Quantized: Physics

Einstein’s Parable of Quantum Insanity

Einstein refused to believe in the inherent unpredictability of the world. Is the subatomic world insane, or just subtle?

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James O'Brien for Quanta Magazine


“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 effect may be 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.

First of all, note that what Einstein describes as insanity is, according to quantum theory, the way the world actually works. In quantum mechanics you can do the same thing many times and get different results. Indeed, that is the premise underlying great high-energy particle colliders. In those colliders, physicists bash together the same particles in precisely the same way, trillions upon trillions of times. Are they all insane to do so? It would seem they are not, since they have garnered a stupendous variety of results.


A monthly column in which top researchers explore the process of discovery. This month’s columnist, Frank Wilczek, is a Nobel Prize-winning physicist at the Massachusetts Institute of Technology.

Of course Einstein, famously, did not believe in the inherent unpredictability of the world, saying “God does not play dice.” Yet in playing dice, we act out Einstein Insanity: We do the same thing over and over — namely, roll the dice — and we correctly anticipate different results. Is it really insane to play dice? If so, it’s a very common form of madness!

We can evade the diagnosis by arguing that in practice one never throws the dice in precisely the same way. Very small changes in the initial conditions can alter the results. The underlying idea here is that in situations where we can’t predict precisely what’s going to happen next, it’s because there are aspects of the current situation that we 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 have full access to reality, according to this argument, the results of our actions would never be in doubt.

Katherine Taylor for Quanta Magazine

Frank Wilczek

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 movement is an illusion. Zeno, a student 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 as follows:

  1. If you know where an arrow is, you know everything about its physical state.
  2. Therefore a (hypothetically) moving arrow has the same physical state as a stationary arrow in the same position.
  3. The current physical state of an arrow 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 future physical state.
  5. The arrow does not move.

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

The foundational achievement of classical mechanics is to establish that the first point is faulty. It 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, one must know not only their positions, but also their velocities and their masses. Armed with that information, classical mechanics predicts the system’s 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 quantum physics. Might that difficulty likewise hint at an inadequate concept of the state of the world?

Einstein himself thought so. He believed that there must exist hidden aspects of reality, not yet recognized within the conventional formulation of quantum theory, which would restore Einstein Sanity. In this view it is not so much that God does not play dice, but that the game he’s playing does not differ fundamentally from classical dice. It appears random, but that’s only because of our ignorance of certain “hidden variables.” Roughly: “God plays dice, but he’s rigged the game.”

Paul Ehrenfest

Niels Bohr (left) and Albert Einstein in 1925.

But as the predictions of conventional quantum theory, free 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 apply to any physical theory that is both local — meaning that physical influences don’t travel faster than light — and realistic, meaning that the physical properties of a system exist 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 avoid Einstein Insanity. The equations of quantum dynamics allow physicists to predict the future values of the wave function, given its present value. According to the Schrödinger equation, the wave function evolves in a completely predictable way. But in practice we never have access to the full wave function, either at present 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 rule-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 opposite of a simple 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 we started with, gives a nice example:

“Naïveté is doing the same thing over and over, and always expecting the same result.”

This article was reprinted on ScientificAmerican.com.

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  • Einstein had amazingly good intuition for the character of physical laws, i.e. what shape the laws of physics must necessarily take. And in this case he was right, too. God doesn't play dice; the universe is deterministic. Unfortunately, he didn't stumble upon the right answer, Many Worlds. I sometimes wonder how much longer it will take popular science writers to stumble upon it, too.

  • Wilczek asserts:
    "In those colliders, physicists bash together the same particles in*precisely the same way*, trillions upon trillions of times."

    Do we actually know trillions upon trillions of particle collisions were *precisely the same* ?

    As we can't measure below the Planck length (some 1.6 to 4.0 x 10^-35m) and Heisenberg uncertainty says we can't know both position and momentum simultaneosuly, how do we know evey collision of these trillions and trillions were precisely the same, within the Planck theoretical limit of position accuracy? How do we know the variations in scattering aren't partly due to variations in collision alignment?

    Is the LHC calibrated to control and measure collisions to within Planck limits?

  • Nice article. But "Naïveté is doing the same thing over and over, and always expecting the same result" is incomplete, it should have said "Naïveté is doing the same incomplete (with hidden variables) experiment, over and over, and always expecting the same result.

  • I believe that this article very much misses the point about Einstein. He was not worried about statistical issues of quantum mechanics but about the issue of locality– that something that happens at one location can't influence events at another location unless there is time for a signal to propagate between the two, (and that signal speed is limited by the speed of light). He made the seemingly very reasonable assertion that any correct physical theory must be local in this sense. He then showed that some of the predictions of quantum mechanics violate this type of locality. Therefore quantum mechanics must be incomplete in some way, and whatever must be added to restore locality will increase the determinism of the theory.

