Einstein's Relativity and the 'Second Major Absurdity' in 1905

Albert Einstein's 1905 paper introduced fundamental concepts that laid the groundwork for modern physics. Among the numerous groundbreaking ideas, there has been much debate and controversy surrounding certain elements of his work, particularly those found in the famous paper on special relativity. This article explores one of the 'major absurdities' often cited in discussions about Einstein's 1905 relativistic theory: the variable x' and the derivation of related derivatives.

Understanding x'

In his 1905 paper, Einstein introduced the notion of x' as a constant to facilitate the analysis of relativistic phenomena. The variable x' represents a spatial coordinate in a frame of reference that is moving relative to a stationary observer. This constant is defined by the equation:

x' x - vt

Here, x is the coordinate in the stationary frame, vt is the contribution of the relative velocity between the two frames, and t is the time.

Derivatives and the Tau Model

Einstein further utilized x' in his tau model, a term he introduced to describe specific temporal and spatial transformations. In this model, x' appears in the calculation of distances traveled and the time taken for light to traverse these distances.

The Derivatives of x'

Einstein applied specific derivatives of x' to derive the fundamental equations of special relativity. Let's examine the four key derivatives he used:

Here, c represents the speed of light, and v is the relative velocity. Notably, the derivation of these derivatives relies on the assumption that x' is a constant, which simplifies the calculations but raises questions about the physical interpretation and the legitimacy of the mathematical handling.

The Criticism and Controversy

Some critics have pointed out what they consider to be a significant flaw in Einstein's approach. They argue that the use of constant derivatives of a constant variable, such as x', is mathematically questionable. A common assertion is that chaining constants with their definitions (such as x' x - vt) leads to erroneous results. However, this criticism overlooks the fact that Einstein was using these derivatives to derive the effects of velocity in a consistent manner.

Another point of contention is the use of the tau model. This model seemed to be based on a scenario with zero velocity, which then required a 'something idiotic' to recover the intended velocity effects. The question remains whether this approach is logically sound or merely a mathematical trickery.

Conclusion

The 'second major absurdity' in Einstein's 1905 paper on relativity centers on the variable x' and its derivatives. While these elements have been criticized, they are integral to the mathematical framework of special relativity. Einstein's work, despite its flaws and controversies, has had a profound impact on our understanding of space and time. Further examination and verification are necessary to resolve these issues and ensure that the concepts remain robust in the face of critical scrutiny.

Keywords: