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Different kinds of physical theories

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Back in the day – even as late as the 19th century1 – many philosophers wanted to explain the world using the "mechanical philosophy". This meant explaining nature in terms of pushing, pulling, levers, pulleys – the kinds of forces a human intuitively understands. Nature was a big mechanical machine, the task is just to guess its inner workings. As Laplace put it (though he didn’t subscribe to a strict mechanical philosophy)2

Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.

Of course, this idea is dead, finished off by quantum mechanics at the latest: we know that quantum mechanics can’t be classical and thus can’t work in terms of point contact forces. However, even Newton’s gravity uses instant long-range forces instead, so the strict mechanical philosophy had already suffered a blow by then.

In more modern times, Einstein spent a lot of time thinking about what kinds of theories are appropriate. He reflected on what sorts of different theories physics has. He divided theories in to two categories: principle and constructive. Let me illustrate by example.

In the kinetic theory of gases, you start from the assumption that a gas consists of a bunch of molecules. You can’t see them directly, but suppose they are there anyway. You can then derive a bunch of facts about thermodynamics that can be directly checked by experiment. Thus we start from some model of what’s really going on – molecules whizzing about – and experimental predictions follow indirectly. This sort of theory is a "constructive" theory: it constructs the empirical facts from an underlying physical model. The mechanical philosophy sought to find a model consisting of contact forces, so they were trying to make a constructive theory.

Principle theories start from the other direction. You take some observed facts and elevate them to immutable facts (principles). Einstein himself had done this with relativity: special relativity starts from assuming that the speed of light and the laws of physics are the same for all inertial observers. Things like length contraction and time dilation then follow by logical necessity. Another example is Newton’s laws, including gravity. He inferred them from observation with no attempt to explain how gravity gets from one point to another, or "what’s really going on".

Which kind of theory is better? When we want to explain something, we seem to automatically reach for a constructive theory. Imagine the following scenario3. An airplane is taking off with a helium balloon inside. It floats towards the cockpit. Why?

Well, it’s quite simple. The airplane’s acceleration causes the air to become packed towards the back of the plane. Helium, being lighter than air, gets pushed towards teh front, where the pressure is lower. We could even explain the specific mechanism in terms of the kinetic theory of gases.

This is certainly a good explanation – it nicely provides us with a picture of what’s happening. There is, however, another potential "explanation".

According to general relativity, one accelerating frame is as good as another. Helium balls in Earth’s gravitational accelerating frame float upwards. So, they must do that in the plane’s accelerating frame too, since there’s no essential difference between the two.

This latter explanation is perfectly true. There is something unsatisfactory about it, though. It doesn’t give us a picture of what’s going on – it just says that IF it floats in gravity, it goes towards the cockpit in the accelerating plane.

Similar principle explanations would be that there can’t be an energy-spawning machine due to conservation of energy. A waterfall can’t fall upwards for the same reason. In special relativity, if we know the length of a rod in one frame, we know how much it contracts in another moving frame.

Since principles are just carefully selected and generalized experimental facts, it is difficult to give them up. So you can use them to constrain further theories – like quantum field theory was constructed by looking for a relativistic quantum mechanics.

On the other hand, constructive theories are easier to change. The entities they are based on are not directly observable, thus "anything goes" as long as the predictions are ultimately correct.

Quantum mechanics is traditionally a constructive theory, starting from quantization rules for particles. Yet a mechanism for explaining measurement is lacking, leading to multiple interpretations of quatnum mechanics. Some have interpreted this problem as quantum mechanics failing to be fully constructive 4. Perhaps we should try to write it as a principle theory instead?5

Constructive theories explain, principle theories constrain 6. To build a constructive theory, one has to be creative in guessing the internal mechanism. To make a principle theory, one has to carefully choose the right experimental facts to start from. Both have their uses. Einstein himself said it best 7:

The advantages of the constructive theory are completeness, adaptability, and clearness, those of the principle theory are logical perfection and security of the foundations.

  1. Even Maxwell in his famous paper "On physical lines of force" (1862) used mechanical devices like gears and idlers to model electromagnetism. ↩

  2. Laplace 1902 ("Philosophical Essay on Probabilities") ↩

  3. Originally problably due to Salmon 1989 ("Four Decades of Scientific Explanation"). ↩

  4. Van Camp 2011 ("Principle theories, constructive theories, and explanation in modern physics") ↩

  5. Clifton, Bub, Halvorson 2003 ("Characterizing Quantum Theory in terms of Information-Theoretic Constraints") ↩

  6. Also discussed in Felline 2011 ("Scientific Explanation between Principle and Constructive Theories") Lange 2014 ("Did Einstein Really Believe that Principle Theories are Explanatorily Powerless?") ↩

  7. Einstein 1919 ("What is the Theory of Relativity?") ↩