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Aesthetics of Light

And yet, along with Newton and Einstein there is a third scientist who was able to successfully link Newton’s universal gravitation and Einstein’s relativity. This is James Clerk Maxwell and he ranks twelfth on Google’s list of the most famous scientists in history. Despite this low ranking, it can be said that modern physics originated in 1865, when Maxwell published an article entitled *A Dynamical Theory of the Electromagnetic Field*. In the article, Maxwell introduces equations that radically change our conception of space, the electromagnetic field, light, and the vacuum. These equations are a textbook example of what physicists mean by beauty and mathematical elegance. They are a summary of discoveries and laws studied by other scientists, but rewritten and adjusted under a new conception of the universe, in which the ‘vacuum’ is no longer conceived of as ‘nothingness’.

Nevertheless, how can Maxwell’s studies of electricity and magnetism act as a bridge connecting Newton and Einstein, whose purpose of study was gravity? To understand this, we must start from what Newton left us with, i.e. the law of universal gravitation. Through this law, Newton was able to describe the force that is established between two bodies with mass placed at a certain distance from each other. These two bodies can be of any kind: the Earth and the Moon, the Earth and the Sun, an apple and the Earth, us sticking to the ground instead of flying away, etc. Newton’s greatness was realising that the force that held the celestial bodies together was the same force that the Earth exerts on us: it is the unification of celestial and terrestrial mechanics. And this force depends on the distance between the two objects: the further apart they are, the more the force weakens.

However, the Newtonian theory of the force of gravity has its weak points. Newton spoke of empty space, but even he was not entirely satisfied with this definition. How can the void, nothingness, carry a force? How can nothingness intervene in the relationship between two objects? Moreover, the way the gravitational force of attraction is formulated, it acts instantaneously between two bodies, it does not need time to establish itself. Two objects on opposite sides of the universe immediately feel each other’s gravitational attraction, and if one of them for some reason changes, for example by moving or exploding into many pieces, the other instantly experiences a difference in the gravitational attraction it was feeling.

Let us imagine, for example, that we could make the Sun disappear with a snap of our fingers. How long do you think it would take the Earth to stop feeling its gravitational attraction and thus break out of its orbit? According to Newton’s formula, the difference would be instantaneous, whereas today we know that it would take about eight minutes for this to happen.

Such results had also been obtained in relation to forces between electric charges. An electric force is established between two bodies that have an electric charge and act at a distance, attracting or repelling each other charges of equal or opposite sign. Moreover, the force between electric charges depends on the distance between the charges in the exact same fashion as the force of gravity. Finally, it too has the same ‘instantaneousness’. The electric force, therefore, has the same characteristics as the gravitational one, the only difference being that instead of attracting masses, it attracts (or repels) charges. Hence, the unresolved doubts about Newtonian gravity are identical to those about electricity.

So, how do we solve these challenges? It was Maxwell who thought of this, with the fundamental contribution of another scientist, namely Michael Faraday. Maxwell can be said to have described Faraday’s intuitions mathematically, formalising them in a decisive manner. In fact, the latter, although gifted with an uncommon imaginative capability, had not followed any canonical studies and had limited knowledge of mathematical language. Maxwell will later describe him as having been able to see a medium where there was not one.

To understand Faraday’s intuition, let us use a practical example. Suppose we take some iron filings (hence iron powder) and place them on a sheet of paper. A magnet is placed under the sheet. The iron filings will begin to arrange themselves on the sheet following precise geometric patterns, they will somehow begin to orient themselves, as if each particle were a tiny compass. So far, nothing new: if for each iron particle we were to calculate the force exerted on it by the magnet, we would see that one by one the particles could only arrange themselves in this manner. Faraday’s intuition was that the geometric arrangement of the iron particles was nothing more than a visualisation of something that existed even before the iron filings were placed on the sheet. This ‘something’ is the magnetic field, and the lines on which the iron filings are oriented are nothing more than its ‘field lines’. They already fill the void. They have been there since the magnet was initially placed. The iron filings merely reveal something that already exists. Behold, the void has been filled with fields.

Electric and magnetic fields then begin to be visualised as fluids permeating space. An electric charge induces an electric field around it and, if another particle appears nearby, there will be an interaction between the field, which is already present, and the new particle. This is radically different from the instantaneous and distant interaction between particles, without any interplay between them.

In the case of the electric field, we can see the field lines as straight lines coming out of a charge and continuing indefinitely into the vacuum (which is therefore no longer empty). A magnet, on the other hand, has lines coming out of the north pole and curving back into the south pole. If we move the electric charge or magnet, we distort the field, but not instantaneously, this distortion propagates at a certain speed, which is no longer infinite as in Newton’ s theory of gravity.

Imagine you are on a giant spider’s web. If a disturbance occurs at a point distant from you, it takes a certain fraction of time for that disturbance to propagate and reach you. The same applies to the electric or magnetic field: it is a ‘web’ of static field lines until you disturb it, and when it is distorted at a point, it takes a certain amount of time for the disturbance to propagate. This solves the problem of the instantaneity of the force.

Maxwell’s equations interpret electric and magnetic fields according to this new understanding. For example, they calculate the electric field passing through a certain imaginary surface, thus taking it for granted that it exists in the ‘vacuum’, beyond the presence or absence of a body capable of perceiving it.

But that is not all, in fact it is only the beginning. Maxwell’s equations demonstrate how the electric and magnetic fields are intrinsically linked: a time-varying electric field generates a magnetic field, just as a time-varying magnetic field generates an electric field. An electro-magnetic stimulation can therefore give rise to a dance between these two fields that continue to mutually generate each other. Maxwell calculated what the propagation speed of this stimulation was: the result is the speed of light. This is how the true nature of light emerges from Maxwell’s equations: it is nothing more than a magnetic and an electric field propagating in a wave-like manner in empty space. We are faced with the unification of electromagnetism and optics.

And the light we observe with our eyes is just a small part of the electromagnetic spectrum: radio waves, microwaves, infrared, ultraviolet waves, X-rays, gamma rays, are all electromagnetic manifestations that obey Maxwell’s predictions.

This is where Einstein will begin to study how the electromagnetic field and light behave in different reference systems. He will realise that electric and magnetic fields are two sides of the same coin and that the speed of light is insuperable. From these observations, he will be able to deduce his theory of relativity. But this is an entirely different story that is worthy of its own article.

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