I have been working my way through Volume III of Feynman’s lectures, the one on quantum mechanics. A few months ago I watched his Quantum Electrodynamics lectures for the lay public and I was fascinated by the beauty and simplicity of the presentation. Now I want to dig deeper.

The basic idea is summarized in the quote (can’t find its source, probably Feynman though :-): “Everything that can happen, does. Physics is then reduced to the problem of finding out what can happen.” This is not philosophical many-worlds garbage postulating the existence of infinitely many alternative universes (I will get to that), but instead the interpretation of the Lagrangian form: if you want to find the probability amplitude of some event, you just add up the amplitudes for all the different ways it could happen. The generality of the principle is astounding, and making only very weak additional assumptions it is possible to completely derive the workings of electrons and photons (except for the mass of the electron, which is still a mystery). The rule is not just for electrons and photons though; those are just the easiest kinds of particles to get at. The entire universe works this way: the amplitude of an event is the sum of all the ways (including classically absurd ones) it could happen.

In the beginning of my studies, I was constantly tripped up by my conception of time. In the double slit experiment, a photon interferes with a version of itself leaving the excited atom *at a different time*. It was very hard to picture this when I was still attached to my idea of time and causality. This is the *logic* of the universe, not the *dynamics*. That is, we aren’t really computing the amplitude of an *event* to *happen* so much as the amplitude that, given some assumptions are true, some other thing about the universe will be true. We phrase the double slit experiment like this: *given* that this atom is excited at *t _{0}*, what is the amplitude that this other atom is exited at

*t*? There is no notion of happening or the flowing of time, it’s just a connection between statements about the universe. Realizing this was an important step in my understanding. Of course, the

_{1}*way*that these two atoms are connected

*does*involve time — that manifests itself in the different “ways it could happen” and thus affects the amplitude.

Ok, so we have this logic which connects facts about the universe together as amplitudes, which are complex numbers. How do we take these amplitudes and get some information we can use? The rule is: the *probability* of an event, er I mean, a fact, is *proportional* to the *absolute square* of the amplitude. Simple enough. So you set up an experiment and calculate the amplitudes for all the different ways it could come out (you have to calculate *all* the ways, because the probability is only *proportional*, so you need to normalize them so they sum to one — I find this unsatisfying). Then you do the experiment, and what *actually happens* at the end of the experiment is one of those ways, proportional to the absolute square of the amplitude for that way.

This is *extremely* unsatisfying to me. Almost all of the resources I have used for learning QM have described it this way and left it at that. I’m pretty sure it’s because nobody really knows the answer to the next question: when, exactly, do you take the absolute square? If you take it too soon, e.g. before “the experiment” is over, then you will lose the interference effects and do not get an accurate answer. But you can’t just delay taking it forever, because then you only ever have amplitudes, not probabilities. There is this arbitrary barrier between the “quantum” world and the “real” world, and that’s when you take the absolute square. This is intentionally ignoring the idea that your experiment apparatus, your measuring devices, etc. are all governed by the quantum logic above as well, because that is too hard to think about. This is the piece I am determined to understand; I am interested in QM philosophically, not practically, so it is not at all satisfying to me to say “it works in practice, get used to it.”

The theory of quantum decoherence provides half of the answer. It shows how this interpretation of the barrier is equivalent to the state of the experimental apparatus (including the state of you, the scientist performing the experiment) becoming entangled with what happened in the experiment. Eventually the whole universe gets entangled with the result of the experiment and that’s what “really happened”. God got a bunch of amplitudes for the way the universe could be; he took their absolute squares, rolled the dice, and picked one. Now the arbitrary boundary has been pushed out as far as it can go — to the edges of spacetime — instead of being between experiment and apparatus. Quantum decoherence shows a sort of compositionality of this quantum logic. This is getting more satisfying.

I love it because it is right on the edge of my ability to conceptualize. All the “decisions” in the entire universe could go this way or that, and if they both lead to the same thing and have opposite amplitudes, they could interfere with each other and make that thing impossible. It is because the universe is a chaotic system, that small changes give rise to large changes, that we can’t observe quantum interference on large scales. These little decisions are very unlikely to lead to the same state. Entropy gives rise to the classical world.

When I get really deep into philosophizing, I explode into the annoying considerations of consciousness. Perhaps God did not pick a universe at random, but our consciousness did. Our memory must conceive of time linearly, it would violate entanglement not to, and that’s why we think there is a single “chosen” universe instead of the explosion of all possibilities. But whether all possibilities exist or there is a single universe chosen at random is likely not an observable distinction, so it is merely fodder for pipe dreams.

