In physics, we speak of systems and states. 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 too – being in 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 of superposition. Let us say, the system has two possible states A and B. If a system is in a pure state it is either in state A or B. However, a system can be in a state of superposition of these two states – state aA + bB, where a2 and b2 are the probabilities of finding the system in state A or B. For example an electron can be in state Up – ↑ or state Down ↓, or it can be in a state of superposition of Up and Down – c1↑ + c2↓ – where c1 and c2 are coefficients that squared give us probabilities of finding the electron Up or Down: pup = |c1|2 and pdown = |c2|2. When we measure the state of the system, we collapse the wavefunction and find the system in one of the states.
When 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 and Schrödinger cat can both dead and alive.
Today we read the Torah portion of Behaalotecha, which gives several examples of superposition of states. One 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, which I want to focus on, is the commandment of Pesach Sheni – the Second Passover. Those people, who were unable to bring Passover sacrifice on time – on the 14th of Nissan – where given the second chance to bring the Korban Pesach (Passover sacrifice) 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 each unleavened bread – matzah (let’s call this state Matzah). On Pesach Sheni, however, we are allowed to each chometz and matzah – in other words, we find ourselves in the state of superposition of (Chometz + Matzah)!
I grew up in Russia in secular family, which did not observe Jewish holidays. We didn’t have Jewish calendar and didn’t even know when the High Holidays – Rosh HaShanah and Yom Kippur – came about. We wouldn’t know about Passover either, if not for my uncle Yosef who lived in Zhitomir, Ukrain, where my mother’s family came from. Uncle Yosef was the only surviving brother of my grandmother Sarah. They had 11 siblings but most of them were murdered either by Kazaks during pogroms or Nazis during the World War II (may God 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 Zhitomir from uncle Yosef with a box of matzahs. We didn’t know exactly when the Passover would start, but we knew it was close, so for a month or so we’d eat every day matzah… and bread. We didn’t know better. All my early Passovers were akin to Pesach Sheini – in a state of superposition (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 mixed state of superposition (Jew + Russian). That is, until I collapsed my wavefunction and chose the state of being a Jew. This is my story told in quantum terms. Pesach Sheini, however, is a story of every ba’al teshuva 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.