    Bell then showed that there was no way to keep the predictions of quantum theory and have locality. Experimental evidence has now shown that the predictions of quantum mechanics are correct, and thus the world is non-local. So Einstein was "mistaken", but what he did was define one of the critical issues in sharp relief, (but unfortunately in a way that was widely misunderstood and unappreciated). To be wrong at this level represents to me a major achievement in moving science forward.

    A good presentation of the arguments of Einstein and Bell, including a discussion of the "play dice" quotation is available in a paper by Maudlin http://arxiv.org/pdf/1408.1826.pdf

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

    Einstein couldn't have said this; he played the violin and must have understood the importance of practice, over and over.

  • Einstein knew nothing about insanity [unlike me but we wont go there]. As for his view of quantum mechanics we all know by now he was against it believing in some sort of pseudo-platonian ur-design within the universe itself. A personal belief that surprisingly clouded is vision. At conference after conference he pushed his barrow luckily to little effect. I think this Einstein obsession is getting tedious. There are so many others who contributed. As for Zeno he was brilliant showing the limits of logic.

  • The infamous quote about insanity is largely misattributed to Albert Einstein and oftentimes to Mark Twain. The quote originally came from author Rita Mae Brown’s novel Sudden Death, published by Bantam in 1983. In the novel, Brown writes:

    "Unfortunatley, Susan didn’t remember what Jane
    Fulton once said. “Insanity is doing the same thing over and over again, but expecting different results.”

    Being a physicist, with experimentation as something fundamental in the field, Einstein quoting something like that sounds highly improbable.

    There has been a solid belief in the internet community about the words coming from Einstein, but we all know how things circulate and amplify, but nonetheless remain false.

    There has been no official or authentic confirmation about the source of the described quote tracing to Einstein.

  • There are many possible interpretations of quantum mechanics including Many Worlds, Debroglie-Bohm, Modal, Von Neuman, etc. Einstein preferred the Ensemble or Statistical interpretation. Since Schrodinger's wave equations really describe probabilities, Einstein thought that quantum theory could only be applied to statistically significant numbers of particles, not single particles. (Assumptions of measuring single photons or single particles should be re-examined.) The most accepted interpretation is the Copenhagen interpretation that assumes the observer (or measuring device) causes a collapse of an indeterminate system of single particles in a smeared out multiplicitity of states (superposition) into one state. The difficulty arises when two entangled particles, separated by a considerable distance, demonstrate linked states when one is measured. "Spooky" action at a distance is not necessary if the particles already have a determined but unknown state, which persists at a distance. Copenhagen interpretation confuses epistemology (knowing) with ontology (being). Not knowing doesn't mean that it doesn't exist. Schrodinger's cat thought experiment was meant to demonstrate the absurdity of this point, but has been distorted to "prove" the opposite. Likewise, Heisenberg uncertainty principle has been applied as a fundamental property of quantum mechanics when it originally was meant to describe limits on our ability to know. Einstein, Heisenberg, Schrodinger and Dirac all were critics of the Copenhagen interpretation espoused by Bohr. Would it hurt to re-examine fundamental assumptions? The particle accelerator experiments don't require indeterminacy, just an acceptance that we cannot know all parameters of any one experiment and therefore cannot precisely predict the outcome.

  • I think the common idea that quantum mechanics mean Universe is unpredictable is nothing more than an assumption. I have never seen any scientific proof about it.
    For example is weather really unpredictable because of quantum mechanics? Can't we really predict dice rolls even if we measure its initial conditions well? Are the orbits etc of planets, stars or galaxies unpredictable because of quantum mechanics?
    I think unpredictability of quantum particles may have practically no effect on macro Universe.

  • I would say rather that naïveté is the inability to expect the unexpected because you unwisely believe you know everything about everything.

  • Why did this get published here? It's a pretty poorly structured piece that says nothing new and does not shed any surprising light on old perspectives. Quanta magazine usually has much higher standards for thinking, writing, and narratives worth our while as readers.

  • I know it's picking nits, but I take issue with your claim that the particles are smashed together in "exactly" the same way. Actually it's only the same speed and direction. There are many factors which make each "smashing" different.

