Saturday, April 27, 2013

History of Science -- Part Sixteen: Copenhagen Interpretation

Werner Heisenberg
The meaning of Newton’s mechanics is clear. It describes a “clockwork universe.” It needs no “interpretation.” Einstein’s relativity is surely counterintuitive, but no one interprets relativity. We get used to the idea that moving clocks run slow or that space is non-Euclidian. It’s harder to accept the quantum theory premise that observation creates the reality observed. That requires interpretation.

Physics is supposed to be about the physical. Now we find we need to interpret what physics has found (and proved), almost like Daniel interpreting King Nebuchadnezzar’s dream. Physics is supposed to be about material things, not supernatural, mental, or spiritual!

Filling that need for interpretation, within a year after Schrödinger’s equation, the “Copenhagen interpretation” was developed at Bohr’s institute in Copenhagen with Niels Bohr as its principal architect. Werner Heisenberg, his younger colleague, was the other major contributor. Although there is no “official” version, there is a general understanding of three principles that make up the interpretation.

Copenhagen softens the interpretation of “observation,” describing it as taking place whenever a microscopic, atomic-scale, object interacts with the macroscopic. When a piece of photographic film or a sensor “observes” the photon, or when a Geiger counter clicks in response to a particle entering a discharge tube, etc., we say the event has been observed.

The three pillars of Copenhagen consist of:

1) The probability interpretation of the wavefunction.

I’ve explained this previously. I described the waviness in a region (technically the absolute square of the wavefunction) as the probability that the object will be found in that region. This is central to the Copenhagen interpretation.

But, remember, it isn’t like the likelihood of winning (or loosing) the lottery. In the “two boxes” experiment the object actually was in both boxes until the wavefunction is collapsed by an observation. I suppose you could consider you might win or loose the lottery before the winning number is drawn, that isn’t what’s going on here. It is sort of as if you have both won and lost … you’ve gotten the money and you’ve torn up the loosing ticket … until the winning number is drawn.

This is hard to grasp. That’s why I keep repeating it. To quote another physicist, Pascual Jordan, one of the founders of quantum theory, “Observations not only disturb what is being measured, they produce it.” That’s the essence of the “superposition state.”

While classical physics is strictly deterministic, quantum mechanics tells of the ultimate randomness in Nature. At the atomic level, God does play dice.

Cosmologist John Wheeler puts it concisely, “No microscopic property is a property until it is an observed property.” Bohr said, “There is no quantum world. There is only an abstract quantum description. It is wrong to think that the task of physics is to find out the how nature is. Physics concerns what we can say about nature.” Some would be even less tactful and just say, “Shut up and compute.”

Einstein rejected Bohr’s attitude as defeatist, saying he came to physics to discover what is really going on, to learn “God’s thoughts.” Schrödinger also rejected the Copenhagen interpretation.

Would Bohr actually deny that a goal of science is to explain the natural world? Perhaps not; he once said, “The opposite of a correct statement is an incorrect statement, but the opposite of a great truth may be another great truth.”

Is there another “great truth” out there still to be discovered? Is this just an episode of the “X Files”? Yeah, I sometimes think that. So, am I Fox Mulder or Dana Scully? What about you? Are you the believer or the skeptic?

2) The Heisenberg uncertainty principle.

Bohr’s assistant, Heisenberg, showed that any demonstration to refute the Copenhagen interpretation’s claim of observer-created reality would be frustrated.

His principle describes a fundamental limit to measurement. If one choses to measure the position of a particle very accurately, then you can’t measure the velocity accurately. And, vice-versa attempts to measure the velocity accurately, limit the ability to measure the location.

For example, to observe an atom with a microscope, one must bounce a photon off the atom that is then reflected into the microscope. But the photon will change the motion or position of the atom. The measurement has limits … and it is not just that the scientist needs to build a better measurement tool. It is not the tool at fault, it is the principle. Sure, the impact of measuring either position or motion will change the other. But it is really more of a fundamental issue, not just a statement about the experiment apparatus.

