Quantum Astronomy: The Heisenberg Uncertainty Principle

In the first article, we discussed the double-slit experiment and how a quantum particle of light (a photon) can be thought of as a wave of probability until it is actually detected. In this article we shall examine another feature of quantum physics that places fundamental constraints on what can actually be measured, a basic property first discovered by Werner Heisenberg, the simplest form known as the "Heisenberg Uncertainty Principle."

In scientific circles we are perhaps used to thinking of the word "principle" as "order", "certainty", or "a law of the universe". So the term "uncertainty principle" may strike us as something akin to the terms "jumbo shrimp" or "guest host" in the sense of juxtaposing opposites. However, the uncertainty principle is a fundamental property of quantum physics initially discovered through somewhat classical reasoning -- a classically based logic that is still used by many physics teachers to explain the uncertainty principle today. This classical approach is that if one looks at an elementary particle using light to see it, the very act of hitting the particle with light (even just one photon) should knock it out of the way so that one can no longer tell where the particle actually is located -- just that it is no longer where it was.

Smaller wavelength light (blue, for example, which is more energetic) imparts more energy to the particle than longer wavelength light (red, for example, which is less energetic). So using a smaller (more precise) "yardstick" of light to measure position means that one "messes up" the possible position of the particle more by "hitting" it with more energy. While his sponsor, Nehls Bohr (who successfully argued with Einstein on many of these matters), was on travel, Werner Heisenberg first published his Uncertainty Principle Paper using this more-or-less classical reasoning just given. (The deviation from classical notion was the idea of light comes in little packets or quantities, known as "quanta," as discussed in article one). However the uncertainty principle was to turn out to be much more fundamental than even Heisenberg imagined in his first paper.

Momentum is a fundamental concept in physics. It is classically defined as the mass of a particle multiplied by its velocity. We can picture a baseball thrown at us at 100 miles per hour having a similar effect as a bat being thrown at us at ten miles per hour; they would both have about the same momentum although they have quite different masses. The Heisenberg Uncertainty Principle basically stated that if one starts to know the change in the momentum of an elementary particle very well (that is usually, what the change in a particle's velocity is) then one begins to lose knowledge of the change in the position of the particle, that is, where the particle is actually located. Another way of stating this principle, using relativity in the formulation, turns out to be that one gets another version of the uncertainty principle. This relativistic version states that as one gets to know the energy of an elementary particle very well, one cannot at the same time know (i.e., measure) very accurately at what time it actually had that energy. So we have, in quantum physics, what are called "complimentary pairs." (If you'd really like to impress your friends, you can also call them "non-commuting observables.")

One can illustrate the basic results of the uncertainty principle with a not-quite-filled balloon. On one side we could write "delta-E" to represent our uncertainty in the value of the energy of a particle, and on the other side of the balloon write "delta-t" which would stands for our uncertainty in the time the particle had that energy. If we squeeze the delta-E side (constrain the energy so that it fits into our hand, for example) we can see that the delta-t side of the balloon would get larger. Similarly, if we decide to make the delta-t side fit within our hand, the delta-E side would get larger. But the total value of air in the balloon would not change; it would just shift. The total value of air in the balloon in our analogy is one quantity, or one "quanta," the smallest unit of energy possible in quantum physics. You can add more quanta-air to the balloon (making all the values larger, both in delta-E and delta-t) but you can never take more than one quanta-air out of the balloon in our analogy. Thus "quantum balloons" do not come in packets any smaller than one quanta, or photon. (It is interesting that the term "quantum leap" has come to mean a large, rather than the smallest possible, change in something, and the order of the dictionary definitions of "quantum leap" have now switched, with the popular usage first and the opposite, physics usage second. If you say to your boss, "We've made a quantum leap in progress today" this can still, however, be considered an honest statement of making absolutely no progress at all.)

When quantum physics was still young, Albert Einstein (and colleagues) would challenge Nehls Bohr (and colleagues) with many strange quantum puzzles. Some of these included effects that seemed to imply that elementary particles, through quantum effects, could communicate faster than light. Einstein was known to then imply that we really could not be understanding physics correctly for such effects to be allowed to take place for, among other things, such faster-than-light connectedness would deny the speed-of-light limit set by relativity. Einstein came up with several such self-evidently absurd thought experiments one could perform, the most famous being the EPR (Einstein, Podolski, Rosen) paradox, named after the three authors of this paper, which showed that faster-than-light communication would appear to be the result from certain quantum experiments and therefore argued that quantum physics was not complete-that some factors had to be, as yet, undiscovered. This led Nehls Bohr and his associates to formulate the "Copenhagen Interpretation" of quantum physics reality. This interpretation, (overly simplified in a nutshell), is that it makes no sense to talk about an elementary particle until it is observed because it really doesn't exist unless it is observed. In other words, elementary particles might be thought of not just as being made up of forces, but that some constituents of it that must be taken into account are the observer or measurer as well, and that the observer can never really be separated from the observation.

