Most of us who follow physics know Einstein's famous response to quantum mechanics (QM): "God does not play dice!" Many writers consider this quote as an indication of his refusal to accept the randomness of QM phenomena, and they consider it to be one of Einstein's biggest mistakes. The author of "Is The Cosmos Random?" in Scientific American's September 2015 issue, having reviewed much of Einstein's written work and correspondence, argues otherwise (a subscription is needed to read it online). A fresh look at what Einstein thought about QM could lead to new approaches to how we think about quantum phenomena, especially how we interpret the experiments that reveal its trademark quirky behaviours.
Einstein's "hidden variable theory" – that there must be one or more underlying variables to explain the seemingly random (and spooky) nature of certain particle processes - was debunked by John Bell in the 1960's. Based on his theorem, a series of elegantly designed experiments were carried out in the 70's and 80's to test the hidden variables theory. Those results argue very convincingly against hidden variables (at least local variables). The principle of locality means that an object can only be directly influenced by its immediate surroundings, whether it is an object pushing it, for example, or energy or a force field acting upon it. In this case there is no evidence that some hidden force field, or as yet unknown particle, acts on the subatomic particle in question, influencing its behaviour. It's just, according to any observations we can make of it, autonomously random.
Subatomic particles do some very weird things. Their behaviours point to a built-in randomness at the quantum level of reality. Particles also don't seem to play by the same rules of space and time that we do at our everyday scale of physics.
Excited atoms, for example, emit one or more photons when they return to ground state, but exactly when and in what direction those photons are emitted are entirely random. Similarly, exactly when a particular radioactive atom emits a beta or gamma particle, or a gamma photon, is purely random. Despite this, both radioactivity and the emission of light follow predictable rules of physics at the macro or everyday level, so that such phenomena can be drawn as predictable curves on graphs even though the individual particles themselves act entirely randomly.
In one version of the famous double slit experiment, electrons are shot one at a time through a barrier, which contains two thin slits, toward a detector screen. Electrons are used in this example but in theory this experiment can be carried out with any subatomic particle because they all follow the same quantum rules. Individual impacts are recorded as discrete points on the detector, as we might expect. However, the impacts are randomly placed on the detector, even though each electron is shot in an identical manor. Like the previous examples show, the electrons have a probabilistic (random) nature, revealed here by where they hit the detector.
This built-in randomness at the particle level cannot be explained by classical mechanics. In classical mechanics, one action always leads directly, and reliably, to another action. Classical mechanics describes a clockwork universe in other words, where every outcome in nature is ultimately predictable. The double slit experiment reveals that at the subatomic (quantum) level, nature is not predictable but entirely random EVEN THOUGH those same electrons, observed at the macro scale, follow Michael Faraday and James Maxwell's predictable classical rules of electromagnetism. You have here two layers of reality, where predictable physics is built upon an unpredictable probabilistic base.
The double slit experiment reveals an additional and even more perplexing subatomic reality. When electrons continue to be shot through the slits, another phenomenon emerges. An interference pattern builds up, like waves interfering with one another in a wave tank. This is not only direct evidence for the dual particle/wave nature of subatomic particles. It also reveals that individual particles, each one hitting the detector in a purely random location, somehow manage to build a distinct pattern AS IF they know how future electrons will contribute to the interference pattern. The experiment can be repeated over and over. Electrons will hit the detector in different random order each time but every time the same interference pattern builds up. This implies that the particles are acting outside the boundaries of time, as we understand it. A particle somehow "knows" the end result as it leaves the electron gun. According to special relativity, no particle can travel faster than the speed of light, back in time in other words, to plot out its contribution.
Space somehow also seems to have a different meaning on the subatomic scale. This example involves quantum entangled particles. To make an entangled pair, for example, you can allow an unstable spin zero particle to decay into two spin ½ particles. One will be spin up and one will be spin down. Other than their opposite spins, these particles will have identical quantum numbers. They will be identical twins in other words. When the entangled particles are shot off in two different directions, they seem to communicate information to one another, instantly, even though one particle may, by the time it's measured, be across the universe from its entangled partner.
