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In a letter published in the May 1975 issue of Reciprocity I stated that I preferred not to comment on articles submitted for publication because “I believe that it is very desirable to encourage free and open discussion of the (Reciprocal) theory and its applications, so that we can have the benefit of as many points of view as possible in extending and clarifying the theoretical structure. I want to avoid saying or doing anything that might give the impression that I am trying to discourage dissenting opinions.” These considerations are still applicable, but I think that we have now reached the point where it would be appropriate to discuss the general situation with respect to the extension and refinement of the theory. The article by Dr. Nehru in the Autumn 1982 issue provides a good example of some of the points that need to be emphasized.

The first fact that should be noted is that the theory is derived in its entirety from the fundamental postulates; that is, it consists entirely of the postulates and their necessary consequences, without any content from other sources. This is very important, because it provides the basis for verifying the validity of the theory by application of the probability principles. In physical matters we cannot obtain mathematical certainty: a condition in which the probability of error is zero. We have to settle for what we may call physical certainty: a condition in which the probability of error is so small that it is negligible. This is attained by making a very large number of comparisons with the data from experience. Every comparison of this kind is a test of the theory, and each additional test that is made without finding a discrepancy reduces the probability that any discrepancy exists anywhere. But the theory cannot be tested by comparison with what little is known about a poorly understood phenomenon such as the pulsars. The definitive test is the comparison with the observational knowledge about phenomena that are well known and clearly understood. Since the Reciprocal System has already passed this test in thousands of comparisons, its validity is as clearly established as is possible for a physical theory (even though this fact is not yet realized by the scientific community in general).

It needs to be recognized, however, that the fixed character of the theory that enables establishing its validity also imposes some severe constraints on its further development. In particular, it prohibits introducing any additional assumptions, or anything from observation, in developing the details of application of the theory to specific areas. In order to preserve the status of the theory as a single, integral entity that can be tested as a whole these details must be derived in the same manner as the major conclusions; that is, as necessary consequences of the basic postulates. During the years that have elapsed since the founding of what is now the ISUS, many of those who have participated in the activities of the organization have decided that they would be better satisfied if the conclusions derived from the theory in certain areas were modified. But as I have just pointed out, the chief merit of the theory, the characteristic that enables us to verify its validity, is its status as a fixed structure, one that we cannot modify to suit our preferences or prejudices.

It does not follow that those of us who have undertaken to develop the details of the theory have necessarily arrived at the correct conclusions in every case. None of us makes any claim to infallibility. Thus it is entirely in order for anyone to take exception to a previous conclusion, providing that he can show that a different conclusion can be derived from a development of the consequences of the fundamental postulates. But if the dissenting opinion is based, either totally or partially, on considerations other than those derived from the postulates of the Reciprocal System it is an expression of a different theory, and it has no claim to a favorable reception by those of us who are working to extend and amplify the Reciprocal System.

This task that we now have ahead of us is to enlarge our area of coverage and apply it to more of the details, meanwhile reexamining and refining the conclusions previously reached that may involve uncertain aspects. We are not looking to see if the theory can produce the right results. We already know, on the strength of the laws of probability, that it is capable of producing the answers that we want. Whether or not we actually find them is not a test of the theory; it is a test of our ability to apply the theory. Even though we have the correct foundation, the answers do not appear automatically. Sometimes they are quite obvious, but more often we have to dig them out.

There are, of course, a multitude of areas still to be covered by the theoretical development. But the issues involved in these areas, such as the list of questions in Dr. Nehru's article, are not “tests of the Reciprocal System,” as he calls them. The required tests have already been carried to the point where the results of additional tests have no significance. Dr. Nehru's questions merely amount to a list of some of the things that should be investigated by anyone who undertakes to extend the previous consideration of the pulsars into more detail. This kind of information serves a useful purpose, and we should welcome Dr. Nehru's contribution, but the only thing it “tests” is out ability as investigators.

As it happens, I have considered all of the points mentioned by Dr. Nehru in the course of the investigations that I have undertaken during the past several years in connection with the preparation of the new edition of The Structure of the Physical Universe. These investigations have disclosed that in all of the cases that Dr. Nehru mentions, the development of the Reciprocal System of theory produces answers that agree with the known facts. In one instance some modification of the previously published conclusions is required. In all of the other cases my finding is that the previous conclusions are correct, as far as they go.

