Uncertainty Principle

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The Tree of Knowledge as a Quantum-Mechanical Metaphor

To Mendel Almost three years ago, in December of 2019, I posted an essay, "The Tree of Knowledge as a Metaphor for Superposition of States and Heisenberg’s Uncertainty Principle." The manuscript of that essay contained an addendum with a short primer on the superposition of states in quantum mechanics and quantum-mechanical treatment of the primordial sin. It expressed the ideas of Maimonides about primordial sin in precise mathematical formulas proving the exact parallel between the fruit of the tree of knowledge of good and evil and a quantum eraser. Realizing that only people familiar with the formalism of quantum mechanics would understand that part of the essay and fearing losing my readers, I decided to omit the addendum entirely. However, the addendum is arguably the most interesting part of the essay, because it [...]

Akeida in Parallel Universes

Michael Frayn’s 1998 play, Copenhagen, concerns a meeting between two great physicists, Niels Bohr and Werner Heisenberg, in 1941 in Copenhagen. In this play, the spirits of Heisenberg, Bohr, and Bohr’s wife, Margrethe, come together in the afterlife to answer Margrethe’s question, “Why did Heisenberg come to Copenhagen?” Bohr and Heisenberg worked closely together in Copenhagen in the 1920s while developing atomic physics, resulting in the formulation of quantum mechanics. Bohr was already an accomplished scientist when the young German Heisenberg joined his group, and Bohr began mentoring him. Heisenberg became one of the leading figures in formulating the new quantum mechanics. Later, Heisenberg joined the group of German physicists developing nuclear weapons for Nazi Germany. Why did Heisenberg return to Copenhagen in 1941? Denmark was at that time already occupied by Germany. [...]

Tzimtzum III—Renormalization—Sweeping Infinites Under the Rug

Sweeping Infinities Under the Rug—or Renormalization Having dealt with internal contradictions in the previous section (see Physics of Tzimtzum I — The Quantum Leap and Physics of Tzimtzum II — Collapse of the Wave Function), we are left with another problem—infinity. Although G‑d concealed His self-contradictory nature by “sweeping paradoxes under the rug” in the process akin to the collapse of the wave function, the Light of the Infinite (Ohr Ein Sof) filled the whole of existence with infinite Divine emanation. This infinite radiation left no room for any finite creation to emerge. What was G‑d to do? Having aced the exam on quantum field theory with flying colors, G‑d employed the favorite trick of theoretical physicists in sweeping infinities under the rug using what is called “renormalization.”[1] Roughly speaking, renormalization solves the [...]

Abel and Cain Conflict—Wave-Particle Duality

…And Abel was a keeper of sheep, but Cain was a tiller of the ground. And in process of time it came to pass, that Cain brought of the fruit of the ground an offering unto the Eternal. And Abel, he also brought of the firstlings of his flock and of the fat thereof. And the Eternal had respect unto Abel and to his offering; but unto Cain and to his offering He had not respect. And Cain was very wroth, and his countenance fell. And the Eternal said unto Cain: “Why art thou wroth? and why is thy countenance fallen? If thou doest well, shall it not be lifted up? and if thou doest not well, sin coucheth at the door; and unto thee is its desire, but thou mayest rule over it.” And Cain spoke unto Abel [...]

The Tree of Life and Wave Mechanics

As we discussed in the earlier post, The Tree of Knowledge as a Metaphor for Superposition of States and Heisenberg’s Uncertainty Principle, the Heisenberg uncertainty principle is a direct consequence of wave-particle duality. If so, shouldn’t we expect to see some hints at the wave nature of reality in the narrative of the Garden of Eden? And the Tree of Life (Etz HaChaim): what was it doing in Eden? It appears in the narrative only twice—in the very beginning and at the very end of the story of the primordial sin—almost as if to put a frame around the picture. At the start of this narrative, the verse states: And the Lord G‑d planted a garden eastward, in Eden; and there He put the man whom He had formed. And out of the ground [...]

