### God Throws Dice

I am one of those rare theologic birds --- I actually understand a bit of Relativity Theory, the Uncertainty Principle and Quantum Mechanics. I took an overview course at the end of my sophomore year of engineering school, and the course covered most of the important mathematics, which, at least at the time, was comprehensible to me. I didn't do brilliantly in the course --- I was composing a full-length ballet score at the time, and actually inked the orchestral score during the lectures, which occurred in a large basement auditorium.

I remember being told that, less than fifty years prior, a small classroom could hold all the people in the world who actually understood the theory, although much of the world had heard of Einstein and wanted to know what it was all about. Nowadays, physics has gone way beyond that handful of theories, the math is still tough but taught all over the world, and books on the nature of the universe are best-sellers.

Over the years, however, it has been my great misfortune to read interpretations of the original theories written by artists, theologians, social critics, entertainers, and even scientists and engineers, who obviously have no idea what they are talking about. I was thinking, lately, about how theologically incorrect such nineteenth-century influential thinkers as Darwin, Marx, and Freud were (this is what I think about around the house), and then I remembered that Einstein has also often been cited as having a major impact on twentieth-century thought. Then I recalled his "God doesn't throw dice" line, and like Proust after smelling cookies, a flood of related memories and thoughts was released, which I have affixed herein.

What bothers me most, of course, is the "E=mc2" bandied about by everyone from school children to advertising people. I was taught that what was really important was "delta E = delta m times c squared." In other words, adding energy to a system (or object) increased its mass, so that attempts to increase the speed of an object by adding energy would increase the mass of the object, so that more and more energy was required for faster and faster speeds. C, the speed of light, was a constant, and mass could not travel at that speed. Only by removing mass from the system, and creating pure energy, could one attain the speed of light.

It was not that a mass could be reduced to energy, but certain processes, like a nuclear reaction, reduced a large mass into smaller masses, and the sum of these smaller masses did not equal the original large mass; the difference was released as energy, and a lot of it! The idea that mass was on one side of the equation and energy on the other, and the speed of light a constant, had enough radical ramifications without imagining that a mass could be reduced all the way down to pure energy, or that mass could be created from energy. But I guess most people don't take Calculus, so adding the deltas would make the formula inaccessible and incomprehensible to most. My problem is, it is incomprehensible --- to everyone.

It's that constant which is the most bothersome, which is why we refer to the "Theory of Relativity." It is intuitively correct to believe that if a train moves 1 foot per second relative to a track, and a man on the train moves 1 foot per second relative to the train, then the man will move 2 feet per second relative to the track. Intuitively correct, but in reality, incorrect! The man will actually be travelling a tiny bit slower. If the train moves at half the speed of light relative to the track, and the man at half the speed of light relative to the train, the slowing is significant --- I vaguely recall it having something to do with the square-root of one minus the ratio of the velocity to the speed of light squared, or (1 - .52).5, which is .866, but I may have forgotten something. Anyway, .5 plus .5 ain't 1.

Philosophically, what's important to me is not that one's observation of the speed of an object depends on the speed of the observer and so on, but that the actual behavior is incomprehensible to anyone. I don't believe there is a sentient being on this planet who can mentally picture that man on the train not going 2 feet per second. That's a radical shake-up of the world-view --- that a phenomena that can be detected with instruments cannot be imagined by humans.

The particle-wave dichotomy is similarly shocking. You take a baseball and throw it out of a building with two open windows. In fact, you take a whole bunch of baseballs and throw them out of those windows. On the other side of the window is a screen where you record the hits. Now, as you throw those baseballs, one at a time, two very neat patterns should form from the baseball passing through one of the two windows, right? Wrong! A very tiny diffraction pattern, as if the baseball was passing through both windows at once, will result. When the baseballs are electrons, and the windows tiny slits, this behavior is quite observable, and it doesn't matter if you fling the electrons all at once or one at a time!

As I understand it, it's not that an electron is both a wave and a particle, it's that our idea that a particle (an object restricted to a particular location) and a wave (a disturbance in a continuous aggregate of objects) exists is wrong! What is actually going on we are unable to imagine. I mean, once you've been exposed to electron clouds and potential wells, and understand that the electron whizzing around the water molecule in the glass of water in your hand has a very small but very real probability of being on the moon at some point in time, you might as well give up trying to form a mental image of the universe!

