And he [Abraham] lifted up his eyes and looked, and, lo, three men stood over against him…  (Gen. 18:2)

On this blog, we often discuss a collapse of the wavefunction as the result of a measurement. This phenomenon is called by some physicists the “measurement problem.” There are several reasons, why the collapse of the wavefunction—part and parcel of the Copenhagen interpretation of quantum mechanics—is called a problem. Firstly, it does not follow from the Schrödinger equation and is added ad hoc. Secondly, nobody knows how it happens or how long it takes to collapse the wavefunction.  This is not to mention that any notion that the collapse of the wavefunction is caused by human consciousness leading to Cartesian dualism is anathema to physicists. It is a problem, no matter how you look at it. What is the alternative, you may ask? —The many-worlds interpretation of quantum mechanics.

Hugh Everett

Proposed by Hugh Everett  in 1957 (H. Everett, Review of Modern Physics, July 1957) and developed by Bryce de Witt, (B. S. DeWitt and N. Graham, The Many-Worlds Interpretation of Quantum Mechanics, Princeton Univ. Press, 1974) the many-worlds interpretation of quantum mechanics is, perhaps, the most outlandish, but yet the cleanest interpretation of the Schrödinger equation.  This theory suggests that every transition between quantum states splits the universe into multiple copies or “branches,” in which all of the possible states are realized.

Bryce de Witt

This approach, as weird as it sounds, is actually the most straightforward interpretation of the mathematical formalism of quantum mechanics, because it does not have to rely on an ad hoc collapse of the wavefunction, which in no way follows from the Schrödinger equation. Recall that Schrödinger equation does not describe the evolution of physical system per se, but the evolution in time of the wavefunction of the system.

Max Borne

Max Borne interpreted the wavefunction as the measure of the probability of finding the system in a particular state. More precisely, square of the amplitude of the wavefunction is the probability of finding the system in a certain region of the configurational space. Thus we cannot say anything certain about finding the system in any particular state. We can only speak of probabilities of finding the system in a particular state or place. However, when we measure parameters of the system such as its position, or momentum, we always get a particular value of the parameter we measure. It is as if the cloud of probabilities has suddenly collapsed to a single point—the value we find in an experiment. Hence, the measurement problem.  Instead, Everett suggested that no collapse takes place, but that all of the possible states are realized in different universes.  Every time-irreversible event, be that a transition between quantum-mechanical states or measurement splits the world into as many branches as there are possible outcomes, which are realized in respective branches of the universe.

A more recent variation on this theme is a parallel-universe interpretation.  It differs from Everett’s original idea in two important aspects.  Everett and DeWitt spoke of branching every time there was a transition between quantum states.  So the world’s history looks like a huge tree, with the trunk in the past and an ever-increasing number of branches as time goes on.  In the parallel-universe version, the multitude of universes exists ab initio, and a wavefunction of a quantum-mechanical system is partitioned among these parallel universes.  Another difference is that, unlike the many-worlds theory that completely prohibits any communication between different branches, parallel universes can merge under certain circumstances, such as an interference experiment.  For example, in a double-slit experiment, a wavefunction of a photon is partitioned between two universes: in one, the photon passes through one slit, and in another, it passes through the second slit in a completely deterministic manner.  After that, due to interference, the two universes merge together producing a single tangible photon.

On this level, parallel universes remain an optional interpretation of quantum mechanics, which has its followers and its skeptics.  On the level of quantum cosmology, however, we are almost compelled to adopt this interpretation.  Indeed, in the quantum cosmology described by the Wheeler-DeWitt equation, the universal wavefunction Ψ(h, F, S) is defined on an ensemble of all possible space-like universes, and is interpreted as a probability amplitude to find a particular manifold S with a particular geometry h and non-gravitational fields F.  The Anthropic principle is usually invoked to select that universe which allows for emergence of life and intelligent beings that are capable of asking the question: which particular universe we live in.