  • @I normally love quanta but…: Right you are. Nor is the article helpful in any way. Philosophical determinism is something like solipsism (it is so structured that there ALWAYS is an argument to 'prove' that the determinist is right: "we don't know yet, and we cannot know either, but it has to be so", or: "you are predestined to be ignorant and disagree with me, just as I am predestined to think I'm right, and this whole discussion is futile". No room for Karl Popper's demand for falsification). Many folks in the natural sciences tend passionately toward determinism because they believe their science (and with it their jobs, and their own importance and social standing, and their inflated asocial view of themselves) depend on it. Ultimately, determinism will go the way of the phlogiston theory. Why? Because it's determined to be so. 🙂

  • As Mermin points out, “quantum theory is the most
    useful and powerful theory physicists have ever devised.
    Yet today, nearly 90 years after its formulation, disagreement
    about the meaning of the theory is stronger than
    ever. New interpretations appear every day. None ever

    I think we need to be a bit more careful about calling
    ideas naive while the jury is still out (90 years of indecision!).

    And, conventional QM still looks like a non-physical
    black-box model to many natural philosophers, even those
    without a dog in the game.

    Fractal Cosmology (because new ideas are badly needed)

  • Frank Wilczek apparently conflates Einstein’s realist thesis with determinism. The issue for Einstein was not “to regain a deterministic description of nature”, or whether or not “God does not play dice”, but rather that certain interpretations of the quantum formalism clash with some of our most basic assumptions about physical reality such as relativistic causality etc.
    Pauli aptly clarified this confusion in a letter to Born dated 31 March, 1954 (The Born-Einstein Letters, p216, Macmillan 2005). After reporting that Einstein said that Born was a person who will not listen, Pauli writes: “This agrees with the impression I have formed myself insofar as I was unable to recognise Einstein whenever you talked about him in either your letter or your manuscript. It seemed to me as if you had erected some dummy Einstein for yourself, which you knocked down with great pomp. In particular, Einstein does not consider the concept of ‘determinism’ to be as fundamental as it is frequently held to be (as he told me emphatically many times), and he denied energetically that he had ever put up a postulate such as ‘the sequence of such conditions must also be… deterministic’. In the same way, he disputes that he uses as criterion for the admissibility of a theory the question: ‘Is it rigorously deterministic?’”.
    Why the same confusion persists is rather perplexing. Yet it would appear that what has been knocked down again with great pomp is only a ‘dummy Einstein’, and a ‘dummy EPR argument’, as the EPR argument nowhere asserts “that nature is deterministic”, contrary to what Wilczek and others believe. For naivete (Wilczek’s epigram) is telling the same ‘dummy Einstein’ story over and over again, and always expecting the same confusion rather than a different result, and might explain why the same confusion persists for so long (over 61 years).
    Whether or not relativistic causality, and by implication locality, are properties of nature, we agree with Wilczek that a definite experimental test is certainly needed before we decide Einstein was wrong. As a fitting tribute to Einstein, who regarded ideas and theories (including his own) as merely temporary, would Wilczek perhaps help to elicit nature’s verdict on Einstein’s question: Must we give up relativistic causality, or must we admit the incompleteness of the theory of the quantum formalism? Einstein’s question has been formulated in terms of a new and simple inequality. The inequality has been waiting for a test (since 2002) that would help decide whether or not Einstein is right (or whether or not Bell is right).

  • Instead of always quoting“God does not play dice.” it would be interesting in this context to quote Einsteins "Insofern sich die Saetze de Mathematik auf die wirklichkeit beziehen, sind sie nich sicher, und insofern sie sicher sind, beziehen sie sich nicht auf die wirklichkeit" (A. Einstein: Geometrie und Erfahrung"). Mathematical descriptions, models and proofs can only be an approximation of reality.

  • Experiments are key, everything else – theories, equations, egos are secondary and change over time. 20, 50, 100 yrs in the future it will all have been thrown out and replaced with the new. But there just isn't enough practical experimentation, I don't know why. Is it being done in secret by the military? The rest of us only get their discarded science when it's declassified and no longer useful. Because an awful lot of cleverly designed experiments should have been done in the last few decades to tackle questions unanswered for a century. Practical experiments are all that matter, and instead we have hot air; it's ridiculous. I can't believe these questions are really unanswered, just top secret. Many worlds is nonsense, though.

  • I greatly respect Frank as a physicist, he's brilliant. However, this drivel of an article is beneath someone of his intellect and suggests that scientists don't tend to make great philosophers. This is a bad caricature of how nuanced Einstein's position actually was – and the benefits to the field of his criticisms have, as evinced here, been grossly unappreciated (see EPR experiment). Einstein didn't believe in determinism as a fundamental criterion of a physical theory, nor was he, at heart a determinist (the conflation is a sad myth). He did, however, take umbridge with Bohr's false characterization of the wave function as an ontological truth rather than an epistemological truth (something Bohr never seemed to grasp). Heisenberg, interestingly, reinforces Einstein's position by emphasizing that the Uncertainty Principle is a mathematical model used to show the LIMITS of what we can know about a given system and should not be interpreted as a physical representation of the system itself. This is a conceptual distinction physicists till this day don't fully seem to grasp. Einstein's second gripe with QM was the idea that by measuring the spin/velocity/position of a given particle (or system of particles) we somehow interact with the system and collapse the wave function, thereby implying that those physical properties cease to "exist" until we "look" at it (i.e. Measure). This was the genesis of his now famous refrain to Bohr, "do you truly believe the moon is not there when you don't look at it?" We now know this reading of quantum measurement in Copenhagen Interpretation to be wrong.

