Physics · Science

“God Does Not Play Dice With the Universe:” Albert Einstein

This is a summary of an article in Scientific American, published on Sept 15, 2015.  The article is titled, Einstein’s Assertion That God Does Not Play Dice With the Universe has Been Misinterpreted.  The article is by George Musser.

Einstein accepted that quantum mechanics was indeterministic: ie randomness and statistics rule. Actually Einstein was the one who had discovered Quantum indeterminism; what he did not accept was that this indeterminism, this randomness was fundamental to Nature.  Einstein thought that indeterminism was rising from a deeper level of reality that Quantum theory was failing to capture.

The problem of whether the universe is a clockworks or a craps table is important.  In the past it has often been thought that if there are simple natural laws that underlie the diversity of nature, then nature is deterministic.  It means that things are happening for reasons.  It means that rational enquiry can be successful and science is possible.  But, on the other hand, if even some things happen for no reason, then the universe is random, there are no laws that nature must always follow,  we will never be able to figure anything out since nature is not predictable.  

So if reason and science are to work, the universe must be deterministic.  But determinism negates many important things like free will, human responsibility, law and justice.

Actually, we can have both determinism and indeterminism, the universe can be either.  They just exist at different levels:

“The distinction between determinism and indeterminism is a level-specific distinction,” says Christian List, a philosopher at the London School of Economics and Political Science. “If you have determinism at one particular level, it is fully compatible with indeterminism, both at higher levels and at lower levels.” The atoms in our brain can behave in a completely deterministic way while still giving us freedom of action because atoms and agency operate on different levels. Likewise, Einstein sought a deterministic sub-quantum level without denying that the quantum level was probabilistic.”

Einstein actually came up with the basis for Quantum theory in 2005 with his discovery of quanta (discrete particles of energy) and the idea that light can act as both particle and wave. It was his thinking about wave physics that Schrodinger built on to develop quantum theory in the 1920’s.  Also Einstein showed in 1926 that when atoms emit photons the timing and emission was random.  

“But Einstein and his contemporaries faced a serious problem. Quantum phenomena are random, but quantum theory is not. The Schrödinger equation is 100 percent deterministic.”

Schrodinger’s equation equation is actually more deterministic than even Newton’s laws of motion.   

“It does not lead to muddles such as singularities (where quantities become infinite and thus indescribable) or chaos (where motion becomes unpredictable).

The theory leaves open what exactly the wave function is and whether it should be taken literally as a real wave out there in the world. Thus, it also leaves open whether observed randomness is intrinsic to nature or just a facade.”

Heisenberg was another early pioneer of quantum theory.  He

“envisioned the wave function as a haze of potential existence. If it fails to pinpoint unequivocally where a particle is located, that is because the particle is not, in fact, located anywhere. Only when you observe the particle does it materialize somewhere. The wave function might have been spread out over a huge region of space, but at the instant the observation is made, it abruptly collapses to a narrow spike at a single position, and the particle pops up there. When you so much as look at a particle— bam!—it stops behaving deterministically and leaps to an end result like a kid grabbing a seat in musical chairs. No law governs collapse. There is no equation for it. It just happens.”

This idea of collapse became the key idea of the Copenhagen interpretation of quantum mechanics.  Copenhagen takes the observed randomness of quantum physics at face value.  It doesn’t realize that behind this facade, nature may be deterministic.   Einstein did not accept this Copenhagen interpretation.  He said it was nuts that the act of measurement could cause a break in the continuous evolution of a physical system.  This is what he meant, specifically when he said that God doesn’t roll dice.  

Below is a summary of the main idea of this essay.  This was a box in the article.

“I at any rate, am convinced that He is not playing at dice,”Albert Einstein wrote to a colleague in 1926.

Repeated over the years, this sound bite became the quin­tessential put­down of quantum me­chanics and its embrace of randomness. Closer examination, though, reveals that Einstein did not reject quantum mechanics or its indeterminism, al­though he did think—for solid scientific reasons—that the randomness could not be a fundamental feature of nature.

Today many philosophers argue that physics is both indeterministic and de­terministic, depending on the level of reality being considered.

