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 the opposite values of their physical characteristics. Thus, for example, in a pair of two entangled electrons, they will always have spins pointing in the opposite directions. Moreover, the electrons are in a linear superposition of two states: spin up and spin down, which means that they are spinning, if it were, in the opposite directions; we just don’t know which is pointing up which is down. Measuring the spin of one electron in this entangled pair immediately fixes the spin of the second electron in the opposite direction: if we find the first electron spinning clockwise (spin up), the second electron immediately begins to spin counterclockwise (spin down).
So these two parshioth, which are really one, have the opposite themes as one would expect from the entangled parshioth. The Rebbe learns a lesson from this apparent paradox for our practical avodah – a Jew must stand strong, i.e. be firmly rooted in Jewish tradition, yet a Jew must be always on the move progressing higher and higher in the Divine service. In QM language, a Jew must be in a state of superposition of standing and moving. Just as with the example of two entangled electrons, as soon as a Jew is caught standing, he must start moving not being satisfied with his spiritual status quo. And as soon as he is caught moving, he must check how firmly he is grounded in his roots. This dichotomy is the quintessential property of the Divine service, which always embodies a superposition of opposite states – moving and standing, striving for spiritual while remaining physical, rotzo v’shov.
This duality is exemplified by mezuzah, which, on the one hand, must be firmly affixed to a doorpost so that the mezuzah doesn’t move (or one is not yotzeh with the mitzvah of mezuzah), on the other hand, the shoresh of the word mezuzah is zuz – to move. This duality is further exemplified by the way we affix a mezuzah on a doorpost. According to Rashi it should be vertical (or, more precisely, not horizontal) but according to Rabeinu Tam, it should be horizontal (or, more precisely, not vertical). Thus the mezuzah, like the Schrödinger cat, is in the state of linear superposition of two opposite states: vertical and horizontal. Since, quantum superposition is a property of the micro world and cannot be easily realized in the macro world in which we live, we simply acknowledge this superposition by placing the mezuzah on diagonal.
Speaking of entanglement, the main message of parshah Nitzavim is that all Jews are entangled. The laws of arvus – mutual responsibility – are learned from this parshah. “You all stand together – netzavim kulchem…” – we are all entangled, which will allow us in a few days to be yotzeh tekias shofar by listening to the baal tokeah, who will exempt us with his tekios.