How The Laws Of Physics Lie

The title is Nancy Cartwright’s, from her book of the same name, and from an article which forms Chapter 3, “Do the Laws of Physics State the Facts?” No, she says, and we agree. I thought it well to summarize this chapter before we review work by David Deustch.

I have no proof of it, but physicists must use the same PR firm computer scientists do. The names these guys come up with are brilliant: neural nets, black holes, artificial intelligence, quasars, realism. This last is the philosophical position that says physicists’ models are Reality, and not just models of Reality. “Anti-realist” critics of this view start back on their heels (“What? You’re against Reality!?”), a great disadvantage.

I don’t like “anti-realism”. So I shall call Cartwright’s view (which I share) Pro-Reality, and will call the other view Model Reification.

Cartwright takes the Pro-Reality view. In my words, this pronounces an anathema on all forms of the Deadly Sin of Reification, even the popular ones.

Now you don’t need this review. The link above is to the book, and you can read it. I will be leaving out much, and adding my own gloss. Consult the book for greater detail.

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Cartwright says “that the laws of physics do not provide true descriptions of reality”, and that “that our explanatory laws do not tell us what they do. It is in fact part of their explanatory role not to tell.”

She proves this starting with the “law” of gravitation, which you will recognize:

F = GMm/r^2,

where F is the force, G is a constant, M and m the masses of two bodies, and r the distance between them.

Cartwright asks if this “law” accurately describes how bodies behave. “Assuredly not,” she says. You might quail at that. But suppose the two bodies are two magnets; or, in her example, two electrically charged bodies. Or suppose there are more than two “neutral” or massed bodies in the universe. Or suppose there is air between them, hence friction, or even a so-called quantum vacuum lies between, in which particles are supposed to pop in an out of existence.

Speaking more carefully, the law of universal gravitation is something like this:

If there are no forces other than gravitational forces at work, then two bodies exert a force between each other which varies inversely as the square of the distance between them, and varies directly as the product of their masses.

She allows that this might be true, “But it is not a very useful law.” Because, as is obvious, of that no other forces bit. Which never happens. The gravity “law” only explains ideal, which is to say unobservable, or approximate situations. Saying the “law” is universal involves an extrapolation in thought, an induction to what cannot be observed; i.e. no observational verification is possible of the situation where only—the word is strict!—gravity between M and m is in play. You must grasp this before moving on.

Most scientists think “nature is governed by a small number of simple, fundamental laws.” We observe “complex and varied phenomena, but these”, scientists think, “are not fundamental.” Complexity arises, most scientists say, “from the interplay of more simple processes obeying the basic laws of nature.”

In other words, it’s all “laws”, which is why, most physicists believe, we’ll some day find a “general unified theory”, a single equation that governs all behavior.

That will never happen, because the Model Reification view gets it all backwards. Once you get this, which you won’t on first reading, and especially if you’ve had training in the sciences, you see everything fresh and new.

The “laws” view itself comes from the drive to reduce everything to abstractions. The yen to make models of Reality and say those models are Reality. When what we really want—and this will be no surprise to regular readers—is knowledge of cause.

An objection that will have occurred to you is this: why not treat the forces of the “laws” acting on (say) the magnets from gravity and also separately from magnetism? Indeed, most scientists have the “presumption […] that the explanatory laws ‘act’ in combination just as they would ‘act’ separately…actual [observed] behaviour is the resultant of simple laws in combination.” Like a tug-of-war game.

With my emphasis:

Our example, where gravity and electricity [or electromagnetism] mix, is an example of the composition of forces. We know that forces add vectorially. Does vector addition not provide a simple and obvious answer to my worries? When gravity and electricity are both at work, two forces are produced, one in accord with Coulomb’s law, the other according to the law of universal gravitation. Each law is accurate [they say]. Both the gravitational and the electric force are produced as described; the two forces then add together vectorially to yield the total ‘resultant’ force.

The vector addition story is, I admit, a nice one. But it is just a metaphor. We add forces (or the numbers that represent forces) when we do calculations. Nature does not ‘add’ forces. For the ‘component’ forces are not there, in any but a metaphorical sense, to be added; and the laws that say they are there must also be given a metaphorical reading…

In interaction a single force occurs—the force we call the ‘resultant’—and this force is neither the force due to gravity nor the electric force. On the vector addition story, the gravitational and the electric force are both produced, yet neither exists.

She gives the example of motion: “When a body has moved along a path due north-east, it has travelled neither due north nor due east. The first half of the motion can be a part of the total motion; but no pure north motion can be a part of a motion that always heads northeast.” Yes, we can model the motion as a vector addition, and model it well—but the body isn’t doing the math!

All is not lost. It is not that the “laws” are wrong in every way. Indeed, they can be saved. The way to save gravity and Coulomb and so on is via the composition of causes: the “laws” aren’t laws in the sense they are strict operative proscriptions by Nature. They instead “describe the causal powers that bodies have.” That means the objects themselves act by the powers they possess, or they are acted on by other bodies with the powers they have, but nothing is being acted on by “laws”. “Laws” are not forces: things have causal powers.

[T]he law of gravitation claims that two bodies have the power to produce a force of size GMm/r^2. But they do not always succeed in the exercise of it. What they actually produce depends on what other powers are at work, and on what compromise is finally achieved among them…the laws we use talk not about what bodies do, but about the powers they possess.

In contrast to “fundamental laws” like gravity there are phenomenological descriptions, which are closer to Reality, because they model directly observations or phenomena. She gives examples like Fourier’s law for heat flow and Ohm’s law for current. They are “ceteris paribus” descriptions, saying only what will happen if all else equal.

The basic laws on influence, like Coulomb’s law and the law of gravity, may give true accounts of the influences that are produced; but the work of describing what the influences do, and what behavior results, will be done by a variety of complex and ill-organized laws of action: Frick’s law [of diffusion] with correction factors and the like.”

To play the role in explanation we demand of them, these laws [of nature] must have the same form when they act together as when they act singly. In the simplest case, the consequences that the laws prescribe must be exactly the same in interaction, as the consequences that would obtain if the law were operating alone. But then, what the law states cannot literally be true, for the consequences that would occur if it acted alone are not the consequences that actually occur when it acts in combination.

If we state the fundamental laws as laws about what happens when only a single cause is at work, then we can suppose the law to provide a true description. The problem arises when we try to take that law and use it to explain the very different things which happen when several causes are at work.

Simple summary: there are no “laws” of nature operating on objects; there are objects with causal powers operating on other objects, and where we can grasp or model these powers to some extent.

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