There were men who were ritually unclean [because of contact with] a dead person, and therefore could not make the Passover sacrifice on that day. So they approached Moses and Aaron on that day. Those men said to him, “We are ritually unclean [because of contact] with a dead person; [but] why should we be excluded so as not to bring the offering of the Lord in its appointed time, with all the children of Israel? Moses said to them, “Wait, and I will hear what the Lord instructs concerning you.” The Lord spoke to Moses saying: “Speak to the children of Israel saying, Any person who becomes unclean from [contact with] the dead, or is on a distant journey, whether among you or in future generations, he shall make a Passover sacrifice for the Lord. In the second month, on the fourteenth day, in the afternoon, they shall make it; they shall eat it with unleavened cakes and bitter herbs. They shall not leave over anything from it until the next morning, and they shall not break any of its bones. They shall make it in accordance with all the statutes connected with the Passover sacrifice.” (Numbers 9:6-12)
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 or tails. A top also has two possible states—it can be spinning clockwise or counterclockwise. Light can have two states as well—being in vertical polarization or horizontal polarization. In classical mechanics, a system can only be in a single state, i.e., at any given point in time, a coin can be either in the state “heads” or in the alternative state “tales”. A top can either be spinning clockwise or counterclockwise.
In quantum mechanics, a system can also be in a state of superposition. Let us say, the system has two possible states A and B. If a system can be in a state of superposition of these two states, this state is denoted in Dirac bra ket notations as |C〉= a|A〉 + b|B〉, where a and b are, roughly speaking, the probabilities of finding the system in state A or B. For example, an electron can be in state spin-up |↑〉 or spin-down |↓〉. Electron’s spin can be in a state of superposition of spin-up and spin-down: c1|↑〉 + c2|↓〉 – where c1 and c2 are coefficients that squared give us probabilities of finding the electron in a state spin-up or spin-down.
A wave function is a mathematical object that describes the state of our knowledge about the quantum mechanical system. According to Born Rule, the probability (more precisely, the probability density) of finding a system in a given state, when measured, is proportional to the square of the amplitude of the system’s wave function at that state. The wave function obeys the Schrödinger equation—the main equation of quantum mechanics—which predicts the probability distribution of finding the system in various states. Because the Schrödinger equation is linear, any linear combination of its solutions is also a solution of this equation. Therefore, quantum mechanics allows the existence of a superposition (that is, a linear combination) of many states. When we measure the state of the system, we “collapse” the wave function and find the system in one of these states.
When a system is in a state of superposition, strange things can happen. For instance, an electron can be “spinning” clockwise and counterclockwise at the same time (in reality, an electron is not spinning, it behaves as if it was spinning, generating a magnetic field and angular momentum), and Schrödinger cat can be both dead and alive or neither dead nor alive.
Torah gives us many many examples of the superposition of states. One such example is manna, which was in a state of superposition of all possible tastes (whichever food a person eating manna would imagine, that is how it tasted).
Another example is the commandment of the Second Passover, Pesach Sheni, described in the Torah portion Behaalotecha. Those people, who were unable to bring the Passover sacrifice on time, that is, on the 14th of the month of Nisan, were given a second chance to bring the Passover sacrifice (Korban Pesach) a month later, on 14th of Iyar.
The amazing thing, however, was that while eating Passover lamb with matzot, those who brought Korban Pesach on Pesach Sheini were allowed to eat bread. Let’s think about it. Usually, the whole year we eat leaven bread, chometz (let’s call this state “Chometz”), while on Passover we must remove all chometz from our houses, and we are only allowed to eat unleavened bread, matzah (let’s call this state “Matzah”). On Pesach Sheni, however, we are allowed to eat chometz and matzah. In other words, we find ourselves in the state of superposition of |Chometz〉 + |Matzah〉! (One could argue, of course, that every day, except for Passover, we can eat bread and matzah because there is no prohibition of eating matzah during the year. The point is that on Pesach Sheini, those who did not have a chance to offer Passover sacrifice in its proper time, got a second chance to bring this sacrifice on the 14th of Iyar. Eating Korban Pesach, however, requires eating it with matzah. So for those bringing Passover sacrifice on Pesach Sheini, eating of matzah was mandatory—it was a mitzvah, although no prohibition to eat bread applied.)
I grew up in Russia in a secular family, which did not observe Jewish holidays. We didn’t have a Jewish calendar and didn’t even know when the High Holidays came about. We wouldn’t know about Passover either, if not for my Uncle Yosef who lived in Zhytomyr, Ukraine, where my mother’s family came from. Uncle Yosef was the only surviving brother of my grandmother Sophia (Sarah). They had eleven siblings but most of them were murdered either by Kazaks during pogroms or by Nazis during World War II (may G‑d avenge their blood!). My grandmother and Uncle Yosef were the only ones who made it alive. Every year, in the spring, we would receive a package from Zhytomyr from Uncle Yosef with a box of matzahs. We didn’t know exactly when the Passover would start, but we knew it was close, and for a month or so we’d eat every day matzah… and bread. We didn’t know better. All my childhood Passovers were akin to Pesach Sheini—in a state of superposition of |Chometz〉 + |Matzah〉. Growing up in a secular culture among Russians left me confused: was I a Jew or a Russian? I grew up in a state of superposition of |Jew〉 + |Russian〉. That is, until I collapsed my wavefunction and chose the state of being a Jew. This is my story told in terms of quantum physics.
Pesach Sheini, however, is a story of every ba’al teshuva, a person who returns to his or her roots and who has to choose between two states. Luckily, the story of Pesach Sheini teaches that it is never too late.