It is remarkable that the many-worlds interpretation or parallel universes idea boasts among its supporters such luminaries as Richard Feynman, Steven Hawking, Murray Gell-Mann, Steven Weinberg, and some of the other best theoretical physicists of the twentieth century.

The classical Jewish sources are replete with the notion of multiple worlds and parallel universes.  Consider, for example, the universes of Tohu (Chaos) and Tikun (Restoration) that coexist parallel to each other.  Or the four worlds of ABYA: Atzilut (the world of Splendor), Briyah (the world of Creation), Yetzirah (the world of Formation) and Assiya (the world of Action), each of which is said to be subdivided into a myriad of parallel worlds.  Needless to say, all these “universes” denote spiritual rather than physical worlds.

The most troubling aspect of the many-worlds approach is that it suggests that the observer also splits into multiple copies completely oblivious of each other – “schizophrenia with a vengeance!”

Let’s look at this week’s Torah portion—Vayeira. The second verse says, “And he [Abraham] lifted up his eyes and looked, and, lo, three men stood over against him…  (Gen. 18:2)” The Zohar suggests that the three persons who came to visit Abraham in Mamre where no other than Abraham, Isaac, and Jacob.  Here we have a “celestial copy” of Abraham visiting the “terrestrial copy” of Abraham, the two coexisting in parallel universes. This idea is further stressed by the way we read the Torah scroll. According to the Messorah—the Jewish Rabbinical tradition—the Torah scroll is read using cantillation marks (taamey ha-miqra or “trope”) that one can find in Tikun Sofrim or in most printed editions of the Chumash (Pentateuch). Later in this Torah portion, in the story of the Akeida, an angel called to Abraham from heaven and said, “Abraham! Abraham!” (Gen. 22:11). There is a vertical line between the first Abraham and repetition of the name: “Abraham | Abraham.” This sign tells the reader to pause between the first Abraham and the second Abraham when reading the Torah scroll. The Kabbalah and Chassidic philosophy (see, for example, Hemshech Samech Vav) explain that the pause is required to distinguish between the celestial Abraham and terrestrial Abraham.

Abraham and three Angels, 1966 – Marc Chagall

In this Torah portion, at least in the Zohar’s interpretation, we read about the terrestrial Abraham meeting his celestial counterpart. This situation is analogous to the parallel universe interpretation of quantum mechanics, which allows for the occasional merger of parallel universes. Indeed, it is as if the spiritual universe—the abode of the celestial Abraham—merged for a moment with the physical universe—the abode of the terrestrial Abraham—to allow for their face-to-face encounter.

Biblical commentators struggle to explain the meaning of the language used by the Torah in the last weeks portion Lech Lecha, when God tells Abram “lech lecha,” lit. go to yourself. Seemingly, it does not make sense in a literal translation. Some translators simply read out “to yourself” part,  others translate it as “for your own good,” which is far from the literal meaning. Given our explanation above, perhaps it simply means a commandment for Abram to go to himself—his higher self, his celestial counterpart, of which we read in this Torah portion.

Each of us has such celestial counterpart, our high self—it is called the Godly soul—nefesh Elokit.  When Abram was told by God to leave his land and his father’s house and go to his higher self, Abram was not a Jew yet—this was before the covenant God made with him, before he was given a new name—Abraham. He only merited to meet his higher self after his circumcision, after he became the first Jew. Children of Abraham, the Jewish people, have their higher self, their Godly soul, inside. As the Tanya says, every Jew possesses nefesh Elokit, which is helek Eloka memaal mamash—“a piece of God from above indeed.” Thus, our task is not going outside ourselves to seek our higher self, as our forefather Abraham had to do, but to direct our attention inward, to return to our true Godly self. That is why the word teshuvah should not be translated as “repentance” but as “return,” which is what it literally means—return to our higher self. Our father Abraham paved the way for us.

“Abraham Serving the Three Angels” by Rembrandt, oil on canvas, 1646.