Particle A's spin might be measured (it has a 50% chance of being either spin up or spin down) at some point. When A is measured and found to be spin up, at that instant, Particle B's spin is confined to spin down. Before measurement, both particle spins are said to be in a superimposed up/down state. Collapse of one into spin up instantly forces the other, wherever it might be located, to collapse into spin down state. This experiment reveals the spookiness of the EPR (Einstein/Podolsky/Rosen) paradox, and it can be reviewed on Wikipedia both here and here. Both entries describe the phenomenon in great detail. The question for us is how does one particle "communicate" wavefunction collapse to its partner instantly across any distance? This goes further than breaking the light speed barrier because it is instant. It is as if physical space does not exist for the entangled pair. They are instead acting like one single particle.
All these phenomena have been exhaustively experimentally verified. As we try to swallow those facts, we seem to be left with two unsavoury choices: Either we accept at face value the fact that phenomena occur randomly and in ways that don't make sense in terms of how we understand space and time. Or, we cling to the hope that there is some predictable and sensible underlying reality and we just haven't found it yet. If we chose the latter option, we are treading toward Einstein's ruled out hidden variables.
George Musser, the author of the Scientific American article, offers us possible outs for both of these choices. First, there is good evidence that reality is actually like a layer cake, where probabilistic and predictable phenomena are layered on top of one another. Which type of behaviour you observe depends on which scale you are observing. If you are focused on behaviours the quantum scale, you will find probabilistic behaviour. Zoom out and look at the same physical system at the everyday scale and you will likely find predictable classical behaviour. What looks purely random at one scale averages out to be predictable behaviour on a grander scale. For example, consider a single isolated atom in the vacuum of space. It could have any random kinetic energy, but it has no temperature.* If you place that atom together with a few million of its friends, you can now measure a specific temperature that is reliably determined by measuring the average kinetic energy of the atoms EVEN THOUGH that mixture consists of atoms that have all kinds of random kinetic energies as they mill about and collide with one another. Temperature is a predictable phenomenon that follows classical rules. It is also an emergent phenomenon that does not exist at the quantum scale.
Musser offers even more layers of phenomenon in the example of weather. At the quantum level, the gaseous particles in air behave randomly. Get them together in measurable volume and you find they perfectly follow predictable gas laws of behaviour (again, it is thanks to averaging out billions of atoms). Now put two or more different large-scale air masses together and you've got the unpredictability that accompanies any weather forecast. The more days out you try to forecast, the more unpredictable it gets because now you are dealing with the physics of chaos theory. Chaos emerges from a non-chaotic initial state. Take a long view of weather over several seasons and once again the numbers come back into predictable line as climate data. Perhaps, considering this, it isn't too much to accept that our predictable world is built upon the zany behaviours of quantum particles.
Second, we can wonder if there is any possibility of some kind of reality underlying the quantum scale of physics, implying that QM is actually only part of an as yet unfinished theory. This, according to Musser, is really what Einstein was getting at: He wasn't arguing against randomness so much as he was arguing against taking the random behaviour observed at face value. There's a subtle difference between taking that stand and resorting to a hidden force or particle. The layer underpinning QM could once again be deterministic in nature. Consider this possibility: All the countless random directions in which a photon can be emitted from an atom could represent countless possible realities at our scale (the multiverse people thoroughly explore this possibility). Here is where I veer off: We observe just one of these possibilities but on its scale, its reality could consist of ALL the possible directions, simultaneously. We observe the photon emitting in just one specific direction, and it looks totally random to us. But add all the countless possible angles of emission and imagine all these realities simultaneously coexisting, from the photon's perspective. From its perspective, it actually achieves all possible emissions. This, then, is what the quantum world looks like to the quantum particle. We, on the other hand, see only one emission and it is random. If we follow the SA article's logic, we can call this difference an abrupt transition from one scale to the next (while maintaining that both realities are valid WITHIN their own scale).
