Scientists’ greatest pleasure comes from theories that derive the solution to some deep puzzle from a small set of simple principles in a surprising way. These explanations are called “beautiful” or “elegant”. Historical examples are Kepler’s explanation of complex planetary motions as simple ellipses, Bohr’s explanation of the periodic table of the elements in terms of electron shells, and Watson and Crick’s double helix. Einstein famously said that he did not need experimental confirmation of his general theory of relativity because it “was so beautiful it had to be true.” See:2012 : WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION?
See which comments resonate with you. Some of my picks as I go through was by :
Professor of Theoretical Physics, Berkeley
My Favorite Annoying Elegant Explanation: Quantum Theory …….General Relativity, in turn, is only a classical theory. It rests on a demonstrably false premise: that position and momentum can be known simultaneously. This may a good approximation for apples, planets, and galaxies: large objects, for which gravitational interactions tend to be much more important than for the tiny particles of the quantum world. But as a matter of principle, the theory is wrong. The seed is there. General Relativity cannot be the final word; it can only be an approximation to a more general Quantum Theory of Gravity.
But what about Quantum Mechanics itself? Where is its seed of destruction? Amazingly, it is not obvious that there is one. The very name of the great quest of theoretical physics—”quantizing General Relativity”—betrays an expectation that quantum theory will remain untouched by the unification we seek. String theory—in my view, by far the most successful, if incomplete, result of this quest—is strictly quantum mechanical, with no modifications whatsoever to the framework that was completed by Heisenberg, Schrödinger, and Dirac. In fact, the mathematical rigidity of Quantum Mechanics makes it difficult to conceive of any modifications, whether or not they are called for by observation.
Yet, there are subtle hints that Quantum Mechanics, too, will suffer the fate of its predecessors. The most intriguing, in my mind, is the role of time. In Quantum Mechanics, time is an essential evolution parameter. But in General Relativity, time is just one aspect of spacetime, a concept that we know breaks down at singularities deep inside black holes. Where time no longer makes sense, it is hard to see how Quantum Mechanics could still reign. As Quantum Mechanics surely spells trouble for General Relativity, the existence of singularities suggests that General Relativity may also spell trouble for Quantum Mechanics. It will be fascinating to watch this battle play out.
Physical Reality Could Be Hugely More Extensive Than the Patch of Space and Time Traditionally Called ‘The Universe’ …..As an analogy (which I owe to Paul Davies) consider the form of snowflakes. Their ubiquitous six-fold symmetry is a direct consequence of the properties and shape of water molecules. But snowflakes display an immense variety of patterns because each is molded by its distinctive history and micro-environment: how each flake grows is sensitive to the fortuitous temperature and humidity changes during its growth.
If physicists achieved a fundamental theory, it would tell us which aspects of nature were direct consequences of the bedrock theory (just as the symmetrical template of snowflakes is due to the basic structure of a water molecule) and which cosmic numbers are (like the distinctive pattern of a particular snowflake) the outcome of environmental contingencies. .
An Explanation of Fundamental Particle Physics That Doesn’t Exist Yet…..What is tetrahedral symmetry doing in the masses of neutrinos?! Nobody knows. But you can bet there will be a good explanation. It is likely that this explanation will come from mathematicians and physicists working closely with Lie groups. The most important lesson from the great success of Einstein’s theory of General Relativity is that our universe is fundamentally geometric, and this idea has extended to the geometric description of known forces and particles using group theory. It seems natural that a complete explanation of the Standard Model, including why there are three generations of fermions and why they have the masses they do, will come from the geometry of group theory. This explanation does not yet exist, but when it does it will be deep, elegant, and beautiful—and it will be my favorite.
A Sphere….Most scientific facts are based on things that we cannot see with the naked eye or hear by our ears or feel by our hands. Many of them are described and guided by mathematical theory. In the end, it becomes difficult to distinguish a mathematical object from objects in nature.
One example is the concept of a sphere. Is the sphere part of nature or it is a mathematical artifact? That is difficult for a mathematician to say. Perhaps the abstract mathematical concept is actually a part of nature. And it is not surprising that this abstract concept actually describes nature quite accurately.
Gravity Is Curvature Of Spacetime … Or Is It?……We do not yet know the full shape of the quantum theory providing a complete accounting for gravity. We do have many clues, from studying the early quantum phase of cosmology, and ultrahigh energy collisions that produce black holes and their subsequent disintegrations into more elementary particles. We have hints that the theory draws on powerful principles of quantum information theory. And, we expect that in the end it has a simple beauty, mirroring the explanation of gravity-as-curvature, from an even more profound depth.