Why the first humans were not allowed to eat from the Tree of Knowledge

As always in science, every answered question breeds new questions. Now that we understand that the Tree of Life and the Tree of Knowledge are metaphors for, respectively, the wave function and the collapse of the wave function (see my earlier post, "The Tree of Knowledge as a Metaphor for Superposition of States and Heisenberg’s Uncertainty Principle"), we are faced with more questions. Why did G‑d not want Adam and Eve to eat from the Tree of Knowledge? And what was so terrible about the forbidden fruit that eating it warranted capital punishment?[1] Let us recall that, according to our tradition, Adam and Eve were prohibited from eating from the Tree of Knowledge only for three hours. Adam and Eve were created on the sixth day—the Eve of the Sabbath (Erev Shabbat). With [...]

The Tree of Knowledge as a Metaphor for Superposition of States and Heisenberg’s Uncertainty Principle

And out of the ground made the Lord G‑d to grow every tree that is pleasant to the sight, and good for food; and the tree of life also in the midst of the garden, and the tree of the knowledge of good and evil. (Genesis 2:9) And the Lord G‑d commanded the man, saying: “Of every tree of the garden thou mayest freely eat; but of the tree of the knowledge of good and evil, thou shalt not eat of it; for in the day that thou eatest thereof thou shalt surely die.” (Genesis 2:16–17) Upon creating Adam and Eve, G‑d permitted them to eat any fruit from the Garden of Eden, except for the forbidden fruit—the fruit of the Tree of Knowledge. Disregarding this injunction, Adam and Eve ate the forbidden [...]

Ẓiẓit, Koraḥ, and Wave-Particle Duality

The Lord spoke to Moses, saying: Speak to the children of Israel and you shall say to them that they shall make for themselves fringes [ẓiẓit] on the corners of their garments, throughout their generations, and they shall affix a thread of sky blue [wool] on the fringe of each corner. (Num. 15:37,38) They [Koraḥ and his men] assembled against Moses and Aaron, and said to them, “You take too much upon yourselves, for the entire congregation are all holy, and the Lord is in their midst. So why do you raise yourselves above the Lord's assembly” (Num. 16:3) The Torah portion Shelach deals primarily with the fiasco of the spies sent by Moses to scout out the land of Canaan. The portion ends, however, seemingly out of turn, with the commandment to [...]

Second Adar – The Month of Quantum Physics

Today is Rosh Chodesh Adar Bet – the New Moon and the beginning of the second month of Adar.  If we ever to have a month commemorating quantum physics, there would be no more appropriate month for that than the second month of Adar – Adar Bet.  A state of superposition is a physical state unique to quantum theory.  In classical physics (such as Newtonian mechanics or thermodynamics) a physical system is either in one state or the other, say in a state A or a state B. Only in quantum physics a system can be in a blended state C which is a linear superposition of states A and B. For example, the spin of an electron can be either Up or Down.  However, an electron can be in a blurred state of [...]

Splitting of the Sea

Do you like riddles?  Here is a riddle – what do these two figures represent in the context of Exodus?   No Idea?  How about a hint? Still no idea? Okay, here is the answer: Yes, the first figure represents two doorposts and the lintel marked with the blood of Passover sacrifice, as it says: וְלָקְחוּ, מִן-הַדָּם, וְנָתְנוּ עַל-שְׁתֵּי הַמְּזוּזֹת, וְעַל-הַמַּשְׁקוֹף--עַל, הַבָּתִּים, אֲשֶׁר-יֹאכְלוּ אֹתוֹ, בָּהֶם And they shall take of the blood, and put it on the two side-posts and on the lintel, upon the houses wherein they shall eat it.  (Ex. 12:7) The second picture is of the splitting of the sea, as it says: וַיָּבֹאוּ בְנֵי-יִשְׂרָאֵל בְּתוֹךְ הַיָּם, בַּיַּבָּשָׁה; וְהַמַּיִם לָהֶם חוֹמָה, מִימִינָם וּמִשְּׂמֹאלָם And the children of Israel went into the midst of the sea upon the dry ground; and the [...]

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