Introduction

The following essay, written some years before the present work was begun, arose as little more than an offhand attempt to explain a T-shirt slogan, but it soon grew into a rather-speculative piece concerning the relationship between science and religion.

Maxwell’s Equations: On the Dance of Science and Religion

A popular T-shirt bears the following inscription, replacing the words ‘Let there be light’ in Genesis in the Bible:

And God said:

and there was light.

Why replace the easy Biblical words with these four rather complicated-looking equations? The general reaction to this T-shirt display is likely to be consideration of its wearer as a science or math geek who doesn’t appreciate the simple truth behind the original words. But it may be worth looking a little deeper into the substitution to understand its meaning.

The perfection of the Biblical words ‘Let there be light’ in our eyes arises from their generative power – a power lacking in the same words spoken as a mere human utterance.

Infinite distinction separates the generative Word of the Creator from the words we use in human life. The Báb set forth the distinction in many places, among them this from His Prayer for Protection:  ‘He createth whatsoever He willeth by His word of command ‘Be!’, and it is.’ We can say the word ‘Be!’, and of course nothing happens; it is not our station in this world to effect such commands.

But it is within our capacities to explore the meanings and modes of operation of the commands of the Creator. Although we may never understand them fully, we are gifted with the power to penetrate their mysteries to a greater and greater degree. That’s what we see here on the T-shirt. These cryptic-seeming symbols give us Maxwell’s equations, named after James Clerk Maxwell, who consolidated equations of Gauss and Faraday, added his own insights, and revealed the unity of light and all other forms of electromagnetic radiation. His 1865 paper on the theory of the electromagnetic field was a pioneering work in physics.

Maxwell’s equations unfold some aspects of the deeper meaning of the command ‘Let there be light’. Here is the author’s limited understanding of the connections between the science and the command.

First, a separate insight had already bound electricity and magnetism into a single very special relationship that enabled our construction of electric motors and generators. We knew at that stage that electricity and magnetism were intimately related.

Second, Maxwell’s equations revealed an insight: that light itself is nothing more or less than a form of electromagnetic energy, a property shared by radio waves, gamma rays, and other forms of radiation all part of one huge energy spectrum.

Third, the relationship between electricity and magnetism extends through space and time, perfusing our universe with a wash of electromagnetic signals that we can detect and read, even back to the cosmic microwave background radio waves that reveal the very beginnings of our universe’s existence: that moment of ‘Let there be light.’  Our astrophysics and cosmology depend almost completely on our readings of the vast range of electromagnetic signals the universe offers us.

The equations themselves specify in strict, accurate terms the connections and behavior of electromagnetic fields. Put very sketchily, a changing electrical field can generate a magnetic field, and vice versa; this interrelationship allows self-sustaining movement of electromagnetic radiation such as light.

So if we consider that the Creator set forth these very detailed, accurate, and specific laws, they amount in this case to ‘Let there be light.’  And of course the accuracy of our understanding of these laws continues to develop as we penetrate the cosmic mysteries more and more deeply. That is one of our most sacred tasks and obligations, and the unity of religion and science impels us to fulfill such obligations as well as we can.

How do we read the equations of ‘Let there be light?’  The four equations shown above are perhaps the simplest forms of Maxwell’s equations to explain. Here they are once more:

First, the symbols alone. E stands for the electric field, B for the magnetic field, q_enc is charge, the little epsilon with a zero subscript (ε₀) is a constant reflecting the way space passes along electric charge, the little mu with a zero subscript (μ₀) is a constant reflecting the way space passes along magnetism, and dA is what is called an ‘area element’, like a tiny rectangle marked in some surface like a sheet of paper. If you want to know what the whole surface is, you use the integral, loosely speaking, to total up all the dA‘s in the surface. The term ds, in similar usage, represents a ‘line element’, like a tiny snip of a linear thread, and you add up all the snips to get the length of the line.

