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Einstein's relativity theory teaches us that an observed phenomenon by different observers, may result in different relative observations.

However, we also know that in a real world, it would be (almost) impossible to establish two "absolutely" identical observations. If not using precision instruments, human perception and cognition would be relative and fluctuating, moreover two human observers could not realize at the very same time and location the same observation. If applying precision instruments, other obstacles may arise, dependent on the experimental design.

Would it make rather sense to imply a stochastic model to observation of such phenomena, rather in the tradition of quantum mechanics: Every observation associated with a probability and such that at any location and time all observations would be probable but certain one of maximum entropy?

Questions:

  • What would be the consequences of such a probabilistic approach to relativity theory?
  • Is there further literature/research in this field which you could recommend?
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    $\begingroup$ This is what is done all the time in experiments of all kinds. You use statistics to model and analyze your observations, because experiments are never perfect. $\endgroup$
    – Javier
    Nov 6, 2021 at 14:24
  • $\begingroup$ @Javier that is from experimental design point of view correct, however, I was rather thinking about stochastic models (e. g. based on quantum type of states and probability density functions etc.) to deliver a general theoretical approach, rather than statistical models such as error analysis. $\endgroup$
    – al-Hwarizmi
    Nov 6, 2021 at 15:57
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    $\begingroup$ If you want stochastic models of general relativity you can look up what is called stochastic gravity $\endgroup$
    – Slereah
    Nov 6, 2021 at 16:17
  • $\begingroup$ @Slereah very interesting, thank you very much. Amazing, that it refers to Langevin equation (for the dynamical conjugate momentum) and a Fokker-Planck equation (for probability distribution). May you suggest a good comprehensive introduction to this theory (book/article)? $\endgroup$
    – al-Hwarizmi
    Nov 6, 2021 at 16:29

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The probabilistic quantum mechanical approach to relativity is called quantum field theory. The oldest and most well known quantum field theory is quantum electrodynamics. To date, this model is consistent with all known electromagnetic phenomena. Both probability and relativity are built into its foundations.

https://en.wikipedia.org/wiki/Quantum_electrodynamics

https://en.wikipedia.org/wiki/Quantum_field_theory

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  • $\begingroup$ Thank you. As far as I know, these very special fields only address particles. Are there similar theories on rather mesoscopic or macroscopic level? $\endgroup$
    – al-Hwarizmi
    Nov 6, 2021 at 15:53
  • $\begingroup$ Physics at macroscopic scales is not probabilistic $\endgroup$
    – Dale
    Nov 6, 2021 at 23:13
  • $\begingroup$ Oh yes there is. For instance: You can derive macroscopic Langevin equations directly from Fokker Planck or Master equations for Chemical reactions but also the laser. It is generally just a matter of at which level you define your observer. $\endgroup$
    – al-Hwarizmi
    Nov 7, 2021 at 4:05
  • $\begingroup$ I disagree with that interpretation. Ignorance does not imply probabilistic physics. Those equations describe ignorance. Similarly, using strictly non-probabilistic Newtonian physics, like ballistics, you nevertheless come up with a probability density function representing measurement outcomes due to unknown effects such as imperfections in the launching device, disturbances in the environment, and imperfections in the measurement. This is not probabilistic physics. The only place where physics is probabilistic is QFT and QM. $\endgroup$
    – Dale
    Nov 8, 2021 at 17:41

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