Is causality absent from physical laws?

Is it true, as Bertrand Russell claimed, that the laws of nature as we know them involve only functional relations between successive states, with no reference to “causes” and “effects”?  And if it is true, is that because of all the possible laws of nature, acausal ones turned out to be the ones that are instantiated, or are acausal laws the only ones we’ve ever formulated to model the real world with?

In fact, when using the equations intended to describe the physical world, one most often does have an idea which term is the cause and which term is the effect.  For example, in Newton’s Law


everybody intuits that it is the force that causes the acceleration and not vice versa.  Or when considering the diffusion of heat

\frac{\partial T}{\partial t} = \nabla\cdot(D \nabla T)

we know that it’s the temperature gradient that drives heat, rather than vice versa.  Or in the Schroedinger equation

i\hbar \frac{\partial}{\partial t}\Psi = H\Psi

the Hamiltonian operator drives the evolution, not vice versa.

The question is whether this asymmetry is in the equations themselves or is imposed by a metaphysical intuition of their users.

For equations like the above, we might postulate that the effect is always the term that appears under the highest time derivative.  This rule does match my intuition in every case I’ve thought of.  One source of confusion, I think, is that philosophers tend to insist on seeing causes and effects as existing at different instances of time.  I think it would be closer to the truth to say that cause and effect are always simultaneous.  The effect is not the subsequent state, but the time derivative itself, which exists simultaneously with its cause.

Question:  is the language of causality inappropriate for relations that don’t involve time derivatives?  I’ve been reading John Losee’s Theories of Causality (following its mention on Edward Feser’s blog), and it seems that some philosophers have said this.  I do have an intuition that in

\nabla\cdot E = 4\pi\rho

it’s the field that’s the effect of the charge density.  However, this intuition is not as strong as the other.  One could reduce this case to the previous ones by noting that the above is actually the time component of the equation

d*F = 4\pi *J

and the spatial components (Ampere’s Law) have time derivatives in them.  However, my intuition was there long before I knew this.

One might ask what I make of this

\nabla\cdot B = 0

Would I say that zero is the cause of the magnetic field having no divergence?  That would be silly.  I suppose one could add a magnetic monopole density to the right hand side and say that the cause of \vec{B} having no divergence is that this density happens to be zero.  However, I’m uncomfortable with ascribing real causative power to absences and with irreducible references to couterfactuals (issues that also comes up a lot in Losee’s book).  The alternative is to say that being divergenceless is the default for things like the magnetic field, that given its nature it needs an external cause only to explain deviations from this.

Causality is something I’m very interested in but that I’ve only just started thinking about seriously, so I’m going to hold off on making any conclusions, except for the following.  It is not clear that asymmetries in physical equations cannot be used to distinguish causes from effects.

18 Responses

  1. Another thing to remember is that universals cause particulars, rather than vice versa.

    Thus gravity causes acceleration, for instance, because there are universal laws regarding how gravity functions, however there are no such laws regarding how objects accelerate, except as derived from laws regarding gravity, EM, and the like.

  2. In his sadly neglected Grammar of Assent, Bl John Henry Newman expresses a sceptical view of physical causality. The [passage is worth quoting at length:-

    “One of the first experiences of an infant is that of his willing and doing; and, as time goes on, one of the first temptations of the boy is to bring home to himself the fact of his sovereign arbitrary power, though it be at the price of waywardness, mischievousness, and disobedience. And when his parents, as antagonists of this wilfulness, begin to restrain him, and to bring his mind and conduct into shape, then he has a second series of experiences of cause and effect, and that upon a principle or rule. Thus the notion of causation is one of the first lessons which he learns from experience, that experience limiting it to agents possessed of intelligence and will. It is the notion of power combined with a purpose and an end. Physical phenomena, as such, are without sense; and experience teaches us nothing about physical phenomena as causes…

    As time goes on, and society is formed, and the idea of science is mastered, a different aspect of the physical universe presents itself to the mind. Since causation implies a sequence of acts in our own case, and our doing is always posterior, never contemporaneous or prior, to our willing, therefore, when we witness invariable antecedents and consequents, we call the former the cause of the latter, though intelligence is absent, from the analogy of external appearances. At length we go on to confuse causation with order; and, because we happen to have made a successful analysis of some complicated assemblage of phenomena, which experience has brought before us in the visible scene of things, and have reduced them to a tolerable dependence on each other, we call the ultimate points of this analysis, and the hypothetical facts in which the whole mass of phenomena is gathered up, by the name of causes, whereas they are really only the formula under which those phenomena are conveniently represented.”