The first two equations are credited to Karl Friedrich Gauss. The first one tells us that if we enclose an electrically charged object inside a closed surface like a sphere, the intensity of the charge q_enc (‘enc’ for ‘enclosed’) on the enclosed object determines the strength of the electric field E at the surface of the enclosure. We get that strength by integrating, which is indicated by the integral sign: the elongated script ‘S’ with the little ellipse around its middle. The ellipse means that the surface or sphere is closed.

The second equation tells us that if we surround an object having a magnetic field B with a closed surface like a sphere, the total net field inside is zero. This does not mean that it is nonexistent, but only that magnetism from one part of the surface is always matched by opposite magnetism from another part.

These first two equations merely describe a static picture. At that level there’s no insight into electromagnetism or the interaction between electricity and magnetism. But the next two are the gems that bring time into our picture, and this is critical.

The little ‘dt‘ you see at right in the denominator in both of these last two equations signifies a tiny slice of time, and the ‘d-phi’ (dΦ) in the numerator is the flux (a measure of intensity). The ‘ds‘ you see at left in both equations signifies a tiny distance in space.

The first of these second two equations, also called Faraday’s Law, tell us that a changing magnetic field, here signified by dΦ_B/dt, generates an electric field (E). This means that if you rotate a magnet inside a winding of conductive wire, it generates electric current in the wire. Hence our everyday electric generators.

The second equation of the last two turns its predecessor around, but it throws in an added part:  The last part, μ₀i_enc, or ‘mu-i’, tells us simply that an enclosed electric current flow i_enc creates a magnetic field (B). That μ₀i_enc part is what’s called Ampère’s Law.

But Maxwell found the connection between electricity and magnetism that makes these electromagnetic fields possible. The right-hand part of the equation starting with μ₀ε₀ reveals the connection. A changing electric field (dΦ_E/dt) generates a magnetic field (B). This means that if you change the electrical charge (dΦ_E/dt) on an object over time, the change also generates a magnetic field.

To put it in very rough terms, if you put these two equations together, and you move the electric and magnetic fields through space, both are changing, so that each one feeds the other, and so we have propagation of electromagnetism as a wave. This is light, in the broadest possible sense.

It is exciting to realize that Maxwell was able to calculate from his equations – NOT from direct observation – the speed of light. He used the known values of μ₀ and ε₀, derived from other definitions and experiments, to calculate the speed of the waves[1]. These constants together give us the value for the speed of light, which itself had been measured independently in various ways by that time. The relationship is defined in this formula:

The experimentally-measured speed agreed with Maxwell’s results: a clear example of anticipatory use of a mathematical idea, since until he had made the connection between μ₀ and ε₀ and the speed of light, no one had understood that such a connection existed.

This presentation of Maxwell’s equations is necessarily superficial because it omits the many mathematical and logical details which the physicist must traverse in the course of applying the laws. The student who wishes to perform the actual calculation of the forces and other effects produced by electricity and magnetism using the equations above must understand mathematics at the level of differential and integral calculus of several variables, in particular in the form of vector calculus.

Reaching Out Farther

Because these four equations apply in our everyday world with great precision, we can use them freely in everyday applications within the scale of our perceptions. But the human species has expanded its understanding to realms beyond our immediate senses. When we move to the realm of relativity and curved spacetime, the equations take on a form and content suitable for that realm. Or when we move to the realm of quantum physics, the same is true. In each of these realms, Maxwell’s equations require modification due to important differences between these realms and our everyday world.

Why all the equations? In the physical world, we want to make predictions of effects, and we want them to be as accurate as possible. The equations allow us to compute highly-accurate predictions. We can even use their modified forms to make accurate predictions in both the relativistic and the quantum realms. From the Maxwell equations we’ve gained useful insight into a sweeping range of physics. But from them we can also derive a much deeper sense of the command ‘Let there be light.’[2]

Humanity has experienced a progression of understanding of electromagnetism, from the first simple insights into the seeming action-at-a-distance of an electric charge or a magnet all the way to the bewildering but amazingly-accurate complexities of relativistic quantum field theory. We have ascended a ladder of understanding one rung at a time.

