The use of the velocity of light, or more generally, the velocity of propagation in vacuum of the electromagnetic waves as a fundamental constant, comes from James Maxwell's Electromagnetic Theory. It is believed that he was the first to say that Light is an electromagnetic phenomenon and to identify its velocity as a fundamental constant.

But if we review Maxwell's original work, this is not exactly true. He never said that the velocity of Light is an universal constant. What he said was that the relation between the electric and the magnetic phenomena is a fundamental constant and that this constant has the units of a velocity and a numerical value of the same order of magnitude as the velocity of light.

The following references are from "A TREATISE ON ELECTRICITY AND MAGNETISM" by James Clerk Maxwell, Dover Publications Inc., reprint of the Third Edition published by the Clarendon Press in 1878 after Maxwell's death, but largely unchanged from the Second Edition which he reviewed personally.

Here we have clearly and undoubtedly stated that the fundamental constant is the relationship between the electric and the magnetic phenomena and Maxwell immediately felt its importance. Unfortunately, after more than 100 years, the physical meaning of this fundamental constant is still misunderstood. Maxwell's constant, having the units of a velocity, is not the velocity of any physical phenomena, be electric, magnetic, luminous, gravitational or any other kind. The velocity represented by Maxwell's constant is a physical barrier that can be reached only after expending an infinite amount of energy, which of course is impossible.

If this is true, why do we believe that the photon reached this barrier and became massless? The answer is a few pages later. After giving several different ways to measure the ratio of the units, and even estimating the probability of error in each proposed experiment, Maxwell concludes:

Please notice that Maxwell always refers to the Ratio of Units and the Velocity of Light as two different quantities that may have an equal numerical value.

We can not blame the great master for this very unfortunate comparison. Without offering a proof, only a probable reason, he expresses an opinion in line with the knowledge available at the time. The Theory of Relativity was still unborn and he could not imagine the way science was going to be misguided by this remark.

The mistake is understandable because the comparison between these two quantities was almost unavoidable. We shall remember that at the middle of the last century, light was the only known physical phenomenon with such a velocity. The subatomic world, with particles that travel at speeds near or even faster than light itself (the Cerenkov radiation is one example), was unknown and still waiting to be discovered.

Even if he is one of the greatest physicists of all times, in my opinion perhaps second only to Newton, his work is not free of flaws. For instance, Maxwell's Theory was based upon Electricity being a continuous fluid. Even more, he rejects the already known but then less popular Atomic Theory of Electricity. Discussing Electrolysis he says:

This does not diminish at all the general validity of his work. Unfortunately, in spite of the specific statement that more careful measurements were needed before the equality of both quantities were to be fully established, his word of caution was not followed.

At the beginning, some experiments were conducted to measure the ratio of the units (Rowland in 1870, Rosa in 1889, Rosa and Dorsey in 1905). The precision available at the time didn't allow to find any difference and too soon they were declared equal and a race began to determine the velocity of light as precisely as possible, while the experiment to measure the ratio of units felt into oblivion.

Nevertheless, with the adoption of the velocity of Light as the fundamental constant, the difference was masked but did not go away. It disturbs all electrical measurements and keeps showing every time an electric unit is experimentally determined, specially the Ohm (the units of Resistance are the inverse of a velocity). Because there is not a theoretical explanation for it, they simply call it the difference between the absolute and the practical or international Ohm.

One of the best documented experiments that proves the existence of the difference is "Neue Bestimmung des absoluten Ohm" by E. Grüneisen and E. Giebe, published in 1922 by the Physical Technische Bundesnstalt. They arrived to the following value:

To repeat this kind of experiment is considered today as pointless. As the determination of the next decimal place of the Ohm's absolute value it may be, but it is also the proof that the velocity of Light is not the Universal Constant.

If Relativity had come first, nobody would doubt the Ratio of the Units being the bigger of both quantities. When more than 30 years later, Albert Einstein presented his Theory of Relativity, Maxwell's constant had been almost forgotten and the velocity of Light was firmly in place as the fundamental constant. The fact that the photon resulted without mass was not questioned as absurd as it should be, but was reluctantly accepted instead as another proof that light was a wave.

