Riding High Amongst the Wave… Functions

Wave functions.

They are the probable darling (get it?) of quantum mechanics. A wave function is one of the most important aspects of quantum physics, actually, as the wave function contains all the measurable information about a particle (or group of particles). Thing is, it’s not like we just look at a wave and get a particle’s medical history, CV, and Facebook profile. Alas, all of our information is tied up in these hazy webs of probability. In fact, that’s what a wave function actually describes in practice- a set of probabilities. In order to take any measurement of a particle, we poke at that set of probabilities, which collapses the wave function, causing all the probable measurements to collapse and the particle to take on a definite value.

Note that we often refer to collapsing wave functions as being “observed,” which causes the collapse. Observation is the simplest way of taking a measurement- by seeing something, we’ve “measured” its location in space.

Anyway, up until now, that wave function has really just been a statistical tool. In mathland (where equations frolic and graze freely, waiting to be herded into a little slate corral for the scrutiny of many a fluffy-haired mathematician), we use symbols to denote certain physical properties and objects. And if we don’t know the physical meaning of a symbol in an equation, we can usually figure it out by looking at the physical units you would use to measure it. For a wave function, however, the units don’t make any goddamn sense.

So, to prevent the rampant spread of migraine-impeded physicists, most of the scientific community1 decided to simply use the wave function for calculations. It may be a handy statistical tool, but it doesn’t have a concrete existence.

Egg on face time… potentially.

A recent paper authored by Matthew F. Pusey, Jonathan Barrett, and Terry Rudolph challenges this idea, claiming “the statistical interpretation of the quantum state is inconsistent with the predictions of quantum theory” and that, therefore, the wave function has to be “real.”

“I don’t like to sound hyperbolic, but I think the word ‘seismic’ is likely to apply to this paper,” says Antony Valentini, a theoretical physicist at Clemson University.

Now, what is it that makes our trio of scientists believe the wave function must be a real thing as opposed to just a statistical tool? From what I’ve been able to gather, there are essentially two reasons why the wave function as statistical tool doesn’t work.

The first has to deal with entangled particles (two or more particles can be entangled so that measuring one affects the outcome of measuring the others, no matter how far apart the objects are). If the wave function were purely a statistical tool, even quantum states that are unconnected across space and time would be able to communicate with each other. As this appears to be categorically untrue according to quantum physics, the wave function must be real.

The second reason is that a purely statistical wave function will not always give the same results as a real, concrete wave function.

Imagine there are two machines, each programmed to create a single photon. Each machine is designed to produce only “good” photons, but every so often, one of them will get its wires crossed and uses a different method that produces a “bad” photon. And let’s assume that we cannot measure which method (the right one or the wonkity one) was used to produce the photon. The only way we know which type of photon was created was by measuring said photon.

And, as we know, the measurement of something is oh-so-important in the world of wave functions.

Now, each machine produces a photon. And those photons are popped over to a detector to be measured. With two photons, we have four different measurement results (good-good, good-bad, bad-good, bad-bad). We have to measure in a roundabout way, though, by determining which states the photons are NOT in.

If the wave function is a real object, then one of those possibilities always has a zero probability- the wave function is either representing the “good” state or the “bad” state, but not both (individual quantum systems must “know” exactly what state they have been prepared in). If, however, the wave function is statistical in nature, then both “good” and “bad” states are described equally well in that probability haze, and there is always a chance that the bad-bad detector will click even though one of the photon-preparing machines sent it a “good” photon.

Basically, the probability maps for the statistical wave functions and real wave functions don’t match up.

I guess, in actuality, the first reason is why the statistical wave function doesn’t work according to the laws of quantum physics, while the second is more of a reason why we need to determine, once and for all, whether the wave function is a concrete thing or not. Because the fact that real wave functions and statistical wave functions can produce different results means that one of them is wrong (unless there’s a wave function for wave functions, which is just entirely too meta for science).

Interestingly enough, if the wave function is proven to be a concrete thing… that makes wave function consequences real as well. Of particular note is the wave function in relation to those entangled particles. In the past, many have attempted to measure the speed with which the wave function collapse travels between entangled particles. We’ve determined that it’s faster than light (and those pesky neutrinos). A real wave function would mean that a real wave would be traveling much faster than the speed of light.

This simple little theory could have a monumental impact on physics (but, for most folks, it’s less in-your-face exciting when compared to FTL neutrinos, so it isn’t getting the same amount of hype). At the very least, it’s going to force a series of experiments to settle the matter one way or another. But this idea rattles a primary aspect of quantum theory, which could have far-reaching (and, as of yet, unpredictable) effects on the realm of quantum physics.

Let’s just say, I’m going to be keeping a very interested eye on this.

1 Fun Fact: Niels Bohr favored the statistical wave function, as did Einstein. Schrödinger, however, backed the idea of a real wave function.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s