I'm getting ahead of myself, of course, because that's Quantum Mechanics, and we all know the Uncertainty Principle came first. Citations of this principle in popular literature are most offensive, because some people use it as a cute form of Murphy's Law. Even those who think it just has to do with the observability of a phenomenon haven't grasped the whole picture. The Principle states that the more you know about an object's location, the less you can know about its momentum, and vice versa. One ramification is that the physical act of observing the object's location mucks up the accuracy of apparatus that's supposed to measure the momentum, but I believe it's more disturbing than that. It's not that the momentum really could be observed, if you were just ingenious enough to devise a testing device to do it, say observing it earlier and projecting forward. It's that the set of possible explanations for what you observe the momentum to be increases as the set of possible explanations for what you observe the location to be decreases. Just because the location can be observed as (X,Y,Z) plus or minus something, and the momentum can only be observed as P plus or minus something worse, doesn't mean you can claim that P is actually some single number plus or minus whatever accuracy you want. It's my understanding, and it sounds like nonsense, that observing (X,Y,Z) really does squash P out to that mushy range, whatever that means.

And here's where Einstein really started getting upset, and threw in the towel. You see, as long as that equal sign held, Einstein still had his clockwork universe, even though that universe was impossible to imagine. But then probability theory stepped in in the form of wave phenomena and Quantum Mechanics and said, "YOU CAN'T KNOW," and Einstein complained, "God doesn't throw dice."

Now some people have taken it quite calmly --- after all, physicists are still in business. Once you've accepted that the math describes things that cannot be imagined, who cares whether the math involves observable constants or random blotches? The wave equations are just as limiting, in their way, as the mass- energy equation, in that they reduce reality down to paper. But, without misusing the theories and principles as misguided metaphors for theories of art, politics or philosophy ("relativism"), let's think a little about the physics itself.

Aren't we, theologically, butting right up against the unknowable? If God is finite and infinite, in the world and outside of the world, knowable (through revelation) and unknowable, everywhere and yet transcendent, too, isn't God, then, in Relativity Theory, the Uncertainty Principle and Quantum Mechanics, and yet outside of them, too? It's the clockwork universe, as desired by Einstein, that limits and constrains God, and makes for bad theology. There is humility and awe in realizing that reality, as it actually is, cannot be imagined by human beings. But beyond that, why shouldn't God be able to create a universe where Quantum Mechanics works? Why can't God throw dice, if God wants to?

There are readers out there who are already picking up pad and pencil to write angry letters about numina, holy wars and technical publications. For once, spare me the knee-jerk reaction and think about what it means to be a human being, why you are an engineer, and what is really important to you. A very scientific, very accurate survey recently determined that over 90% of Americans are religious. It certainly isn't science's goal to prove the existence of God, or to come up with a working definition of God, but becoming an engineer does not mean you automatically must approach the world at every second as a rational, logical, perfect (ideal?) realist. Nor are engineers expected to reject their upbringing, their beliefs and obligations, their culture and society.

Perhaps we seek knowledge as an attempt to disprove the existence of God. A reality circumscribed, limited and reducible to natural laws and formulas is a reality stripped of miracles, wonder and values. What bothers me about Einstein's "God doesn't throw dice" maxim is not that Einstein believes in God, but that the God Einstein wants to believe in is not allowed to make the rules. Similarly, Darwin's theory of natural selection is wrapped up in egotistical notions of progress, not adaptation to external phenomena which might be outer directed. Marx's utopian visions of a stateless, faithless society marred his analytical gifts and made all of his predictions wrong. And Freud's excitement over dreams leaves no room for the horrors and joys of real on-going experience based on free will, rather than predetermining events of one's childhood.

What all four never face, and what their blind followers lose sight of, is why they chose to observe what they did in the first place. Attempting to do science for science's sake leads, inevitably, to theological questions outside of science's realm. What each of us must ask ourself is whether, when faced with these questions, we should form our own religion or open ourselves to those who have travelled the paths before. This choice is made by each individual. While scientific treatises are rife with the theologies of those who have chosen the former route, we should not deny the opportunity to those who seek the latter.

In honor of my 50th birthday, I received this letter in praise of many essays in this collection, and this essay in particular.

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