Alexander I. Poltorak

Fitting Pieces of the Puzzle Together

Meditations on the Maaseh Merkavah – IV

This is the fourth and the final installment in the series of posts related to Ezekiel’s prophesy, Ma’aseh Merkava, “The Making of the Chariot.” For background information, refer to the previous posts, “Space – Between Future and Past,” “Relational Space,” and “Collapse of the Wave Function.”

Regular readers of my blog may be wondering about my last post “Futurist Interpretation of Quantum Mechanics,” which was about my new interpretation of quantum mechanics. This is not a physics blog, however; the Quantum Torah blog is about Torah and physics (or, more broadly, Torah and science). What did the last post have to do with Torah? Hopefully, it will all now become clear.

Last Shavuot I had a very unusual experience. Sitting in shul listening to the reading of Ezekiel’s prophesy, Maaseh Merkava, got me thinking about the meaning of the four faces of “living creatures”— Chayot—the angelic beings in Ezekiel’s vision. According to Kabbalah, these four faces correspond to the four letters of the ineffable name of God, Havayah or Tetragrammaton – Y-H-W-H. I had several distinct thoughts in rapid succession, which were all fully formed and crystal clear as if placed into my head from the outside. Although seemingly disconnected, they were all related to various aspects of physics about which I had been thinking on and off over the years.

As I described in my first post on this topic, “Space – Between Future and Past,” Chokhmah (the sefirah corresponding to the letter Yud of the Tetragrammaton) is the spiritual precursor of the aspect of time we call the past. Binah, (the sefirah corresponding to the letter Heh of the Tetragrammaton) is the spiritual precursor of the aspect of time we call the future. Six sefirot (Chesed, Gevurah, Tiferet, Netzach, Hod, and Yesod collectively called partzuf Zeer Anpin and corresponding to the letter Waw) is the spiritual precursor of space. The reason Kabbalist associate space with Zeer Anpin (Z”A) is because our three-dimensional space has six directions (up-down, front-back, right-left) represented by the gematria (numerical value) of the letter Waw.

I later thought that the letter Waw may be better related to a six-dimensional space called the phase space which is made of three special coordinates (X, Y, Z) and three components of momentum (Px, Py, Pz). The state of any particle is represented by its position in the phase space. In the phase space, every degree of freedom is represented by a dimension (an axis) in a multi-dimensional space. (see 613 Degrees of Freedom and Maarat HaMachpelah – Double Cave.) The phase space is used in Hamiltonian mechanics and in quantum mechanics, which uses Hamiltonian formalism. I thought that, perhaps, Zeer Anpin better represents this six-dimensional phase space, which is used in quantum mechanics.

The structure of the Tetragrammaton suggested to me that the space-time geometry may not be like Minkowski spacetime of special relativity, where time and space are fused together in a four-dimensional continuum, but rather like a fiber bundle, where each point of a one-dimensional timeline is replaced by or corresponds to a three-dimensional space. In this fiber bundle, the time is the base “space” (the word “space” is used here as an abstract mathematical space, not the physical space we live in), and the three-dimensional space we leave in is the fiber.  I also realized that space is identical to what we perceive as the present moment “positioned” between the future and the past, serving as an interface between past and future, as it were. As we travel through time (base), we jump from one 3-D space (fiber) to the next, which is perceived by us as the flow of time (or time-flux).

There is a direct connection to quantum mechanics. From the Special Theory of Relativity, which preceded the development of quantum mechanics by almost 20 years, we became accustomed to working with four-dimensional Minkowski spacetime. However, in quantum mechanics, even though it was developed later, we continue to use time and three-dimensional space separately as in pre-relativistic Newtonian physics. (The relativistic version of quantum mechanics was developed by Paul Dirac in 1928, but is only used as quantum electrodynamics or, more generally, quantum field theory). This is considered by some as one of the impediments to developing the quantum theory of gravity. I realized (which was a confirmation of my long-held belief that space-time was a fiber bundle) that the structure of the Tetragrammaton hints at the validity of separating space and time—the approach used in quantum mechanics. Moreover, it hints at the use of the six-dimensional phase space, which is indeed used in quantum mechanics.

As I described in the second post on this topic, “Relational Space,” my next insight was that space is relational. Although I thought so for as long as I can remember, the thought connecting this concept with the letters of the name Havayah was very satisfying. The connection to quantum physics lies in the fact that the relational spacetime made of spin foam is the basis for the quantum loop gravity, as I wrote in that post. What followed was the realization that the lines forming the underlying network represent interactions between particles due to gravitational coupling.

In my third post, “Collapse of the Wave Function,” I described how the first two letters of the name Havayah relate to the quantum-mechanical phenomenon known as the collapse of the wave function. I suggested that the letter Heh symbolizes the wave function describing the system in a superposition of states, and the letter Yud symbolized the collapsed wave function.

Let us recall now that the first three sefirot of the Tree of Life, Chokhmah, Binah, Da’at, represent in Kabbalah respectively past, future and present. The pseudo-sefirah, Da’at, is often associated in Kabbalah with partzuf Zeer Anpin (Z”A).  Now to bring all this together:

Yud  י  Chokhmah, Abba  Past  Collapsed wave function
Heh  ה  Binah, Imma  Future  The wave function
Waw  ו  Six Sefirot (Z”A)  Present  Space


We can now see the relevance of my last post, “Futurist Interpretation of Quantum Mechanics.” The collapse of the wave function is caused by the synchronization of the clocks bringing the future time of the quantum-mechanical system into the observer’s present and past. This also explains the position of one of the founders of quantum mechanics, Niels Bohr, which forms the basis of the Copenhagen interpretation, that the state of the quantum-mechanical system is only defined at the moment of measurement. Indeed, this state of a particle is defined as a point in the phase space, which only emerges at the present moment.

Now the puzzle is complete and all pieces fit together.

Kabbalists say that one can gain an understanding of the physical workings of the universe from the Ma’ase Merkava – the Work of the Chariot. It is hard, however, to translate the mystical vision of angelic beings into the language of physics, unless one studies both, Jewish mystical tradition and physics. This Shavuot, I was blessed with a glimpse of how the two beautifully fit together.

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About the Author
Dr. Alexander Poltorak is Chairman and CEO of General Patent Corporation. He is also an Adjunct Professor of Physics at The City College of New York. In the past, he served as Assistant Professor of Physics at Touro College, Assistant Professor of Biomathematics at Cornell University Medical College, and Adjunct Professor of Law at the Globe Institute for Technology. He holds a Ph.D. in theoretical physics.
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