Einstein's Contributions to Understanding Light

Albert Einstein is often credited with establishing the Special Theory of Relativity through his renowned 1905 paper "Zur Elektrodynamik bewegter Körper" (On the Electrodynamics of Moving Bodies). However, he was not the only thinker grappling with the intriguing outcomes of the Michelson-Morley experiment, which demonstrated that velocities do not combine with the velocity of light ( c ) in the intuitive, Galilean manner that low-speed velocities do. He was neither the first nor the only one to explain these results by positing that Maxwell's Equations—the framework for light propagation—must undergo transformations between moving reference frames in a manner that preserves their form, thereby ensuring the constancy of the speed of light. Both Hendrik Lorentz and Henri Poincaré had previously engaged with these concepts.

In Maxwell's formulation, ( c ) is defined using fundamental constants derived from electrostatics and magnetostatics. Therefore, if the structure of Maxwell's equations remains unchanged, the speed of light remains constant.

While Lorentz and Poincaré proposed ideas involving "effective time" to elucidate their findings, they stopped short of asserting that the time ( t ) measured by clocks in different reference frames is the actual time. Their reluctance to confront the implications of time measurement across moving frames left them lacking in boldness. Einstein, on the other hand, boldly embraced the radical notion that clocks observed by different observers in relative motion do indeed tick at varying rates, making this assertion a cornerstone of his academic discourse.

In the years following Einstein's seminal paper, Vladimir Ignatowski delved deeper to identify the minimum set of assumptions that could delineate the Lorentz transformation between relatively moving coordinate frames. He concluded that Galileo's relativity alone suffices to derive this transformation's form, leading to the entire family of Lorentz transformations parameterized by an unknown constant ( c ). Ignatowski's theory thus provided the accurate form of the Lorentz transformation, with the value of ( c ) being determined through experimentation. If one, like Galileo, were to assume too much by believing that time is measured uniformly across all frames, one would retrieve the Lorentz transformation limit for an infinite ( c ).

The Michelson-Morley experiment serves as a pivotal moment in determining the unknown constant ( c ) within Ignatowski's framework. Maxwell's equations, therefore, retain their form across moving frames due to Ignatowski's theory and the experimental implications of the Michelson-Morley experiment that established the value of ( c ).

This connection is, by “pure coincidence” (or, as I will elaborate later, the physics of photons), significant. As stated earlier, Maxwell's equations and the concept of light are not even considered in Ignatowski's theory. Consequently, the Michelson-Morley experiment identifies a phenomenon traveling at ( c ). Furthermore, Ignatowski's theory implies that only one such unique universal speed ( c ) exists. Hence, the Michelson-Morley experiment experimentally substantiates the critical intuition suggested by Maxwell's equations, revealing that we inhabit a universe characterized by a finite ( c ), which coincidentally is also the speed of light.

Isn't that elegant? It seems that this realization may have led Einstein to reflect on his earlier disregard for the elegance of mathematics. Ignatowski’s approach adeptly intertwines several profound questions with elegant, straightforward group-theoretic concepts, contrasting with Einstein’s cluttered methodology that includes electromagnetism, which distracts from fundamental principles and results in an overwhelming array of equations that can be difficult for contemporary readers to interpret.

Einstein did, however, receive some mathematical guidance, particularly from his lifelong friend and mathematician Marcel Grossmann, prior to formulating the General Theory of Relativity.

Thus, we should now conceptualize ( c ) as the distinctive speed consistently measured across all inertial frames, with light experimentally observed to travel at this speed. An additional implication stemming from the Michelson-Morley experiment, when considering light quanta, is that the rest mass of the photon is negligible. Areeba Merriam further explicates this notion in her discussion of the relationship ( E^2 - p^2 c^2 = m^2 c^0 ) that I introduced earlier, which indicates that the Minkowski length of the momentum four-vector for a particle equals its energy in its rest frame. Photons exist on the light cone (a concept to be explored in a later article), possess no rest frame, and their total energy is entirely derived from their motion.

Light's Universal Nature

Part 2 of this exploration will attempt to outline Ignatowski's reasoning. Before proceeding, it is worth noting that recent experimental confirmations have established that ( c ) is more fundamental than light. A monumental finding of this century was the confirmation that the universal signaling speed ( c ), which also coincides with the speed of light, is identical to that of gravitational waves, as evidenced by the detection of event GW 170817 in 2017.

On the remarkable day of August 17, 2017, the gravitational wave observatories, US LIGO and European (near Pisa) VIRGO, recorded a massive gravitational wave lasting several minutes from the elliptical galaxy NGC 4993. This unmistakable signal indicated the merging of two neutron stars. Precisely 1.7 seconds post-merger, both the Fermi and INTEGRAL Earth-orbiting gamma-ray telescopes detected gamma-ray bursts emanating from the same direction, prompting observations worldwide.

The source of this event was the merger of two neutron stars located 144 million light-years away. The 1.7-second delay serves as an impressive validation that both light and gravity propagate at the same speed to within 1.7 seconds in 144 million times 32 million seconds (the duration of a year). This represents an extraordinary precision of four parts in ten to the power of sixteen (10¹?). In simpler terms, that means one followed by sixteen zeros. However, scientists often prefer exponential notation for convenience, as it avoids cumbersome names that can differ across languages.

In Europe, this translates to four hundred parts in one trillion; in the US, that’s four hundred parts in a quintillion (where US quintillion equals European trillion = 10¹?).

What’s even more remarkable is that astrophysicists, when calculating how long it took for light to emerge from the debris cloud generated by the neutron star merger, managed to account for over 1.6 seconds of that delay, leaving merely about a tenth of a second unexplained—resulting in a confirmed precision of one part in ten to the power of seventeen (10¹?). This equates to ten parts in one quintillion in the US, and ten parts in one trillion in Europe.

While General Relativity predicts that gravitational waves travel at the speed ( c ), it is unlikely that any serious physicist was surprised by the findings. Nevertheless, on that day, I felt something profound and emotionally overwhelming; it was astonishing to witness the fundamental significance of ( c ) reaffirmed as something far beyond merely the speed of a specific process.

For further insights, click below for Part II of "What's So Special About the Speed of Light?"

title:	What's So Special About the Speed of Light? Part II
description:	Is the cosmic signal speed limit enforced by a relativistic copper man? Or is there even a limit? Vladimir Ignatowski…

References

I provide links to the annotated German and English Wikisources for Ignatowski’s original works, which detail his discoveries:

Ignatowski, W.: “Einige allgemeine Bemerkungen über das Relativitätsprinzip”, Physikalische Zeitschrift. 11. Jg. 1910, S. 972–976

More contemporary interpretations of Ignatowski's insights regarding Special Relativity are discussed in my next article:

• English Version: “Some General Remarks on the Relativity Principle”
• Jean-Marc Lévy-Leblond, “One more derivation of the Lorentz transformation”, Am. J. Phys. 44
• Palash B. Pal, “Nothing but Relativity,” Eur. J. Phys. 24:315–319, 2003
• Berzi & Gorini, “Reciprocity Principle and the Lorentz Transformations”, J. Math. Phys. 10, 1968