Richard Feynman is considered to be one of the greatest theoretical physicists of all time. The 1965 Nobel laureate, is not just popular for having an exceptional brain during his time and his amazing bongo-playing skills but also his unique teaching pedagogy and methodologies. Feynman had the ability to explain any complicated concept in an extremely simple and playful manner in a way that even someone from a non-scientific community could grasp the concept.

Feynman gave a series of introductory physics lectures at Caltech during 1961-1963, which gave rise to the three volumes of Feynman Lectures on Physics which are considered to be the most popular physics books ever written. The first volume of the book is about Mechanics, radiation, and heat, the second volume of the book is primarily about Electromagnetism and matter, and the third one is about quantum mechanics.

Richard Feynman lecturing at Caltech, 1964. The lecture title is “Motion of the Planets around the Sun.” Caltech Archives Image.

In one of his Lectures about electromagnetism, Feynman focuses upon the “underlying unity” of nature where he talks about why certain equations in physics, despite being associated with various fields, have an “underlying” similarity.

Why are the equations from different phenomena so similar? We might say:
“It is the underlying unity of nature.” But what does that mean? What could
such a statement mean? It could mean simply that the equations are similar for different phenomena; but then, of course, we have given no explanation. The “underlying unity” might mean that everything is made out of the same stuff, and therefore obeys the same equations. That sounds like a good explanation, but let us think. The electrostatic potential, the diffusion of neutrons, heat flow are we really dealing with the same stuff? Can we really imagine that the electrostatic potential is physically identical to the temperature, or to the density of particles? Certainly o is not exactly the same as the thermal energy of particles. The displacement of a membrane is certainly not like a temperature. Why, then, is there “an underlying unity”?

Feynman then goes on to explain that the mathematical equations of different subjects in physics are actually not ‘identical’ in the ‘bigger picture’ but when analyzed closely, at the most individual level, things turn out to be slightly different.

A closer look at the physics of the various subjects shows, in fact, that the
equations are not really identical. The equation we found for neutron diffusion is only an approximation that is good when the distance over which we are looking is large compared with the mean free path. If we look more closely, we would see the individual neutrons running around. Certainly the motion of an individual neutron is a completely different thing from the smooth variation we get from solving the differential equation. The differential equation is an approximation, because we assume that the neutrons are smoothly distributed in space.

Feynman then adds to the statement, explaining that most of the complicated phenomena in physics is made simple and understandable as it is imitated by simple differential equations.

Is it possible that this is the clue? That the thing which is common to
all the phenomena is the space, the framework into which the physics is put?
As long as things are reasonably smooth in space, then the important things
that will be involved will be the rates of change of quantities with position in
space. That is why we always get an equation with a gradient. The derivatives
must appear in the form of a gradient or a divergence; because the laws of
physics are independent of direction, they must be expressible in vector form. The equations of electrostatics are the simplest vector equations that one can get which involve only the spatial derivatives of quantities. Any other simple problem or simplification of a complicated problem must look like electrostatics. What is common to all our problems is that they involve space and that we have imitated what is actually a complicated phenomenon by a simple differential equation.

That leads us to another interesting question. Is the same statement perhaps
also true for the electrostatic equations? Are they also correct only as a smoothed-out imitation of a really much more complicated microscopic world? Could it be that the real world consists of little X-ons which can be seen only at very tiny distances? And that in our measurements we are always observing on such a large scale that we can’t see these little X-ons, and that is why we get the differential equations?

Feynman also discusses the ‘underlying’ differences in details between the ‘smooth’ looking equations and their analysis at the most minute scale. He further focuses upon the problem with the combination of quantum mechanics and relativity in terms of its fundamental resemblance with the equations of electrostatics and that it might lead to an internal contradiction.

Our currently most complete theory of electrodynamics does indeed have its difficulties at very short distances. So it is possible, in principle, that these equations are smoothed-out versions of something. They appear to be correct at distances down to about 10^(-14)cm, but then they begin to look wrong. It is possible that there is some as yet undiscovered underlying “machinery,” and that the details of an underlying complexity are hidden in the smooth-looking equations as is so in the “smooth” diffusion of neutrons. But no one has yet formulated a successful theory that works that way. Strangely enough, it turns out (for reasons that we do not at all understand) that the combination of relativity and quantum mechanics, as we know them, seems to forbid the invention of an equation that is fundamentally different from the equations of electrostatics, and which does not at the same time lead to some kind of contradiction. Not simply a disagreement with experiment, but an internal contradiction. As, for example, the prediction that the sum of the probabilities of all possible occurrences is not equal to unity, or that energies may sometimes come out as complex numbers, or some other such idiocy.

Feynman, along with his astounding explanation of multiple aspects of physics in both theoretical and mathematical manner, has also provided insights on different ‘issues’ and contradictions in physics thereby explaining why and how these drawbacks need to be addressed.

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