Albert Einstein and Hermann Minkowski’s Space-time Formalism

Vesselin Petkov writes: “Minkowski’s contributions to modern physics have not been fully and appropriately appreciated. […] Einstein called Minkowski’s approach ‘superfluous learnedness’. Also, Sommerfeld’s recollection of what Einstein said on one occasion can provide further indication of his initial attitude towards Minkowski’s development of the implications of the equivalence of the times of observers in relative motion: ‘Since the mathematicians have invaded the relativity theory, I do not understand it myself any more’. […] Despite his initial negative reaction towards Minkowski’s four-dimensional physics Einstein relatively quickly realized that his revolutionary theory of gravity would be impossible without the revolutionary contributions of Minkowski”. x

First let us correct a myth here: it is not quit true that Minkowski’s contributions have not been appreciated. Hermann Minkowski was Einstein’s former mathematics professor at the Zürich Polytechnic. During his studies at the Polytechnic Einstein skipped Minkowski’s classes; but Einstein also skipped Prof. Carl Friedrich Geiser’s lectures as much as he skipped Prof. Adolf Hurwitz’s classes… They were all mathematicians. Einstein never showed up the classes of mathematicians. At that time Einstein was less interested in mathematics than in the visible process of physics. He found it difficult to accept for a long time the importance of abstract mathematics, and found high mathematics necessary only when developing his gravitation theory – he discovered the qualities of high mathematics around 1912

Einstein and his wife around 1905

Second, On September 21, 1908, in the 80th annual general meeting of the German Society of Scientists and Physicians at Cologne, Minkowski presented his famous talk, “Space and Time”. x


May years later his assistant, the physicist Max Born wrote: “I went to Cologne, met Minkowski and heard his celebrated lecture ‘Space and Time’, delivered on 21 September 1908. […] He told me later that it came to him as a great shock when Einstein published his paper in which the equivalence of the different local times of observers moving relative to each other was pronounced; for he had reached the same conclusions independently but did not publish them because he wished first to work out the mathematical structure in all its splendor. He never made a priority claim and always gave Einstein his full share in the great discovery”. x

Scott Walter writes, “This story of Minkowski’s recollection of his encounter with Einstein’s paper on relativity is curious, in that the idea of the observable equivalence of clocks in uniform motion had been broached by Poincaré in one of the papers studied during the first session of the electron-theory seminar. It is possible, of course, that Poincaré’s operational definition of local time escaped Minkowski’s attention, or that Minkowski was thinking of an exact equivalence of timekeepers”. [In the
summer of 1905, Minkowski and David Hilbert led an advanced seminar on electrodynamical theory]. x

Before 1905 Poincaré stressed the importance of the method of clocks and their synchronization by light signals. He gave a physical interpretation of Lorentz’s local time in terms of clock synchronization by light signals, and formulated a principle of relativity. However, Poincaré did not pronounce “the equivalence of the different local times of observers moving relative to each other”. Einstein was the first to do so


 John Stachel explains Poincaré’s clock synchronization: “Poincaré had interpreted the local time as that given by clocks at rest in a frame moving through the ether when synchronized as if – contrary to the basic assumptions of Newtonian kinematics – the speed of light were the same in all inertial frames. Einstein dropped the ether and the ‘as if’: one simply synchronized clocks by the Poincaré convention in each inertial frame and accepted that the speed of light really is the same in all inertial frames when measured with clocks so synchronized”. x

Einstein in the Patent Office

In the text of the lecture of the Cologne talk immediately after presenting Lorentz’s local time it is written: “However, the credit of first recognizing sharply that the time of the one electron is just as good as that of the other, i.e., that t and t’ are to be treated the same, is of A. Einstein”. And Minkowski referred to Einstein’s 1905 relativity paper and to his 1907 review article

Read my short paper (a note) on Einstein, Minkowski and Max Born’s recollections of Minkowski’s work


2 thoughts on “Albert Einstein and Hermann Minkowski’s Space-time Formalism

  1. after years of studing physics I am now convinced that Minkowski four-velocity has no physical menaing.

    A particle at rest in 3D space moves with the velocity of light c=300.000 Km/s in the 4D Minkowski space-time. This is not physics this only mathematical crap.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s