This view dissolves the much debated dilemma between determinism and free will. Even if everything that parti­cles do is preordained, the choices we make can be completely open because the low-­level laws governing particles are not the same as the high-­level laws governing human consciousness.”


Einstein thought that collapse could not be a real process, because this would require what physicists now call “spooky action at a distance” and this idea had not been discovered yet.  Einstein thought this was impossible.  Actually, many historians say that Einstein was trying to explain randomness, not explain it away.  Basically, Einstein thought that quantum randomness was just what the surface looked like, that actually it was the product of deeper goings-on.  


The basic idea of this article is that free will is real, because even if everything that parti­cles do is preordained, the choices we make can be completely open because the low-­level laws governing particles are not the same as the high-­level laws governing human consciousness.  The quotes below elaborate on this idea.  These are all direct quotes.

“In his [Einstein’s] estimation, quantum mechanics is a broad- brush theory that expresses the overall behavior of nature’s building blocks but lacks the resolution to capture individual cases. A deeper, more complete theory would explain the motion in full without any mysterious jumps.

If you roll a six-sided die and it lands on, say, four, the range of one to six “collapses” to the actual outcome of four. A godlike demon, able to track all the atomic details affecting the die— the exact way your hand sends the cube tumbling across the table—would never speak of collapse.

Einstein’s intuitions were backed up by his early work on the collective effects of molecular motion—studied by the branch of physics known as statistical mechanics—in which he had demonstrated that physics could be probabilistic even when the underlying reality was deterministic.

In 1935 Einstein wrote to philosopher Karl Popper, “I do not believe that you are right in your thesis that it is impossible to derive statistical conclusions from a deterministic theory. Only think of classical statistical mechanics (gas theory, or the theory of Brownian movement).”

Although Einstein’s overall project failed, his basic intuition about randomness still holds: indeterminism can emerge from determinism. The quantum and subquantum levels—or any other pair of levels in the hierarchy of nature—consist of distinct types of structures, so they abide by different types of laws. The laws governing one level can leave a genuine element of randomness even if the laws underneath it are completely regimented. “A deterministic microphysics does not induce a deterministic macrophysics,” says philosopher Jeremy Butterfield of the University of Cambridge.

Is the world deterministic or indeterministic? The answer depends not only on the basic laws of motion but also on the level at which a system is described. Consider five atoms in a gas moving deterministically. They start at nearly the same location and gradually spread out. On a macroscopic level, though, one would not see individual atoms but an amorphous puff of gas. After a time, the gas might split at random into multiple puffs. This macro-level randomness is not an artifact of an observer’s ignorance about the micro-level;it is an objective feature of nature, reflecting how atoms agglomerate. Analogously, Einstein suspected that a deterministic subrealm of the universe leads to the randomness of the quantum realm.

Think of a die at the atomic level. It can be constructed from zillions of atomic configurations that look utterly indistinguishable to the eye. If you track any one of these configurations as the cube is rolled, it will lead to a specific outcome—deterministically. In some configurations, the die ends up showing one dot; in others, two; and so on. Therefore, a single macroscopic condition (being rolled) can lead to multiple possible macroscopic outcomes (showing one of six faces).  

Although the higher level builds (in the jargon, “supervenes”) on the lower one, it is autonomous. To describe dice, you need to work at a level where dice exist, and when you do so, you cannot help but neglect atoms and their dynamics. If you cross one level with another, you commit the fallacy of a category mistake, which is like asking about the political affiliations of a tuna sandwich.“When we have phenomena that can be described at multiple levels, we have to be conceptually very careful in not mixing levels,” List says.

For this reason, the die roll is not merely apparently random, as people sometimes say. It is truly random. A godlike demon might brag that it knows exactly what will happen, but it knows only what will happen to the atoms. It does not even know what a die is because that is higher-level information.

The demon never sees a forest, only trees. It is like the protagonist of Argentine writer Jorge Luis Borges’s short story “Funes, the Memorious,” a man who remembers everything and grasps nothing. “To think is to forget a difference, to generalize, to abstract,” Borges wrote.

