"Symbols of Religions". Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons Several recent atheist commentators have rightly condemned ISIS, citing it as an example of religion gone horribly wrong. But then they go further, usi...
So, I was reading some philosophy tonight. I finished David Hume's An Enquiry Concerning Human Understanding , which - at the end of a book with no abstract reasoning of quantity or number or really any experimental reasoning - has the following as the fina...
Okay, I am really sick and tired of reboots. I've reached my limit, and the idea that there might be a reboot of the classic Ghostbusters is enough to push me over the edge. For a while, there have been rumors of another sequel that introduced a new team. T...
There is something about Bell's Theorem that I don't understand.
As I understand it, Bell starts with Schrödinger's Wave Equation, which (as Schrödinger conceived it) applies to a single particle. Using Schrödinger's formulation, an observer can expect to find the particle at some location, (x,y,z), at some time, t, with the probability given by Schrödinger's formula.
In the EPR Paradox, instead of reckoning one particle, we are given a pair of twin particles sharing a common "birth certificate" going off in opposite directions from each other.
How are we to apply Schrödinger's Wave Equation, which applies to a single particle, to a pair of particles separated by arbitrary distances in space?
Bell blithely takes Schrödinger's Wave Equation and straightaway applies it to both particles, as if they comprised a "singlet" -- a system of two particles acting as if they were one particle.
But here is where I fall off the boat. There is but one parameter, t, for time in Schrödinger's Wave Equation. What is Bell supposed to plug in for "system time" for reckoning events (measurements) occurring at two different locations in space?!?
One of the first things we learn from Einstein's Relativity is that there is no such thing as "Universal Cosmological Time." Indeed there is no such thing as "simultaneity" for events taking place at separate locations.
It occurs to me that Bell is abusing Schrödinger's Wave Equation by extrapolating from the special case for which Schrödinger constructed his formula -- a single particle -- to embracing an arbitrary distributed system of particles.
How in the name of Schrödinger and Einstein does Bell get away with that?!?
Both Schrödinger and Einstein died before Bell constructed his Inequality. Had they been alive, I reckon both of them would have objected to extrapolating the Wave Equation to a distributed system, especially since doing so required the adoption of the unrealistic concept of a common "system time" to plug into Schrödinger's ad hoc formula.
It is instructive to consider two quotes here from Richard Feynman:
"Where did we get Schrödinger's wavefunction from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger."
"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."
Moreover, Schrödinger was not entirely comfortable with the implications of quantum theory. Schrödinger wrote about the probability interpretation of quantum mechanics, saying: "I don't like it, and I'm sorry I ever had anything to do with it." I reckon he was worried someone would someday misapply it.
Nonetheless, Bell hypothesized that it was realistic to extrapolate Schrödinger's Wave Equation from the case of a single particle to the case of a distributed system, even though that created the dilemma of inventing the unrealistic concept of a unified "system time" that pervaded the cosmos. Was his hypothesis defensible? This is where Feynman's second quote comes into play.
Under the questionable hypothesis, Bell constructed an Inequality that was soon disconfirmed by Alain Aspect's experiments. That's not very surprising, and it means that the ad hoc single-particle Wave Equation cannot reasonably be extrapolated to a distributed system. In other words, Bell's Inequality is "inoperative" because it's constructed from an unrealistic assumption about the existence of a "universal system time" that extends throughout the cosmos.
Does anybody really know what time it is?
First, let me say that I've done this before, back in 2008, so here's a link to that list (although please ignore all of the begging to join BookWise ... it was a clever book-oriented multi-level marketing system which, sadly, did not survive the digital a...
- Wabash CollegePhysics, Mathematics, Philosophy, 1995 - 1999
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