By S. K. Smith
Einstein has been called the Father of Relativity. But there was a Scotsman who beat Einstein by about 40 years. Read on…
December 31, 1999, Time Magazine declared Albert Einstein as “The Person of the Century.” It was a much deserved title. Einstein’s work has rewritten the science text books and has resulted in a paradigm shift that has affected our world view. Below are just a taste of his many accomplishments:
Einstein’s Theory of Relativity corrected Newton’s Laws, Kepler’s Laws, and Galilean Relativity. His explanation of the Photoelectric effect (for which he won the Nobel Prize) gave birth to the concept of photons and more credence to the emerging theory of quantum mechanics. Einstein’s famous equation, E = mc^{2}, corrected the laws of conservation of mass and conservation of energy and catapulted the new disciplines of nuclear and particle physics. His work on Brownian motion confirmed the existence of atoms and molecules and revolutionized thermodynamics. And most of this was accomplished by the time Einstein was 25.
There is an old saying; “Does man make the times or do the times make the man?” Albert Einstein was at the right place at the right time to precipitate the shift from the absolute world view of Newton to the modern world view of relativity, quantum mechanics, and the atomic age.
At the turn of the century (19^{th} to 20^{th}), scientists had thought they had the universe pretty well figured out. Newtonian physics was strongly entrenched, describing the motion of objects in the heavens and on earth like clockwork. Galilean relativity is experienced in everyday life. Mass is conserved. Lengths of rulers remain unchanged. Clocks tick at the same rate throughout our universe. For relative velocities, our experience is simple vector addition.
In his Autobiographical Notes, Einstein wrote about a thought experiment he performed in 1895 when he was 16. In the context of Galilean relativity, he pictured himself catching up to a light wave much like a surfer would a water wave. When he caught up, the light wave would seem to be frozen. Since light, an electromagnetic wave, would cease to vibrate in this frame, it would disappear. This was impossible according to the classical electromagnetic laws and it had never been observed. This got Einstein to thinking that there was no inertial frame in which a light wave was at rest.
In 1905, Albert Einstein, then 25, submitted a paper “On the Electrodynamics of Moving Bodies,” The Principle of Relativity. It is now distinguished as Einstein’s Theory of Special Relativity. (General Relativity came later and that is another story.)
Special Relativity is based on two postulates:
Postulate I:
The laws of physics are the same, or invariant, in all inertial systems – that is, the mathematical form of a physical law remains the same.
Postulate II:
The speed of light in a vacuum is a constant, independent of the inertial system, the source, and the observer.
From these two postulates, nature becomes surreal when observing objects approaching the speed of light. The observer at rest sees lengths contracting, clocks ticking at slower rates, mass increasing, and velocities not following simple vector addition (since light is the limiting velocity)for objects in motion. Yet, these weird results at high velocities have been measured and confirmed in the laboratories. At relatively low velocities, special relativity reduces to Newtonian physics, that which we experience in our everyday life.
Now, the Scotsman comes into the picture.
No doubt Albert Einstein was brilliant. In 1895, though, he was heavily influenced by a Scotsman when he was doing his thought experiment about light. In the field of special relativity, this same Scotsman beat Albert Einstein by about 40 years.
James Clerk Maxwell (1831 – 1879), a Scottish mathematician and theoretical physicist, developed the classical theory electromagnetism. Maxwell studied the works of scientists that had preceded him, such as Gauss, Ampère, and Faraday. He synthesized previous unrelated observations, experiments and equations of electricity, magnetism, and optics into a consistent theory. Finally, he published a purely mathematical theory in “On a Dynamical Theory of the Electromagnetic Field” (1865).
His four simple set of equations, known ever since as Maxwell’s equations, demonstrated that electricity, magnetism and even light are all manifestations of the same phenomenon: the electromagnetic field.
Serious students of physics and electrical engineering study “Maxwell’s Equations” in one form or the other. For this article, I will present the differential form (vector calculus) for empty space.
Maxwell’s Equations in Differential form
(for empty space):
Names

