Foundations of Physics

, Volume 41, Issue 5, pp 905–918

Fundamental Problems in the Unification of Physics


DOI: 10.1007/s10701-011-9535-6

Cite this article as:
Heller, M., Pysiak, L. & Sasin, W. Found Phys (2011) 41: 905. doi:10.1007/s10701-011-9535-6


We discuss the following problems, plaguing the present search for the “final theory”: (1) How to find a mathematical structure rich enough to be suitably approximated by the mathematical structures of general relativity and quantum mechanics? (2) How to reconcile nonlocal phenomena of quantum mechanics with time honored causality and reality postulates? (3) Does the collapse of the wave function contain some hints concerning the future quantum gravity theory? (4) It seems that the final theory cannot avoid the problem of dynamics, and consequently the problem of time. What kind of time, if this theory is supposed to be background free? (5) Will the dynamics of the “final theory” be probabilistic? Quantum probability exhibits some essential differences as compared with classical probability; are they but variations of some more general probabilistic measure theory? (6) Do we need a radically new interpretation of quantum mechanics, or rather an entirely new theory of which the present quantum mechanics is an approximation? (7) If the final theory is to be background free, it should provide a mechanism of space-time generation. Should we try to explain not only the generation of space-time, but also the generation of its material content? (8) As far as the existence of the initial singularity is concerned, one usually expects either “yes” or “not” answers from the final theory. However, if the mathematical structure of the future theory is supposed to be truly more general that the mathematical structures of the present general relativity and quantum mechanics, is a “third answer“ possible? Could this third answer be related to the probabilistic character of the final theory? We discuss these questions in the framework of a working model unifying gravity and quanta. The analysis reveals unexpected aspects of these rather wildly discussed issues.


Unification of physics Noncommutative geometry Nonlocality Measurement Probability Singularity 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Michael Heller
    • 1
    • 3
  • Leszek Pysiak
    • 2
  • Wiesław Sasin
    • 2
  1. 1.Vatican ObservatoryVatican CityVatican City State
  2. 2.Department of Mathematics and Information ScienceWarsaw University of TechnologyWarsawPoland
  3. 3.Copernicus Center for Interdisciplinary StudiesCracowPoland

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