Quasi-elegance….As a young student first reading Weyl’s book, crystallography seemed like the “ideal” of what one should be aiming for in science: elegant mathematics that provides a complete understanding of all physical possibilities. Ironically, many years later, I played a role in showing that my “ideal” was seriously flawed. In 1984, Dan Shechtman, Ilan Blech, Denis Gratias and John Cahn reported the discovery of a puzzling manmade alloy of aluminumand manganese with icosahedral symmetry. Icosahedral symmetry, with its six five-fold symmetry axes, is the most famous forbidden crystal symmetry. As luck would have it, Dov Levine (Technion) and I had been developing a hypothetical idea of a new form of solid that we dubbed quasicrystals, short for quasiperiodic crystals. (A quasiperiodic atomic arrangement means the atomic positions can be described by a sum of oscillatory functions whose frequencies have an irrational ratio.) We were inspired by a two-dimensional tiling invented by Sir Roger Penrose known as the Penrose tiling, comprised of two tiles arranged in a five-fold symmetric pattern. We showed that quasicrystals could exist in three dimensions and were not subject to the rules of crystallography. In fact, they could have any of the symmetries forbidden to crystals. Furthermore, we showed that the diffraction patterns predicted for icosahedral quasicrystals matched the Shechtman et al. observations. Since 1984, quasicrystals with other forbidden symmetries have been synthesized in the laboratory. The 2011 Nobel Prize in Chemistry was awarded to Dan Shechtman for his experimental breakthrough that changed our thinking about possible forms of matter. More recently, colleagues and I have found evidence that quasicrystals may have been among the first minerals to have formed in the solar system.
The crystallography I first encountered in Weyl’s book, thought to be complete and immutable, turned out to be woefully incomplete, missing literally an uncountable number of possible symmetries for matter. Perhaps there is a lesson to be learned: While elegance and simplicity are often useful criteria for judging theories, they can sometimes mislead us into thinking we are right, when we are actually infinitely wrong.
The Higgs Mechanism……Fortunately that time has now come for the Higgs mechanism, or at least the simplest implementation which involves a particle called the Higgs boson. The Large Hadron Collider at CERN near Geneva should have a definitive result on whether this particle exists within this coming year. The Higgs boson is one possible (and many think the most likely) consequence of the Higgs mechanism. Evidence last December pointed to a possible discovery, though more data is needed to know for sure. If confirmed, it will demonstrate that the Higgs mechanism is correct and furthermore tell us what is the underlying structure responsible for spontaneous symmetry breaking and spreading “charge” throughout the vacuum. The Higgs boson would furthermore be a new type of particle (a fundamental boson for those versed in physics terminology) and would be in some sense a new type of force. Admittedly, this is all pretty subtle and esoteric. Yet I (and much of the theoretical physics community) find it beautiful, deep, and elegant.
Symmetry is great. But so is symmetry breaking. Over the years many aspects of particle physics were first considered ugly and then considered elegant. Subjectivity in science goes beyond communities to individual scientists. And even those scientists change their minds over time. That’s why experiments are critical. As difficult as they are, results are much easier to pin down than the nature of beauty. A discovery of the Higgs boson will tell us how that is done when particles acquire their masses.
The True Rotational Symmetry of Space…..Although this excercise might seem no more than some fancy and painful basketball move, the fact that the true symmetry of space is rotation not once but twice has profound consequences for the nature of the physical world at its most microscopic level. It implies that ‘balls’ such as electrons, attached to a distant point by a flexible and deformable ‘strings,’ such as magnetic field lines, must be rotated around twice to return to their original configuration. Digging deeper, the two-fold rotational nature of spherical symmetry implies that two electrons, both spinning in the same direction, cannot be placed in the same place at the same time. This exclusion principle in turn underlies the stability of matter. If the true symmetry of space were rotating around only once, then all the atoms of your body would collapse into nothingness in a tiny fraction of a second. Fortunately, however, the true symmetry of space consists of rotating around twice, and your atoms are stable, a fact that should console you as you ice your shoulder.
Remember even though I pick some of these explanations does not mean I discount all others. It’s just that some are picked for what they are saying in highlighted quotations. Lisi’s statement on string theory is of course in my opinion far from the truth, yet, he captures a geometrical truth that I feel exists.:) You sort of get the jest of where I am coming from in the summation of Paul Steinhardt