A4      Einstein Cuts the Gordian Knot

Einstein declared R and M to be valid without any restrictions and showed how one must modify N, so that everything fits together without contradiction. He placed at the beginning of his theory, which today we call the special theory of relativity (STR), the following postulate:

m R m
All inertial frames are equal. The laws of nature, including the values of the constants arising therein, are the same in all inertial frames
m M
Maxwell's electrodynamics is valid without restrictions

In the last section we saw that R and M imply that the speed of light c has the same value in all inertial frames and is therefore a universal constant. In the usual mks system of units this value is

c = 299,792,458 m/s

The equals sign is correct: Since 1983 the meter is no longer a fundamental value, but is defined by this value of c and the second! Thus today the STR is the basis even for the definition of our basic metrics! The absoluteness of the speed of light in the STR firmly couples space and time together. A distance of approximately 300,000 km length corresponds to one second of time.

The boldness of Einstein's idea is oftly praised in today’s text books. So do Roman Sexl, Ivo Raab and Ernst Streeruwitz in their very recommendable physics book for high school students (translation by Samuel Edelstein):

“Finally in the year 1905 a formerly unknown technician of the Swiss federal patent office in Berne stepped into the public eye with a new idea. His name was Albert Einstein, and his article 'On the Electrodynamics of Moving Bodies' proceeded from the idea that perhaps one could not measure the earth’s movement through the ether because the ether does not exist!”  [11-10]

Wilhelm Wien suggested in 1912 to award the Nobel Prize for physics in equal parts to Lorentz and Einstein:

"From a purely logical point of view, the relativity principle must be considered as one of the most significant accomplishments ever achieved in theoretical physics.  ... [Relativity] was discovered in an inductive way, after all attempts to detect absolute motion had failed.  ...  While Lorentz must be considered as the first to have found the mathematical content of the relativity principle, Einstein succeeded in reducing it to a simple principle. One should therefore assess the merits of both investigators as being comparable.  ... "  [10-153]

Einstein would have agreed with this. He himself had designated only one of the 5 works of his 'annus mirabilis' as "quite revolutionary", namely the one concerning the photoelectric effect! When Einstein in 1921 finally received his long overdue Nobel Prize, the reason also specifically emphasized that work. Einstein always spoke of Lorentz with the greatest respect. All 5 works were by the way published, along with good introductions, by John Stachel in [09].


Albert Einstein and Hendrik Antoon Lorentz (1921)

In the STR one can also replace the postulate M with the special requirement that c is a universal constant. In the following chapters we will demonstrate in detail, how one can derive the STR from the relativity principle and the constancy of c. Fortunately, a complete presentation of the STR requires only modest mathematical knowledge. We will not have to struggle like Kepler, who writes in his introduction to the “Astronomia Nova” :

“I, who consider myself a mathematician, quickly fatigue the power of my brain through the re-reading of my work, in an attempt to recognize the sense of the proofs, which I indeed originally inserted with my own understanding into the diagrams and the text, and from which diagrams I again want to glean an understanding. If I obviate the heavy comprehensibility of the material by interspersing detailed descriptions then I appear to be garrulous in mathematical things and that is the opposite mistake."

(translation by Samuel Edelstein from [08-19])