– By Byron Jennings, Theorist and Project Coordinator
July 17 marks the 99th anniversary of the death of Henri Poincaré. Henri who? You may well ask. He was just an ordinary, run of the mill genius: engineer, mathematician, physicist and philosopher. Believe me, you have to be a genius to be both an engineer and a philosopher. As an engineer he carried out the investigation into the 1879 Magny mining disaster. As a physicist he introduced the ideas of relativity, using light beams to synchronize watches and is attributed by some as the real inventor of special relativity. In mathematics, he is known for the Poincaré conjecture in topology and the beginning of chaos theory. But it is his philosophy that I want to explore here.
Poincaré was the father of what is known in philosophical circles as conventionalism: what others regarded as laws derived by the scientific method he regarded as convenient hypotheses or conventions. Two examples he gave are the geometry of space-time and Newton’s laws of motion. The following is typical of this thought (Science and Hypothesis, 1904): “Whether the ether exists or not matters little – let us leave that to the metaphysicians; what is essential for us is, that everything happens as if it existed, and that this hypothesis is found to be suitable for the explanation of phenomena. After all, have we any other reason for believing in the existence of material objects? That, too, is only a convenient hypothesis; only, it will never cease to be so, while some day, no doubt, the ether will be thrown aside as useless.” For him, even the existence of material objects was just a convenient hypothesis. This might seem extreme but he was spot on about the ether, a cornerstone of physics in 1904, but which Einstein’s paper the following year demolished.
To put more flesh on the idea of conventionalism and show that it is not ridiculous, consider the notion of a fixed earth: this is the old Copernicus vs Ptolemy or Galileo vs the Catholic Church story. Poincaré would have regarded it as a convention that the earth is not stationary. Ah you say, did not Galileo give the definitive answer with his telescope? Not at all. While the telescope did get rid of the Ptolemaic system, Tycho Brahe came up with an alternative: a fixed earth orbited by the sun and the other planets then orbiting the sun (the Duhem-Quine Thesis strikes again). So, is there any way to settle the question of the absolute motion of the earth? No, all we can measure is the motion of earth with respect to something else: the sun, the center of Galaxy, the fixed stars, the cosmological three degree microwave background or specified inertial frame. Take any arbitrary frame you like (I prefer the one where I am the center of the universe, your mileage may vary) and there is a well-defined mathematical transformation from any of the previously mentioned frames to this new one. We can use that transformation to write all the laws of physics consistently in the new frame.
This is not relativity – either special or general – which has the same laws in different frames. Here the laws are different in the different frames – different but well defined. The earth fixed description has some peculiarities:
- The laws of physics depend on the distance from the center of the earth. But hey, since we have assumed the earth is the center of the universe this is good and proper.
- There are forces, generated by the above-mentioned mathematical transformation, that depend on the behavior of cosmological microwave background (perhaps Mach’s principle).
The choice of frame is due to convenience. Tycho Brahe’s model lost to Copernicus’s due to the difficulty of using it for planetary motion. However for the motion of stars within the Galaxy, we do not use a sun-center frame but a Galaxy centered frame and for cosmological calculations we use a still different frame. But the most widely used frame of all is that of a fixed earth. Ptolemy rules! Good models never die. Consider giving directions from TRIUMF to the UBC physics department (about a mile away, to use obsolete units). Now in a sun-centered frame, UBC is rapidly moving due to the rotation of the earth and its orbital motion. Thus the directions would have to be time dependent and even a small mistake in following them would have the person lost in space. Even worse then not taking that left ‘toin’ in ‘Albakoikie’ (Bugs Bunny, Herr meets Hare, 1945).
That’s classical mechanics, quantum mechanically things are even worse. What is well defined in classical mechanics may become ambiguous in quantum mechanics. A prime example is the unitary transformation that changes all kinds of things around but leaves observations untouched. One of the most commonly used concepts in both classical and quantum mechanics is the potential. The gravitational potential holds us on the earth and the earth in its orbit (sun-centered frame). The nuclear potential holds the nucleus together, but, but, but, the potential can change dramatically under unitary transformations, from strongly repulsive at short distances to highly non-local. The actual form used is no more and no less than a convention – a convenient hypothesis.
How do you choose the best convention? That is simplicity itself.
– to be continued –
