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Beauty is Truth? (interview)

#1
C C Offline
http://iainews.iai.tv/articles/beauty-is-truth-auid-484

=EXCERPT= [...QUESTION:] Why is it rational to use the simpler theory to explain phenomena? Could using this approach lead us to something which is beautiful but untrue? Is beauty perhaps a distraction?

JOE BUTTERWORTH: Given that science is experimental, it’s unlikely to settle on something that’s actually wrong, because in the end it has to be judged against what we observe. But yes, it’s certainly true that beauty could be a distraction, that people could place too much weight on the aesthetic concerns when really the data is telling us something different. It’s certainly true that we could go the wrong way because of our prejudice to follow what we think is the simpler model or simpler theory. But you have to use whatever guide you can find. In the end, the data keep you honest. If you’re not meeting the data, you’re not really doing science; you’re doing maths or something else entirely....
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#2
Magical Realist Offline
The data will not tell you how to assess the data, what parts of it you will selectively emphasize or ignore, and what theory will be used to make sense of it. And even then, there may NOT be a simple and beautiful equation behind it all. One had hoped after all the elaborate mathematical reductions of relativity and quantum mechanics over the last century we'd be left with beautifully simple explanation of ferromagnetism. Alas, twas not to be. Here's that explanation in all of its contrived and muddled messiness:

"The Bohr–van Leeuwen theorem, discovered in the 1910s, showed that classical physics theories are unable to account for any form of magnetism, including ferromagnetism. Magnetism is now regarded as a purely quantum mechanical effect. Ferromagnetism arises due to two effects from quantum mechanics: spin and the Pauli exclusion principle.

Origin of magnetism

One of the fundamental properties of an electron (besides that it carries charge) is that it has a magnetic dipole moment, i.e., it behaves like a tiny magnet. This dipole moment comes from the more fundamental property of the electron that it has quantum mechanical spin. Due to its quantum nature, the spin of the electron can be in one of only two states; with the magnetic field either pointing "up" or "down" (for any choice of up and down). The spin of the electrons in atoms is the main source of ferromagnetism, although there is also a contribution from the orbital angular momentum of the electron about the nucleus. When these magnetic dipoles in a piece of matter are aligned, (point in the same direction) their individually tiny magnetic fields add together to create a much larger macroscopic field.

However, materials made of atoms with filled electron shells have a total dipole moment of zero, because every electron's magnetic moment is cancelled by the opposite moment of the second electron in the pair. Only atoms with partially filled shells (i.e., unpaired spins) can have a net magnetic moment, so ferromagnetism only occurs in materials with partially filled shells. Because of Hund's rules, the first few electrons in a shell tend to have the same spin, thereby increasing the total dipole moment.

These unpaired dipoles (often called simply "spins" even though they also generally include angular momentum) tend to align in parallel to an external magnetic field, an effect called paramagnetism. Ferromagnetism involves an additional phenomenon, however: The dipoles tend to align spontaneously, giving rise to a spontaneous magnetization, even when there is no applied field.

According to classical electromagnetism, two nearby magnetic dipoles will tend to align in opposite directions, so their magnetic fields will oppose one another and cancel out. However, this effect is very weak, because the magnetic fields generated by individual spins are small and the resulting alignment is easily destroyed by thermal fluctuations. In a few materials, a much stronger interaction between spins arises because the change in the direction of the spin leads to a change in electrostatic repulsion between neighboring electrons, due to a particular quantum mechanical effect called the exchange interaction. At short distances, the exchange interaction is much stronger than the magnetic dipole-dipole interaction. As a result, in a few materials, the ferromagnetic ones, nearby spins tend to align in the same direction. In certain doped semiconductor oxides RKKY interactions have been shown to bring about periodic longer-range magnetic interactions, a phenomenon of significance in the study of spintronic materials.[10]

The exchange interaction is related to the Pauli exclusion principle, which says that two electrons with the same spin cannot also have the same "position". Therefore, under certain conditions, when the orbitals of the unpaired outer valence electrons from adjacent atoms overlap, the distributions of their electric charge in space are further apart when the electrons have parallel spins than when they have opposite spins. This reduces the electrostatic energy of the electrons when their spins are parallel compared to their energy when the spins are anti-parallel, so the parallel-spin state is more stable. In simple terms, the electrons, which repel one another, can move "further apart" by aligning their spins, so the spins of these electrons tend to line up. This difference in energy is called the exchange energy.

The materials in which the exchange interaction is much stronger than the competing dipole-dipole interaction are frequently called magnetic materials. For instance, in iron (Fe) the exchange force is about 1000 times stronger than the dipole interaction. Therefore below the Curie temperature virtually all of the dipoles in a ferromagnetic material will be aligned. The exchange interaction is also responsible for the other types of spontaneous ordering of atomic magnetic moments occurring in magnetic solids, antiferromagnetism and ferrimagnetism. There are different exchange interaction mechanisms which create the magnetism in different ferromagnetic, ferrimagnetic, and antiferromagnetic substances. These mechanisms include direct exchange, RKKY exchange, double exchange, and superexchange."===http://en.wikipedia.org/wiki/Ferromagnetism
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