Condensed matter theories are notorious for not being able to predict spectacular results/effects before the experiments were done. What they often do is to rationalize experimental results that are already known. I agree that there are a few exceptions to this rule. The brilliant exceptions are: (1) Josephson effect, (2) Abrikosov flux lattice, (3) fractional quantum Hall effect etc. Are there many more of such brilliant theories in condensed matter physics? Can you please elaborate? Even BCS theory is useless to predict and find a new superconductor! In contrast theories like Newtonian mechanics, quantum theory and relativity showed spectacular predictive power and often the experiments were only done well after the prediction. Of course condensed matter theory is hardly fundamental in that sense and is actually applied quantum mechanics (not everyone will agree) of many particle systems.
Magnetoelectricity has first been predicted (somewhat naive) Pierre Curie and later Dzyaloshinskii following Landau and Lifshitz predicted, based on symmetry analysis, that chromia would be a candidate to show the linear magnetoelectric effect. One year later in 1960 Astrov measured the linear magnetoelectric effect in chromia. In general, symmetry analysis makes prediction about all sorts of possible effects some of them have been demonstrated others are still waiting to be found.
I am well aware of the emergent aspect of condensed matter physics and also the famous Anderson slogan "More is different". Surely more is different and surely fundamental laws of nature, the so-called theory of everything (TOE) that the particle physicists are hoping to pin down in near future is actually a 'theory of nothing" for the vast natural world of condensed matter and biology. Heisenberg cannot explain "a blade of grass"; the nature that we see in front of our eyes does not have the symmetry of the fundamental laws and it is hardly possible to reproduce this complexity of the nature from these laws directly. The symmetry breaking is the most fundamental principle to understand the visible world; the consequent emergent phenomena lead to the shape and nature of the universe. To understand this is not too difficult but to produce a predictive theory of the condensed matter and more complex biological world is certainly another thing. The story of the prediction of finding such and such planet in such and such position of the sky simply from the calculations of Newtonian mechancis and focusing the telescope and finding the planet at exactly the same position is an wonderful experience. Or think of Einstein's prediction of the bending of light in the strong gravitational field and his complete confidence that Eddington's experiment will either find that or his experiment is completely flawed. This is something that fascinates us. (Max Plank could not sleep well because he was worried about the outcome but Einstein slept very well because he was confident - the story goes!). Well condensed matter theory has not predicted anything as dramatic and we do not also expect that. Now take the example of the theory of supercoonductivity. It took almost half a century to produce a theory (BCS) after the experiment established this most dramatic emergent phenomenon of the condensed matter. But this theory does not help you really to find a new superconductor! Do you call this a predictive theory?
It may be worthwile pointing out that predictions are rarer than you might think. What are the predictive successes of quantum mechanics? The hydrogen atom was known well before. The great triumphs were rather to *explain* such phenomena as the specific heats of metals and gases, black-body radiation, molecular binding, radioactive decay and more other effects than I can think of. But which were predicted? Bell inequality violations are the one and only that occur to me (but that may be my lack of knowledge). Even for Newtonian mechanics: we have LeVerrier's discovery of Neptune as an extraordinary prediction, but that can hardly be called the best argument in favour of Newtonian dynamics. Again, the important achievements of Newtonian mechanics lay probably more in what it explained than in what it predicted. In this respect, I believe condensed matter does quite well.
I disagree. First, the fractional quantum Hall effect was not predicted before the experiment. Second, there have been many predictions which have been successfully confirmed later.
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