And he took him all these, and divided them in the midst, and laid each half over against the other… And it came to pass, that, when the sun was going down, a deep sleep fell upon Abram; and, lo, a dread, even a great darkness, fell upon him… And it came to pass, that, when the sun went down, and there was thick darkness, behold a smoking furnace, and a flaming torch that passed between these pieces.
Gen. XV, 10-17
The above verses from this week’s parshah (Torah portion) Lech Lecha (Gen. XII,1–XVII,27) describe the Covenant between the Parts (a.k.a. the Covenant of the Pieces), when God entered into eternal covenant with Abraham (at the time called Abram) – a covenant symbolized by halved animals. The simple meaning of this ritual is apparent: just as a halved animal only appear as two separate halves, in reality, they are two parts of one animal – so too making a covenant between two apparently separate entities – Jewish people represented by their forefather Abraham on the one hand and God on the other hand – unites them forever into an indivisible oneness. As the Zohar says, “Israel, Torah and God are all one.”
Another symbolism of the Covenant between the Parts is that it is a perfect metaphor for quantum entanglement. As we discussed many times on this blog, quantum entanglement is a unique property of quantum mechanics where two separate quantum-mechanical objects – particles or even whole atoms – are described by a single wavefunction (or a single state vector). Two entangled particles are truly one object. No matter how far they may be from each other – even in the opposite corners of the universe – each particle reacts instantaneously to a change in the state of the other particle. Say two particles are born as a result of a decay of another particle. Such particles remain entangled. If they have a spin, the law of conservation of angular momentum demands that their spins remain always in the opposite state. In other words, if one particle has its spin up (it “spins” clockwise, as it were), the other particle must have its spin down (it “spins” counterclockwise, as it were). After a while, these two particles move very far from each other while remaining entangled. Initially, the spin of both particles is in a state of superposition of up and down. If we collapse the wavefunction of one particle fixing its spin in a down direction, the other particle’s wavefunction collapses simultaneously, no matter how far removed, fixing the spin of that particle in the up direction. Einstein was deeply troubled by this phenomenon and called it a spooky action at a distance. However, it has been proven experimentally beyond reasonable doubt. Entangled particles act as a single object no matter what distance separates them.
More generally, two objects are entangled if, when we obtain information about one object, we improve our knowledge of the other object. For example, if we buy a pair of gloves packed in two boxes with each glove packed in its own box, if we open one box and find a right-handed glove, we don’t have to open the second box to know it contains a left-handed glove.
The Covenant between Parts is a perfect metaphor for the entanglement:
- Abraham was commanded to take several animals and split them in half. This is a metaphor for the fact that the primary source of entangled particles is a decay of another particle – when a large particle is “split” into two or more smaller particles, they remain entangled. However, just as two halves of one animal is still one animal, two entangled particles represent a single quantum-mechanical object described by a single wavefunction (or a single state vector).
- Like two gloves, two haves of an animal are asymmetrical – one is the right side, the other is the left side. Looking at one half and discovering that it is the right half allows us to immediately know that the other half is the left half without even looking at it. Thus, obtaining information about one half of the animal improves our knowledge of the other half, which is the definition of entanglement.
- The birds that were not split in half symbolize this oneness – just as they remain whole, divided animals in certain sense also remained whole. Similarly, two entangled particles only appear to be two separate objects while, in reality, they are one object.
- The animal halves are placed one opposite the other – this symbolizes the fact that, due to conservation laws, certain quantum-mechanical properties of entangled particles, such as spin, must be always in the opposite state.
- What unites two entangled particles separated by distance, is a single wavefunction (or a single state vector), which they share. This is symbolized by the torch of fire that passed between the parts: “and a flaming torch that passed between these pieces.” A torch is a metaphor for a state vector. A torch produces light, which is an electromagnetic wave – a metaphor for the wavefunction. Biblical commentators explain that this torch reunited and fused separate parts together. Indeed, it is the wavefunction that binds two separate entangled particles into a single object.
- “…Behold a smoking furnace…” – the smoke appeared together with the torch of light between the parts. As we discussed in several posts on this blog, smoke represents uncertainty as it blurs the vision. Quantum entanglement is inextricably tied with quantum uncertainty.
- “…When the sun was going down, a deep sleep fell upon Abram; and… even a great darkness, fell upon him.” Sleep and darkness both symbolize diminishing information. Our senses are dulled during sleep and we are deprived of information about our surroundings. Similarly, we can’t see in darkness and lack information about our environs. This is a metaphor for the probabilistic nature of quantum mechanics. An observer lacks sufficient information about whereabouts of a particular particle and, at best, can predict the probability of finding the particle in a certain area. Einstein was equally troubled by this fuzziness of quantum theory, which he helped to conceive. He famously told his friend, Niels Bohr, “God doesn’t play dice. To which Bohr replied, “Quit telling God what to do!” Einstein felt that quantum mechanics provides an incomplete description of the reality and that there must be some hidden variables that supply the rest of the information. Unfortunately for Einstein, in 1964, physicist John Stuart Bell proved that there are no hidden variables. Bell’s Theorem proves that no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. Physicist Henry Stapp described Bell’s theorem as “the most profound discovery of science.” There are no hidden variables; and physical reality, on its most basic subatomic level, is fundamentally fuzzy. This inherent dream-like fuzziness and a bit of “darkness” (i.e., lack of information about hidden variables) are hinted at by this biblical verse.
Interestingly, on October 21st, 2015, when this post was first written, during the week when we read that year parshah Lech Lecha, The New York Times published an article “Sorry, Einstein. Quantum Study Suggests ‘Spooky Action’ Is Real.” This article reported a landmark experiment conducted by physicists at Delft University of Technology in the Netherlands that provided so far the strongest evidence of quantum entanglement and Bell’s Theorem. The group led by Ronald Hanson, a physicist at the Dutch university’s Kavli Institute of Nanoscience, describe their experiment as a “loophole-free Bell test”. The timing of this article was uncanny.