Logical Limitations of Physical Laws

Logical Limitations of Physical Laws

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There are some fundamental logical difficulties in accepting science-derived laws of nature as being the intrinsic or eternal characteristics of the physical universe.

To begin with, whatever physical laws we hold to be true, we have become aware of them only through our experiences on this planet; and, since recently, on some other celestial bodies. However, these are only infinitesimal sections of a grand universe that is known to be stretching to billions of light years. Moreover, the experiences on which we base our understanding have been during a very short time span in the considerably longer history of the cosmos: just a few thousand years compared to the billions of years during which the universe seems to have been existing. The question then is: Are we justified, on the basis of these limited spatiotemporal data, in asserting that these laws have operated all through time and are valid in every nook and corner of the universe?

Before the rise of modern science, there used to be a clear cut distinction in the minds of investigators between the physics on the terrestrial plane and the physics of the heavens. In the Aristotelian view, it was believed that in the celestial sphere entirely different laws opera­ted: there, for example, all motion took place only in perfectly circular orbits, no changes ever occurred, and matter never decayed. Science no longer holds such views. Indeed, a necessary step for the development of modern science was the recognition of the universality of the laws of nature. Although the Copernican Revolution was generally looked upon as removing humans from the coveted center of the universe, thus humiliating our ego, one could just as well regard it as result­ing in the merger of our abode with the heavens – a magnifying experience.

On the other hand, one could also argue from a purely logical point of view that the Aristotelian world view was not unreasonable: for according to it, extrapolation of our limited experiences into the domain of the totally unknown and (apparently) unreachable was not logically justified. For example, suppose that we had known in precise quantitative terms that all falling bodies accelerate at a certain rate here on earth, but were unaware of the law of gravitation. If we had concluded from this that bodies on Jupiter or on the moon would also fall down with the same acceleration, it would have been wrong

Thus, at least at the quantitative level, things do not behave in quite the same manner everywhere in the universe. We now have an explanation for why the rate of fall depends on the mass of the planetary body: the law of gravitation. But there is also another parameter which determines the rate of fall. And that is the gravitational constant G. We believe that this has the same value on the moon, on Jupiter, and everywhere in the universe. Indeed the gravitational constant is one of many other such universal constants that play a fundamental role in determining the general features of the universe we observe. In connection with them also, certain important questions may be raised.

To see this, consider the following: There are a number of physical laws whose quantitative aspects involve fundamental constants, such as the velocity of light, the charge on the electron, etc. We do not know why these constants have the specific values they have. The situation could well be compared to pre-Newtonian physics when the acceleration due to gravity was known, but one did not understand why it had that particular value. If it turns out that these constants have the observed values because of some local properties of the galaxies, it is conceivable that we may have to restrict some of our ideas as to the universality of physical laws.

Or again, the second of thermodynamics has no meaning in the context of a very small number of particles and at very small dimen­sions – a fact which was not as apparent when the law was first formulated in the mid­dle of the l9th century. Likewise, for extremely short time intervals, the principle of energy conservation may be violated. More generally, we know that the laws govern­ing the microcosm are in many ways different from those at much larger scales. If the universe is indeed oscillating (expanding and contracting, to be re-formed and to re-expand) it could well be that in each phase of existence it is governed by different sets of laws.

This said, there are at least two reasons why physicists believe in the spatiotemporal universality of the laws of nature. The first is that there is no evidence to the contrary. From spectroscopic analyses of the nature of matter in distant stars and observations of their motion there is little reason to suspect that they are governed by different laws. More importantly, the whole enterprise of a rational coherent science would be impossible without the assumption of uniformity in the universe at large.

We may still grant that science can never be absolutely certain about the eternal and universal validity of physical laws. However, three things must be borne in mind while considering these im­perfections of science. First, that they arise from the human being’s inherent limita­tions as an organism in the physical universe, and thus are part of every other competing effort to interpret the world of experience. Secondly, humans have been able to accomplish much, both intellectually and practically, in spite of these logical con­straints. Thirdly, the human mind has not yet developed a methodological system or conceptual framework with which one can achieve even a fraction of the results that modern science has been able to do.

Thus, we must be clear about two aspects of the scientific enterprise. It does not aim at, nor pretend to, absolutely certain knowledge. But science does offer proofs for whatever tentative knowledge it proclaims. In religious doctrines, on the other hand, while one is assured of the eternal veracity of the views, one is not always given logi­cal or evidential supports. Hence the statement that science is proof without cer­tainty, whereas religion is certainly without proof.