Using the wave equations formulated for quantum particles by Erwin Schr?dinger, Max Born was the first to make the suggestion that these elementary particle waves were not made up of anything but probabilities! So the constituents of everything we see are made up of what one might call "tendencies to exist" which are made into particles by adding the essential ingredient of "looking." Looking as an ingredient itself, it must be noted, took some getting used to! There were other possible interpretations we could follow, but it can be said that none of them was consistent with any sort of objective reality as Victorian physics had known it before. The wildest theories could fit the data equally well, but none of them allowed the particles making up the universe to consist of anything without either an underlying faster-than-light communication (theory of David Bohm), another parallel universe branching off ours every time there is a minute decision to be made (many worlds interpretation), or the "old" favorite, the observer creates the reality when he looks (the Copenhagen Interpretation).

Inspired by all these theories, a physicist at CERN in Switzerland named John Bell came up with an experiment that could perhaps test some of these theories and certainly test how far quantum physics was from classical physics. By now (1964) quantum physics was old enough to have distinguished itself from all previous physics to the point that physics before 1900 was dubbed "classical physics" and physics discovered after 1900 (mainly quantum physics) was dubbed "modern physics." So, in a sense, the history of science in broken up into the first 46 centuries (if one starts with Imhotep who built the first pyramid as the first historical scientist) and the last century, with quantum physics. So, we can see that we are quite young in the age of modern physics, this new fundamental view of science. It might even be fair to say that most people are not even aware, even after a century, of the great change that has been taking place in the fundamental basis of the scientific endeavor and interpretations of reality.

John Bell proposed an experiment that could measure if a given elementary particle could "communicate" with another elementary particle farther away faster than any light could have traveled between them. In 1984 a team led by Alain Aspect in Paris did this experiment and indeed, this was undeniably the apparent result. The experiment had to do with polarized light. For illustrative purposes, let's say that you have a container of light, and the light is waving all over the place and -- if the container is coated with a reflective substance, except for the ends -- the light is bouncing off the walls. (One might picture a can of spaghetti with noodles at all orientations as the directions of random light waves.) At the ends we place polarizing filters. This means that only light with a given orientation (say like noodles that are oriented up-and-down) can get out, while back-and-forth light waves (noodles) cannot get out. If we rotate the polarizers at both ends by 90 degrees we would then let out back-and-forth light waves, but now not up-and-down light.

It turns out that if we were to rotate the ends so that they were at an angle of 30 degrees to each other, about half of the total light could get out of the container -- one-fourth from one side of the bottle and one-fourth through the other side. This is (close enough to) what John Bell proposed and Alain Aspect demonstrated. When the "bottle" was rotated at one end, making a 30-degree angle with the other side so that only half the light could escape, a surprising thing happened. Before any light could have had time to travel from the rotated side of the "bottle" (actually a long tube) to the other side, the light coming out of the opposite side from the one that was rotated changed to one-fourth instantaneously (or as close to instantaneous as anyone could measure). Somehow that side of the "bottle" had gotten the message that the other side had been rotated faster than the speed of light. Since then this experiment has been confirmed many times.

John Bell's formulation of the fundamental ideas in this experiment have been called "Bell's Theorem" and can be stated most succinctly in his own words; "Reality is non-local." In other words, not only do the elementary particles that make up the things we see around us not exist until they are observed (Copenhagen Interpretation), but they are not, at the most essential level, even identifiably separable from other such particles arbitrarily far away. John Muir, the 19th Century naturalist once said, "When we try to pick out anything by itself, we find it hitched to everything else in the universe." Well he might have been surprised how literally -- in physics as well as in ecology -- this turned out to be true.

In the next essay we will combine the uncertainty principle with the results of Bell's Theorem and increase the scale of the double slit experiment to cosmic proportions with what Einstein's colleague, John Wheeler, has called "The Participatory Universe." This will involve juggling what is knowable and what is unknowable in the universe at the same time.

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For more information:

Werner Heisenberg: http://www.aip.org/history/heisenberg/

Nehls Bohr: http://en.wikipedia.org/wiki/Niels_Bohr

Albert Einstein: http://scienceworld.wolfram.com/biography/Einstein.html

John Bell: http://physicsweb.org/articles/world/11/12/8

Erwin Schr?dinger: http://scienceworld.wolfram.com/biography/Schroedinger.html

Max Born: http://en.wikipedia.org/wiki/Max_Born