If there were some device that could measure some things about the universe, without disturbance, set up in such a way as to negatively interfere with itself when its measurements were “undesirable”, it could potentially control the way the universe would go. Now you see where the title of this post comes from. I have not been able to sketch this device as a black box, nor fully understand why it should be impossible. I suspect it has something to do with the uncertainty principle, the derivation of which I have yet to completely understand.

Quantum Mechanics is fascinating to me, and I am trying to keep my mind open to the deep, philosophical, passionate curiosity it invokes without descending into the insanity of a quantum crackpot. It is a challenge.

Hi Luke,

Good thoughts there! You are not alone: I am not sure that anyone really understands how quantum theory maps across to physical reality!

A small team of us made an attempt of our own to make a mapping, and came up with some really curious results. Yes, we could answer fundamental questions, e.g. resolve wave particule duality, define force and time at the next more fundamental level, explain Schrodinger’s Cat, observer dilemmas, etc., but the results suggest that there is a deeper reality, and quantum mechanics is only an approximation of it.

It’s a pretty extreme fringe theory, and we don’t make any guarantee that it’s right! But it might give you some other perspectives to think about. We call it the cordus conjecture. http://cordus.wordpress.com/

Dirk

Have you read this?

http://blog.sigfpe.com/2007/03/independence-entanglement-and.html

Paul.

This book is good on these questions: http://www.amazon.co.uk/Lectures-Quantum-Theory-Mathematical-Foundations/dp/1860940013/ref=sr_1_1?ie=UTF8&qid=1316076125&sr=8-1

He chapters on Kocken-Secker Theorum and Bells Theorum are very good.

N

“Inspiring you to be a quantum crackpot too? ”

Absolutely :)

If you’d like to be not mainstream but less of a crackpot, I recommend looking at David Hestenes’ work. I recommend 7 and 8 on this page: http://geocalc.clas.asu.edu/html/GAinQM.html for a reformulation of the Dirac equation (the [relativistic] equation that governs the motion of an electron) in a manner that is much simpler and more revealing than the standard approach. This reformulation strongly suggests an interpretation of the parts of the solution to the Dirac equation. This formulation uses no complex numbers and directly explains the complex numbers that arise in the usual formulation.

From the interpretation supplied by this reformulation, Hestenes has formed his own interpretation of what an electron is. This is his Zitterbewegung Interpretation which is a modern, more compellingly motivated version of Schrödinger’s early idea. This is covered in paper 9 above and in several papers here http://geocalc.clas.asu.edu/html/Impl_QM.html which cover interpretation of QM more generally.

In a different vein, much of the difficulty with interpreting quantum mechanics comes from difficulties interpreting probability theory. E. T. Jaynes is the one to go to for clearing up those misconceptions. A good way to enter his written works is through the paper “Clearing up mysteries” located here: http://bayes.wustl.edu/etj/node1.html

As a caveat, both of these authors are very intent in making quantum mechanics “make sense.” If your goal is to make unverifiable, semi-mystical claims about ill-defined problems, these papers will not help at all.

The universe is lazily evaluated.

(And we are the ones doing the forcing?)

@Derek, thanks for all the great links! I am very interested in making quantum mechanics “make sense”, however, what that means for me is difficult to define. As Feynman says, you say you don’t understand, but what you mean is you don’t

accept. I find some interpretations satisfying, and others unsatisfying, and I have no idea why.@illissius, as inhabitants of the universe, its evaluation model is necessarily hidden from us. We are semantics, not implementation. :-)

I’m not interpreting your statement as being directed at me, but I will respond nevertheless. I have not said that I do not (or do) understand many proposed interpretations/explanations, but I will outright say that I do not accept most of them. Most of the time it’s because such proposals are completely non-predictive, unfalsifiable, ill-specified, and, in many cases, actively discourage attempting further understanding. In such cases, I do not gain anything by accepting them, and I do lose something.

The problem with quantum mechanics is that the experiments and mathematical theory vastly outstripped any conceptual understanding. Compounding this, early conceptual mistakes from murky understandings of probability, entropy, and the often new mathematics being used have been enshrined into the foundations of quantum mechanics. Hestenes shows that the Pauli, Schrödinger, and Dirac equations are not just poorly interpreted, but actually wrongly interpreted, i.e. are not even self-consistently interpreted. Jaynes, in his neoclassical electromechanics*, demonstrates that many results that are considered quintessentially quantum mechanical actually follow from classical electromechanics calling into question things like zero point energy. In the paper I linked Jaynes demonstrates how misunderstandings of probability make Bell’s theorem true but irrelevant. In my view most of the colofulness of quantum mechanics interpretations comes from attempting to give physical significance to subjective probabilities, unfortunately I have to agree with Jaynes that in the typical formulations the probabilistic and physical aspects of the problem are completely hashed together.

* I’m pretty sure neoclassical electromechanics was not intended by Jaynes to be a replacement of quantum mechanics but just a foil for it.