olegt
Posts: 1405
Joined: Dec. 2006
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Granville Sewell does a great impression of one blind man and the elephant in his post Fine-tuning of the constants AND equations of Nature? He writes some silly things about the Schroedinger equation.
| Quote | | The Schrodinger partial differential equation of quantum mechanics is the heart of atomic physics. This elegant PDE governs the behavior of all particles under the fundamental forces, but, unlike other PDEs, it cannot be derived from simpler principles. Like time, space, matter and energy, it “just is”. To quote from one of my PDE books, “Schrodinger’s equation is most easily regarded as simply an axiom that leads to the correct physical conclusions, rather than as an equation that can be derived from simpler principles…In principle, elaborations of it explain the structure of all atoms and molecules and so all of chemistry.” |
First, Schroedinger's equation is a good first approximation for the understanding of atomic physics (electrons plus nuclei), but it won't work for two other fundamental forces: weak and strong interactions. You need a relativistic quantum theory for those and the Schroedinger describes the non-relativistic limit. No creation or annihilation of particles, no photons even! Second, it can be derived from a more fundamental theory: it is the non-relativistic limit of the Dirac equation in quantum electrodynamics. Schroedinger's equation misses the relativistic spin-orbit coupling (a rather significant interaction at the heavier end of the periodic table), while Dirac's gets it right.
| Quote | | The Schrodinger equation contains a parameter, h, called Planck’s constant, which is one of the many constants of Nature that is very “fine-tuned”: change it a little bit and you get a universe that cannot support any imaginable forms of life. Now I know enough mathematics and physics to be sure that most changes to this equation itself would result in a universe that could not have supported life; the properties of the elements in the periodic table certainly depend sensitively on the properties of this magnificent PDE. There may be some ways to modify it without disasterous results (I doubt it); but there is no doubt that the Schrodinger equation itself is very fine-tuned for life. |
Actually, Planck's constant is now simply viewed as the conversion factor between frequency and energy, in the same sense as the speed of light c is the conversion factor between the units of time and length (the SI no longer has an independent standard of length: it is based on the standard of time). The one and only* physical parameter in atomic physics is the fine-structure constant alpha = e^2/h-bar c. This parameter determines the properties of atoms and thus affects chemistry. For a while, physicists have tried to find out "why" alpha has the value of approximately 1/137.036. Now we know that alpha is not a fundamental constant of nature: the Standard Model of particle physics predicts (and particle experiments confirm) that alpha grows at higher energies. One can of course say that the parameters of the Standard Model are fine-tuned for life, but sooner or later we'll find what determines them and creationists will just move on to the next gaps in the knowledge.
| Quote | | So I think to explain our existence without design, we not only have to imagine some cosmic random-number generator which churns out values for Planck’s constant and the other constants, but also a cosmic random-equation generator. Are we to assume that in all these other universes imagined by man to explain our existence, the behavior of particles is still governed by the Schrodinger equation, but the forces, masses and charges, and Planck’s constant have random values? Or perhaps the behavior of particles is governed by random types of PDEs in different universes, but there are still many universes in which Schrodinger’s equation holds, with random values for Planck’s constant? No doubt there were some universes which couldn’t produce life because the governing equation looked just like the Schrodinger equation, but with first derivatives in space where there should be second derivatives, or a second derivative in time where there should be a first derivative, or the complex number i was missing, or the mass was in the numerator, or the probability of finding a system in a given state was proportional to |u| rather than |u|^2?? |
Ironically, Dirac's equation is linear in the spatial derivatives and it is valid in our Universe. What a bunch of nonsense!
*ETA: apart from the electron mass.
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