that indivisibility is important for the idea of atoms which does date from antiquity (and is paid homage to in Newtons Principia).

  • The distinction between induced versus induced properties is definitely interesting when applied to thermodynamics like this. (I might try to respond to this, maybe via Spinoza -- though it would help if you might talk a little more about what you might be reading around this/have found out already)
    – Joseph Weissman
    May 27, 2013 at 3:31
  • Meillassoux also seems possibly relevant here (I am thinking of the arguments about contingency in After Finitude.)
    – Joseph Weissman
    May 27, 2013 at 13:45
  • @Weissman: I do know that the idea of substance occupies a central role in Spinozas philosophy, but my understanding is that he's not aiming towards physical understanding - would you care to expand a little? May 27, 2013 at 14:00
  • @weissman: I'm not familiar with After Finitude - it certainly looks interesting. Badiou, in the preface points out he makes all the laws of nature contingent - which isn't I think quite what the idea of substance is about. Were you thinking of something else? May 27, 2013 at 14:02
  • Well, I think I'm probably struck most here at this possible convergence between univocal substance and radical contingency (in Spinoza and Meillassoux); the fact we don't know (the limits of) what a body (the universe!) can do... :)
    – Joseph Weissman
    May 27, 2013 at 14:48

3 Answers 3


But when we look at energy as a substance, that is something that remains conserved through accidental change, we see in fact that the conservation of energy is a law that characterises the meaning and the substance of energy.

Conservation of (mass-)energy isn't the only conservation law. IMO, that wrecks the second paragraph of the question.

  • fair enough, but historically conservation of mass was the first discovered. Perhaps the name substance may even refer to it. But you're right, one needs to consider the possibility of no substances or a plurality of substances. May 27, 2013 at 14:06

Firstly, as Gugg correctly points out, there exist other converved quantities. Hence, you can't say "energy is the quantity which is being preserved*, because then you have no way of distinguishing energy from, say, total mass, or total momentum.

Secondly, it is a fairly non-trivial fact that there exist conserved quantities. To the best of my knowledge, physicists (and mathematicians) have done a fair amount of research into the question of existence of such quantities - see for instance Noether's Theorem. Hence, you can't just "characterise the meaning and the substance of energy" by the conservation law, until you have established that there is a conserved quantity out there to be characterised - and to do that, you have to identify the quantity in any case.

  • yes, I do realise that noethers theorem establishes a link between symmetries of a space and conserved quantities; and this can be used to deduce new spaces and symmetries for quantities that are conserved but for which no sensible space is immediately apparent; for example local U(1) space for the electromagentic charge. I'll change my question as you and Gugg are correct in that the is inappropriate. May 27, 2013 at 13:14
  • Of course, once one decides that there is a plurality of substances then one must needs identify them. The angle I'm going for is that conservation is important, in the same way indivisibility in atoms is important too. May 27, 2013 at 13:42

One must be careful when contemplating about the potential existence (or abstaction of) "substance" for the cases where we observe something conserved. The danger is that an ordinary "property" which one may not consider calling as a "substance" would be what is actually conserved. Consider the conservation of various properties of (say, the velocity of) "center of mass" in certain kinds of multi-partical interactions when there are no external forces. In that case, "velocity of the center of mass" remains constant! Who would call "velocity of center of mass" of such self-interacting particals as a "substance"?

As another thing, as noted by @Feanor above, Noether's Theorem requires that there must be a related symmetry whenever there is a physically preserved quantity. Before calling the preserved quantity as substance or associating it with a substance-as-a-philosophical concepty/entity, one must examine the related symmetry and see if it is closer to be associated with a "substance" than the related quantity. It is not immediately clear whether the symmetry comes first (broader than) or the conserved quantity if one is tempted to talk about existence of a related substance. Independent of your view, one must see that at least the relation between the symmetry and conservation law is symmetric and in certain aspects in certain cases, related symmetry seems to be more general than the observed conservation law (and conserved quantity).

Based on this, for the energy example, we would have philosophical/mathematical/metaphisical reasons to avoid assigning a substance to energy; instead we could see it as an ordinary property (as ordinary or arbitrary as "velocity of center of mass") which do not deserve any philosophical interest compared to "space/time invariance" of the natural forces. I mean a more meaningful allocation of "substance" would be not with energy but time-invarience because of the reasons above. So the related laws may not be seen about the nature of "substance" (of energy).

  • Is the velocity of the centre of mass a conserved quantity? Consider a stone thrown through the air. May 27, 2013 at 21:43
  • Yes, given that there are NO EXTERNAL forces as I noted in the answere! In your example there is GRAVITATION! Even in this case, when there is an external force like gravitation, this time "accelaration of the center of mass" is a constant! Just replace velocity property with acceleration and you give yet another example of an invariant property.
    – mami
    May 27, 2013 at 23:13
  • Somehow, if i could not make myself clear in the original answer, you may try this: If you be too hasty to call "energy" as a kind of substance, you may be expected to assing some kind of substance to "velocity / acceleratio etc. of center of masss" as well. Are you volunteer to do that? I am trying to warn about a possible trap here. Because of seemingly more essential symmetries (of natural forces), you may find many conserved quantities which might be byproduct (like momentum for instance) and you may never be willing to contemplate a substance about them. Why should be energy different?
    – mami
    May 27, 2013 at 23:23

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