Dear Steven,
Last week we addressed your question concerning simulation theory, and this week we shall touch upon your fascinating thoughts about quantum entanglement.
In part, you asked:
“… However, my views have evolved a lot lately … quantum physics and ideas like entanglement — that two particles in two different places can be entangled and cooperate at a quantum level — that go so completely against what we can observe about our universe. For example, I’ve long wanted to understand more about the mechanics of how mitzvot and prayer affect the world, and science now has the language — courtesy of quantum entanglement — to describe how doing one thing in one place might instantly affect something else in another place, without any passage of or through time and space.
“In other words, perhaps the mechanics of quantum entanglement are identical to the mechanics of how a mitzvah or tefilla here might affect an outcome somewhere else.”
I must say that you have, with your connection between entanglement and the effects of mitzvot and prayer upon the universe, touched upon one of the deepest Kabbalistic principles regarding the effect of our actions upon the universe.
Let us first mention that, as it is well-known, entanglement embodies one of the most baffling conundrums of quantum physics. Two sub-atomic particles which are essentially “entangled,” for example which emanate from an atom in a way which necessitates them to hold opposite spin patterns, will retain those opposite characteristics, hence remain entangled, no matter how far apart they may be. Even if they travel light-years apart they remain entangled, and if the spin of one particle is changed, that will have an immediate effect of the spin of its entangled particle. This effect will transpire instantaneously, as if they’re still attached, light-years away! This seems to defy Einstein’s principle in special relativity that nothing can ever travel faster than the speed of light!
Physicists have struggled to explain that this, indeed, does not contradict relativity, because nothing “travels” between the two particles; rather they are in some way “attached at the hip” no matter how distant they are from each other in space.
This is profoundly similar to our understanding of how the actions of a human being affect even the far-flung reaches of the universe instantaneously. This is predicated on the understanding of the soul. We usually think of the soul as a spark of Godliness which the Creator has imbued us with. This is true, but it goes far beyond that. In fact, the deeper sources of Jewish thought, the Kabbalistic works, teach us that the part of the soul within our bodies is merely the sparks of the lowest level of the soul. It compares our bodies to a “shoe”; although our bodies stand in our shoes, it’s only the lowliest part of one’s body held within the shoe. The main part of one’s body towers far above the reaches of the shoe. Also the main parts of our souls tower light-years above our physical structures. The root of the soul reaches above all the 10 levels of Sefiros, or celestial worlds  from which emanate different aspects of Godliness; hence every thought, matter of speech and action a person does instantaneously affects all of those heavenly worlds. Hence the actions, speech and thoughts immediately affect the entire universe, as the celestial worlds are the core and spiritual foundation for the entire physical universe. This is the spiritual side of our “entanglement” with the higher spheres of the spiritual, and hence physical, universe.
When one contemplates this concept, there’s truly no room for a condition which plagues our generation, the lack of self-esteem. Rather than feeling puny and inconsequential in face of the billions of galaxies we know to exist, one should feel proud to embody a soul so high and powerful that it can affect all of those galaxies! This is the true meaning of our creation in the image of God!