Not Much Uncertainty Principle
January 29, 2011
by William P. Meyers

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The Heisenberg Uncertainty Principle, or less pretentiously, the uncertainty relationship, is a fact of nature, discovered as part of quantum mechanics (a subset of the more general quantum physics).

Philosophies and religions that believe in an observer-created reality have interpreted the uncertainty relationship as proof of their viewpoint. They claim that reality is subjective, not objective, and this supports or interweaves with other aspects of their viewpoint. Some, but not all, New Age and Eastern (Hinduism, Buddhism and Taoism) religious sects propose that human individuals "create their own world," and that by learning to control their minds can thereby control the world. They may also claim that the world is an illusion, thus justifying not paying attention to it, or basing decisions on faith in religious leaders or scriptures.

These claims warrant examination.

The uncertainty relationship was discovered in 1927, capping a four year period of rapid discoveries in quantum physics which solved problems that had been on the table for decades. It is fair to say that the discovery of the electron (1897), or minimal unit of electric charge, and of the light quanta, or photon in 1905, had started what we now call quantum physics. But in 1923, even though it was believed that electrons associated with atoms obeyed quantum laws, no one could correctly model the spectra (specific frequencies of light) emitted by heated molecules of differing elements.

In September of 1923 Louis de Broglie proposed that electron, like the photon, obeyed the law associating a frequency with its energy level. Energy (E) would equal frequency (f) times Planck's constant h:

E = f x h

In fact he proposed that all forms of matter and energy were governed by that relationship, and thus had a wave property, frequency, associated with them.

Much happened in 1924, but in 1925 Werner Heisenberg cracked the basic math for the frequency of atomic spectra problem. He decided he would use no model of atoms at all, but would instead base his Quantum Mechanics only on observable facts, in the first instance, the frequencies of light emitted by atoms. With considerable help from friends (Born, Jordan, and Pauli), and because all the spectral data had been available for decades, the new system was shown to be essentially correct. In addition Erwin Schrodinger in January 1926 solved the hydrogen spectrum with his wave formulation of quantum mechanics. Physics guys liked that because the math was more familiar to them than Heisenberg's, but soon the two maths were shown to be equivalent.

Max Born issued his first paper on the probability interpretation of quantum mechanics in June of 1926, which is of great philosophical importance, but which won't be followed in this essay. In March of 1927 physical experiments first showed that de Broglie was absolutely right: electrons, thought of as particles, did have frequencies and acted like waves in certain situations.

Which brings us back to Heisenberg, and March 23, 1927. His uncertainty relationship was based on the nature of the math used in quantum mechanics to correctly predict spectra, and on a thought experiment (later carried out with real experimental apparatus). It is important to understand the equation:

The "p" represents momentum, "x" can be taken as the location in space, and the triangles in this case indicate the latitude or slack available for their attached variables. The total slack, or uncertainty, from multiplying the observed momentum with the observed locations in space is greater than or equal to Planck's constant (h) divided by 2 times pi (3.14), or about h/6. The best case scenario for accuracy is when the two sides of the equation are equal.

Which is to day if you have really great experimental apparatus and are trying to simultaneously measure something's momentum and position in space, the best you can do overall is get it to within about h/6. If you try to make p smaller (more accurate or certain), x becomes less accurate or certain. If you double the certainty of p, you halve the certainty of x.

Yet on this uncertainty whole philosophies and religions try to defend their metaphysical speculations from the discipline of nature. How much uncertainty are we talking about?

Planck's constant is an experimentally determined number of energy units multiplied by time. Given that our everyday science energy units are on our scale, it is a small number: about 6.626 times ten to the negative 34th Joule seconds. In other words, put down a decimal point, then 33 zeros, then 6626:

.00000000000000000000000000000006626 Joule seconds

You probably have no more sense of how small atomic particles are than I do, but the result is that uncertainty is pretty significant for a light quanta, roughly corresponding to its wave length, and is significant for a single electron. However, it really is not all that significant, most of the time, even for something as light as a hydrogen atom (one proton with one electron). The uncertainty is for the entire experimental system; it does not increase as we work on objects of larger mass.

Upscale to something we think of as really small, say a virus particle, and the uncertainty is still about h/6, which means that determining the momentum and position of our virus is going to be limited by our experimental apparatus and our lack of caring, rather than by the uncertainty relationship.

So how certain were scientists about positions real world things before Heisenberg? The answer is no one had really thought about it clearly. Quick, give me the exact position and momentum of that cloud in the sky over there. See, classical physics was filled with uncertainty, just as life is. But arguing the cloud is not real because you can't tell me to 99 decimals where its center of mass is right now, is foolish. In theory in classical physics the moon has an exact position in space and an exact momentum, but no one was ever able to measure the moon or for that matter anything that would have caused their experiments to be affected by Heisenberg's certainty limitations.

Heisenberg found the uncertainty principle because it finally mattered to scientists. Things that matter in the quantum world of electrons and photons may not matter in our gigantic human everyday scale. The rules of quantum physics apply only to very, very, very small things. In aggregate they average out to ordinary, everyday physics and to our intuitive understanding of dealing with our everyday lives.

What Heisenberg really showed is that we can be highly certain about physical reality if we are willing to put in the effort. Even in the case of electrons.

If you are a carpenter, and are used to your hammer, you know how to hit a nail on the head. There is plenty of uncertainty at a human scale, but its nature is different.

Understand this, and you are probably ready to understand the issue of observation affecting what is observed in the domain of quantum physics. That will be a separate essay.

Key take away: uncertainty is a fact of nature, but in the sense of the Heisenberg Uncertainty Principle, it is very, very small.

[special thanks to Abraham Pais for Inward Bound , pages 252-262 and those who have contributed to Wikipedia articles on quantum physics]

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