This post is a logical extension of the previous one – a sequel if you like – and, for that reason, it should be read in conjunction with it.
One of the things I learnt, from researching for that post, was that Schrodinger was attempting something else to what he achieved. He didn’t like the consequences of his own equation. I believe he was expecting to obtain results that would reconcile quantum phenomena with classical physics and that didn’t happen. His famous Schrodinger’s Cat thought experiment confirms his disbelief in Bohr’s and Heisenberg’s interpretation of the wave function collapse: only when someone makes an observation or a measurement does reality occur. Prior to this interaction, the quantum state exists as a superposition of states simultaneously. His thought experiment was to take a quantum phenomenon and amplify it to a contradictory macro-state: a cat that was dead and alive at the same time. His express purpose was to illustrate how absurd this was.
Likewise, he apparently wasn’t happy with Born’s probabilities, yet it was Born’s insightful contribution that actually gave Schrodinger what he wanted: a connection between his quantum wave function and classical physics. To quote Arthur I. Miller in Graham Farmelo’s book, It Must be Beautiful; Great Equations in Modern Science:
[Born’s] dramatic assumption transformed Schrodinger’s equation into a radically new form, never before contemplated. Whereas Newton’s equation of motion yields the special position of a system at any time, Schrodinger’s produces a wave function from which a probability can easily be calculated… Born’s aim was nothing less striking than to associate Schrodinger’s wave function with the presence of matter. (My emphasis)
I think this is the key point: Born was able to provide a mathematical connection between quantum physics and classical physics via probabilities. The fact that these probabilities agreed with experimental data is what cast Schrodinger’s equation in stone and gave it the iconic status it still has in the 21st Century. As Wikipedia points out: Schrödinger's equation can be mathematically transformed into Richard Feynman's path integral formulation, which is the basis of his QED (quantum electrodynamics) analytic method, and the current ‘last word’ on quantum mechanics.
I re-read Feynman’s ‘lectures’ on QED after writing my post and one can see the connection clearly. But it’s Born’s influence that one sees, rather than Schrodinger’s, which is not to diminish Schrodinger’s genius. His attempt to create a ‘visualisable’ wave function, as opposed to Heisenberg’s matrices, is what set the course in quantum mechanics for the rest of the century.
But whilst Schrodinger and Einstein argued over the philosophical consequences of quantum mechanics with Bohr and Heisenberg, Feynman (a generation later) was dismissive of philosophical considerations altogether. In a footnote in QED, Feynman argues that the probability amplitudes are all that matters, and that the student should ‘avoid being confused by things such as the “reduction of a wave packet” and similar magic.’
If Feynman professes a philosophy it is by this credo:
‘I’m going to describe to you how nature is – and if you don’t like it, that’s going to get in the way of your understanding it… So I hope you can accept Nature as She is – absurd.’
However, the discontinuity between quantum mechanics and classical mechanics that arises from a ‘measurement’ or an ‘observation’ is hard to avoid. As I said in my previous post, it is entailed in Schrodinger’s equation itself, because the wave function is continuous yet all quantum phenomena are discrete. Roger Penrose, and others (like Elwes, quoted in previous post) point out that Schrodinger’s wave function is continuous until the quantum phenomenon in question is physically resolved (observed), whence the wave function effectively disappears.
What this tells me is that everything seems to be connected. It’s like nothing can come into existence until it interacts with something else. But it also implies that the quantum world and the classical world – what we call reality – are distinct yet interconnected. It reminds me of Plato’s cave, where our reality is akin to the ‘shadows’ projected from a quantum world that only mathematics can describe with any precision or purpose.
Our reality is a veneer and the quantum world hints at a substratum that obeys different rules yet dictates our world. It’s only through mathematics that we are able to perceive that world let alone comprehend it – particle smashers play their role, but they only provide windows of opportunity rather than a panoramic view.
This is a subtly different concept to the ‘hidden variables’ philosophy proposed by David Bohm (and some say Einstein) because I’m suggesting that the quantum world and the classical physical world obey different rules.
In a not-so-recent issue of New Scientist (30 April 2011, pp.28-31) Anil Ananthaswamy explains how different parties (Mario Berta from the Swiss Federal Institute of Technology, Robert Prevedel of the University of Waterloo Canada and Chuan-Feng Li of the University of Science and Technology of China in Hefie) have all reduced the limits of Heisenberg’s uncertainty principle through quantum entanglement.
Their efforts were apparently in response to theoretical suggestions by 2 Dutch physicists, Hans Maassen and Jos Uffink, that information gained through quantum entanglement (knowing information about one entangled particle or photon axiomatically provides information about its partner) would affect the limits of Heisenberg’s uncertainty principle. For example: if 2 particles go in opposite directions after a collision, they theoretically have the same momentum, yet Heisenberg’s uncertainty principle states that the information would be necessarily fuzzy, juxtapose knowing its position. However, measuring the momentum of one particle automatically gives knowledge of the other that subverts the uncertainty principle for the second particle.
Entanglement is an example of quantum interaction that classical physics can’t explain or even duplicate. That there appears to be a correspondence between this and the uncertainty principle supports the view that the quantum world obeys its own rules.
In my introduction, I suggested that this post needs to be read in conjunction with the previous one. This post focuses on the philosophy of quantum mechanics whereas the previous one focused on the science. Whereas the philosophy of quantum mechanics is contentious, the science is not contentious at all. That’s why it’s important to appreciate the distinction.