    Comte had drawn a similar distinction between “laws” and “causes.”

  3. Cardinal Newman’s understanding here seems to me to be basically the same as Hume’s, save more elegantly worded and sophisticatedly reasoned out.

  4. The first section of Feser’s Scholastic Metaphysics is about causality and is a good primer on various problems.

  5. John K

    I would suggest Newman’s effectively limiting “causality” to volition owes more to Bishop Berkeley than to Hume.

  6. Michael Paterson-Seymour,

    That is fair enough, but as I understand him, he still reaches a rather Humean conclusion with regards to physical causality – according to him, what appears to us to be the causality of physical things is, at bottom, simply “constant conjunction” mistaken for volition.

    At any rate, I don’t quite see why leaning on either Hume or Berkeley (or Comte, for that matter) is supposed to lend credence to Newman’s argument.

  7. Newman goes astray with most of the rest of the tradition, in my opinion, in thinking of effects as subsequent to causes rather than simultaneous, and he holds to a regularity view of causality that I would reject. From Losee’s book, it seems that philosophers have multiple things in mind when they design causality theories: what causality is, how we first become aware of it, and how it can validly be inferred. I am only interested in the first. The psychological fact that we become aware of causality through our own acts of volition and the epistemic fact that we infer causality through observed regularities and correlations concern other issues.

  8. Bonald,
    Physics is not reducible to equations and formulae.
    “The physicist seeks through mathematics an understanding that is not entirely mathematical.”
    CS Lewis — The Discarded image.
    It is this non-mathematical understanding that we call “causality”.
    Eg Are anthropogenic CO2 emissions causing global warming?
    This question is meaningless unless causality exists.
    Causality is an arrow between two different things.

  9. The Einstein equation G=8*pi*T, we intuit that the stress-energy T “causes” the space to curve. So explicit time-dependence is not necessary,
    PS I would replace “metaphysical intuition” with “physical intuition”.

  10. Effect is consequent to the cause, rather than subsequent. That is, there must exist a particular relation between the two things. The relation which is intuited by the mind from observations but does not reduce to observations (that would be regularity view).

  11. Bonald

    As to your question, “what causality is,” the obvious answer is that it is an abstraction. To ask “What is causality?” and to ask “How is the word ‘causality’ used?” are two forms of the same question.

    I can easily imagine a language that had no word for “cause,” but that had a great many words that we, with our notion of “cause,” should identify as “causal” verbs – scrape, push, wet, carry, eat, burn, squash, hurt and so on.

    As to how we learned to use those “causal verbs,” the answer is simple enough. As children, in the same way that we learned to report from seeing it that the cat was on the table, we also learned to report, from observation, that the cat knocked over the milk jug and lapped up the milk, that the dog made a funny noise, or that things were cut or broken by whatever we saw cut or break them.

    Hume muddied the waters by assuming that, if an effect occurs in one case and a similar effect does not occur in an apparently similar case, there must be a further relevant difference. Now, this may or may not be true, but it cannot possibly be derived from observation and why should we assume that necessary connection is implicit in the notion of cause and effect? I could use and understand all the “causal verbs” I have listed without making that particular assumption.

  12. > The Einstein equation G=8*pi*T, we intuit that the stress-energy T “causes” the space to curve. So explicit time-dependence is not necessary

    Yeah, but there are time derivatives in G.

  13. > I could use and understand all the “causal verbs” I have listed without making that particular assumption.

    Quite true. Invariable effectiveness is not part of what we mean by causality.

  14. […] Last time I suggested a couple of rules on efficient causality. […]

  15. I had in mind Hume’s definition, “The idea of cause and effect is derived from experience, which informs us, that such particular objects, in all past instances, have been constantly conjoined with each other: And as an object similar to one of these is supposed to be immediately present in its impression, we thence presume on the existence of one similar to its usual attendant.”

    That is why I selected examples that do not fit it very well, if at all.

  16. I don’t know if you read comments on your older posts, but at any rate it seems to me, that your idea of the highest time derivative necessarily being the effect is wrong.

    Consider e.g. Faraday’s law: -dB/dt=rot(E)
    Would you really claim that the electromotoric force in a generator with rotating magnets is the cause of the changing magnetic field?

    Generally, dA/dt=B simply means that if there is some B then A must be changing in time, and if A changes in time there must be some B, but I don’t see that it makes sense to call either one the cause of the other in general. I strongly suspect that one needs a temporal sequence to speak of causality in any meaningful way.

  17. That’s a very good counter-example. I’ll think about it.

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