By Bodhi Dhanapala, Quebec, Canada.

Some of us who studied in village schools a half-century or more ago remember very well our old teachers. They had no hesitation in using the cane or giving knocks on the head, condemning the not-so bright students as having no brain”. The teacher would claim that how ever much effort”  he puts into teaching such students, their brains don’t change. Of course, if such put-downs were attempted in this modern age, then some parents would take up cudgels and even attempt to sue such teachers.

Here, when the teacher  says that the dumb student has no brain”, he does not actually mean that the child does not have any gray matter inside his/her skull. He means, in an abstract sense, that the child has no intellectual capacity. If the teachers puts up a pedagogic effort P, and if the change in the pupil’s understanding is D, then the teachers expects, at least in lowest order, that D would be proportional to P. Hence, introducing a proportionality constant m, we can write a simple equation.

D=mP                (1)

Since this is the first equation in this text, we have denoted it by (1). Even with a very big pedagogic effort P, if the pupil’s understanding D remains unaffected, we can in fact conclude that the constant m is zero, i.e., m=0. Hence it is clear that when the teacher says this fellow has no brain”, he is correct.

The pupil’s understanding D etc are measured by holding tests and giving marks”. If we take a physical property like gravity, we measure it by taking the pointer reading of a balance or a weighing machine. This number is a perfectly concrete observation and there is nothing abstract about it. Similarly, we measure acceleration by recording the pointer readings of instruments that measure time and speed. The time is nothing abstyract here. It is read off  from the needle of a clock. If the needle of the speedometer of a car indicates 20 miles per hour, and 10 minutes later it indicates a speed of  30 m.p.h, then the mean acceleration A of the car  during that time is (30-20)x(60/10) or, 60 miles per hour, per hour. Note that the per hour” occurs twice. Unfortunately, the Vidusara article had been re-typed l and these crucial points have been dropped by the typist. He or she probabaly didn’t understand how acceleration is measured.

Scientific data are gathered as far as possible in a quantitative manner, as pointer readings which can be read by any one, independent of his culture or his geographic location. Scientific laws are then presented as relations that exist between sets of data. For example, it could be between data for acceleration and data for the force applied.  It should be emphasized that the laws are not based on observing, say,  100 crows and because we find all of them to be black,  then claiming  a law” saying that all crows are black”. Science does NOT proceed in that manner. Typically, a  bright and innovative scientist with a wide command of the “subject” comes up with a bright idea or hypothesis regarding the existence of a relationship or law” connecting one set of data with another, and then he tests it out, and proposes a theory.  That is in fact how Galileo proeeded. A theory is a statement about connections between sets of pointer readings. Of course, the theory is expected to be valid only within the length scales, time scales and energy scales that limit  the experimental capabilities of the age. Every new theory must go beyond the previous theories, and explain” all observations within the length scales and time scales  of the new theory,  without any exceptions.

Let us now consider the laws of motion that are associated with Galileo and Newton. According to Newton’s second law of motion, if a force F is applied to an object, its speed increases (i.e., accelerates) in a manner proportional to the applied force. Hence, introducing a proportionality constant m, we can write Newton’s second law as

F=mA                    (2)

The quantity M is called the mass of the object.  Forces are always exerted in a definite direction. Hence a force is a vector quantity. The acceleration A also occurs in some definite direction. Hence A is also a vector quantity. To indicate that A , F are vectors, we write them within parenthesis  as (A) and (F). Now, the quantity m which links (A) to (F) cannot be a simple number, because it links each of the three component of (F) to the three components of (A). Hence m is a 3×3 object called a tensor. To indicate the tensor character of m, we write it with two sets of parenthesis ((m)).  Thus  equation (2) can be more correctly written as (F)=((m))(A).

But,  Newton’s second law of motion says something additional. It says  that if the object is in empty space, then the acceleration A is always in the same direction as the applied force F. This means the tensor becomes diagonal and all its diagonal elements become identical. Hence we can ignore the tensor character of ((m)) and simply use its scalar value m in simple discussions of particles in free motion”. This is, of course not so for motion in a medium.

As the intellectual level of a dumb-head” did not change even with many knocks  given by the teacher, we concluded that the dumb-head had  ”no brain, i.e., its m=0. In the same way, what ever force F  we apply to a photon, its acceleration remains zero because its speed is a constant. Hence, we have to conclude that the mass of a photon must be zero under all circumstances. That is,

F=mA;  A is zero what ever the value of F, hence the mass m=0                 (3)

However much we explain the above to a brainless” person, that person’s position will not change.  There are three types of such brainless” persons. Some may in fact not have this abstract capacity that we call the intellect”. Other’s may seem to be ”brainless” and continue to hold patently false views simply because of their pride, and because of their inability to admit that they do not understand simple physics. In the old days, our old teachers knew how to deal with such people. But today we cannot use such methods. The third type of brainless” persons  is simply made up of older people whose  brains are cluttered up with  age, and they simply cannot deal with new knowledge.

Some brainless person may try to be clever”  by arguing that his brain consumes energy  and hence, according to Einstein’s E=mC2 law, this energy is mass. Hence he can attempt to assign” a mass to the “mass-less” brain. Some people have used similar mis-guided arguments and tried to assign a mass” to the photon. We must emphasize that such notions don’t belong to physics, but belong to the phantasies of such individuals.
Some individuals can attempt to assign anything to anything with no attention to rhyme or reason.  The Schrodinger equation  is the most important quantum physics equation as far as everyday materials is concerned.  It was first presented at seminars in 1925. However, someone may try to re-assign history by claiming that the seed idea for the Schrodinger equation was presented by de Broglie in 1927 at the famous Solvey conference!!!

This is not history, but histrionics. Attempting to hold public debates on such matters would be nothing but a fools’ comedies. Some individuals can even come wearing masks, and invoke Gods, spirits and claim that such beings exist. However, it is of little use to ask them whether these beings exist in the abstract” or not.

Some promoters of show business attempted to promote a fools’ comedy by putting out a bait of   $1500 to inveigle performers for the show. However, the bait did not fool anyone. Finally the promoters had to behave like the fox in La Fontaine’s fables. The fox, failing to get the bunch of grapes on the vine, declared that the grapes are sour. The promoters of the fools’ comedy also claimed  that the show is in fact not worth a tuppence and retreated to the bushes.

Although we do not needs fool’s comedies, most science teachers know that if one can mix in a bit of humour during a lesson, then the students enjoy the class, and even the brainless may suddenly show some brain! Hence explaining Newton’s equations of motion, or the non-existence of a mass of the photon in this manner should be considered a desirable pedagogic maneuver.