On explanations and causality within physics

I recently watched a video by philosophers Massimo Pigliucci (City University of New York) and Daniel Kaufman (Missouri State University) discussing differences in styles of explanation between the natural sciences and the social sciences. There’s a lot in the video that I agree with, but I want to dissent on one issue. That is, I don’t agree that causality is as central to explanations within physics as the video suggests, and thus the differences with the social sciences are less pronounced than suggested. (Though, having said that, I do agree that there is one very big difference in that biological entities exhibit purpose and intention, whereas physical entities do not.)

Pigliucci and Kaufman suggest that “explanations” within the physical sciences are typically in terms of causation, and thus are of the form of pointing to antecedent causal events that are sufficient to explain subsequent events. They also discuss “laws of physics” as being “widely generalisable causal relations”.

I would instead say that physical laws are often not about causes and are just descriptive. They would thus be “widely generalisable descriptive relations”. The meaning of “explanation” within physics is also much broader than just causal explanations. More generally, “explanations” are linkages between descriptions of different aspects of the system. All systems, simple or complex, can be (partially) described in different ways, and if we show how those descriptions link together then we “explain”.

I’ll illustrate the above with some examples, starting with one of Kepler’s laws of planetary motion.

Kepler’s first law states that the orbit of a planet is an ellipse with the Sun at one of the two foci. That is not a causal law, since it makes no statement about what causes the planet to move that way and instead only describes the motion.

We now know that the planet moves in an ellipse because gravity obeys an inverse-square law. It was Newton’s great breakthrough that showed that elliptical motion would follow from a centripetal force whose magnitude scales as the inverse-square of the separation. Yet the statement that gravity obeys an inverse-square law is also descriptive rather than causal. That is, the statement is not in the form of pointing to antecedent events which cause subsequent ones.

If we then ask why gravity can be modelled with an inverse-square law, we could reply that it is because space is three dimensional, and thus that, as gravitational influence spreads out, the space over which the influence spreads increases as the surface area of a sphere, which scales as the radius squared. Again, though, this explanation is not one in terms of causation, in the sense of pointing to antecedent events that cause subsequent ones.

If one wanted a causal account of this in terms of events, one could give an account in terms of gravitons travelling between the Sun and the planet, thus causing the planet to move as it does, but there would then be quite an involved train of explanation between the causation by gravitons and Kepler’s descriptive laws.

As a second example, let’s turn to the gas laws, and in particular take Boyle’s Law, which states that, if one takes a given quantity of gas and keeps the temperature constant, then the product of its volume times the pressure is a constant. If one doubled the volume, one would halve the pressure.

Again, that is descriptive rather than causal, since it doesn’t attempt to explain why that is the case. If we were to explain Boyle’s Law we’d say something like this: if one increased the volume of a container, then gas molecules would have further to travel before bouncing off a wall, and so would do so less often. It is the molecules hitting against the wall that causes pressure, and so less frequent hits means lower pressure.

That indeed is a causal explanation (“molecules hitting against the wall that causes pressure”), but note that it is not about one event that causes a subsequent event, it is about the aggregate of events within the container. Further, “pressure” is not an “event”, rather it is an accounting concept that summarises the effect of the aggregate of events. Thus the concept of pressure is not of the form “Event X causes Event Y”, it is rather a commentary about the behaviour of the ensemble.

So, again, what counts as explanation in physics is much broader than the basic causality of an antecedent event explaining a subsequent event.

For another example let’s turn to the First Law of Thermodynamics, which is the concept that energy is conserved. What is “energy”? It is not a “thing” (not an ontological entity) and it is not an event. Rather, “energy” is a commentary about a system. It so happens that, from the description of a system, one can construct the accounting concept “energy”. For example, taking half the mass of a particle and multiplying it by the square of its velocity gives one form of energy (though there are also other forms).

The reason that this accounting concept is useful is that the energy does not change with time (it is “conserved”) and thus keeping track of it is useful for analysing the behaviour of a system. The reason that “energy” does not change with time is that, at a very basic level, the behaviour of physical stuff is the same at all times.

It was the great mathematician Emmy Noether who proved that if a physical system has a “symmetry”, for example showing the same basic behaviour at all different times, then there would be an accounting-concept quantity that could be measured and would be conserved, and in this case that concept is energy.

Again, none of the above is about basic causation of the form “Event X causes Event Y”, instead it is about descriptions of the system as an ensemble, and it is about how different descriptions in terms of different concepts link to each other. And those linkages between descriptions are what we call “explanations”.

Explanations directly in terms of causation are one form of explanation. They are a very important form, and indeed we can say that we do not understand a system unless we can give causal explanations, or at least outlines of causal explanations, for its behaviour. But other forms of explanation are just as important and are often just as useful.

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