IIB. The Successes and Unity of Quantum Mechanics.

We need to see how successful quantum mechanics is, for two reasons.  First, it convincingly shows us that the physical universe is governed by mathematical laws.  And second, we will see that its successes are sufficient to warrant basing a metaphysical scheme of existence, at least in part, on it.  

1. Never Wrong.

Where it can be applied, quantum mechanics never gives a wrong answer.  There is an enormous range of phenomena to which quantum mechanics can be applied (see what follows), and there are only two kinds of situations where it cannot be applied.  The first is when the calculations are too complicated--for example, in trying to calculate the properties of large molecules.  And the second is gravity; quantum mechanics and gravity have not yet been reconciled.  I do not feel that this implies there is anything fundamentally wrong with quantum mechanics.

2. Classical Physics.

Some of classical physics can be derived from quantum mechanics.  (Properties like friction are too complicated to derive from quantum mechanics.)  So the successes in predicting the orbits of planets, trajectories of charged objects in electromagnetic fields and so on ultimately rests with quantum mechanics.  Further all the classical particlelike properties—mass, energy, momentum, angular momentum and charge—with all their attendant characteristics, are a consequence of the equations of quantum mechanics.

3. Atomic Properties.

The electronic structure of each atom can have many different possible energy levels, and the differences of those energies can be measured by measuring the wavelength of light given off.  Quantum mechanics predicts those energy levels, many of them to an accuracy of better than one part in a hundred million.  It also correctly predicts the chemical properties of the atoms.

4. Properties of Semiconductors.

The properties of the semiconductors used in all modern electronic devices—used to make the chips in computers and so on—are correctly predicted by quantum mechanics.  Through these applications, it is estimated that one third of the GDP depends on “quantum” devices.

5. Lasers.

Lasers are designed using quantum mechanics, and their properties are correctly predicted by the theory.

6. Nuclear Properties.

As in the atom, each nucleus has many different energy levels, and the differences can be measured by measuring the wavelengths of the light (or x-rays) given off.  Quantum mechanics also predicts these energy levels, but not with the precision of the atomic levels.  This understanding of nuclear properties allows astrophysicists to correctly predict many properties of stars.

7. Elementary Particles.

There are a host of successful applications here, especially from the Standard Model of strong and electroweak interactions.  There currently is no known failure of quantum mechanics in this area.  And even if there were a failure, there is a good chance it would be in the details (of the Hamiltonian) rather than in the basic principles (linearity, relativistic invariance and internal symmetry groups).

8. Unity.

The argument in favor of quantum mechanics being “the” theory of the physical universe does not rest only on successes in particular areas.  Its unity is truly astonishing.  All the phenomena of nature follow from very few equations.  As one example, the properties of electric and magnetic fields, light, infrared radiation, ultraviolet radiation, x-rays and gamma rays all follow from the four Maxwell equations (which are the quantum mechanical equations for lightlike wave functions).  And these same equations can be extended to include the weak nuclear interactions.

9. The Anomalous Magnetic Moment.

One last example.  The electron and muon are elementary particles.  How they act in a magnetic field is determined in part by their magnetic moments (roughly, related to how fast “the particles” are spinning).  The variation of the magnetic moment from its simple value of 2 has recently been measured to a few parts in a hundred billion.  To compare theory and experiment, over 800 quantum mechanical calculations (one for each Feynman diagram) had to be done.  Experiment and theory agreed (to within experimental error).  One could hardly ask for a more striking example of the mathematical nature of the physical universe!

10. Summary

The successful range of applications of quantum mechanics to the inanimate world is enormous.  When this is coupled with item 1 above, it seems clear that the physical universe is governed by mathematics (all is number, says Pythagoras).  Further, it seems reasonable to use quantum mechanics to deduce something of the true nature of physical reality.