There is a most challenging and beautiful phrase that expresses the way in which patterns of meaning can be interrelated. It takes a form that bears directly on the subject of this essay. In the Tajalíyyat, or Effulgences, of Bahá’u’lláh, He writes:

The third Tajallí is concerning arts, crafts and sciences. Knowledge is as wings to man’s life, and a ladder for his ascent. Its acquisition is incumbent upon everyone. The knowledge of such sciences, however, should be acquired as can profit the peoples of the earth, and not those which begin with words and end with words. Great indeed is the claim of scientists and craftsmen on the peoples of the world.[3]

Two points emerge immediately from this passage: 1) knowledge serves to elevate human life, and 2) that acquisition of knowledge should benefit humanity. The first of these two points shows the way knowledge progresses from a lesser to a greater pattern, as in moving step by step up the rungs of a ladder. The second point directs the choice of such progressions to fields that offer human benefit.

The field of physics offers immense benefits to the entire human race, if we choose to accept them. Maxwell’s equations opened the floodgates to a stunning range of potentials in communications, basic physics research, and much more. But physics, in all its predictive power, does not address the ways in which humans use its potentials. To take steps up the rungs of the ladder of knowledge urges us to find ways to turn those material potentials to beneficial human use. Finding such ways is not just the business of physics; it is the business of society.

The Heart of the Dance

Society without a shared core of ethical and spiritual belief lacks the qualities necessary to grow into maturity in a healthy, nondestructive pattern. Our patterns of history make this point clear. The human species has found ways to share its central beliefs, but in every age these shared beliefs dissipate to the point where even the most obvious beneficial truths become buried in heaps of superstitious and dogmatic rubbish[4].

One most-effective way to sweep aside the rubbish is to apply both scientific and spiritual principles that show mutual consistency. If a principle pronounced by a faith is inconsistent with clearly-understood scientific principles, it can’t be used. And since scientific principles are intended to address only material matters, any non-material application of a strictly-material scientific principle is impossible. When one remembers this method of eliminating confusion, the meaning of ‘Let there be light’ can be understood and appreciated both at a material scientific level and at a spiritual and religious level. At the physical level, we have Maxwell’s equations showing us the laws by which light operates; at the spiritual level, we have the burst of light at the Universe’s creation showing us the wonder of the very existence of those equations newly called into being.

We live in a universe in which we identify four dimensions, three of space and one of time. In a wonderful essay asking why this is true, physicist Hermann Weyl wrote:

For the moment I assume that the world is an n-dimensional flat manifold (which is true to great approximation)… Suppose a single candle is burning in the world. Now blow this candle out; what will happen according to the Maxwellian laws? You probably think it will grow dark, pitch dark, in a sphere around the candle which expands with the velocity of light. And you are right – provided the number n is even, especially in our world for which n = 4. But it would not be so in a world of odd dimensionality. … ‘And God said, Let there be light: and there was light.’, so tells the story of Creation in Genesis, Chapter I. If He wished to keep the possibility open for Himself to say ‘Let there be darkness again’ and to accomplish this by blowing out His candles then He had to make the world of even dimensionality.[5]

The complete harmony of science and religion distinguishes the Bahá’í teachings from all others in their precision and clarity. Other teachings make allusions and parallels to many scientific truths, but only in this time have we had the inner and outer meanings of those allusions and parallels unfolded to us with such lucidity and detail. The book has been opened wide. Now that the book is opened, the learning can truly begin.

NOTES

[1] See https://www.physicsforums.com/threads/determining-c-from-maxwells-equations.894375/ for a starting point on the history of c.

[2] Genesis 1:3.

[3] Bahá’u’lláh, Tablets of Bahá’ú’lláh, ‘Effulgences’ (Tajallíyát).

[4] The entropy of physical systems – their tendency to move toward a state of undifferentiated disorder or noise – is mirrored by the same tendency in social and religious systems. It is for this reason that flows of information are revealed to humanity periodically, for the purpose of moving us progressively toward states of higher order and informational content.

[5] Hermann Weyl, ‘Why is the World Four-Dimensional?, in Levels of Infinity, p. 211.