Superposition

/Superposition

Day Six – the State of Superposition

And God saw all that He had made, and behold it was very good, and it was evening and it was morning, the sixth day. (Gen. 1:31)   The Biblical narrative of creation concludes with the above verse. Rabbi Shlomo Yitzchaki (a.k.a. Rashi) comments on this verse: the sixth day: Scripture added a “hey” on the sixth [day], at the completion of the Creation, to tell us that He stipulated with them, [“you were created] on the condition that Israel accept the Five Books of the Torah.” [The numerical value of the “hey” is five.] (Tanchuma Bereishith 1). Another explanation for “the sixth day”: They [the works of creation] were all suspended until the “sixth day,” referring to the sixth day of Sivan, which was prepared for the giving of the Torah (Shab. 88a). [...]

Sabbatical Year – when the Wavefunctions are Collapsed

The Torah portion, Re’eh, talks about the Sabbatical Year—in Hebrew, Shemitah—the Seventh year. When the Sabbatical year comes, all loans are forgiven, and Jewish servants go free. This is difficult to understand. Why would a lender forgive a loan just because it’s the seventh year in the Shemitah cycle? Why would slaves be set free just because it’s the Sabbatical year? Another question is why do we translate Shemitah as the “Sabbatical year”? Besides the fact that it is the seventh year, and Shabbat is the seventh day, what connects the word “shemitah” with Shabbat? As Rabbi Yehoshua Steinberg writes in Biblical Hebrew Etymology, (see Re’eh: The Slippery Year? – The Wonders of the Holy Tongue), the three-letter root of the word “shemitah” – Shin-Mem-Tet – connote falling, collapsing, slipping, weakening, or disintegration. The two-letter [...]

Re’eh – the Power of Seeing the Blessings

The Torah portion Re’eh, begins with the verse: Behold, I set before you this day a blessing and a curse. (Deut. 11:26) The first word of this verse, re’eh, literally means “see” in Hebrew. So, literally, this verse should be translated as: See, I set before you this day a blessing and a curse Why did Moses implore people to see, as he was about to set before them a blessing and a curse? To understand this, we need to look at the following verses defining the blessing and the cure: The blessing, if ye shall hearken unto the commandments of the Lord your God… (Deut. 11:27) …and the curse, if ye shall not hearken unto the commandments of the Lord your God… (Deut. 11:28) Does this remind you the setup of the [...]

Symmetry and Love — Jewish Chromodynamics

Ye are standing this day all of you before the Lord your God: your heads, your tribes, your elders, and your officers, even all the men of Israel, your little ones, your wives, and thy stranger that is in the midst of thy camp, from the hewer of thy wood unto the drawer of thy water; that thou shouldest enter into the covenant of the Lord thy God—and into His oath—which the Lord thy God maketh with thee this day. (Deut. 29:9-11) The above verses at the beginning of the Torah portion Nitzavim that is always read in the week preceding the Jewish New Year, Rosh HaShanah, are usually interpreted in terms of the unity of Jewish people: You are standing this day all of you [read: standing together in perfect unity]. This is not [...]

Half-Shekel – Metaphor for Entanglement

This they shall give, everyone who goes through the counting: half a shekel according to the holy shekel. Twenty gerahs equal one shekel; half of a shekel shall be an offering to the Lord Ex. 30:13 In this week’s Torah portion, Ki Tisa (Ex. 30), Jewish people are given the commandment of donating a coin as atonement, not just a coin – half a coin. But why half? If God thought, twenty gerahs would be too much, He could have commanded Moses to mint another coin worth ten gerahs. But no, the coin was to remain what it was—worth twenty gerahs—and Jews were to give half a coin. Don’t you find it peculiar? I don’t, because half-coins are my favorite metaphor when explaining entanglement to my physics students. What is entanglement? When obtaining [...]

Chanukah Menorah, Burning Bush and Sotah

As I wrote in my previous post, Schrödinger  Menorah:  Burning  And  Not  Burning, the Lubavitcher Rebbe explains the miracle of Chanukah as a paradox of the menorah burning and not burning, thereby embodying the absolute nature of God, who is not limited by His infinity but combines all possibilities including infinitude (ko’ach bli gvul) and the finitude (ko’ach hagvul). The notion of the menorah burning and not burning easily lends itself to be cast in terms of the quantum superposition of states of burning and not burning. I couldn’t help myself to call it a Schrödinger Menorah. There a couple of problems, however, with this idea. Firstly, as the Rebbe wrote in 1971 in a letter to the editor of the Journal of the Association of Orthodox Jewish Scientists, “The idea of miracles implies [...]

Schrödinger Menorah: Burning and not Burning

The miracle of Chanukah revolves around a single-day-supply of olive oil burning for eight days during the rededication of the Holy Temple in Jerusalem (Bet HaMikdash), after Maccabees liberated Israel from the occupation by the Seleucid empire. There are countless explanations of the miracle of the oil lasting eight days. The Lubavitcher Rebbe offers a unique explanation. The Rebbe dismisses any explanation of the miracle that relies on the miraculous nature of the oil itself. The Rebbe maintains that to be kosher for the Menorah, the oil had to be natural olive oil, not some miraculous oil. According to the Rebbe, the miracle was that the natural oil was burning and not burning at the same time. The Rebbe draws an analogy with the dimensions of the Ark (Aron HaKodesh) in the Holy [...]

Quantum Thoughts on Nitzavim and Vayelech

According to the Saadia Gaon, these two parshioth are really one parshah, which sometimes is split into two.  In the language of Quantum Mechanics (QM) the two parshioth are entangled and have one state vector, i.e., they are described by the single wavefunction.  Needless to say, this is not meant in a literal sense, as QM describes physical objects, whereas these biblical chapters are certainly not.  Nevertheless, b’derech drush, we can loosely say that these parshioth are entangled, i.e., they are joint into one.  These two Nitzavim and Vayelech speak of the opposite themes – “nitzavim” connotes standing( lit., you stand), while “vayelech” connotes walking (lit., …and he walked). As much as it seems paradoxical at first, from the physicist’s point of view, it is not surprising at all.  Typically, entangled objects have [...]

When was the World Created?

There is a dispute in the Talmud as to when was the world created. According to Rabbi Eliezer, the world was created in the month of Tishrei. According to Rabbi Yehoshua, the world was created in the month of Nisan (Tr. Rosh Hashanah (10b)). The Chasidic thought attempts to reconcile these opposite opinions suggesting that both opinions are correct—the world was created in Nisan in thought, whereas in deed, it was created in Tishrei. The problem with this approach is that for halakhic (Jewish ritual law) purposes of calculating Jewish calendar, the planets are deemed to have commenced their heavenly orbits in Nisan, not in Tishrei! How could planets that haven’t yet been actually created, start their orbital movements in Nisan?! This can be explained by using the approach I suggested in my post [...]

Pesach Sheini – in a State of Superposition

In physics, we speak of systems and states. A system is a collection of physical objects (particles, waves, etc.). A system can be in various states. For example, a coin could have two states – heads and tails. A top also has two possible states – it can be spinning clockwise or counterclockwise. Light can have two states as well – being in the vertical polarization or horizontal polarization. In classical mechanics a system can only be in a pure state, i.e., at any given point in time, a coin can be either in a state “Heads” or the alternative state “Tales”. A top can be spinning either clockwise or counterclockwise, each of which is a pure state. In quantum mechanics, a system can be in a pure state or in a state [...]

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