Deducing the Stars

The following cartoon recently appeared on my Facebook feed, courtesy of Beatrice the Biologist.

This provides a neat illustration of the difference between how a biologist approaches nature and how a physicist approaches nature. Here is perhaps the greatest astrophysicist of the twentieth century, Sir Arthur Stanley Eddington, in his book “The Internal Constitution of the Stars” (1926, pg. 16).

We can imagine a physicist on a cloud-bound planet who has never heard tell of the stars calculating the ratio of radiation pressure to gas pressure for a series of globes of gas of various sizes, starting, say, with a globe of mass 10 gm., then 100 gm., 1000 gm., and so on, so that his nth globe contains 10ⁿ gm. Table 2 shows the more interesting part of his results.

The rest of the table would consist mainly of long strings of 9’s and 0’s. Just for the particular range of mass about the 33rd to 35th globes the table becomes interesting, and then lapses back into 9’s and 0’s again. Regarded as a tussle between matter and aether (gas pressure and radiation pressure) the contest is overwhelmingly one-sided except between Nos. 33-35, where we may expect something interesting to happen.

What “happens” is the stars.

We draw aside the veil of cloud beneath which our physicist has been working and let him look up at the sky. There he will find a thousand million globes of gas nearly all of mass between his 33rd and 35th globes — that is to say, between 1/2 and 50 times the sun’s mass. The lightest known star is about 3 x 10³² gm. and the heaviest about 2 x 10³⁵ gm. The majority are between 10³³ and 10³⁴ gm. where the serious challenge of radiation pressure to compete with gas pressure is beginning.

If Sir Tube Worm Eddington is clever enough, then he would be able to work out possible sources of energy in the universe. Building on the work of Spider Crab Newton, Fangtooth Maxwell and Viperfish Schrodinger, T.W. Eddington could reason as follows.

• Given the crush of gravity, the Earth cannot be too large or it could not be supported by atomic forces. Gravity will have moulded the Earth into a sphere, and there must be an upper surface to the water. The entire universe cannot be rock and water.
• The laws of thermodynamics and radiation imply that the Earth is cooling at a certain rate, radiating energy into space. This rate is too fast for hydrothermal vents to maintain a liquid ocean. There must be another energy source.
• Following A.S. Eddington’s argument above, our wormy friend could discover that an astronomical body in which the crush of gravity was countered by thermal pressure could ignite and sustain nuclear reactions, and so radiate copious amounts of energy for billions of years. Gravity could maintain a planet in a stable orbit around such a “star”.

(It is interesting to think about how – and, especially, whether – a physicist underwater could discover what we’ve discovered about the laws of nature. The step from Aristotle to Newton would have been much more difficult, as fluid resistance is essentially never negligible underwater. But that is a topic for another day.)

If, on the other hand, if T.W. Eddington’s predecessor’s had discovered that their universe’s gravity is a “one over radius cubed” (rather than squared) law that will not allow stable planetary orbits, or that nuclear ignition temperatures are too high for stable stars to form, then they could conclude that such an energy source will not be found shining on the ocean surface.

The moral: if you know the laws of nature, at least in the relevant regimes, then you know what kinds of objects are stable, and thus what kinds of objects one might expect to find in the universe. This is not mere presumption or hubris – this is astrophysics. In fact, this is how many good astrophysicists textbook begin (e.g. Padmanabhan). Also, if you can see a couple a tens of billions of light years into the universe, and if the laws of nature that you have discovered are doing a sterling job of explaining your observations, then your inferences about what kinds of objects are possible and likely are on a firm footing.

There is more to physics than raw observation. We have discovered mathematical laws, the kinds of simple laws that living things just don’t seem to follow. This does not reflect a failing on the part of biologists, but rather the complexity of biology. Faced with questions like “what kind of thing could emit energy?”, a physicist would not answer “well, let me go check my 2015 Illustrated Field Guide to Energy Emitters”.