From Quanta Magazine ( notice original story hither ).

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

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

Start of all, note that what Einstein describes equally insanity is, according to quantum theory, the fashion the world actually works. In breakthrough mechanics you tin do the same affair many times and get different results. Indeed, that is the premise underlying smashing high-free energy particle colliders. In those colliders, physicists bash together the same particles in precisely the same style, trillions upon trillions of times. Are they all insane to practise so? It would seem they are non, since they take garnered a stupendous variety of results.

Of grade Einstein, famously, did non believe in the inherent unpredictability of the world, proverb "God does not play die." Still in playing dice, nosotros deed out Einstein Insanity: We exercise the same thing over and over—namely, roll the dice—and nosotros correctly anticipate different results. Is information technology really insane to play dice? If and then, information technology'due south a very mutual grade of madness!

Nosotros tin evade the diagnosis by arguing that in practice one never throws the dice in precisely the same style. Very small changes in the initial weather can alter the results. The underlying idea hither is that in situations where we can't predict precisely what'south going to happen next, it'due south because in that location are aspects of the current situation that we haven't taken into business relationship. Similar pleas of ignorance can defend many other applications of probability from the allegation 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 actions would never be in doubt.

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 farther back in history.

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

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

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

The foundational accomplishment of classical mechanics is to plant that the first signal is faulty. It is fruitful, in that framework, to allow a broader concept of the character of concrete reality. To know the state of a system of particles, one must know non but their positions, just too their velocities and their masses. Armed with that data, classical mechanics predicts the system's time to come development completely. Classical mechanics, given its broader concept of physical reality, is the very model of Einstein Sanity.

With that triumph in mind, let us return to the apparent Einstein Insanity of quantum physics. Might that difficulty likewise hint at an inadequate concept of the state of the globe?

Einstein himself thought so. He believed that there must be hidden aspects of reality, non yet recognized within the conventional formulation of breakthrough theory, which would restore Einstein Sanity. In this view it is non so much that God does not play dice, but that the game he's playing does not differ fundamentally from classical dice. Information technology appears random, simply that's only because of our ignorance of sure "hidden variables." Roughly: "God plays dice, merely he'south rigged the game."

But as the predictions of conventional quantum theory, free of hidden variables, have gone from triumph to triumph, the wiggle room where one might adapt such variables has get small and uncomfortable. In 1964, the physicist John Bell identified certain constraints that must apply to any concrete theory that is both local—meaning that physical influences don't travel faster than low-cal—and realistic, meaning that the physical properties of a system exist prior to measurement. Just decades of experimental tests, including a "loophole-free" test published on the scientific preprint site arxiv.org last month, show that the world we alive in evades those constraints.

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

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

"Naïveté is doing the aforementioned thing over and over, and always expecting the same outcome."

Frank Wilczek was awarded the 2004 Nobel Prize in physics for his work on the theory of the stiff force. His near recent volume is A Beautiful Question: Finding Nature's Deep Design. Wilczek is the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology.

Reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by roofing research developments and trends in mathematics and the physical and life sciences.