    I suggest reading Douglas Stone's brilliant work, Einstein and the Quantum: The Quest of the Valiant Swabian. It is a fantastic book investigating the true, undistilled history of quantum mechanics with Einstein playing it's narrative centerpiece. The interesting revelation from the book is that Einstein, above all his contemporaries, was responsible for discovering most of the fundamentally novel concepts in quantum mechanics. Not Bohr (who didn't even BELIEVE in the particle description of nature years after Einstein's work on the photoelectric effect – i know, ironic), not de broglie (overrated by Stone's estimation), not even Born, Dirac, Heisenberg or Schrodinger (at least until, after the fact). Of course, these genuises would form much of the edifice of QM but it was Einstein that truly launched the revolution (and it certainly was not fueled by his love for determinism).

    His work on the Photoelectric Efffect, on Brownian Motion and his equations for calculating Avogrado's number, his work on the specific heat of solids, his work on wave-particle duality (that presaged de broglie's work), his work on probability waves as applied to photons (work which, years later Born would essentially take and apply to electrons – though he was honorable enough to give einstein all the credit), bose-einstein condensates, his work on the quantization of chaos (1919), his work on spontaneous and stimulated emission (i.e. the LASER), his work on quantum entanglement (yes, einstein was the first scientist to actually predict entanglement – though he meant it as a disproof of QM), and numerous other publications. Make no mistake, Einstein is the Godfather of QM, and were it not for Bohr's erroneous arguments in their infamous tussle and his insistence that the observer's presence affects the empirical reality of the object measured (e.g wave collapse), Einstein would've probably been more open to working with QM.

    From 1925 until the late 70's QM was (and still is) VERY poorly conceptually understood by many working scientists. Hell, Richard Feynman was averse to the notion of the field until Julian Schwinger's work on QFT made it an inexorable staple of QM. Particles interact, and they do so in what we conceptually determine to be a field (or a medium of interaction).

    Einstein has nothing to apologize for; the randomness of QM is not necessarily a stochastic function of it's theoretical foundation but rather a reflection on the limits of human knowledge. There are variables we presumably cannot see (particles that perhaps DO descend smaller and smaller ad infinitum) and interactions that are too weak to measure with current technology (e.g. gravitons for instance).

    Read and enjoy (and this is no quack, he's the head of Applied Physics at Yale University and one of the leading theoretical physicists – in particular LASER systems – in the world): http://blog.press.princeton.edu/2013/09/25/qa-with-douglas-stone-author-of-einstein-and-the-quantum/

  • While I do find Wilczek's article sub par compared to his pedigree, I am much more depressed by the regurgitation of hidden variables nonsense in the comments. Oddly enough, such drivel is not usually posted under physics articles that do not mention Einstein. It seems we need to establish a new Godwin-type law, I'm afraid.

  • Well, John, why is the gauge boson (the photon) represented as a quark-antiquark pair in QCD? This is a perfect example of hidden variables, sometimes called partons or neutrino-antineutrino pairs. Another example might even be the threshold gammaray, responsible for pair formation.

  • Varioous people like to talk about Einstein` "insanity". The Brownian motion is a good example of this children frightening determinism. The models of the quantum particles fluctuations under the unknown ,but quite real forces, does not wake the enthusiasm of "God plays dice" idea followers.

  • The irony of einsteins statement he continued to use the same methods that gave him great results(thought experiments) and they later failed to give him the same results.

  • Nice old photograph there, is there missing a person in this picture? Was this reason for question between Niels Bohr and Albert Einstein, like : "To behave or to misbehave?" -.
    "Aint you misbeheaving !?"

  • Why do we look at non-locality as a physical property (like a connection that we can measure with our technology)? Isn't this entire field of science about non-physical connections that aren't measurable by us mere mortals? If we think of quantum mechanics, and agree that is indeed strange, why would we apply classical physics to measure it? The fabric of the universe…..isn't it all interconnected? If so, why would we be surprised that entanglement is a part of that connection? It seems to me if we are to walk in this strange land, we must leave our tools and expectation behind…..

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