One of the oldest philosophical questions is whether the Universe is deterministic or indeterministic. In a strictly deterministic universe everything that happens unfolds, causally, from the previous configuration of the universe. In such a universe, the thinking typically goes, man has no Free Will. We do what we are compelled to do by the rules of the Universe, or by the gods, if you prefer religious terminology. Our lives are controlled by Fate.
The advent of quantum physics threw a monkey wrench into the deterministic view of the universe constructed by scientists between 1600 and 1900. After considerable debate and experimentation, quantum physicists decided that at least some things in the universe happened by chance. This gave strength to the Free Will schools of philosophy and religion.
As far as I know my favorite philosopher, Ludwig Wittgenstein, did not decree the universe to be deterministic, or indeterministic either. Wittgenstein was a philosopher's philosopher. He offered no direct guidance to living life, unlike say Friedrich Nietzsche or Henry David Thoreau. In fact it is hard to find a place where he said anything definite about the universe, at least not after his earliest work, the Tractatus Logico-Philosophicus.
In his later works, including Philosophical Investigations, you might say that Wittgenstein deconstructs philosophy. But he is not a nihilist. For Wittgenstein the universe exists, it is no illusion. Instead what gives the aura of illusion to much philosophy, religion, and magical thinking is a swarm of errors that result from careless reasoning and the inexact nature of English and the other languages we use to do our thinking.
So what can best be learned from Wittgenstein is a technique, a critical attitude. It is similar to the ancient Socratic method of asking questions that lead a student to a correct, if complex, viewpoint. The trick to the Socratic method is asking the correct questions. I've never seen a formula for generating the correct questions. Wittgenstein provides no explicit formula, but his later works provide large numbers of examples of trying to apply an analytic (but often intuitive) process to philosophy itself. Frequently we are led to conclude that philosophy, like religion, is riddled with nonsense. Eliminating nonsense is one Herculean task that must be done if you want a clean stable for your ideas about the world.
Based on looking at many human and natural phenomena, we don't need to abandon the terms deterministic and indeterministic. What we have to do is use them more carefully and to realize that in certain situations there are shades of gray between them, and even room for both to be present in the same phenomena.
One of the most interesting and well-examined domains is probabilistic phenomena. We can speak of the probabilities of drawing an inside straight in poker, of an atom of radium decaying within the next pico second, of fog in the morning in London in February, or of Aunt Betty calling unexpectedly. But probability is another big word that may be misleading if we over generalize. Does shuffling a deck of cards create the same sort of probability as weather or quantum uncertainty?
Probability can exist in both a determinate world and an indeterminate world. From Newton's time until Heisenberg every throw of the dice was believed by scientists to be subject to the laws of (what we now call) classical physics, laws that were totally deterministic. Sure, with 2 dice, snake eyes came up every so often, and seven came up a reliable percentage of the time, but that was because humans had devised this method to introduce randomness. The dice were supposed to be shook up or thrown hard, making slight variations in muscle movements, too small to consciously control, result in outcomes that the thrower could not predict. A man of skill, throwing carefully, might cause dice to produce specified results at least some of the time, but other men monitored such cheating. The end result, fair or cheat, was determined by the placement of the dice in space, the momentum of the throw (including angular momentum), the exact characteristics of their bounces, and even the friction of the air.
When quantum physicists first discovered random atomic events many thought that there would prove to be underlying non-random, deterministic events that could explain the randomness. Much like Newtonian physics could explain, at least in theory, any particular throw of the dice. Einstein, for instance, believed that. But they were wrong, as far as anyone can tell. Many atomic and subatomic events do follow classical physics. Momentum, for instance, is preserved in atomic collisions. But decay processes, including radioactive decay and the emission of a light quanta by an electron "falling" from a high energy "orbit" to a lower energy orbit seem to be random events. At least within an envelope.
An envelope? They always leave that factoid out when religious gurus who specialize in the mechanics of separating their followers from money are elevating Quantum Physics to a Recipe for Mysticism. An envelope, here, is a metaphor for bounded probabilities. For instance, no matter how many times you role a pair of dice, the results are limited to the numbers between 2 and 12. That in itself is a kind of fuzzy determinism. Casinos, the old-fashioned kind with roulette wheels and people dealing cards, were built of fuzzy determinism. You could not predict which gamblers would win or lose any given hand or turn of the wheel, but at the end of the night the casino had more money than it started with.
Likewise a radioactive atom. You can't know when a particular atom will decay, but you can bet on a large group of atoms of the same element and not lose your shirt because the group emits radiation at a very predictable rate.
Once you start putting atoms together you quickly reach a point where quantum physics becomes pointless and you might as well fall back on classical physics. Yet engineers can build machines that make use of quantum mechanics for devices humans use, as shown by almost every electronic device made since the invention of the transistor. We use quantum uncertainty in our devices, yet we do that to increase predictable, deterministic behavior. If our devices get a glitch, the most likely sources are not quantum mechanical fluctuations outside the expected envelope but the failure of old classical components like a battery or solder joint.
So be careful about philosophical extrapolation. Or remember the modern key to all knowledge and wisdom: It's Complicated. You are made up of the same stuff of the rest of the universe, the arrangement is just different. We are arranged like mammals, only more so. Thinking about Free Will or Not Free Will will not help you make a decision. So take a deep breath and know that causality and randomness, determinism and indeterminism, are both going on all the time, within you and without you.
This essay is offered as a sacrifice to the Roman goddess Fortuna, and to the lucky Roman soldiers who won Jesus Christ's clothes at the crucifixion.
More quantum physics and philosophy
Showing posts with label uncertainty. Show all posts
Showing posts with label uncertainty. Show all posts
Wednesday, January 16, 2013
Sunday, January 30, 2011
Not So Much Uncertainty
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]
Natural Liberation Philosophy
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]
Natural Liberation Philosophy
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