The level logic works the other way, too. Indeterministic microphysics can lead to deterministic macrophysics. A baseball can be made of particles behaving randomly, yet its flight is entirely predictable; the quantum randomness averages out. Likewise gases consist of molecules executing enormously complicated—and effectively indeterministic—movements, yet their temperature and other properties follow laws that are dead simple.

When you think in terms of levels, the worry that indeterminism might mark the end of science evaporates. There is no big wall around us, cordoning off a law-abiding chunk of the universe from the anarchic and inexplicable beyond. Instead the world is a layer cake of determinism and indeterminism.

The earth’s climate, for example, supervenes on Newton’s deterministic laws of motion, but weather reports are probabilistic, whereas seasonal and longer-term climate trends are again predictable.

Biology, too, supervenes on deterministic physics, but organisms and ecosystems require different modes of description, such as Darwinian evolution. “Determinism doesn’t explain everything,” says Tufts University philosopher Daniel C. Dennett. “Why are there giraffes? Because it was ‘determined’ that there would be?”

Human beings are embedded within this layer cake. We have the powerful sense of free will. We often do the unpredictable, and in most of life’s decisions, we feel we were capable of doing otherwise (and often wish we had).

To be free, we need indeterminism not at the particle level but at the human level. And that is possible be- cause the human and particle levels are autonomous. Even if everything you do can be traced to earlier events, you can be the author of your actions because neither you nor the actions exist at the level of matter, only at the macrolevel of mind. “This macro-indeterminism riding on micro-determinism may secure free will,” Butterfield says. Macroin-determinism is not the cause of your decision. It is your decision.

Some might complain that you are still a puppet of the laws of nature, that your freedom is an illusion. But the word “illusion” itself conjures up desert mirages and ladies sawed in half: things that are unreal. Macro-indeterminism is not like that. It is quite real, just not fundamental. It is comparable to life. Individual atoms are completely inanimate, yet enormous masses of them can live and breathe.

It would be a category mistake, not to mention completely unenlightening, to describe human decisions as the mechanics of atoms in your brain.

To be sure, List’s arguments do not explain free will fully. The hierarchy of levels opens up space for free will by separating psychology from physics and giving us the opportunity to do the unexpected. But we have to seize the opportunity. If, for example, we made every decision on a coin toss, that would still count as macro-indeterminism but would hardly qualify as free will in any meaningful sense. Some people’s decision making may be so debilitated that they cannot be said to act freely.

This way of thinking about determinism also makes sense of an interpretation of quantum theory that was developed in the years after Einstein’s death in 1955: the many-worlds interpretation. Advocates argue that quantum mechanics describes a collection of parallel universes—a multiverse—that behaves deterministically in the large but looks indeterministic to us because we are able to see only a single universe.

For instance, an atom might emit a photon to the left or to the right; quantum theory leaves the outcome open. According to the many-worlds interpretation, that is because the same situation arises in a zillion parallel universes; in some, the photon goes deterministically left, and in others, it goes right. Not being able to tell which of those universes we reside in, we cannot predict what will happen, so the situation from the inside looks inexplicable.

“There is no true randomness in the cosmos, but things can appear random in the eye of the beholder,” says cosmologist Max Tegmark of the Massachusetts Institute of Technology, a prominent proponent of this view. “The randomness reflects your inability to self-locate.”

That is very similar to saying that a die or brain could be constructed from any one of countless atomic configurations. The configurations might be individually deterministic, but because we cannot know which one corresponds to our die or our brain, we have to think of the outcome as indeterministic. Thus, parallel universes are not some exotic idea out there in the cosmos. Our body and brain are little multiverses, and it is the multiplicity of possibility that endows us with freedom.”

Below is a list of additional sources to explore:

Freedom Evolves. Daniel C. Dennett. Viking, 2003.

Laws, Causation and Dynamics at Different Levels. Jeremy Butterfield in Interface Focus, Vol. 2, No. 1, pages 101–114; February 2012.

Free Will, Determinism, and the Possibility of Doing Otherwise. Christian List in Noûs, Vol. 48, No. 1, pages 156–178; March 2014.

Our Mathematical Universe: My Quest for the Ultimate Nature of Reality.

Max Tegmark. Knopf, 2014.

Portland Head Light, Maine.  Picture by Hanselmann Photography. 

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