Quantum Diaries

Is science accumulative? Is the Pope a Catholic? Some things are truly self-evident. The accumulative nature of science is one of them. But the different ways science is accumulative does hold some surprises. Consider home improvement. We can add onto the top, build out from the side, fix the broken window, or build down from the foundations. Science is accumulative in all these directions. Think of classical mechanics and planetary motion. After Isaac Newton (1642 – 1727) introduced his three law of motion, various people, most notably Joseph-Louis Lagrange (1736 – 1813) and William Hamilton (1805 – 1865), developed more mathematically sophisticated treatments of classical motion. They used Newton’s work as a starting point and built new stories onto the superstructure. Pierre-Simon Laplace (1749 – 1827) added onto Newton’s work in other ways. He found an error in Newton’s calculation of planetary stability and added the nebular hypothesis to describe the origin of the solar system. The first of these corrected the structure Newton had built—replaced the broken window if you like—while the second, the nebular hypothesis, added a new room on the side. It extended Newton’s ideas beyond where they were originally applied. The discovery of Uranus by William Herschel (1738 – 1822) can also be considered a sidewise extension to planetary system; the discovery left the original work intact but extended it outward.

These advances all left the paradigm of classical mechanics intact but built on the foundation Newton had laid. But quantum mechanics was a whole different story. It left the superstructure intact but changed the foundation; like the magician’s trick of pulling the table cloth off the table while leaving the dishes in place. The advent of quantum mechanics did not require the recalculation of planetary orbits. The work of Newton, Laplace, Lagrange, and Hamilton could still be applied as before but only to a fixed range of phenomena. Quantum mechanics kept all the successes of classical mechanics, but put it on a new foundation.

Now, quantum mechanics frequently is seen as a complete overthrow of classical mechanics and if you are looking at the metaphysics, that is true. However, no one should take metaphysics seriously anyway. From the point of view of the person calculating planetary orbits, nothing changed when Schrodinger introduced his eponymous equation. Schrodinger built on the work of Hamilton just as much as Hamilton built on the work of Newton. (Quantum mechanics is built on Hamilton’s formulation of classical mechanics.) Whereas Hamilton added to the superstructure, Schrodinger helped replace the foundation.  Both added to the existing structure rather than demolishing it, and the smoke went up the chimney just the same[1]. Or rather, the planets went round the sun just the same.

Replacing the foundation is largely synonymous with Thomas Kuhn’s idea of paradigm change. This is the reductionists dream and the foundations in various fields of science are indeed frequently replaced: quantum gravity will replace quantum field theory, which replaced quantum mechanics, which in turn replaced classical mechanics. But only the foundation was replaced, the superstructure was left intact.  A similar process happened with this sequence: indivisible atoms, atom structure, nuclear structure, nucleon structure, and the standard model.

Thus, we see how science advances: fixing errors (Laplace), refining formalisms (Hamilton, Lagrange), extending to new areas (Laplace, Herschel), and replacing the foundations (Schrodinger). But these are all extensions to the existing knowledge. When we forget this, mistakes are made. When quantum chromodynamics was introduced, it changed the foundation of nuclear physics, but left most of the previous understanding of nuclear physics intact. The overzealous proponents of the quantum chromodynamics did not understand this and claimed that nuclear physics would have to be largely redone. But that was nonsense; we made a few minor changes and carried on. Science is amazing in that it can easily change the foundation without major damage to the superstructure. Try doing that with a sky scraper or even a two story house.

The reason this all works is that science is modular, with fairly well defined interfaces between the models. Consider chemistry. At one side, quantum chemistry is closely related to physics and share a common formalism: quantum mechanics. In the middle, chemistry developed independently of physics and did not depend on the quantum chemistry foundation.  But then, parts of biology and applied science use chemistry as a foundation to build on; interlinked but each progressing separately.

So science oozes onwards in all directions: upward, downward, sideways, and inward. It discards what is no longer useful—yet, for the most part, the older models provide the scaffolding to support the new, and the more recent insights are obtained without destroying the older ones. And science unfolds as it should, building knowledge one room at a time.

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod.