Why, in all this years the error has not been discovered and corrected? There are several and very valid reasons:

Let's see what Maxwell's constant real value is. In Maxwell's original work, the relationship between units was called v, but since v is normally used to name any velocity, to avoid confusion I will call it b . In any case, by definition, the value of b is:

b = ( m₀ * e₀)^-½                                                               (1)

where m₀ is the magnetic permeability and e ₀ is the electric permittivity, both measured in vacuum.

The values of m₀ and e₀ are not independent but are function of the units of measurement to be used. If we make e₀ equal to one and use to centimeter, the gram and the second (c.g.s.) as units of measure, we have the absolute electrostatic system. In this case, the value of m₀ has to be obtained by measurement.

Another system of units is the absolute electromagnetic system in which the units of measure are the c.g.s. and the value of m₀ is equal to 4p . In this case, the value of e₀ is the one that has to be obtained by measurement.

These two systems of measurement have several drawbacks: the magnitude of the electric and magnetic units used in everyday practical problems are either too large or too small. Furthermore, their dimensions have fractional exponents. To avoid these problems a practical system of units was needed.

In 1901, Giovanni Giorgi, following an idea originally proposed by Maxwell, discovered that a practical system of units could be constructed choosing as a fourth fundamental magnitude, the magnitude of any electromagnetic unit: charge, resistance, current, etc. Then, instead of finding the value of e₀ or m₀ by experiment, they can be calculated in function of this fourth magnitude without any measurement.

The system that Giorgi proposed, known as the practical system, uses the meter, the kilogram and the second (M.K.S.) as units of measure and assigned to the constant K in Coulomb's Law the following value:

K = 9 * 10⁹ Nm²/ Coulomb²                                              (2)

Beginning with this value e ₀ and m ₀ can be derived:

                      = 1.256637 * 10^-6 Henry/meter                                  (3)

and

                1             Coulomb
e₀ = ----------------- -------------
          4p * 9 * 10⁹  Volt * m

                      = 8.841941 * 10^-9 farad/meter                                   (4)

using this two values in (1), the value of b is:

                       = 3 * 10⁸ meters/second                                             (5)

This is Maxwell's constant true value. It is exact by definition because the units of measure were chosen that way. But as soon as the practical system began to be used, a fact became evident: the velocity of light was slightly smaller than the exact value that theory predicted for b . By then, Maxwell's Electromagnetic Theory already passed without doubt many rigorous tests and there was not a single indication that his theory should be reviewed.

The difference was first accepted within the experimental error range and when the measurement techniques improved and the difference persisted, it was already too late: the velocity of light was wrongly established as the fundamental constant and all units of measure were to be calculated in function of it.

By a reason not clear to me (somewhere I read because magnetism is more fundamental than electricity, which in some sense is true), the value of m₀ was accepted exact by definition and e₀ was changed to be calculated in function of c instead of its true value. The best accepted measured value of the velocity of light is:

                c = 2.997927461 * 10⁸ meters/second                              (6)

and using this value, the new value of e ₀ became:

e₀ = 1 / (m₀ * c²)= 8.854171 * 10⁻¹² farad/meter                (7)

 and K, instead of the originally intended exact value, became:

                  K = 8.987569 * 10⁹ Nm² / Coulomb²                                (8)

The value of b is only 1.00069 times c. The difference is so small that may be seen as negligible, and in every day life it is, but in this particular case, that small amount makes a big difference: the photon has a non zero rest mass and many concepts in modern Physics will have to be reviewed, Relativity included.

The only remaining problem is to confirm experimentally the value of Maxwell's constant. The latest reference I could find for the direct determination of the ratio of the units is around 1905, when the available experimental techniques were not precise enough as to stablish a difference.

The direct measurement of the Ratio of the Units using modern technology will prove that the product ( m₀ * e₀ ) is different than the value of c^-2 and this will make a big impact in our understanding of matter. Once we accept the photon having rest mass, the relationship between the rest mass of all known stable particles becomes evident and their structure can be established in function of a single elementary particle, the fundamental building block from what everything is made of, from atoms to the largest celestial body, including of course, all forms of life.

Felipe O. Bertrand
Bertrand36@aol.com