Consider Gallup’s post to be restated mathematically, in the context of quantum mechanics, as:
where represents the position state vector, represents a position internal to the orbital cloud, and a position external to the cloud. We see that the probability of being inside is
and the probability of being outside is
However, the statement that “5% of me is not in me” is conceptually incorrect. In the actual case, a process known as quantum Darwinism acts via three* mechanisms – entanglement, einselection, and decoherence – to ensure that, in this universe, the wavefunction always collapses onto a classical state. Our boundary settings are as follows:
- Consider Mistri’s body to constitute a quantum system with state vector
- Consider the surrounding environment to be a quantum system with state vector
- In the quantum-classical transition, entangles with such that
We now invoke Zurekian quantum Darwinism to model what happens in this situation. Entanglement–the first principle of quantum Darwinism–has been completed. Next, the process of environmentally-induced superselection, or einselection, during the wavefunction collapse sifts out the pointer state–which is as the entirety of Mistri’s body (allegedly) exists in this universe. Furthermore, the act of measurement through environmentally induced interactions* triggers decoherence on the quantum state such that:
in all observable cases.
We believe that the point “one of an atom’s electrons could be on the other side of the known universe from its nucleus” was the basis for the logic in the comment. However, in the post above, we conceptually proved that, in the limit of macroscopic objects such as the human body, quantum Darwinism acts as an upper bound on and actually causes state collapse onto
Alternatively, one can restate the comment in another way: consider one hundred parallel universes, each containing one copy of Mistri. If we invoke the many-worlds interpretation and apply it to the first equation, we see that in five of those universes, no such body will exist. That is, the probabilistic nature of decoherence will yield five universes where quantum Darwinism acts to collapse onto
* there are four mechanisms, but the discussion of einvariance has been left out in this post.