Probability Outcomes In Physics: Describing Is Not Understanding

born einstein

Max Born tells us that in Classical physics, every experiment begins with “initial conditions”– those things which we take for granted as the starting-point of our research. Such initial conditions are “not determined by natural laws,” he says, but are assumed— a sort of artificial freeze-frame we impose upon the system under analysis so as to provide us a starting-block for our investigations. One must simply take on faith that the starting configuration has been– indeed, is even capable of being– precisely measured in every relevant way. Otherwise, says Born, “one has to be content with a statement of probability.”

To provide my own example… suppose we want to do an experiment concerning a ball which starts at rest and then rolls down a certain-length plank. We must assume that, at the beginning of the experiment, the ball is no-wise in motion or being acted upon by some unaccounted-for force. And we must assume that the ball is at rest precisely against the starting line.

But in reality, notes Born, “even the best measurements offer only statistical evidence, which is more or less restricted by the scatter of the initial configuration.” The best we can say or hope-for is that most of the ball –most of the time– is at (relative) rest behind the line (which itself is mostly where we think it is). Even if we are able to measure within 1-oompth of exactness, any movement of the ball or line less than 1-oompth will simply not be measurable.

Says Born… “An exact description of the state of a physical system presupposes that one can make statements of infinite precision about it.”  To Born, “this seems absurd.”   For him, “infinitely precise statements about the initial position and the initial velocity” are nothing but “metaphysical nonsense.”

In the notes he wrote to accompany the publication of his multi-decade correspondence with Albert Einstein, Born explains that, “together with many other physicists, I have been gradually converted as a result of experience in the field of quantum phenomena to the point of view that” … “at any given moment, our knowledge of the objective world is only a crude approximation from which, by applying certain rules such as the probability laws of Quantum Mechanics, we can predict unknown (e.g. future) conditions.”

Personally, I have to admit some frustration when I read early 20th century physicists such as Born expounding upon the subject of probability, for — in spite of what they claim– their minds have not altogether switched over to the new “quantum” way of thinking, and so they are not always clear or consistent. For instance, in the above statement, Born appears to be claiming nothing revolutionary at all, merely that, because we can’t measure a certain system exactly, we cannot exactly know its present state, and thus cannot exactly predict its future state. After reading his statement, one does not come away thinking that he has abandoned all belief in some underlying reality or in the mechanism of cause-and-effect.

And yet, Born and other scientists in the dominant camp of theoretical physics are commenting elsewhere that such abandonment is precisely what they demand — that the belief in some underlying, objective reality must be rejected, and that faith in a Universe run strictly by cause-and-effect must be jettisoned.

Typically, in Born’s day as in our own, physicists discover the distribution of situational outcomes only after repeating an experiment many, many times. They then retroactively create and assign probability-equations describing the situational outcomes within some acceptable margin-of-error. The problem is that these handy-dandy equations are sometimes impossible to interpret as actual, physical behavior.

For instance, if the equations describing a certain experimental situation and its outcomes return an undefined value (or infinity!) for certain locations along a particle’s trajectory, then the physical interpretation may very well be that the particle “disappears” at that value, only to reappear later at other values and continue on. This is similar to what a “quantum leap” is supposed to be for electrons, and how such an idea was ever arrived-at in the first place.

Basically, probability equations have proven so successful at predicting the outcome of multi-event scenarios, that when physicists feel forced to choose between math and a rational, physical explanation, they choose the math.  In their defense, in much of the day-to-day work of physics, the rational, physical explanation is irrelevant– what matters is that the situation is predictable and manipulatable.  What Uranium electrons are exactly up to during nuclear fission is, in a practical sense, irrelevant, as long as the nuclear power plant keeps running as it is predicted to.

I think one danger of the purely mathematical approach is that sometimes equations can be found to fit the data by a sort of coincidence, or as a neat trick, but such equations tell us nothing about the real situation, and indeed, can sometimes be misleading.

