From Quanta Magazine ( discover original story here ).

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

That witticism—I'll phone call information technology "Einstein Insanity"—is usually attributed to Albert Einstein. Though the Matthew effect may exist operating hither, it is undeniably the sort of clever, memorable 1-liner that Einstein often tossed off. And I'm happy to give him the credit, because doing and so takes the states in interesting directions.

Showtime of all, notation that what Einstein describes as insanity is, according to quantum theory, the way the earth actually works. In quantum mechanics you can do the same matter many times and become different results. Indeed, that is the premise underlying peachy high-energy particle colliders. In those colliders, physicists fustigate together the aforementioned particles in precisely the same style, trillions upon trillions of times. Are they all insane to do so? Information technology would seem they are non, since they have garnered a stupendous variety of results.

Of course Einstein, famously, did not believe in the inherent unpredictability of the earth, saying "God does not play dice." Yet in playing dice, we act out Einstein Insanity: We exercise the same affair over and over—namely, curl the dice—and we correctly conceptualize different results. Is it really insane to play die? If and then, it's a very mutual form of madness!

We can evade the diagnosis by arguing that in exercise one never throws the dice in precisely the same mode. Very modest changes in the initial atmospheric condition tin alter the results. The underlying idea hither is that in situations where nosotros can't predict precisely what's going to happen next, information technology's because in that location are aspects of the electric current state of affairs that we oasis'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 have total access to reality, according to this argument, the results of our actions would never be in dubiousness.

This doctrine, known as determinism, was advocated passionately by the philosopher Baruch Spinoza, whom Einstein considered a great hero. But for a better perspective, we need to venture even further 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 motility is an illusion. Zeno, a student of Parmenides, devised iv famous paradoxes to illustrate the logical difficulties in the very concept of motion. Translated into mod terms, Zeno's arrow paradox runs as follows:

  1. If you know where an pointer is, yous know everything about its concrete land.
  2. Therefore a (hypothetically) moving arrow has the same physical state equally a stationary arrow in the aforementioned position.
  3. The electric current physical state of an pointer determines its future physical state. This is Einstein Sanity—the denial of Einstein Insanity.
  4. Therefore a (hypothetically) moving arrow and a stationary arrow have the same time to come physical state.
  5. The arrow does non move.

Followers of Parmenides worked themselves into logical knots and mystic raptures over the rather blatant contradiction betwixt indicate five and everyday experience.

The foundational achievement of classical mechanics is to establish that the commencement point is faulty. Information technology is fruitful, in that framework, to permit a broader concept of the character of physical reality. To know the state of a system of particles, i must know non only their positions, but besides their velocities and their masses. Armed with that information, classical mechanics predicts the system'south future evolution 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 breakthrough physics. Might that difficulty likewise hint at an inadequate concept of the state of the earth?

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

But every bit the predictions of conventional quantum theory, gratuitous of hidden variables, have gone from triumph to triumph, the wiggle room where one might accommodate such variables has become small and uncomfortable. In 1964, the physicist John Bell identified certain constraints that must utilise to any physical theory that is both local—meaning that physical influences don't travel faster than light—and realistic, pregnant that the physical properties of a organisation be prior to measurement. Only decades of experimental tests, including a "loophole-gratis" test published on the scientific preprint site arxiv.org concluding calendar month, show that the earth nosotros live in evades those constraints.

Ironically, conventional quantum mechanics itself involves a vast expansion of physical reality, which may exist enough to avert Einstein Insanity. The equations of breakthrough dynamics allow physicists to predict the time to come values of the wave function, given its present value. According to the Schrödinger equation, the moving ridge function evolves in a completely anticipated way. Only in exercise nosotros never have access to the full wave role, either at nowadays or in the future, so this "predictability" is unattainable. If the wave function provides the ultimate description of reality—a controversial issue!—we must conclude that "God plays a deep yet strictly dominion-based game, which looks like die to us."

Einstein'due south great friend and intellectual sparring partner Niels Bohr had a nuanced view of truth. Whereas co-ordinate to Bohr, the reverse of a simple truth is a falsehood, the opposite of a deep truth is some other 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 i nosotros started with, gives a nice example:

"Naïveté is doing the same thing over and over, and always 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's Deep Design. 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 enhance public understanding of science by covering enquiry developments and trends in mathematics and the physical and life sciences.