Albert Einstein, Objective Reality, and Randomness

"No one knows anything. The whole affair would have been a delight to Jesuit fathers."
—Albert Einstein on the first international meeting on quantum physics, Solvay, 1911

Albert Einstein (1879-1955) is famous for many things. Mostly, now, he is remembered as the genius who changed scientists' (and other educated peoples') view of the nature of space and time through his theories of Special Relativity and General Relativity.

The second most famous thing about Einstein is that he showed this genius later in life. It is common knowledge that he did poorly in school as a child. This story is beloved by parents who feel their child's self-esteem is more important than actually hitting the books and proving they have done it with good grades. Unfortunately the story is not true. Little Albert's grades were quite good from elementary school to graduate school. [The best Einstein biography for advanced readers, including Philosophy students, is Subtle Is the Lord: The Science and the Life of Albert Einstein]

The third most famous thing about him was his support for the U.S.A. developing an atomic weapon, followed by his regret that an atomic weapon was developed and used to destroy two cities filled with people in Japan. Albert was a peace activist well before World War I began, and remained so until the end of his life.

Albert Einstein was interested in philosophy from at least as early as his college days. Possibly the fourth most famous thing he was famous for was not being able to reconcile with the science of quantum physics, even though he was one of the inventors and major contributors to that branch of science.

Quantum physics developed slowly. Its origin is usually marked by Max Plank's paper on radiation in 1901, which to jump to a later interpretation said that electromagnetic radiation (including light) comes in energy packages, or quanta. This went along with the ongoing development of the atomic theory, which had shown that electric charge also came in packages, which came to be called electrons. There were many weird things about the new theory, most notably that these light quanta, or photons, and electrons sometimes acted like waves and sometimes acted like particles.

The parts of quantum theory that Einstein could never except had to do with randomness. Einstein wanted to see reality as objective. That does not mean that it is just made up of objects. Rather, he wanted the objects (which could include wave-like objects) to be subject to the laws of causality, as he saw them. A number of results of quantum physics collided with Einstein's view of causality, including the Uncertainty Principle [Heisenberg's] and such random events as the decays of nuclear physics (resulting in radioactivity) and in particular the random timing of transitions of electrons when near an atom that result in electromagnetic radiation.

Younger physicists had no problem accepting quantum physics. They seldom saw it as posing a philosophical problem, much less a science one. Einstein's assumption that to have science you need causality, and specifically causality as defined by Isaac Newton, does not hold much weight today among people with PhD's in physics.

Einstein worked until he was on his death bed to find the underlying causes of quantum randomness and probabilities. Long after his death it was postulated, and is now generally believed, that the proton and neutron consist of smaller entities called quarks (more particle like) and gluons (more wave or force-like). If there were some way to measure the positions and velocities of the particles making up the neutrons and protons of an atom, then perhaps it would be possible to predict when a specific atom of a radioactive element would decay. But it is not likely that these decays are the result of the quarks reaching some particular configuration.

Consider dice and solar flares.

Ordinary fair dice, the kind used in casinos and board games, are governed by classical physics. [If you could make them small enough, say a few atoms across, they might start to display true quantum randomness.] They produces random results as long as they are thrown fairly. In theory (and to a surprising degree in practice) you can predict the results if you can sufficiently control how they are thrown and know enough about the surfaces they bounce against before coming up snake eyes, or boxcars, or whatever.

Einstein wanted atomic physics to work like ordinary dice. That would preserve his classical physics version of causality.

Consider solar flares. Scientist know there are patterns to them, but within the envelopes of those patterns they are random. They are mainly classical physics phenomena. They would be predictable if you knew enough about the matter and energy of the sun that gives rise to them. But how would you know that, in advance? You would need some sort of probe that can survive within the sun and send you detailed information about the pre-flare setup.

In fact there are a lot of things we can't know with certainty, for a wide variety of reasons. That does not mean that reality isn't objective. It is because objective reality is complicated. Very to the power of 30 complicated.

For much of my life I tended to favor Einstein's objections to quantum randomness. At some point, however, I realized the problem was more semantic than scientific. In other words, the problem was with how Einstein defined the words objective and causality.

Randomness in quantum physics doe not mean that anything can happen. The randomness in quantum physics is in envelopes. Just as when you roll a pair of dice you may bet any result from 2 to 12, but get 7's more often than other results, in quantum physics you mostly individual get results around a central number, and statistical results from a large set of data are also typically very close to that number.