Again Planck’s constant appears. That is the true limit. As you design an experiment to measure either property precisely, you disturb the other property and the product of the measurement accuracy is always greater than or equal to Planck’s constant. (That’s a non-precise statement of Heisenberg’s equation. It is the “delta” or variation of the position measurement times the delta of the velocity measurement must be greater than or equal to Planck’s constant.) If you reduce the delta of one of the measurements, that must cause the uncertainty or delta of the other to increase.

Like most of these quantum theories, Heisenberg’s uncertainty principle has also been proven time and time again by all kinds of ingenious experiments.

Heisenberg’s uncertainty applies to other quantum characteristics too, such as energy or spin. The uncertainty principle can also be derived directly from the Schrödinger equation.

The uncertainty principle comes from the wave-like property of quantum mechanics and the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.

This basic limitation to both experiment and interpretation is now well accepted, regardless of other views and theories. Yet it isn’t quite enough to prevent certain contradictions in accepted quantum theory.

That leads to the third principle:

3) Complementarity

Copenhagen invokes the “complementarity” principle to confront a spooky aspect of observation: the instantaneous collapse of an object’s wavefunction everywhere by an observation anywhere.

Bohr understood that the two possibilities of an object being both a wave, spread-out and probabilistic as well as a real particle when observed is contradictory. So he supposed a concept called “complementary,” which allows the contradiction since we must consider only one aspect at a time. That’s what we mean when we say the wavefunction collapses upon observation. The contradictory view disappears, leaving us with a physical object. This covers both Schrödingers equations and the observed dual nature of both waves like electromagnetic waves and photons as well as matter such as electrons and atoms also having this dual nature and wave-like properties.

Recall that the spread-out wave could cover a lot of space. So the collapse to a physical object would suddenly put all the matter, or all the information, in one specific location. If the wavefunction really were spread-out matter, then that matter (or even energy or information) would have to move faster than the speed of light to collect in one place. As crazy as all we’ve talked about so far, we don’t think that happens. As kooky as the probability wave interpretation seems to be, it would be downright impossible to believe the object is actually smeared out across space. Remember, there is only the wave, not the wave and the particle, it is just the wave … until observation. Then there is just the particle.

What we are left with is the view that all we can understand is the results of our experiments. Stop worrying about what “really” happens. That we can’t know. We just know the click of the Geiger counter, the trail in a cloud chamber, the flick of a meter, the view in the microscope, the computer printout of the sensor data … all macroscopic phenomenon.

This almost appears to eliminate all physical objects at the atomic level. It appears that all we have are the measurements of our instruments and the design of our experiments. We can’t speak of atoms directly because we can’t observe them directly like we can a rock or water.

(This is no longer true. IBM labs produced one of the first photographs of actual atoms — atoms of argon. They even moved them around and spelled out “IBM.” So this “we can’t see or know” explanation is getting a bit thin. Modern, young physicists are continually challenging these explanations, even if they have been accepted as Gospel for almost one hundred years.)

This calls back Newton’s response when asked just what gravity “is.” He answered, hypothesis non fingo which means, “I make no hypothesis.” He didn’t claim to explain gravity. His equations simply predicted how it works. Einstein did extend that, giving great insight into the nature of space and time. Will some new “Einstein” eventually describe what is really going on in quantum physic?

Essential to the Copenhagen interpretation is a clear separation of the quantum microworld from the classical macroworld. May we some day eliminate the need for the Copenhagen interpretation in favor of a true story of Nature?

Only time will tell. So far we haven’t. Copenhagen is the primary explanation used today. Sure there are others like the “Many Worlds” explanation so popular with science fiction writers, and several more, but Copenhagen has stood the test of time and it is what is taught today.

So what about Einstein? Did he try to come up with an interpretation. You bet. That’s next.

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