Most of these matters require more explanation than I can give here, but the first three are relatively simple, and a few comments about them will serve to illustrate the points that I have been making. Dr. Nehru's first question is why the quasars do not pulse as the pulsars do. The answer is that they actually do pulse as they pass through the pulsation zone, but we cannot detect the pulses because they originate from billions of stars and the radiation from these stars is not.synchronized. In the second item he points out that the duration of the pulse should be in the range of one unit of time, rather than in seconds, as observed. But the unit of time applies to the unit of mass. The observed pulse is a composite of a vast number of sub-pulses, and it continues as long as there are mass units in the line of travel.

The third item is the reason for two peaks in the pulses of some pulsars. Dr. Nehru says that “no explanation has been offered for this from the framework of the Reciprocal System.” This is true. But it is true only because, prior to my recent studies, the results of which have not yet been published, no one had gotten around to examining the question. Just as soan as I had occasion to take a look at the situation, I found the answer obvious. From the explanation of the nature of the pulsars that we derive from theory, it follows that the shape of the pulse is determined by the shape of the pulsating object, specifically its radio structure. The young pulsars, type S as they are known to the astronomers, have pulses with single peaks, which are quite evidently produced by globular structures. The older pulsars, type C, have had time to develop the typical dumbbell form of radio structure, and the double peak simply reflects the existence of this double structure.

These results are typical of those that I have obtained in the astronomical investigation (which I expect to complete in a few more months). Throughout the astronomical field I have found that the application of the Reciprocal System of theory provides simple and logical answers to the outstanding problems. Inasmuch as the extreme conditions to which astronomical objects are subjected stretch physical theory over the widest possible range of application, the fact that the principles and relations developed in the more accessible realms of physical science can be extended to astronomical phenomena without any serious difficulty is very significant.

I do not mean to imply, however, that this is an easy task. In a separate communication Dr. Nehru has raised another issue that brings out the point that exploration of a totally new field of thought, such as that which we are undertaking, is not a simple matter. He notes that my explanation of the destruction of the heavy elements at the stellar temperature limits asserts that the combined space displacement of the ionization and thermal motion neutralizes the rotational time displacement of the atom, and reduces all motion to the linear form. In order to accomplish this, Dr. Nehru comments, the thermal motion must, in some way, be converted to rotation. “The thermal motion, being a Linear space displacement, cannot directly destroy the atomic rotation,” he says. Actually this is not correct. It would be true if we were dealing with vectorial motion, but all of the motions with which we are here concerned are scalar, and the scalar situation is quite different.

This is a good illustration of the fact that, even though the theory has the answers that we are looking for, these answers are by no means self-evident. I believe that I have a reasonably good understanding of the primary consequences of the postulates of the Reciprocal System. Furthermore, I recognized the scalar nature of the basic motion, and emphasized it in my first book, published in 1959. But it was not until two or three years ago that I had a clear enough understanding of scalar motion to be able to answer the point that Dr. Nehru now brings up, if anyone had raised the issue earlier.

The key to this situation (and to most other questions about the basic motions as well) is a recognition of the way in which rotational scalar motion differs from rotational vectorial motion. The difference can easily be seen if the motion of a point the surface of a rotating ball (a vectorial motion) is compared with that of a point on the surface of a rotating expanding balloon such as the one that I described in The Neglected Facts of Science. In the vectorial case the primary motion of the point is transverse, and the acceleration toward the axis of rotation causes it to move in a circle around that axis. In the scalar case the primary motion of the point is radial, and the rotation of its representation in the reference system causes the point to move spirally outward. The rotation of the atom is a scalar motion similar to the rotation of the expanding (or contracting) balloon. The thermal motion is a linear scalar motion that simply adds to, or subtracts from, the magnitude of the radial motion whose direction is being changed by the rotation. Attainment of equality between the scalar magnitudes, the space and time displacements, thus destroys the rotation.

In my opinion, there is no doubt that whatever problems may exist in other physical areas can similarly be solved by application of the basic principles and relations that we have derived from the postulates. I am therefore suggesting to those who.are inclined to tackle these problems that you ought to approach them with the firm conviction that the answers exist, and that they can be obtained if sufficient time and effort are applied, along with a little ingenuity.

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