## Interplay of Theory Development with Physical Reality

What’s the relation of theories of physics to the actual physical reality they are describing? A naive answer would be something like “Theories are formed by making enough experiments and deducing a common law from the results. As more experiments are made, the theory with its laws becomes a more correct description of reality”. This, however is a simplistic way to describe the situation, as no amount of supporting special cases counts as an actual logical proof for a general statement, and usually there’s a need to already have at least some degree of a “pre-theory” before one can even make any experiments.

Suppose someone wants to study the behavior of matter at different temperatures. The things measured could involve thermal expansion of a metal rod, pressure changes upon heating a gas in a rigid container, or something similar. Actually, to even be able to measure a temperature, one has to make several assumptions about the physical laws related to it. When we immerse one end of a thermometer in a kettleful of hot water, we assume that only the temperature of the thermometer changes significantly, and the hot water stays at a very close to constant temperature as the thermometer and water reach thermal equilibrium. So there we already need to have some kind of a common-sense notion of heat capacity, whatever we decide to call that thing at that point of constructing a theory of thermodynamics. In particular, we assume that if an object has either a very small mass or small volume, it takes only a small amount of “thermal energy” to change its temperature.

Also, the concept of thermal equilibrium itself requires some assumptions that are not obvious in principle. The Zeroth Law of Thermodynamics says that if Object 1 and Object 2 are in thermal equilibrium with each other, and Object 2 is in equilibrium with Object 3, then the Objects 1 and 3 are also in mutual thermal equilibrium. A kind of an equivalence relation, but this time in physics instead of pure mathematics (another example of an equivalence relation in physics is found when forming a set of all scalar-vector potential combinations resulting in the same electric and magnetic fields). We need to do this assumption before we can measure temperatures based on the thermal expansion of some material, as the equilibration needs to be able to be transmitted forward through the material that we are trying to expand by heating it. So, to measure temperature we need to have some kind of an intuitive notion of thermal equilibrium, and also assume that the length of a metal rod or column of mercury or ethanol is a single-valued function of temperature in the range of conditions we are doing the experiments in. This may seem like a chicken-and-egg problem where we need to define temperature to study thermal expansion, and also know a law of thermal expansion to be able to define temperature. The same situation is apparent in the SI definition of the unit of length as an exact fraction of the distance travelled by light in a second, despite the fact that distance measurements were done by people for quite a long time before someone even got the idea of the constancy of speed of light. This circularity problem doesn’t cause as much trouble as one may think, as you can try different kind of theories combining assumptions about temperature and thermal expansion and make a lot of tests on every theory, trying to find a contradiction between the theory and experimental fact, and trust that in the case of wrong assumptions it will become apparent that something fishy is going on. Or of course if there’s a logical contradiction in the theory with itself then it must be wrong no matter what the experiments tell.

Some things that are usually assumed about thermal equilibration include that it proceeds monotonously towards its conclusion, and doesn’t do strange things like the thermometer reading oscillating around some value before setting to equilibrium (in other words, the thermal impact given to the thermometer by the hot liquid doesn’t cause an effect similar to how a mechanical impact affects a physical pendulum in absence of supercritical damping). This assumption is not always true in thermodynamics, as oscillating chemical reactions like the BZ reaction show (first academic papers about oscillating reactions were actually initially rejected from publication because they were so much against the common sense notions about chemical kinetics and thermodynamics at the time).

The temperature/thermal equilibrium example was a rather simple one, but a lot more difficult problem are the differences of the theory of relativity and quantum mechanics to the classical Newtonian mechanics, where one finds out a necessity to accept physical laws that are very difficult to form a mental image about and that are against conventional common sense (however, it must be admitted that even the classical Newton’s first law is not intuitively obvious on the surface of the Earth where there are frictional forces damping almost every form of motion).

Philosophical theories about the nature of successive scientific theories include the Karl Popper’s theory where the most important feature of a scientific theory is thought to be its falsifiability, which means that the theory must be “vulnerable” to experimental evidence in the sense that the theory can’t be somehow cleverly bent to fit any possible experimental results (in the same way how illogical features in a religious belief system can be justified by saying “Inscrutable are the Lord’s ways”). Other philosophers who have investigated the subject include Thomas Kuhn and Paul Feyerabend. In Kuhn’s theory in particular, the very concept of “objective physical reality” is questioned, and it’s said that to be able to talk about physical reality one always has to do that in reference to some particular theoretical framework.

Actually I recently got (for free) a book related to this subject, C. Dilworth’s “Scientific Progress – A Study Concerning the Nature of the Relation Between Successive Scientific Theories”, and it seems to contain a lot of interesting material but I haven’t managed to read very far through it. I hope the links in this blog post help someone who’s trying to find info about this subject.

## About the NASA’s TRAPPIST-1 findings

Yesterday, I was excitedly following the NASA press conference about the exoplanets found orbiting the star TRAPPIST-1 located 39 light years from earth. When I heard the day before that they’re going to announce something, the first idea that came to my mind was that they must have observed a combination of organic molecules and oxygen in some distant planet’s atmosphere, which would be a chemical nonequilibrium state that is difficult to explain without some kind of biology being present. Yes, of course you can’t have an atmosphere where there’s something like a mixture of methane and oxygen that is within flammability limits, but even very small concentrations of hydrocarbons and other organic compounds are apparently possible to notice from the IR spectrum of a distant object.

Actually, they didn’t have any spectral data yet, which could be used to make conclusions about the chemical composition of the atmospheres (that will be obtained later), but they had information about the masses, orbit radii and cross-sectional areas of the planets (these can be deduced from the oscillation of the star’s apparent position, see link “reduced mass“, and from the dimming of the light of the star when a planet temporarily moves past it), and the planet densities were too large for them to be gas-planets. Also, the temperatures of three of them seemed to be in the range where water can exist as a liquid at reasonable pressures.

Actually, a planet doesn’t necessarily need to even be in the so called habitable zone to possibly have liquid water – even on Mercury, the hottest planet on our Solar system, there are places that are always in shadow and can actually get quite cold because the rate of heat conduction through large masses of rock is slow compared to the rate of radiative heat loss to space. Therefore liquid water could exist in such places if contained inside some kind of “pocket” that would also protect it from low pressures. Also, the icy surface of Jupiter’s moon Europa can hide liquid water beneath it, because the tidal forces from Jupiter cause viscous (frictional) heating inside the moon, despite it being way too far from the Sun to be inside the definition of “habitable zone“.

So, more interesting stuff is probably coming, as the astronomers obtain infrared spectra from that star system.

Also, see the related discussion in Physics Forums here.

The featured image is from Wikimedia Commons.