That is causal enough for me. I accept probability and the statistical nature of results as part of the objective reality of the universe. In fact I have found that seeing the relationship of randomness to cause and effect has been very helpful to me.

I could tell you a story about a preacher who always introduced himself to potential victims with the words "Look around you. Do you believe that this all could be random?" But I have covered enough for one essay.

Wittgenstein, Determinism, and Probability

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

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

Lazy Nature, Lazy God

Is nature lazy? It certainly is slow. Look how long it took for life as we know it to evolve.

The ancient Greek philosopher-scientists knew that light was lazy. They showed that when light is reflected from a surface the angle of reflection is equal to the angle of incidence. Whatever the speed of light was, this reflection rule resulted in the shortest, and therefore the fastest, path between a source of light, an observer, and a reflective surface between them. Light takes the shortest path.

In the era historians refer to as the Enlightenment, this came to be called the principle of least action.

Nature has a number of definitions; when I write Nature, I mean the Universe or totality of things, including the principles that cause it to exist and determine the specifics of existence. Primitive people take the ancient idea of a god (tree, rock, ghost, or human) and try to amplify that up until they have a God that created and rules over, or at least within, Nature. Whether you believe in God or Nature, the physics experiments come out the same.

So the principle of least action implies that God is lazy too. God's laziness makes the universe predictable.

You can make a lot out of this simple principle, which applies to solid physical objects as well a light and energy fields. To understand this, unfortunately, the path of least effort leads through the quicksand of something called the calculus of variations. And of course, most people in the world need to start working or fighting or begging before they even get to regular calculus in school. On the other hand, if you do happen to study calculus and then the calculus of variations, you can get anything you want in the world. You will be able to see deeper and further than other humans, and make of it what you will.

With your math magic, you are now ready to do Lagrangian dynamics, among other things. You can see where Newton's Laws come from: a lazy, symmetrical universe (designed by a lazy God). And using only the principle of laziness, you can work out Schrodinger's equation (for the motion of a non-relativistic particle in a potential field) [Byron & Fuller, Mathematics of Classical and Quantum Physics, p. 71]. Thus you have the key to quantum physics. In retrospect it is surprising no one came up with it before Erwin Schrodinger.

Which brings up another important point: Chance. Or probability, if you like the more modern formalism. Many Romans worshipped Chance, or Fortuna (Tyche to the Greeks). In addition to the chance events of human lives, the practice of gambling was already well-developed. Dice pre-exist recorded history, as did other methods of casting lots or determining oracles. The minor Christian god Jesus Christ may have been an incarnation of chance, as it was written in the Bible (King James translation), Mark 15:24, "And when they had crucified him, they parted his garments, casting lots upon them, what every man should take." [Alternate versions found in Matthew 27:25, where this is attributed to fulfilling a Jewish prophecy; Luke 23:34; and John 23:24]

The role of probability in quantum physics, and in particular the Uncertainty Theorem, has led to a lot of guru-driven nonsense spouted in the popular arena of wishful thinking. There is probability in quantum physics, which is to say in Nature, but it is of a type. We say things like "the probability of finding an electron within this space-time region in our experiment is 40%." It sounds like "there is a 40% chance of rain today." But if an experiment where the equations create a 40% expectation is run a few hundred times and the electron is only found 37% of the time, what physicists do is alter their equations. Afterwards it looks like they got the 37% figure from theory, but in fact they got it from practice and molded their theory to their results. See Inward Bound by Abraham Pais for numerous historical examples.

Asking where an electron is in space-time relative to an atomic nucleus is actually simply asking a bad question, although strangely it is fine to ask where the same electron is traversing a vacuum tube. Chance in quantum land is probably best seen in radioactive decay, where it is clearly a result of a probabilistic decay mechanism, not of observational or prediction problems.

The principle of least action leads to quantum probability equations. So in some sense the rules of probability in quantum phyics are themselves predictable. Just as we cannot be sure what any throw of the dice may bring, but we can predict the outcome of large numbers of throws using the rules of probability.

In classical physics, laziness appears to be exact (assuming you know exactly everything about your system), or too pick an exact shortest path. In quantum physics the mask of exactness is removed, but the laziness of Nature is still the rule.