When I first started dabbling in the dark side and told people I was working on the philosophy of science, the most common response from my colleagues was: Oh the foundations of quantum mechanics? Actually not. For the most part, I find the foundations of quantum mechanics rather boring. Perhaps that is because my view of science has a strong instrumentalist tinge, but the foundations of quantum mechanics have always seemed to me to be trying to fit a quantum reality into a classical framework; the proverbial triangular peg in an hexagonal hole. Take wave-particle duality for example. Wave and particles are classical idealizations. The classical point particle does not exist, even within the context of classical mechanics. It should come as no surprise that when the classical framework breaks down, the concepts from classical mechanics are no longer valid. What quantum mechanics is telling us is only that the classical concepts of waves and particles are no longer valid. Interesting, but nothing to get excited about.

The problem with the uncertainty principle is similar. This principle states that we cannot simultaneously measure the position and motion of a particle. Now, classically, the state of a particle is given by its location and motion (i.e. it’s momentum). Quantum mechanically, the state is given by the wave function or, if you prefer, by a distribution in the location-motion space[1]. Now the problem is not that the location and motion cannot be measured simultaneously but that the particle does not simultaneous have a well-defined position and motion since its state is given by a distribution. This causes realists, at least classical realists, to have fits. In quantum mechanics, the position is only known when it is directly measured, ie properties of the system only exist when they are being looked at. This is a distinctly antirealist point of view. Again, this is trying to force a classical framework on a quantum system. If anything is real in quantum systems, it is wave functions, not individual observables. But see below.

Quantum mechanics is definitely weird; it goes against our common sense, our intuition. The main problem is that, while classical mechanics is deterministic, quantum mechanics is probabilistic. To see why this is a problem, consider the classical-probability problem of rolling a dice. I roll a fair dice. The chance of it being 2 is 1/6; similarly for any value from 1 to 6. Now once I look at the dice the probability distribution collapses. Let’s say, I see a 2. The probability is now 1 that the value is 2 and zero for the other values. But for Alice who has not seen me check, the probabilities are still all 1/6. I now tell her that the number is even. This collapse her probability distribution so that it is 1/3 for 2,4,6 and zero for 1,3,5. Now for Bob, who did not hear me telling Alice, the probabilities are still 1/6 for each of the numbers. Two important points arise from this. First, classical probabilities change discontinuously when measurements are made and, second, classical probabilities depend not just on the system but on the observer, ie probabilities are observer dependant.

We should expect the same quantum mechanically. We should expect measurements to discontinuously change the probability distribution and the probability distribution to be observer dependent. The first is certainly true. Quantum mechanical measurements cause the wave function to collapse and consequently the probability distribution[2] also collapses. The second is not commonly realized or accepted, but it should be. The idea that the wave function is a property of the quantum system plus observer, not the quantum system in isolation, is not new. Indeed, it is a variant of the original Copenhagen interpretation of quantum mechanics. But frequently, it is denied. When this is done, one is usually forced to the conclusion that the mind or consciousness plays a large and mysterious role in the measurement process. Making the wave function, or the state description, observer dependent avoids this problem.  The wave function is then just the information the observer has about the quantum system. As Niels Bohr (1885 – 1962), one of the founders of quantum mechanics, said: It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.

Let us consider the wave function collapse in more detail. Consider an entanglement experiment. The idea is to have a system emit two particles such that if we know the properties of one, the properties of the other are also known. One of the two emitted particles is measured by Bob and the other by Alice.[3] Now, Alice is lazy so she has her particle transported to her home laboratory. She also knows that once Bob has done his measurement, she does not have to measure her particle but only has to call Bob to get the answer. Bob is also lazy, but he does go the lab and, if he feels like it, does the measurement and faithfully records it in his log book. One day when Alice calls, she gets no answer. It turns out Bob has died between the time he would have made the measurement and when he would have recorded it in his lab book. Now Alice is very upset. Not that Bob has died—she never liked him anyway—but that she does not know if the momentous event of the wave function collapse has happened or not. Her particle has not arrived at her home yet, but there is no experiment she can do on it to determine if the wave function has collapsed or not. The universe may have split into many worlds but she can never know! Of course, if the wave function is a property of the observer-quantum system, there is no problem.  The information Bob had on the wave function was lost when Bob died and Alice’s wave function is as it always was. Nothing to see here, move along.

So what is the interpretation of quantum mechanics? An important part seems to be that wave functions are the information the observer has on the quantum system, and is not a property of the quantum system alone. If you do not like that, well there is always instrumentalism,[4] i.e. shut up and calculate.

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod.