Institute for Foundational Studies
Hermann Minkowski

Hermann Minkowski
1864 - 1909




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Hermann Minkowski



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As is well-known in the present situation in physics it is difficult to secure funds for projects in fundamental physics that do not fall into the area of the big projects such as LHC and LIGO, for example. Although the research at the Minkowski Institute does overlap with the research at LHC and LIGO, our approach and particularly our research strategy are significantly different.

Due to its specific nature and goals, in the present situation the Minkowski Institute tries to become as independent of uncertain funds and donations as possible; now the only steady but small source of funding is the Minkowski Institute Press and potentially teaching as well once the Institute is granted the right to offer courses. Such an independence ensures that it is solely the Institute which determines its reasearch projects and the number of colleagues invited to work on them as outlined in its Mission.

Due to the limitted funds at this stage the Minkowski Institute acts as a "crystallization centre" of an innovative research strategy (extracted from the methods behind the greatest discoveries in physics), which is now being further developed by testing its potential for accelerating and focusing the research process in different areas of fundamental physics. Once proven to be more productive, it will allow the Institute to act as a "catalyst" in the research in fundamental physics.

Presently the Minkowski Institute is guiding and coordinating the work of researchers who are invited as members of its research teams (and who can afford doing this while holding their University or other positions).

Now the research at the Minkowski Institute is on its first and major research project as outlined below and the Institute continues to invite researchers who are interested in working on this project and its implications as affiliated members. Inquiries by interested researchers are given careful consideration.

Recent graduates (Physics or Mathematics) interested in the research at the Minkowski Institute are especially encouraged to contact Vesselin Petkov at for specific information on how to join the research on the present project.

Minkowski Institute's Major Research Project - Summary

Exploring Minkowski's program of regarding
four-dimensional physics as spacetime geometry

In his groundbreaking talk "Space and Time" in 1908 Hermann Minkowski announced the revolutionary view of the unification of space and time into an inseparable four-dimensional world (with time as the fourth dimension), which we now call spacetime. He arrived at it by successfully decoding the profound message (that the world is four-dimensional) hidden in the failed experiments to detect absolute uniform motion, that is, he revealed the deep physical meaning of the principle of relativity (postulated by Einstein and explained by Minkowski) - physical laws are the same in all inertial refererence frames (otherwise absolute motion can be discovered) because the reference frames in relative motion have different proper spaces and times and the physical laws are expressed in the same way in each frame in terms of its proper space and time; but many spaces and times imply a four-dimensional world (Minkowski remarked that it was Einstein who regarded on equal footing the different times of obsetvers in relative motion, formally introduced by Lorentz, but pointed out that neither Lorentz nor Einstein examined the notion of space, after which he explicitly stated the essence of the physical meaning of the principle of relativity: "Hereafter we would then have in the world no more the space, but an infinite number of spaces analogously as there is an infinite number of planes in three-dimensional space. Three-dimensional geometry becomes a chapter in four-dimensional physics"). Minkowski had clearly realized that four-dimensional physics was in fact spacetime geometry since all particles which appear to move in space and last in time are in reality a forever given web of the particles' worldlines in spacetime. Then Minkowski outlined his program of geometrization of physics:

The whole world presents itself as resolved into such worldlines, and I want to say in advance, that in my understanding the laws of physics can find their most complete expression as interrelations between these worldlines.

Unfortunately, this program has not been fully explored (even in general relativity) mainly due to two reasons:

  1. The reality of the Minkowski four-dimensional world (spacetime) is not an accepted fact in physics since some physicists think that theories are just descriptions of physical phenomena and therefore physics cannot say which theoretical entities have counterparts in the physical world. This metatheoretical issue (whether theoretical entities adequately represent elements of the physical world) might have been hampering the advancement of fundamental physics in the last 80 years. Addressing and resolving it can be done by recalling that part of the art of doing physics is to determine whether different theories are indeed simply different descriptions of the same physical phenomena (as is the case with the three representations of classical mechanics - Newtonian, Lagrangian, and Hamiltonian), or only one of the theories representing given physical phenomena is the correct one (as is the case with general relativity, which identifies gravity with the non-Euclidean geometry of spacetime, and other theories, which regard gravity as a force).

  2. It is often stated that the notion of spacetime cannot accommodate the probabilistic behavior of quantum objects. However, the fact that quantum objects are not worldlines in spacetime only indicates what they are not, and in no way questions the reality of spacetime. Quantum objects might simply be more complex structures in spacetime than worldlines. [1]

Often the issue of the reality of spacetime is ignored by physicists since they regard it as belonging to philosophy. Hardly anything can be wronger than such a position with far reaching negative implications for fundamental physics. The dimensionality of the world is a purely physical question that should be answered by physics alone. Moreover, Minkowski himself forcefully stressed it that the new view of spacetime arose from the domain of experimental physics.

This research project has two main stages:

  • Rigorously examining the relativistic experimental evidence to determine whether it would be at all possible if the world were not four-dimensional.
  • If the reality of spacetime is confirmed, which will confirm Minkowski's discovery that four-dimensional physics is merely spacetime geometry, all possible implications for fundamental physics will be studied, particularly for quantum gravity,[2] gravitational wave physics, and the nature of elementary particles.

  1. ''As an illustration that spacetime can accommodate probability perfectly well, imagine that the probabilistic behavior of the quantum object is merely a manifestation of a probabilistic distribution of the quantum object itself in the forever given spacetime - an electron, for instance, can be thought of (for the sake of the argument that spacetime structures can be probabilistic as well) as an ensemble of the points of its disintegrated worldline which are scattered in the spacetime region where the electron wavefunction is different from zero. Had Minkowski lived longer he might have described such a probabilistic spacetime structure by the mystical expression predetermined probabilistic phenomena.'' V. Petkov, Physics as Spacetime Geometry. In: Springer Handbook of Spacetime (Springer, Heidelberg 2014), Chapter 8. Go back.
  2. A comprehensive exploration of the implications of Minkowski's profound idea of regarding four-dimensional physics as spacetime geometry leads to an interesting and potentially important result - that gravity might not be a physical interaction. Such a stunning explanation of the unsuccessful attempts to create a theory of quantum gravity does not appear to have been examined so far. If Einstein had examined Minkowski's idea thoroughly he would have most probably considered and carefully analyzed this possibility. Had he lived longer, Minkowski himself might have arrived at this radical possibility. In 1921 Eddington even mentioned it explicitly - "gravitation as a separate agency becomes unnecessary" [A. S. Eddington, The Relativity of Time, Nature 106, 802-804 (17 February 1921); reprinted in: A. S. Eddington, The Theory of Relativity and its Influence on Scientific Thought: Selected Works on the Implications of Relativity (Minkowski Institute Press, Montreal 2015)].

    This possible explanation of the failure of quantum gravity does not look so shocking when gravity is consistently and rigorously regarded as a manifestation of the non-Euclidean geometry of spacetime. Then it becomes evident that general relativity does imply that gravitational phenomena are not caused by gravitational interaction since they are fully explained in the theory without the need to assume the existence of gravitational interaction: what has the appearance of gravitational attraction involves only inertial (interaction-free) motion and is indeed nothing more than a mere result of the curvature of spacetime. The actual open question in gravitational physics seems to be how matter curves spacetime, not how to quantize the apparent gravitational interaction (Chapter 8 of the Springer Handbook of Spacetime and Chapter 6 and Appendix C of Inertia and Gravitation). Go back.