Institute for Foundational Studies
Hermann Minkowski

 
Hermann Minkowski
1864 - 1909


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Research Strategy

What, we believe, makes the Minkowski Institute without a counterpart in the world is the development and employment of a research strategy (extracted from the greatest discoveries in physics), whose main components are summarized below.

We employ this research strategy to address and help break the present impasse in fundamental physics by first trying to identify the reasons for the lack of major breakthroughs in fundamental physics in the last 80 years (of the type of relativity and quantum mechanics). We begin every research project by rigorously examining all explicit and especially implicit assumptions involved in it in order to ensure that no implicit assumptions are smuggled into the work on any of our research projects. For example, while thoroughly examining the reasons for the failure so far to create a quantum theory of gravity we are not worried to ask the heritical, but fully legitimate question of whether gravity is a physical interaction; moreover, in 1921 Eddington mentioned it explicitly [1] - "gravitation as a separate agency becomes unnecessary;" two years later, in his fundamental work on the mathematical foundations of general relativity The Mathematical Theory of Relativity Eddington stated it even more explicitly [2]: "An electromagnetic field is a "thing;" gravitational field is not, Einstein's theory having shown that it is nothing more than the manifestation of the metric." This and several more examples are briefly formulated on our blog:

https://doingphysicsright.wordpress.com/

Main Components of the Minkowski Institute Research Strategy

1. Special emphasis on metatheoretical issues because such issues might have been hampering the advancement of fundamental physics in the last 80 years. Perhaps the most important metatheoretical issue is the nature of physical theories, particularly its two main aspects:

1.1. Whether theoretical entities adequately represent elements of the physical world. Some physicists appear to think that theories are nothing more than descriptions [3] of physical phenomena and therefore physics cannot say whether theoretical entities have counterparts in the physical world. Addressing such a misconception 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).

It should be stressed as strongly as possible that an inadequate position on metatheoretical issues can prevent a scientist (no matter how great) from making a discovery. Perhaps the most cruel and sad example in the history of physics is Poincaré's failure to see the revolutionary idea of unifying space and time into a single entity (spacetime) - due to his inadequate view that physical theories are only convenient descriptions of the world (and therefore it is really a matter of convenience and our choice which theory we would use), he failed to comprehend the profound physical meaning of the relativity principle and particularly the deep physical meaning of the geometric interpretation of the Lorentz transformations as rotations in a four-dimensional space with time as the fourth dimension (which he published first but probably discovered independently from Minkowski). As T. Damour stressed it "it was the sterility of Poincaré's scientific philosophy: complete and utter 'conventionality'... which stopped him from taking seriously, and developing as a physicist, the space-time structure which he was the first to discover" [4].

1.2. Whether an accepted (and experimentally confirmed) theory can be found wrong. There is no expiration date for physical theories whose predictions have been experimentally confirmed. Such theories will never be proven wrong in their domains of applicability where they were tested (for example, a thousand years from now bridges will still be built by employing Newtonian mechanics). No future experiments can challenge such theories in the areas where their predictions were experimentally tested because experiments do not contradict one another. Any new theory containing the domain of applicability of the old one (i.e., containing the old theory as a limiting case) will be a representation of the world with a better "resolution" and will not contradict the basic features of that domain captured by the old theory.

2. Nothing in Physics should be taken for granted no matter how self-evident it may look, especially if there have been problems that have not been resolved for years. An example is the failure so far to arrive at a theory of quantum gravity. Although it may seem heretical to some, one of the ways to deal with this problem is to question and examine thoroughly the taken-for-granted assumption that gravity is a physical interaction.

3. Employing the powerful and provenly productive method of exploring the internal logic of an idea. It can be briefly described as deducing all logical consequences of an idea and examining their implications through thought and real experiments.

Probably the thinkers of the Eleatic school of thought (Xenophanes, Melissus, Parmenides and Zeno) were the first who started systematically to develop and employ this method. Galileo beautifully demonstrated its power by exploring the internal logic of the idea of motion and discussing thought experiments (involving everyday situations) which helped him to arrive at two fundamental results - (i) the notion of inertial motion (that bodies moving with constant velocity do not need a mover as Aristotle believed), and (ii) Galileo's principle of relativity (motion with constant velocity cannot be detected by mechanical experiments).

Two other scientists who successfully employed the method of exploring the internal logic of ideas are Einstein and Minkowski:

  • Einstein's analyses of thought experiments led him to his special and general relativity,
  • Minkowski's exploration of the internal logic of the mathematical formalism of classical mechanics, particularly of the fact that "The equations of Newtonian mechanics show a twofold invariance" helped him see the profound physical meaning of Einstein's special relativity - that it is not a theory of objectively relative quantitities, but a theory of an absolute four-dimensional world with time as the fourth dimension (what is relative in Einstein's special relativity is frame-dependent and therefore does not have an objective physical meaning).

To reveal the full potential of the method of exploring the internal logic of ideas, at the Minkowski Institute we employ this method to identify delayed discoveries in physics by demonstrating that they either could have been realistically made earlier or are logically contained in fundamental ideas well known before the actual discoveries. Then we outline possible resolutions of present open questions on the basis of extracted hidden information from the fundamental ideas, involved in the open questions, which is obtained by exploring the internal logic of those ideas.

4. Fully exploiting Wheeler's "first moral principle" [5] - "Never make a calculation until you know the answer" - which is enormously powerful when dealing with issues that demonstrate that one can still do physics at its best even if no calculations are involved.


References

1. 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).

2. A. S. Eddington, The Mathematical Theory of Relativity (Minkowski Institute Press, Montreal 2016) p. 221.

3, Regarding physical theories as nothing more than mere descriptions (which do not represent anything in the external world) appears to be a real problem in physics because some physicists regard issues such as the reality of spacetime as belonging to philosophy, which is an embarrassing misconception and is ultimately physics at its worst - the issue of the dimensionality of the world is pure physics.

4. T. Damour, Once Upon Einstein, Translated by E. Novak (A. K. Peters, Wellesley 2006), p. 52

5. E. F. Taylor, J. A. Wheeler, Spacetime Physics, 2nd ed. (W.H. Freeman & Company, New York 1992), p. 20