Richard Feynman came very close to describing quantum phenomena the same way. To describe electron and photon interactions, he started from the standpoint that the particles are waves and they move from point to point as a wavefront. A wavefront, unlike a point, takes numerous paths to get from A to B, rather than just one path. To translate that into mathematical quantum jargon, you call the particle a probability wave, and it doesn't take numerous paths. It takes ALL paths. This approach assumes that a particle, just like larger objects, follows the principle of least action. By assigning arrows that follow each possible path (in theory there are countless paths remember) and rotating them as you go, you can get a measure of how difficult, or how long and convoluted, each path is. By adding up all the arrows as vectors, you get a final vector called the amplitude of the wavefunction. This is the path integral that the particle takes from A to B, which also happens to always be the shortest route it can take, and also happens to be the path, the straight line, that we observe. This might seem like a pointless exercise, all this fanciness just to get back to the particle's observed trajectory. However, there is an important point to it, that ALL possible trajectories DO contribute to the path integral, even routes that take the photon all around the universe between A and B (those paths don't contribute very much). Conceptually, this process introduces a whole new way to think about a particle. The path integral forms the basis of the famous Feynman diagrams, I'll mention later. I don't know if he ever thought of those infinite paths as a physical reality or strictly as a mathematical method. I don’t think he ever couched it in the kinds of terms where you think of the process as a kind of scale transition from quantum to our macro scale, where one path as an observable phenomenon emerges from a state of "all possible paths taken."
When you think about this, you might see how it mingles with Max Tegmark's multiverse theory, in particular his level III many-worlds interpretation. Feynman himself suggested a closely related multiple histories interpretation of QM.
This underpinning (and unimaginable) possible quantum reality (all paths taken) could be thought of as a kind of nonlocal, or global, hidden variable. It acts not directly on particles but redefines them within their scale instead. It would result in a superimposed multiverse (existing strictly at the quantum scale with only the possible very rare exception of quantum tunneling). It would contain all quantum possibilities of all quantum processes that ever have and ever will occur in the universe. In such a quantum reality, each electron in the double slit experiment does, in fact, take every possible trajectory to the detector. In an instant, each particle has already built the interference pattern. From inside our macro-scale perspective, we observe only an artifact of that reality or, better put, we observe a different (emergent) reality where a single random path is observed and an interference pattern mysteriously builds up. The double slit experiment, therefore, becomes an opportunity to glimpse a direct translation of quantum reality into our "macro language." We don't see the ultimate reality of all those trajectories taking place at once (the source of the random strikes on the detector) and that's why our observations don't make sense to us. They do make sense, however, from the all-paths taken quantum path integral perspective.
We can see that the quantum entanglement phenomenon can also be a translation of quantum reality that we are reading in our macro reality terms. In such a quantum world, each of the two electrons shoot off in every possible direction simultaneously. In that quantum reality they are everywhere at the same time, and they are indeed part of a single entity, because their quantum states are superimposed (they share the same total momenta, angular momenta, and energy).
It seems confusing because most of the time we don't need to look into QM weirdness. In many cases, we can accurately describe a particle's behaviour as if it is a point-like particle that travels in a straight line. Think of the Rutherford gold foil experiment, in which an alpha particle** is shot at a relatively big gold atom. The occasional collisions between that particle and the nucleus can be described using classical dynamics. The alpha particle is deflected as if it were a small hard ball. Many other experiments also reveal the point-like nature of particles. Only experiments cleverly designed to single out quantum behaviour reveal it. Entanglement experiments tell us that it is useless to visualize electrons or photons or any subatomic particles as point-like particles. They never are point-like, except when we translate them into our scale (the alpha particle - nucleus collision though tiny is observed in our scale). Sometimes the translation seems seamless. A particle is observed as clearly a point-like particle or a wave. Sometimes it's almost lost (as in two entangled electrons experiment). What we observe is muddled.
Wave function collapse, from this perspective, is not a process (there is actually no mathematical framework describing this process by the way). Instead it is the transition from the quantum scale to the macro scale. We don't see a quantum particle/wave at all. We don't see any collapse. When we do see a "particle," it is the artifact-like trace of what that path integral represents in our reality, at our scale.
From a statistical standpoint, it looks as if we are measuring only one (random) degree of statistical freedom from within a quantum reality that contains countless degrees of freedom. In most experiments, what we observe is actually the path integral of all the possible degrees of freedom in that quantum system. Because they are path integrals, all the quantum randomness fits seamlessly into our perception of reality, in the same way that temperature makes sense – from a distance. The clever electron version of the double slit experiment is one of the few exceptions where one single (random to us) degree of freedom is plucked out at a time.
