From Quanta Magazine ( notice original story here ).

"Insanity is doing the same thing over and over and expecting different results."

That witticism—I'll call it "Einstein Insanity"—is usually attributed to Albert Einstein. Though the Matthew outcome may be operating here, it is undeniably the sort of clever, memorable one-liner that Einstein frequently tossed off. And I'm happy to give him the credit, because doing and so takes us in interesting directions.

First of all, note that what Einstein describes as insanity is, co-ordinate to quantum theory, the fashion the world actually works. In quantum mechanics you can practice the same affair many times and get different results. Indeed, that is the premise underlying great high-energy particle colliders. In those colliders, physicists fustigate together the same particles in precisely the same mode, trillions upon trillions of times. Are they all insane to do so? It would seem they are non, since they have garnered a stupendous variety of results.

Of grade Einstein, famously, did not believe in the inherent unpredictability of the globe, saying "God does not play dice." Yet in playing dice, we human activity out Einstein Insanity: Nosotros do the same matter over and over—namely, roll the dice—and we correctly anticipate different results. Is it really insane to play dice? If so, it'south a very common grade of madness!

Nosotros can evade the diagnosis by arguing that in practise one never throws the die in precisely the same way. Very modest changes in the initial conditions can change the results. The underlying idea here is that in situations where we tin can't predict precisely what's going to happen next, it'south because there are aspects of the electric current situation that nosotros haven't taken into account. Similar pleas of ignorance can defend many other applications of probability from the accusation of Einstein Insanity to which they are all exposed. If we did accept full access to reality, according to this argument, the results of our deportment would never be in doubtfulness.

This doctrine, known as determinism, was advocated passionately by the philosopher Baruch Spinoza, whom Einstein considered a great hero. But for a meliorate perspective, nosotros need to venture fifty-fifty further back in history.

Parmenides was an influential ancient Greek philosopher, admired by Plato (who refers to "male parent Parmenides" in his dialogue the Sophist). Parmenides advocated the puzzling view that reality is unchanging and indivisible and that all movement is an illusion. Zeno, a pupil of Parmenides, devised four famous paradoxes to illustrate the logical difficulties in the very concept of motion. Translated into modern terms, Zeno's arrow paradox runs every bit follows:

  1. If you know where an arrow is, you know everything well-nigh its physical land.
  2. Therefore a (hypothetically) moving arrow has the same physical state equally a stationary arrow in the same position.
  3. The current physical state of an arrow determines its future physical country. This is Einstein Sanity—the deprival of Einstein Insanity.
  4. Therefore a (hypothetically) moving arrow and a stationary arrow have the aforementioned future concrete land.
  5. The pointer does not motility.

Followers of Parmenides worked themselves into logical knots and mystic raptures over the rather blatant contradiction between betoken 5 and everyday feel.

The foundational achievement of classical mechanics is to establish that the get-go indicate is faulty. Information technology is fruitful, in that framework, to allow a broader concept of the character of physical reality. To know the state of a system of particles, 1 must know not only their positions, merely besides their velocities and their masses. Armed with that information, classical mechanics predicts the system'southward future evolution completely. Classical mechanics, given its broader concept of physical reality, is the very model of Einstein Sanity.

With that triumph in heed, permit u.s. return to the apparent Einstein Insanity of breakthrough physics. Might that difficulty too hint at an inadequate concept of the state of the world?

Einstein himself thought then. He believed that at that place must exist hidden aspects of reality, not all the same recognized inside the conventional formulation of quantum theory, which would restore Einstein Sanity. In this view it is not and then much that God does not play dice, merely that the game he'due south playing does not differ fundamentally from classical dice. It appears random, but that's only considering of our ignorance of sure "hidden variables." Roughly: "God plays dice, simply he'due south rigged the game."

But as the predictions of conventional breakthrough theory, free of hidden variables, take gone from triumph to triumph, the wiggle room where one might accommodate such variables has become pocket-sized and uncomfortable. In 1964, the physicist John Bell identified certain constraints that must use to whatever physical theory that is both local—meaning that concrete influences don't travel faster than lite—and realistic, significant that the physical backdrop of a organisation be prior to measurement. But decades of experimental tests, including a "loophole-free" test published on the scientific preprint site arxiv.org last month, show that the world we live in evades those constraints.

Ironically, conventional quantum mechanics itself involves a vast expansion of physical reality, which may be enough to avert Einstein Insanity. The equations of quantum dynamics allow physicists to predict the future values of the wave function, given its present value. Co-ordinate to the Schrödinger equation, the moving ridge function evolves in a completely predictable style. But in practice nosotros never have access to the full moving ridge part, either now or in the future, so this "predictability" is unattainable. If the wave part provides the ultimate clarification of reality—a controversial outcome!—we must conclude that "God plays a deep nonetheless strictly dominion-based game, which looks like dice to us."

Einstein's great friend and intellectual sparring partner Niels Bohr had a nuanced view of truth. Whereas according to Bohr, the contrary of a uncomplicated truth is a falsehood, the opposite of a deep truth is another deep truth. In that spirit, let us introduce the concept of a deep falsehood, whose opposite is likewise a deep falsehood. It seems fitting to conclude this essay with an epigram that, paired with the one nosotros started with, gives a nice case:

"Naïveté is doing the same thing over and over, and ever expecting the same result."

Frank Wilczek was awarded the 2004 Nobel Prize in physics for his work on the theory of the strong force. His most recent book is A Beautiful Question: Finding Nature'due south Deep Blueprint. Wilczek is the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology.

Reprinted with permission from Quanta Mag, an editorially independent publication of the Simons Foundation whose mission is to heighten public understanding of science past covering research developments and trends in mathematics and the physical and life sciences.