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

On this blog, we often discuss the collapse of the wavefunction as the result of a measurement. This phenomenon is called the “measurement problem.” There are several reasons, for which the collapse of the wavefunction—part and parcel of the Copenhagen interpretation of quantum mechanics—is considered a problem. Firstly, it does not follow from the Schrödinger equation, the main equation of quantum mechanics that describes the evolution of the wavefunction in time, and is added ad hoc. Second, nobody knows how the collapse happens or how long the wave function takes to collapse. This is not even to consider that any notion that the collapse of the wavefunction is caused by human consciousness, as proposed by Von Neumann, leading to Cartesian dualism, is anathema to physicists. It is a problem, no matter how you look at it. What is the solution? The most radical, but the most accepted solution is 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 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—Bryce DeWitt called it “schizophrenia with vengeance”—is actually the most straightforward interpretation of the mathematical formalism of quantum mechanics because it does not rely on an ad hoc collapse of the wavefunction. Recall that the Schrödinger equation does not describe the evolution of a physical system per se, but the evolution in time of the wavefunction describing the state of the system.


Max Born

Max Born interpreted the wavefunction as the measure of the probability of finding the system in a particular state. More precisely, the squared 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 the 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. Instead, all possible states are realized in different universes.  Every time-irreversible event – be that a transition between quantum-mechanical states or the measurement – splits the world into as many branches as there are possible outcomes, which are all 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 our universe branching out 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 all along, 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 during 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 the 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 Tikkun (Rectification) 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 us look into this week’s Torah portion – Vayera. The second verse says:

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

The Zohar suggests that the three persons who came to visit Abraham in Mamre were 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 Mesorah, 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 binding of Isaac, the Akeida, an angel called to Abraham from heaven and said,

Abraham! Abraham! (Genesis 22:11).

There is a vertical line (a cantillation mark) between the first Abraham and the 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 by Rabbi Dovber of Lubavitch) explain that the pause is required to distinguish between the celestial Abraham and the terrestrial Abraham.


Abraham and three Angels, 1966 – Marc Chagall

In this Torah portion, Vayera, 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 the 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 week’s portion Lech Lecha, when G‑d 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, with whom he ultimately meets in this Torah portion, Vayera.

Each Jew, a descendant of Abraham, has a celestial counterpart, the higher self – it is called the G‑dly soul – nefesh Elokit.  When Abram was told by G‑d 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 G‑d 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 G‑dly soul, inside. As the Tanya says, every Jew possesses nefesh Elokit, which is helek Eloka memaal mamash – “a part of G‑d 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 G‑dly 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.