## lördag 28 maj 2016

### Aristotle's Logical Fallacy of Affirming the Consequent in Physics

One can find many examples in physics, both classical and modern, of Aristotle's logical fallacy of Affirming the Consequent (confirming an assumption by observing a consequence of the assumption):
1. Assume the Earth rests on 4 turtles, which keeps the Earth from "falling down". Observe that the Earth does not "fall down". Conclude that the Earth rests on 4 turtles.
2. Observe a photoelectric effect in accordance with a simple (in Einstein's terminology "heuristic") argument assuming light can be thought of as a stream of particles named "photons" . Conclude that light is a stream of particles named photons.
3. Assume light is affected by gravitation according the general theory of relativity as described by Einstein's equations. Observe apparent slight bending of light as it passes near the Sun in accordance with an extremely simplified use of Einstein's equations. Conclude universal validity of Einstein's equations.
4. Observe lift of a wing profile in accordance with a prediction from potential flow modified by large scale circulation around the wing. Conclude that there is large scale circulation around the wing.
5. Assume that predictions from solving Schrödinger's equation always are in perfect agreement with observation. Observe good agreement in some special cases for which the Schrödinger equation happens to be solvable, like in the case of Hydrogen with one electron. Conclude universal validity of Schrödinger's equation, in particular for atoms with many electrons for which solutions cannot be computed with assessment of accuracy.
6. Assume there was a Big Bang and observe a distribution of galaxy positions/velocities, which is very very roughly in accordance with the assumption of a Big Bang. Conclude that there was a Big Bang.
7. Assume that doubled CO2 in the atmosphere from burning of fossil fuel will cause catastrophic global warming of 2.5 - 6 C. Observe global warming of 1 C since 1870. Conclude that doubled CO2 in the atmosphere from burning of fossil fuel will cause catastrophic global warming of 4 - 8 C.
8. Assume that two massive black holes merged about 1.3 billion years ago and thereby sent a shudder through the universe as ripples in the fabric of space and time called gravitational waves and five months ago washed past Earth and stretched space making the entire Earth expand and contract by 1/100,000 of a nanometer, about the width of an atomic nucleus. Observe a wiggle of an atom in an instrument and conclude that two massive black holes merged about 1.3 billion years ago which sent a shudder through the universe as ripples in the fabric of space and time called gravitational waves...
9. Observe experimental agreement of the anomalous magnetic dipole moment of the electron within 10 decimals to a prediction by Quantum Electro Dynamics (QED). Conclude that QED is universally valid for any number of electrons as the most accurate theory of physics. Note that the extremely high accuracy for the specific case of the anomalous magnetic dipole moment of the electron, compensates for the impossibility of testing in more general cases,  because the equations of QED are even more impossible to solve with assessment of accuracy than Schrödinger's equation.
The logic fallacy is so widely practiced that for many it may be difficult to see the arguments as fallacies. Test yourself!

PS1. Observe that if a theoretical prediction agrees with observation to a very high precision, as is the case concerning the Equivalence Principle stating equality of inertial and gravitational (heavy) mass, then it is possible that what you are testing experimentally in fact is the validity of a definition, like testing experimentally if there are 100 centimeters on a meter (which would be absurd).

PS2 Books on quantum mechanics usually claim the there is no experiment showing any discrepancy whatsoever with solutions of the Schrödinger equation (in the proper setting), which is strong evidence that the Schrödinger equation gives an exact  description of all of atom physics (in a proper setting). The credibility of this argument is weakened by the fact that solutions can be computed only in very simple cases.