Differential Form

Explanation

Gauss’ law

s·E = 0

There is no net electric charge emanating from any volume of empty space

Gauss’ law for magnetism

s·B = 0

There is no net magnetic charge emanating from any volume of empty space

MaxwellFaraday equation

s x E = ¶B/¶t

The rate of change of a Magnetic field produces a proportional perpendicular Electric field

Ampère’s circuital law

s x E = ¶B/¶t

The rate of change of an Electric field produces a proportional perpendicular Magnetic field

How did the 19^{th} century James Clerk Maxwell beat Albert Einstein – “The Person of the 20^{th} century?”
If you manipulate Maxwell’s equations, they can be put into the form of the Laplace Wave Equation:
s^{2}u 1/c^{2} _{ }¶^{2}u/¶t^{2} = 0
where c is the speed of the propagation of the wave.
s x E = ¶B/¶t
s x (s x E) = s x ¶B/¶t
s (s · E)  s^{2}E= ¶/¶t (s x B)
Substitute s·E = 0_{ } and s x B = μ_{0}ɛ_{0}¶E/¶t:
s (0)  s^{2}E= ¶/¶t (μ_{0}ɛ_{0}¶E/¶t)
Rearranging terms:
(s^{2}  μ_{0}ɛ_{0 }¶^{2}/¶t^{2}) E = 0
Note: 1/√ μ_{0}ɛ_{0 }= 3 x 10^{8} m/s = c (the speed of light)
therefore
(s^{2} – 1/c^{2} _{ }¶^{2}/¶t^{2}) E = 0
What this wave equation  (s^{2} – 1/c^{2} _{ }¶^{2}/¶t^{2}) E = 0  tells us is that all types of electromagnetic waves (visible light, ultra violet light, infrared radiation, Xrays, microwaves, electromagnetic fields, Gamma rays, etc.) propagate in a vacuum at the speed of light. And this propagation is independent of the source of the electromagnetic wave or its observers.
Written 15 years before Einstein was born (1879), Maxwell’s equations contain the second postulate of special relativity: the speed of light (and all other forms of electromagnetic waves) is a constant in a vacuum independent of its source and/or who is observing it. Given this postulate with the first postulate the laws of physics are invariant in all inertial systems  an observer of objects in motion sees lengths contract, time dilate, masses increase, velocities not following simple vector addition as the speed of light is the limiting velocity, etc. Sound familiar?
Some conclusions:
James Clerk Maxwell is considered one of the most (if not the most) influential 19^{th} century scientist, who impacted physics in the 20^{th} century. Unfortunately, he died at the age of 48, the year Einstein was born. If Maxwell had lived longer and continued to produce, he may have developed more fully the theory of relativity – made famous by Einstein in the 20^{th} century.
Maxwell’s theories influenced Einstein’s thought experiment in 1895. Einstein’s famous equation, E = mc^{2}, was derived from reconciling Maxwell’s equations with the laws of conservation of energy and momentum. In the 1860s, Maxwell’s equations contained the key postulate – that the speed of light is independent of its source or its observers – for the theory of special relativity (1905).
When Einstein visited Cambridge in the 1920s, someone remarked, “You have done great things but you stand on Newton’s shoulders.” His reply was, “No, I stand on Maxwell’s shoulders.”
Maxwell’s equations are still standing in the 21^{st} century. The only adjustments needed are minor ones for quantum fluctuations of virtual particles in a vacuum.
This brings new meaning to the take off on Genesis 1:3, which is seen on some physics posters, bumper stickers (I have one of these), and Tshirts:
And the God said,
s·E = ρ/ɛ_{0 }
s·B = 0
s X E = ¶B/¶t
s X B = μ_{0}J+ μ_{0}ɛ_{0}¶E/¶t
And there was Light!

Note:
s·E = ρ/ɛ_{0
}s·B = 0
s x E = ¶B/¶t
s x B = μ_{0}J+ μ_{0}ɛ_{0}¶E/¶t
are Maxwell’s Equations in SI units for linear materials
© October 1, 2008, S. K. Smith