11. V. Arunasalam, Intrinsic Theoretical Power and Mathematical Beauty of Relativity, and Ultimate Reality

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Volume 16: Pages 104-130, 2003

Intrinsic Theoretical Power and Mathematical Beauty of Relativity, and Ultimate Reality

V. Arunasalam

50 Windsor Drive, Princeton Junction, New Jersey 08550 U.S.A.

The intrinsic theoretical power and mathematical beauty of (special or flat spacetime) relativity and its relevance to ultimate reality are examined in hindsight in sufficient detail. The fourdimensional spacetime continuum nature (or character) of space and time (known as the worldspace or the fourspace or the Minkowski space) and the associated EinsteinPoincaré truly manifestly Lorentz covariance requirements on the mathematical description of any physical system (i.e., on all laws of physics) in this fourspace continuum do indeed lead us to the ultimate physical reality that the mathematical formulas (or laws) of physics are discovered, not invented, and thus are meant to be a true and honest representation of the actual behavior of nature. However, at present, Maxwell's electromagnetic theory is the only existing truly manifestly Lorentz covariant field theory. All other existing manybody theories are not Lorentz covariant theories but are, indeed, “Lorentz invariant” theories only in the sense that they predict Lorentz invariant results (but the mathematical structure of these theories in the worldspace is frame dependent and not form invariant), and thus they are simply mathematical models that we have constructed and/or invented to assist us in the exploration of nature, and nothing more. Specific cases (or instances) that clearly demonstrate the awesome intrinsic theoretical power and mathematical beauty of relativity are presented. Thus we show that the Lorentz transformation is a part of physical reality in the sense that it exists in nature and not necessarily in the human mind (i.e., the laws of physics are nature's laws and not ours). Also, a rather serious attempt is made here (probably for the first time and, of course, with only partial success) to understand “nature's arrow of time” from the point of view of (special) relativity.

Keywords: theoretical power of relativity, mathematical beauty of relativity, laws are discovered not invented, nature's laws and not ours, laws and ultimate reality, covariance and invariance, tardyons, tachyons, pair production, cosmology, PT theorem, CPT theorem, relativity, quantum theory, arrow of time

Received: February 17, 2003; Published online: December 15, 2008