# In Honour of the Memory of Hermann Minkowski

Hello, folks! In this important article, I want us to talk about a great scientist who was also Einstein’s teacher. This man’s name was Hermann Minkowski.

Hermann Minkowski was born on the 12th of June 1864 to Lewin Minkowski and Rachel Taubmann, a Jewish family in Aleksota, in the Kingdom of Poland, Russia.

He studied at East Prussia, in the University of Königsberg, and he earned his doctorate in 1885 under the tutorship of Ferdinand von Lindemann. And *“in 1883, while still a student at Königsberg, he was awarded the Mathematics Prize of the French Academy of Sciences for his manuscript on the theory of quadratic forms.”*

Before his sudden demise on the 12th of January, 1909, he had left his mark in the fields of number theory and relativity.

And in this article, I want us to remember Hermann Minkowski as the genius of geometry. He pioneered some of the geometrical methods applied to solve problems in number theory, mathematical physics, and relativity.

And his achievement in the field of relativity is so profound and enduring that it continues into post-modern physics. *How did this achievement come about?*

Hermann Minkowski discovered in 1907 that the theory of special relativity which his former student Albert Einstein had written could be geometrically understood and represented as a theory of 4-dimensional space-time.

This new formulation became known as *Minkowski space-time*, and in physics, it is aptly represented by the invariant interval:

*Δs ^{2 }= x^{2} – y^{2} – z^{2} – c^{2}t^{2}*, where

*c*is the speed of light.

The above Minkowski space-time shows us explicitly how Minkowski was able to see and derive the geometrical import of relativity as he was able to include time as just the fourth dimension of the universe.

This was how Minkowski introduced us to the flat geometry of the universe that is characterized by the fusion of space and time in relativity, and from then henceforth, space and time were no longer separate entities.

Minkowski geometrical method of describing relativity became well accept that even his former student Einstein had to adopt it in general relativity which was his attempt to extend the principles of relativity to accelerated frames.

And to share my personal experience, Minkowski geometrical formulation assisted me greatly to understand relativity myself.

It is one of the most beautiful experience to understand the different slanted distortions of Minkowski space-time in relativity. It was an indispensable tool for me when I was writing absolute relativity.

This geometrical method really gives one a picture of what relativity is than the mechanistic or purely mathematical presentation.

So, today, I want us to remember Minkowski for his contributions to physics. And personally, I really appreciate his geometrical description or formulation of relativity. It is one legacy that I am convinced will remain until the end of time.

This is because even in *The Theory of the Universe*, we find the application of Minkowski geometrical method to explain the other mysteries of the universe that special relativity did not capture.

And this is possible because, in *The Theory of the Universe*, we find the full realization of the potentials of the Minkowski geometrical method in describing not just the relativity of uniform frames, but also the relativity of accelerated frames.

And by making a beautiful comparison of the geometrical changes or transformations between inertial reference frames and non-inertial reference frames for both the atomic and non-atomic realms, we are able to understand the whole universe using one geometrical method.

And this won’t be possible without the contributions of Hermann Minkowski to physics.

So, we really have to remember and honour the memory of Hermann Minkowski. This is all the more important now that we see his geometrical method applied for the complete understanding of the universe.

And in fact, Hermann Minkowski would always be remembered as the one who opened the door to our geometrical understanding of the universe. His geometrical method, whether it was an accident or by well-calculated procedure applies in the universe.

By the above presented geometrical formulation, Minkowski was able to fuse space and time in a single entity, and he himself captured this better when at *“the beginning part of his address called “Space and Time” delivered at the 80th Assembly of German Natural Scientists and Physicians (21 September 1908)”, *he said:

*“The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”*

The above quote by Minkowski’s has become famous ever since he said it, and the first time I saw it, I mirthful at the magnificent way in which he captured not just his geometrical input to relativity, but also the entire meaning and legacy of the theory of relativity.

And in Minkowski’s lifetime, he was a close friend of another great mathematician called David Hilbert. When Minkowski passed away on the 12th of January, 1909 due to appendicitis, Hilbert penned his obituary thus:

*“Since my student years, Minkowski was my best, most dependable friend who supported me with all the depth and loyalty that was so characteristic of him. Our science, which we loved above all else, brought us together; it seemed to us a garden full of flowers. In it, we enjoyed looking for hidden pathways and discovered many a new perspective that appealed to our sense of beauty, and when one of us showed it to the other and we marvelled over it together, our joy was complete. He was for me a rare gift from heaven and I must be grateful to have possessed that gift for so long. Now death has suddenly torn him from our midst. However, what death cannot take away is his noble image in our hearts and the knowledge that his spirit continues to be active in us.”*

And today, I sometimes remember Hermann Minkowski because even in death, he still speaks to us through his discovered mathematical concepts, and especially through his geometrical formulation of relativity.

He is mostly remembered for this, and it is rightly his greatest legacy. And as a testimony of this, as we proceed deeper into post-modern physics and into the complete understanding of the universe, we would remember and appreciate the intellectual legacy of Minkowski the more.

His geometrical method has real application in nature, and being pushed to its farthest limit, is what now gives us a unified description of the universe.

Until next time,

I will be here.

– M. V. Echa.