This statistical treatment brings to mind recent work done on a mathematical object called the amplituhedron. I wrote an article on it here. Like a multifaceted higher-dimensional jewel, its volume can calculate the probabilistic outcomes of particle collisions inside colliders, a very tedious job that is usually done by large computers, or it could be done by resorting to drawing many hundreds of Feynman diagrams. The amplituhedron is like a shortcut that circumvents those calculations and goes directly to a geometric assessment that can be quickly processed. The researchers also calculated a master amplituhedron that contains an infinite number of facets, analogous to a full circle (where every direction is represented) in two dimensions. Its volume, in theory, represents the total amplitude of all physical interactions in the universe. Lower dimensional amplituhedra live on the faces of this structure and represent our observations when a finite number of particles collide.
Both Feynman diagrams and the amplitudehron seem to do the same thing. The Feynman diagrams take the scenic route (it takes so many of those calculations) and the amplitudehron takes the direct route. Both can predict the probabilities of creating various kinds of particles when two massive particles collide with each other in a collider. Both serve as a kind of translator taking information from the quantum scale that we can't directly access and turning it into a macro-scale form we can observe.
Using a scale approach eliminates the need to make an unsavoury choice between "quantum-scale phenomena are random and don't make sense" and "there must be some hidden variable somewhere." Instead we come to a single consistent conceptual framework and we could say that Einstein was right after all. There is a hidden nonlocal variable in the sense that quantum reality is all possibilities at once. It can differ from reality at the macro scale because phenomena unique to the macro scale are emergent. The shift from one reality to the other is a shift in scale, where emergence takes place.
The question of whether an electron is physically real or not takes a back seat to the question of what scale we're talking about. What does this mean for the reality of a subatomic particle? For those readers who hope for a physically real particle, the picture here once again seems to strongly suggest that reality at its most basic level is strictly built of potentiality. Reality itself is redefined as a scale-dependent concept. We could argue that what we measure and observe in our quantum experiments (an electron doing something funky) is as real as all-paths-taken (the electron being in all places at once) and vice versa. In the same way that temperature is a real phenomenon to us but not to a subatomic particle, a path integral is real at the quantum scale but not to us. To us it is just a particle moving in a straight line from A to B. It might not satisfy some readers to say that a real object such as a chair, for example, consists of a collection of the statistical average of all possible quantum potentialities. How do we even experience the separateness of objects then? I would answer that "chair-ness" is an emergent property that is physically real to us at our scale.
There is an unexpected upside to this approach. The Holographic Universe principle provides a consistent (different) explanation for quantum entanglement but it takes the randomness of free will away in the process, something most people find abhorrent since we sense we can make random choices and change our futures. I tackled that principle a few years ago in this article. Thanks to the layer-cake nature of scale, we can retain our unpredictable free will even though the cells in our brains behave according to established predictable physical and chemical laws (two different scales). What this approach forbids is applying rules that work for one scale to another scale. The branch of psychology that tackles our conception of free will (ego, moral directive, our subconscious dreams, etc.) doesn't use the same language as neuroscience (axons, glial cells, receptor flooding, neurochemical reactions, etc.) for good reason. In physics, it can be all too easy to forget that caution, especially when many of us carry in the back of our heads the idea that there is one ultimate reality that should work in all cases, no matter what our perspective is. When it comes to quantum phenomena, we're lost.
When I say "rules" I don't mean that physical laws change from one scale to the next, nor am I suggesting that spacetime is something different at the quantum scale (no one knows what spacetime is at the quantum scale). I am also not suggesting that quantum phenomena could actually ever be observed (what do you bounce off an electron to "see" it without affecting it?) or verified directly. I mean the rules of observation and interpretation have to be scale-dependent. Just because a particle acts like a tiny hard ball in one experiment doesn't mean that the particle really is a tiny hard ball. I only argue that we can use a scale-dependent approach that borrows from the science of emergent phenomena to interpret what is going on in the double slit and entanglement experiments at the quantum scale.
*Here I mean only classical temperature – thermal motion or the degree of "hotness." The particle will have entropy as well and it can be precisely measured. Those entropies can in theory be added up and averaged to get temperature as well. That's the thermodynamic approach. In fact, temperature theory is quite complex (simply google "temperature"). I intend only the most basic classical kinetic approach in my example.
** An alpha particle is a helium nucleus consisting of protons and neutrons. According to QM, even though it is composite, it has its own specific de Broglie wavelength and acts just like any other singular quantum particle.