Scientific Paradigms





          Newtonian or classical physics is still an important part of science and in use everyday by physicists and engineers. It is still taken as a paradigm form of scientific explanation. But do we really understand how it works on the epistemological level? It is assumed, we would think, that the use of Newtonian Mechanics involves the application of general empirical principles to a particular problem at hand. But if we consider what is arguably the most important of Newton’s Laws, the second law, it is not at all obvious that this is the case.


The Second Law is sometimes expressed as F=MA but more accurately it is that the applied force is equal to the first time derivative of the momentum function. Is this an empirical relationship? If so, how could we test it? Presumably if the law is empirical it is testable, but how is this to be done? There is no test independent of the defining relationship that can determine the magnitude of a force, no other way to come up with or derive the magnitude of a force. The Second Law is really a quantifying definition, not an empirical relationship yet it is of great value. The epistemological problem then is to explain why this is the case.


It could be argued that the First Law cannot be understood without knowing the First and Third Laws: no change in motion without a net applied forcer and action and reaction.  This claim seems reasonable with respect to the First Law, knowing it we can regard the Second Law as a rule for measuring the net force on an object. But then another question develops, namely why is the Second Law useful? The Second Law admits to other formulations. We could use an integral of the second time derivative of the momentum function, i.e. integrate the “jerk” function and get the same results. (Some experts, e.g., Col. Staap in biomechanics think that jerk is more important than acceleration for injury analysis.)This seems to be physically realistic. We might even go to the rate of change of the change in the acceleration, and this too might be physically realistic in certain circumstances. So the Second Law has no unique mathematical formulation, it might admit to several. But does it have any real empirical content?


Suppose we do an experiment. We launch a weight into the air in a vacuum chamber against a constant gravitational field and see how high it goes. We could measure the height with high speed cameras against a scale to a very high degree of accuracy. From the height we can calculate the applied force and the acceleration resulting from the release of the spring. Suppose we do it one day and the weight goes two feet into the air, we do it the next day and it only raises a foot and a half. Now what? Before each test we determine the force deflection constant –K – for the spring; it is the same for both days. Now we have a real problem. We might have to regard the results as miraculous, but do they contradict the Third Law or Newtonian Mechanics?  The weight still rises on the second day, a reaction to the applied force; the Second Law tells us how to measure the forces after the fact and is still applicable. The Third Law is satisfied because there was both an action, the decompression of the spring and a reaction- the motion of the weight. (Other interpretations of the Third Law might be more appropriate here.) So we may have a miraculous event that does not violate the laws of physics. What a revolting development!


If a science does not preclude miracles is it still a science? Now if such a confusing set of events were really to happen the attention would be drawn to the spring. Perhaps K was variable for some obscure reason. Gravity is very constant at any particular spot on earth and a sudden decrease would be very noticeable and problematic, so a change in gravity is ruled out.  But perhaps the mass of the dead weight could somehow change overnight and this might be a solution to our dilemma. Other laws or principles might come into consideration here, like the conservation of mass or various considerations in engineering like the properties of materials. But even if we failed to come up with an explanation for the problematic events we would in no case abandon Newtonianism in domains like this. Why?


As was suggested, the laws weren’t violated; therefore there is no reason to abandon them. But it seems as though their utility has been compromised. The results from the first days experiment do not apply to the second day’s test. But were they suppose to? Is this not an assumption that is not in Newtonian Mechanics?  But the discipline is certainly taken to have predictive power, consider ballistics and statics for example. We would have to abandon our buildings if statics, a related derivative discipline were suddenly to become questionable. Further, anyone doing the experiment and understanding Newtonian Mechanics would tend to assume that the second day’s results would be the same as the previous days. But predictions and expectations based on Newtonian analysis are assumptions about the world which while likely to be true as a matter of experience are not guaranteed by the theory.


Newtonianism is generated by a single important realization, that changes in motion have a quantifiable cause. This is the realization that generates the first two laws. The Third Law is very interesting in that its status is a little less clear; it is neither a direct  observation nor a mathematical rule. It seems as though it is a tautology or a synthetic apriori judgment (Did Kant realize this?). I push on the wall and the wall pushes back. If the wall doesn’t push back then I have no push. If there is no resistance to my push then no force can develop from my efforts. Forces exist only as opposing pairs. It makes no difference what the cause of the resistance is; it could be inertial mass or the mechanical properties of a structure. But in either case the force pair is created at the contact surface through opposing electromagnetic fields. The electrons in my finger tips are repulsed by the electrons in the wall. The third law is based on the principle that like charges repel one another. Something which Newton didn’t know but is implicit in the law.


The problem with Newtonianism is that it is an instance theory and not a system theory. This is why the impossible or miraculous do not necessarily contradict it. While it is possible to apply the theory to long duration events, it basically deals with instantaneous forces and their consequences. While a force might have a complicate and time variant description, e.g.., we introduce a forcing function and integrate it over a time domain to determine the final velocity; the accuracy of the predicted results again depends on considerations not inherent to the laws of motion. (We might have a mathematical description of the variations in the thrust of a rocket engine. The assumption behind the calculated velocity of the rocket is that the engine performs as described.)


The epistemological issue is related to how much of what passes for our knowledge is instance based as opposed to systems based understanding. The world is composed of systems, not of instantaneous processes. The universe never stops working. Even if the notion of Planck time unit is meaningful, most of the events in the universe and most of our experiences involve much longer durations and most importantly many more events than can transpire in this interval. Classical physics succeeds because it defines most of what is going on in the world surrounding the analyzed event as irrelevant. It simplifies and reduces information. This works to a large extent with the sorts of problems it is concerned with but the elimination of complexity and the reduction of information fails when most systems are analyzed.


We can use simplifying models with test tube beakers to produce worthwhile results in chemistry and other disciplines as well may yield significant results when simple laws or models are applied. But with areas with complicated phenomenon, e.g. economics, medicine or politics a law or rule based approach is fundamentally inadequate.



RCE 8/12