Fighting realism
Posted by aogMonday, 12 March 2007 at 11:07 TrackBack Ping URL

Because I am a pedant, I must correct several errors committed by jd watson over at Brothers Judd when discussing quantum mechanics, as these errors seem to be common ones. Watson writes —

The “collapse of the waveform” must be the result of an observation, hence the necessity for an observer, continuously creating reality.

The error here is in taking “observer” to mean much more than it really does. In quantum mechanics, an “observation” is a measurement of some property of a quantum object, which is represented in the theory as the application of an operator to a wave function (math types can think of it as multiplication, progammers as a function call)1. This can arise through any physical interaction and does not require any sort of intelligence or self awareness.

For instance, in the classic double slit experiment, the observer isn’t the scientist doing the experiment, but the screen behind the slits. It works just as well in a lifeless universe as in ours.

Moreover, as far as quantum mechanics is concerned, reality is just as real before the collapse of the wave function as it is afterwards. Reality is not “created” by the collapse, it is simply changed from one state to another (or, more accurately, changed from a mixed state to a single state). There is no reason why any wave function ever has to collapse for reality to exist. In fact, the entire field of quantum computation depends on avoiding wave function collapse for extended periods of time. Taking our macroscopic, collapsed wave function view as being the “real” reality is just realism in action, propagated by realists unable to accept divergent wave functions.

Watson also has this —

QM (Quantum Mechanics) returns to the Pythagorean error and does so in a self contradictory way. Assuming everything, including time, is quantized, it then uses continuous variables to represent the wave function and partial differential operators, which assume continuity to be valid, to derive the observables from the wave function.

There are multiple errors here. The first is that I am unware that QM assumes the quantization of time. There are variants that do, but it’s not a fundamental assumption of the theory. The second is a misunderstanding of quantization. The Pythagorean error was presuming a single quantization, that there is some universal fundamental quantum of, say, length. QM does not assume that. Any particular action is quantized, but there is no necessary relationship between the quantum for action A and action B. That is why continuous functions are appropriate for QM despite the quantization. Moreover, wave functions can evolve continuously, it is only during collapse that quanta matter.

That said, there is this

Finally, there is the metaphysical sin of confusing our knowledge of reality, represented by measured properties and equations or models, with reality itself.

That was actually a key theme in my doctoral thesis, for which I used QM as an example. QM is a breathtaking achievement of mathematics. It provides a functional description of reality that has a precision almost impossible to describe to those not versed in the theory. However, that is, as Watson notes, not the same as being an accurate description of how reality is actually structured. I think it reasonable to, given the precision, take QM by default as being such a description, but that doesn’t make it true.

1 The application of the operator results in a new “collapsed” wave function. The Heisenberg Uncertainty Principle is simply the common description of the fact that the operators are non-commutative. I.e., it matters which order the operators are applied to a wave function. So applying the “location” operator and then the “momentum” operator to a wave function can yield a different result than applying the “momentum” and then the “location” operators. This is an archetypical example of the elegance that so attracts people to the theory.

Comments — Formatting by Textile
erp Monday, 12 March 2007 at 14:10

Nicely said.

I collapsed your error wavefunction.

erp Monday, 12 March 2007 at 19:00

Thank you … I think.

joe shropshire Tuesday, 13 March 2007 at 16:18

I’d like a little more on point 2. Planck’s Constant is in joule*sec, so: if kg*m**2/sec is quantized doesn’t that mean time is in some way?

Annoying Old Guy Tuesday, 13 March 2007 at 17:16

Planck’s Constant isn’t a unit of quantization itself, although it shows up in many. For example, one need only look at the quantization for electron orbitals in a hydrogen atom. There’s no consistent quanta between the levels and, in an otherwise empty universe, for any given amount of energy, no matter how small, one could find adjacent orbitals with a difference less than that amount. That doesn’t work in real life because such orbitals get to be so large (say, multiple kilometers) that there’s no possibility of them not being swamped by other matter or energy.

Another example is the Casimir Effect. This occurs because the approach of the two surfaces quantizes the allowed energies of the vacuum virtual particles. The flip side is obviously that absent those surfaces, any possible energy is allowed, i.e. those energies are not quantized.

Finally, let’s look at a related concept, the Planck Length. Contrary to what many think, this is not the quantum of length, but the shortest meaningful length. Distances shorter than that no longer obey what we consider normal ordering, i.e. one third of a PL is not necessarily shorter than a half of a PL. It does not mean that every length is an integer multiple of the PL.

It’s hard to find an analogy that makes it clearer because it’s just fundamentally different than we experience. You could try think of all of these particles as little cloud balls, about the size of basketballs. Now think of trying to measure how far apart they are in millimeters. You can’t, because the boundaries are not only vague but shift. It’s not that the clouds have to snap to a grid, but that sufficiently short lengths are no longer meaningful.

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