Einstein's Theory of Invariance

by Craig Rusbult, Ph.D.

The famous theory of Albert Einstein is often called his Theory of Relativity, but he thought it should be called a Theory of Invariance, and I agree.  Why?
 

As explained in my Detailed Overview of Scientific Method,
      Another strategy [for inventing theories] is to construct a theory, using the logic of internal consistency, by building on the foundation of a few assumed axiomatic components.
      In mathematics, an obvious example is Euclid's geometry.  An example from science is Einstein's theory of Special Relativity;  after postulating that two things are constant (physical laws in uniformly moving reference frames, and the observed speed of light), logical consistency -- which Einstein explored with mental experiments and mathematics -- makes it necessary that some properties (length, time, velocity, mass,...) will be relative while other properties (proper time, rest mass,...) are constant.

The simple logic of invariance (which is the foundation for Einstein's theory of "relativity") is explained in Chapter 16 of my book, Power Tools for Problem Solving in Physics.  Just read the first two pages and stop when I ask, "Are you convinced?"   { These two pages require no mathematics;  then, if you want to master the basic math, which isn't difficult, you can continue reading. }
 

And here are some views about invariance & relativity from others:

Albert Einstein was unhappy about the name "theory of relativity".  He preferred "theory of invariance".  The reason is that [one] cornerstone of his 1905 theory of relativity is that the measured velocity of light is the same (invariant) regardless of any relative motion between a laboratory and the source of light.  What Einstein feared came to pass when the popular catchphrase of his theory became "everything is relative".  It was snatched up by people not acquainted with the scientific context, who regarded the theory as evidence in support of their own social views.   { Arthur Miller, from a letter in New Scientist }

In actual fact, the theory of relativity is anchored in absolutism — in the concrete of Einstein's two postulates:  The velocity of light is a universal constant, and the laws of physics are constant.  He described these postulates as principles of invariance.  An insightful textual analysis of the introductory sections of the 1905 paper would have recognized that the two "postulates" specify unchanging principles that serve as the foundations of the theory.  In fact, Einstein called his creation an "Invariententheorie," a theory of invariance.  The name "theory of relativity" was coined later in a review by German physicist Max Planck.  Einstein resisted that name for years, although he reluctantly bowed to peer pressure.  The relativistic features of time and space that led to the term "theory of relativity" are derived from the principles of invariance.   { quoted from POSTMODERNIST RHETORIC DOES NOT CHANGE FUNDAMENTAL SCIENTIFIC FACTS by Irving M. Klotz, who is a Morrison Professor, Emeritus, in the departments of chemistry and of biochemistry, molecular biology, and cell biology at Northwestern University }

and Relativity & Quantum Physics from the International Catholic University:
      The fundamental principle underlying the theory of relativity it that the laws of nature always have the same form for all observers.  This follows from our belief that there are laws that describe, precisely and mathematically, the connections between causes and effects.  This invariance of the laws of nature sometimes called the principle of covariance, or the principle of relativity.  It says that the laws of nature are completely objective, and do not depend on who is looking at the phenomena or from what vantage point.
      Einstein began by asking himself a very simple question:  What would a light wave look like to someone who is travelling alongside it?  It was known that a light wave is an electromagnetic wave that is described by Maxwell's equations, so he looked for a solution of these equations that describe a stationary light wave, and found that there is none.  However we describe a light wave, it is always moving with the speed of light.
      This led him to study very carefully the transformation equations that relate the spatio-temporal co-ordinates of events in one frame of reference to those in another frame moving with constant velocity with respect to the first.  It had always been assumed to be obvious that these transformation equations are those due originally to Galileo.  Furthermore, it was also considered obvious, according to the principle of relativity, that our description of phenomena should give the same result whichever reference frame we use.  Einstein realised that Maxwell's equations do not satisfy this condition;  they are not invariant under the Galilean transformation.
      So he asked himself what the transformation would have to be to ensure that the light wave looks the same to all observers, whatever their relative velocities.  This was already known to be the Lorentz transformation.  He then asked what would be the consequences of assuming that the Lorentz transformation applied to all phenomena, not just to light waves, and found that this enabled him to explain many apparently anomalous results, such as that of the Michelson-Morley experiment.  ...<snip>...
      The popularity of the theory of relativity among the general public, reinforced by the image of Einstein as the typical scientist, gave impetus to the idea that physics is relative, and thence that everything is relative.  If Einstein had called his work the theory of invariance, we would perhaps have been spared this nonsense.
 

Copyright © 2007 by Craig Rusbult, all rights reserved