Book references:

Insurance and Casinos

Health insurance is the big issue of the moment. All kinds of politicians made all kinds of promises to all kinds of people during the 2008 elections, and now they are pretending to act on those promises. An improved health care insurance system was promised by many to many. My own expectations are low. But I am happy to debate the issue.

It helps to look at insurance in general, as well as looking at the specifics of insuring people's health.

And to understand insurance, you need to look at it outside the box. A good way to look at something outside its box is to take a look at a similar box, then compare and contrast. The ideal other box to look at, when considering insurance, is the casino, or gambling industry. This is not just my being satirical. It has to do with statistics and probability, which were originally studied and understood by considering games of chance.

Most people know, when they walk into a casino, that the casino is not really in the business of philanthropy. Casinos make money, they don't lose money. People suspend that knowledge by overriding it with another idea. They may get lucky. An individual, going to a casino and playing games of chance for any given period of time, may gain money.

But the money that individual makes is not, except in very unusual circumstances, a concern for the casino. Because other individuals, who are also there hoping to get lucky, are losing a whole lot more money than the individuals who are winning.

Casinos are set up that way. They were set up that way in ancient times before probability and statistics were developed forms of mathematics. Each game in a casino has a return ratio. Over a series of games, the individual outcomes have predictable percentages. This is most obvious in a roulette wheel, where each of the outcomes is equally lightly. Given that, for the casino to win over time the betting odds are simply set to slightly favor the casino. I won't go into the details, but you can find some at Roulette at Wikipedia.

Other games are more complicated, but work on the same principle. In poker the fact that the casino always wins is even more obvious, since a certain amount of each pot is raked off by the casino.

Insurance is remarkably similar. In its simplest form, it is a pool of money. Some people make money (they get more out than they put in); their are expenses for managing the money, and also profits taken out by the owners. As a result, most people get paid back less than they put in. You could argue that as with casinos, if people were rational no one would patronize an insurance company.

But the world is complex, and fear is a primal human emotion. There is an argument that some forms of insurance do make sense for the people who pay for them. This is because decreasing risk has a value to individuals.

Look at auto insurance, for instance. If you get into a car wreck the expenses from it could be enough to bankrupt most people. You probably won't get into a car wreck on any given day or even year, but there is a good chance you will get into one eventually. You fear bankruptcy, so you buy automobile insurance every year. It is expensive, and you are unlikely to come out ahead unless you get into a wreck (make that an expensive collision, not a fender bender) within a year or two after you first take out insurance. Yet it is worth it to many people because it protects them from being impoverished by a random event, an accident.

One can fairly ask, how much is it worth, this diminishment of risk? The auto insurance company has administrative expense and takes out a big chunk of the cash flow as profit to distribute to its investors. So all the people who buy insurance, together, will get paid back less than they pay in. Insurance companies hire actuaries to calculate their long term pay out risks, and set rates high enough to cover that plus administrative costs plus profits. Individuals are not in a position to hire actuaries. All they can do is shop for auto insurance, hoping to find the insurance company that takes the least bite out of the pie.

One other aspect of insurance should be carefully considered: insurance as investment. We see this in some forms of life insurance. The insurance company pays out more in aggregate to the people it insures than they pay in! Even so, the insurance company covers its administrative costs and pays its investors a profit. How can this be?

When an insurance company knows it can hold its incoming revenue stream for a long time (because its actuaries told it so), it can invest its balance of money in bonds, stocks, and real estate. So from an individual insured's perspective, the insurance company resembles a sort of mutual fund. Your family gets paid when you die if you have life insurance, or you get payments from a set starting point until the time of your death if you purchase an annuity policy.

In theory Social Security works like this, as do most old-fashioned (defined benefit) pensions. You pay your social security taxes during your work life. The government invests this money in interest-bearing government bonds. The average person gets more than they pay in. Those who die early are out of luck. Those who live long get far more money than they put in. Of course in reality money put in today goes out today to those who are already drawing Social Security. But it shows the idea of insurance that not only spreads risk, but creates additional income for the entire pool of insured people.

Not that anyone in Congress is going to listen to you unless you gave at least $2000 to their election campaign, but given all this, what kind of federal health insurance would you like?

Should it provide roughly equal benefits for everyone? Should it funnel almost all the money to care for those with the most expensive medical conditions? Should the money that goes in the first year be paid out it once, or should it be accumulated, with interest, for the benefit of those who are doing the paying? Should it be subsidized by taxes, or should it generate a profit to the government that pays for non-medical budget items like the military budget?