Friday, July 19, 2019

Energy conservation

On a Humean metaphysics, energy conservation implies a vast conspiracy in the arrangement of things throughout spacetime, somewhat like this:

  1. Wherever there is a change in energy in one region there is a corresponding balancing change in another region.

In an Aristotelian causal powers metaphysics, energy conservation implies a fact like the following about every physical substance x:

  1. Every causal power of x whose content includes an effect on the energy of one or more substances also includes a balancing reverse effect on x’s own energy.

That no physical substance simply has a power to affect the energy of another substance, without the content of that power having to include a balancing effect on one’s own energy, is deeply surprising. It is a conspiracy almost as surprising as (1).

These conspiracies strongly suggest that neither the Humean nor the Aristotelian metaphysics is the whole story about energy conservation. The conspiracies desperately call for explanation. I know of two putative explanations: an optimalist one (on which reality strives for value, and mathematically expressible patterns are a part of the value) and a theistic one. Both of these explanations, however, really do great violence to the spirit behind Humean metaphysics. But Aristotelian metaphysics with optimalism or theism explaining the conspiracy in (2) works just fine.

Of course, the problem can also be solved by a different metaphysics, one on which the behavior of objects is explained by pushy global laws. But it is harder to fit human freedom and agency into that metaphysics than into the Aristotelian one.


Michael Gonzalez said...

I don't see the problem in the deterministic sort of chain reaction cases (viz., if something is acted on, and the energy produces action on its part, and it thus acts on something else, etc). I can't see where any "new" energy would come from, or why the energy transferred from one step in the chain to another shouldn't just be regarded as (at least, in some important senses) the very same energy that has continually been handed off at each link in the chain.

When it comes to first order, active causation (such as that of a self-mover, like an animal or a person), there is a sort of leap; but, of course, Aristotle himself gives the step between the two levels, namely the "nutritive soul" or the level of explanations characteristic of a living creature. But, still, we do regard the energy we expend in our actions as having been borrowed from the creatures we ate, who in turn borrowed it from the Sun, etc....

Alexander R Pruss said...

On an Aristotelian metaphysics, energy isn't a thing that moves from one substance or another. It's just a way of describing the accidents of the substance. There is no compelling metaphysical reason why when substance A causes substance B to gain an accident of heat, substance A should lose an accident of heat at the same time. For on orthodox Aristotelianism, the accident isn't moving from one substance to another: A loses one accident and B gains another accident.

I see no metaphysical reason why an object couldn't have the causal power to increase the heat of things around it without itself becoming colder. Many Aristotelians are Thomists, and Thomists believe in immaterial angels. An immaterial angel could speak to a group of people. In doing so, it would be making the air vibrate and hence heat up. But the angel wouldn't be losing energy, because immaterial things don't have any energy.

Michael Gonzalez said...

I think on pretty much any view, immaterial beings acting in the material world violates the conservation of energy. But, in any case, I see now what you mean about the Aristotelian view.... Hm. Could we define the powers in terms that necessitate giving something up?

Alexander R Pruss said...

Even if we necessitate giving something up, why should it be *energy*?

(Maybe another thing to investigate is explaining why the dynamics is Hamiltonian. For given that, Noether's theorem will yield conservation of energy from temporal isotropy.)

Walter Van den Acker said...


If energy isn't a "thing" that moves from one subtsnce to another, in what way can substance A be said to "cause" substance B to gain an accident? It seems to me there must be something from A that somehow "goes" to B.

Alexander R Pruss said...


Leibniz thought that, too, which is why he concluded that there was no real causation between distinct substances (unless the cause was God; I am not sure why he thought himself entitled to that exception). But it seems mistaken to think of causation as a transfer of some entity.

Walter Van den Acker said...


Actually, I think it is mistaken not to think of causation as a transfer of some entity. I mean, if an entity X causes another entity Y to do something, 'something' (whatever that something may be) must go from X to Y. If that isn't the case, saying that X causes something in Y doesn't seem to mean anything at all.

Unknown said...

Noether's theorem (or a generalization of) accounts for the big-name conservation laws, even down to QFT. Really anything that can be stated in a Lagrangian (or Hamiltonian) formulation.

I think this does really affect the interpretative work we have to do. For example, the Lagrangian minimizes the Action, and this is given as brute instead of the conservation laws themselves. I think a minimalization-of-action metaphysics of a (largely) symmetrical universe doesn't really seem prima facie bad, and certainly better than "there's just conservation laws". It is as above not inherently teleological since you can just define it to optimize over possible worldpaths, but it fits nicely into a teleological definition as well.

Alexander R Pruss said...

Noether's theorem requires two things:
1. minimization of action
2. symmetries.
Both are puzzling on the Humean and Aristotelian pictures, indeed I think just as puzzling as the conservation laws. (Leibniz talked of how special cases of 1 provided an argument for the existence of God.)