If I remember correctly, this is what happened in the early days of spectral analysis.  Different spectral patterns from luminous objects were discovered, and some mathy-type individuals immediately went to work finding equations which would produce the same patterns.  Sometimes, when this were accomplished, the equation would be highly praised by the scientific and mathematical community.  

But as time went by –and mostly due to steadily advancing technology and methodology– better and more finely tuned spectral analysis was accomplished– and suddenly the nifty equations didn’t describe the situations anymore. So, not only did these equations never really tell us anything about the situation– they were also misleading, since many theoretical physicists can’t help but spend time trying to figure-out what an equation is telling us (I’m certainly in that camp).

If one has the time and computing power at one’s disposal, one can come up with a mathematical equation to fit all sorts of series. But so what? Neat trick is all, sometimes.

To take a simple example, if one is examining the spectrum produced by a certain luminous object, and one finds dark bands occurring in this spectrum at position 3, 5, 7, 9, and 11 — one can come up with a predictive mathematical equation describing this situation, namely: dark band position = 2x +3, with x being the intervals (0, 1, 2, 3, 4…). One may then convince one’s self that he has discovered something by the production of this equation.

But suppose new evidence or better measurements now show that the data stream actually appears more like… 3.1, 5.7, 6.9, 9.2, and 11.8– and maybe an additional term shows up in the middle which was not even discernible previously… Thus, the mathematical equation which once seemed to describe the situation is found to be no longer adequate… or relevant. 

And what do you think physicists do when they have a mathematical “explanation” which they have grown attached to– even built other theories around and ontop of — but which is then proven inadequate in light of new data?  Typically, what they will NOT want to do is to chuck out the math and start over. No, instead they will often attempt to tweak the same fundamental equation until it fits the new data.  Over time — as physicists attempt to keep their equation relevant to the ever-expanding, ever-changing data– what started out as a simple mathematical description such as 2x+3 may become so complex of an equation that it takes half a page to write it all out in most basic terms (of course, mathematicians can make equations look shorter and simpler by substituting complex terms for simple ones).

By the time of Einstein’s death, orthodoxy in physics had accepted the trade-off of physics for math, of meaning for predictions of probability.. “Why?” became no longer the dominant scientific question, but “What is expected?”  And the answer to that question was not deduced, but discovered by repeated experiments.

A few of the more philosophically minded physicists may sometimes still try to EXPLAIN what may be going on physically in a situation, but most physicists have become comfortable with just accepting the after-the-fact mathematical description of results.

Not all acquiesce to this view, of course. There’s me. And then there’s… uhm…

Well, going back to Einstein… Born tells us that Einstein “was firmly convinced that physics can supply us with knowledge of the objectively existing world.”

Einstein refused to give up causality without a fight. One gets the impression that to him, there IS NO physical science without causation, that the most fundamental purpose of physics is to EXPLAIN things, not merely describe them. Indeed, in one letter to Born, Einstein writes… I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will, not only its moment to jump off, but also its direction. In that case, I would rather be a cobbler, or even an employee in a gaming-house, than a physicist.”

Einstein did not have a problem with statistical descriptions of experimental results, but for him, this was not the end-goal of physics. To use my own example, it would be like a doctor being satisfied with a medicine because he could precisely tell his flu patients that, with his methods, they stand a 40% chance of a complete cure and a 60% chance of losing both legs.  Describing is not understanding.

Born, on the other hand, believed that “the statistical interpretation of physics is the final one.”

Einstein was willing to concede the practical results of probability descriptions… “I admit, of course, that there is a considerable amount of validity in the statistical approach,” he writes Born.  But he felt that […] “physics should represent a reality in time and space”… “not probabilities, but considered facts.”

Wolfgang Pauli, in his attempt to explain Einstein’s views to Born, said that Einstein believed in a reality which always had a sharp location– whether one could measure it or not.  Pauli –being, like Born and unlike the rebel Einstein, a supporter of the new physics-orthodoxy — described Einstein’s outlook as a “philosophical prejudice.”  Pauli explains that Einstein (poor old fool that he was) felt that there exists an underlying reality which depends neither upon the experimenter nor upon his experimenting-apparatus.

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