Quantum Uncertainty: Where’s Jane?

Quantum physics is weird for a whole lot of reasons. One of the central reasons is that all things in the quantum realm are stated in terms of probabilities, or uncertainties, or indeterminacy. That’s unlike the realm of classical physics, the realm our normal day-to-day lives are lived in. However, I use an analogy from the classical world to illustrate the realm of quantum uncertainty.

The physical universe is pretty predictable. The rising and setting of the Sun, the phases of the Moon, the tides, the positions of the planets and their satellites, eclipses, etc. can all be predicted to a high degree of accuracy centuries in advance. Applies fall from trees. Two parts hydrogen combines with one part oxygen makes water.  Pure water boils at 100 degrees Centigrade at sea level. Spring follows winter. Entropy increases. Musical instruments play according to design. Bridges bridge according to design. Airplanes fly according to design and so on and so on and so on. Your macro (classical physics) world is as predictable for the most part as is your death and taxes.

On the micro (quantum physics) scale however, quantum effects rule the roost, and that roost is anything but predictable. In other words, uncertainty rules in the tiny world of the micro, for at the heart of quantum physics lays the Heisenberg Uncertainty Principle. In other words, when dealing with all things micro, what you know is only probability. In the world of the macro: The sun will rise tomorrow. In the world of the micro: Any specific atom of a radioactive substance may, or may not decay within an hour, even if it’s near certain that at least one atom will. You can’t predict or know which one. In the world of the macro: You know where the moon is. In the world of the micro: Where is an electron that’s ‘in orbit’ around an atomic nucleus? You don’t know to any precise degree, unlike say, a satellite in orbit around the Earth. The very act of observing or measuring something at the micro level changes the very nature or the properties of what you are trying to observe or measure. You may know the general probability of the value of the property (say the location of an electron in the vicinity somewhere around an atomic nucleus), but never the exact value or location.

From the realm of the classical macro, say an observer observes a pebble on the beach. The observation comes about because photons (light) reflect off the pebble, enter the eyes of the observer, carry sufficient energy to jiggle those retina receptors, causing an electrical nerve signal into the brain which does its brain thingy and ‘sees’ the pebble in a specific place on the beach. The photons, while energetic enough to jiggle the receptors in the retina, aren’t energetic enough to budge the pebble. However, if you replaced a revolver bullet(s) for the photon(s), then the pebble would move, probably to an unexpected, indeterminist place, but with a certain probability of being with a certain radius of where it originally was; an even greater probability of being within twice that distance, etc. Instead of the pebble and the bullet, substitute an electron (pebble), which is small enough to be dislodged by a photon (bullet). You need the photon to see the electron, say in ‘orbit’ around an atomic nucleus, but after that photon enters your eye, the electron has gone walkabout. In other words, the very act of observing the electron changes the position of the electron, so you can’t be certain post-observation where the electron is now and what its new velocity and direction might be. It might not even be in ‘orbit’ anymore. That’s part of the guts of the Heisenberg Uncertainty Principle and better eyeballs or better measuring equipment won’t decrease the level of uncertainty.  The other part  of the uncertainty phenomena is that the electron is behaving as a wave – the wave-particle duality – and thus the electron is not behaving like a little billiard ball and travelling in a nice straight line, or a standard curved orbit at all but waving all over the place like a flag in a still breeze.

So when comparing the macro and the micro worlds, there are two kinds of probability or uncertainty or indeterminacy – call it what you will. There’s uncertainty in the macro world due to lack of knowledge that you in theory could acquire, like is that flipped coin that rolled under the sofa heads or tails? Then there’s uncertainty in the micro world due to lack of knowledge that you can not ever acquire, even in theory. In general, the former tends to represent the classical physics of the macro; the latter, the quantum physics of the micro.

To illustrate, I’ve thought up an example from the world of the classical macro world called ‘where is Jane?’ The starting point is that apparently, according to information on Facebook, Jane is to leave Adelaide, South Australia for Canberra, Australian Capital Territory at 9 am. That much is apparently certain, but that’s all you know. The question is ‘where is Jane?’ at 10 am?

It’s highly probable that Jane will catch a direct flight from Adelaide to Canberra, and knowing the usual speed of a commercial airliner, you can predict where Jane will be at 10 am. BUT, what if Jane missed the flight? What if the flight was delayed? What if the plane hit high headwinds, tailwinds or crosswinds? What if the flight had to go around some nasty weather system? What if the flight was diverted or returned to Adelaide because of a mechanical problem? Then your prediction of where Jane is (latitude, longitude, altitude) at 10 am is fuzzier.

Of course Jane, albeit with less probability, might have flown first to Melbourne hence Canberra. Or perhaps Jane went from Adelaide to Darwin to Brisbane to Canberra - improbable, but not impossible. Even more improbable (but not impossible) is that Jane flew from Adelaide to Perth then on to London via Africa (or the Middle East), hence to New York (or maybe Boston or Washington or Miami) then on to L.A. (or San Francisco) hence to Hawaii, Sydney and Canberra! To predict where Jane is at 10 am, you’d need to consider all those improbably but possible itineraries. 

To complicate things further, there’s a reasonable possibility Jane went to Canberra not by plane, but by train. Or maybe she drove or took a taxi or bus. Maybe she decided to hitchhike, or use her bicycle or walk the distance (say to raise and collect money for charity). 

So, where’s Jane at 10 am? You don’t know exactly, although you can assign various probabilities to all the possibilities and take your best guess. Of course if Jane knows you’re looking for her, perhaps she deliberately took one of the low probability options – and then decided to head for Hobart instead as her port of call! Now you have an idea of how hard it is to pin down any property, such as the position of an electron, in the world of the quantum micro! In fact, it’s even harder than that. You will be indecisive or indeterminate or uncertain that the electron in question is in fact anywhere even near that atomic nucleus it normally ‘orbits’ around. There’s a possibility that the electron went totally walkabout. In our analogy, what if Jane went up – straight up. Maybe, just maybe, however improbable, our Ms. Jane took a suborbital rocket flight from Adelaide to Canberra, perhaps maybe via the Moon, or maybe she is currently heading outward bound towards Mars (and points beyond)!

Actually, to satisfy your curiosity, Jane woke up, decided to hell with going to Canberra, rolled back over and went back to sleep!