[go: up one dir, main page]
Skip to main content
SpringerLink
Log in

A Case Study for Leibnizian Ideas in Wolfram Model

  • Research
  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

We study implications of Leibnizian ideas such as the identity of indiscernibles, and variety (due to Barbour and Smolin) in the context of Wolfram Model, which has been put forward in 2020. We have provided (at the moment) speculative interpretations for Leibnizian and non-Leibnizian hypergraphs. We introduced an action based on variety, to select paths where it is maximized. The specific universe which is of concern here is the one with name ‘wm1268’ from the Registry of Notable Universe Models, which is used as a test case in the present study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. The idea is proposed by Deutsch and used by Barbour and Smolin in Ref. [3] where reference to Deutsch is given. Hence we use these three names to denote the specific choice of variety function we employ in the study. The word ‘BSD’ should not to be confused with the operating system with the same name, where the word BSD is an acronym for ‘Berkeley Software Distribution.’

References

  1. Adamo, T.: Lectures on twistor theory. http://arxiv.org/abs/1712.02196 (2018)

  2. Alexander, S., Cunningham, W.J., Lanier, J., Smolin, L. Stanojevic, S., Toomey, M.W., Wecker, D.: The autodidactic universe. arXiv preprint http://arxiv.org/abs/2104.03902 (2021)

  3. Barbour, J., Smolin, L.: Extremal variety as the foundation of a cosmological quantum theory. http://arxiv.org/abs/hep-th/9203041 (1992)

  4. Barbour, J.: Shape dynamics. An introduction. In: Quantum Field Theory and Gravity: Conceptual and Mathematical Advances in the Search for a Unified Framework, pp. 257–297. Springer (2012). http://arxiv.org/abs/arXiv:1105.0183

  5. Barbour, J.: The End of Time: The Next Revolution in Physics. Oxford University Press, New York (2000)

    Google Scholar 

  6. Dündar, S.F: Wolfram model variety. https://github.com/fsdundar/wolfram-model-variety (2023)

  7. Dündar, F.S.: A use of variety as a law of the universe. Complex Syst. 31(2), 247–260 (2022)

    Article  Google Scholar 

  8. Gorard, J., Dannemann-Freitag, J.: Axiomatic quantum field theory in discrete spacetime via multiway causal structure: The case of entanglement entropies. (2023). http://arxiv.org/abs/arXiv:2301.12455

  9. Gorard, J.: Algorithmic causal sets and the wolfram model. (2021). http://arxiv.org/abs/arXiv:2011.12174

  10. Gorard, J.: Hypergraph discretization of the Cauchy problem in general relativity via wolfram model evolution. (2021). http://arxiv.org/abs/arXiv:2102.09363

  11. Gorard, Jonathan: Some quantum mechanical properties of the wolfram model. Complex Syst. 29, 537–598 (2020)

    Article  Google Scholar 

  12. Gorard, Jonathan: Some relativistic and gravitational properties of the wolfram model. Complex Systems 29, 599–654 (2020)

    Article  Google Scholar 

  13. Hossenfelder, S.: Existential Physics: A Scientist’s Guide to Life’s Biggest Questions. Atlantic Books, London (2022)

    Google Scholar 

  14. Huggett, S.A., Tod, K.P.: An Introduction to Twistor Theory, vol. 4. Cambridge University Press, Cambridge (1994)

    Book  Google Scholar 

  15. Leibniz, G.W.: Discourse on Metaphysics and the Monadology. Courier Corporation. (2005)

  16. Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Sov. Phys. Dokl. 10, 707–710 (1966)

    MathSciNet  ADS  Google Scholar 

  17. Penrose, R.: Twistor algebra. J. Math.l Phys. 8(2), 345–366 (1967)

    Article  MathSciNet  ADS  Google Scholar 

  18. Semih Dündar, F.: Maximal variety Leibnizian strings for large \(N\). In: 9th International Congress on Fundamental and Applied Sciences (2022)

  19. Smolin, L.: Views, variety and celestial spheres. arXiv preprint http://arxiv.org/abs/arXiv:2202.00594 (2022)

  20. Smolin, L.: Views, variety and quantum mechanics. arXiv preprint http://arxiv.org/abs/arXiv:2105.03539 (2021)

  21. Surya, S.: The causal set approach to quantum gravity. Living Rev. Relativ. 22, 1–75 (2019)

    Article  ADS  Google Scholar 

  22. Universe 1268 from the wolfram physics project. https://www.wolframphysics.org/universes/wm1268/ Accessed 4th June 2024

  23. Wolfram Research, Inc. Mathematica, Version 13.2. Champaign, (2022)

  24. Wolfram, S.: A class of models with the potential to represent fundamental physics. Complex Syst. 29, 107–536 (2020)

    Article  Google Scholar 

  25. Wolfram, S.: A Project to Find the Fundamental Theory of Physics. Wolfram Media, New York (2020)

    Google Scholar 

Download references

Acknowledgements

This study has been supported by a TÜBİTAK 1002-A project under the grant number 122F297. We would like to thank the anonymous referee with whose comments the paper has much improved. We are grateful to Tınaz Ekim for useful discussions. The numerical calculations reported in this paper were partially performed at Harran University High Performance Computing Center (Harran HPC resources). We would like to thank Abdulkerim Eneş for help as regards the use of the mentioned HPC environment. The codes we developed for this study is available in Ref. [6] under the GPLv3 license. All the figures have been drawn with Mathematica [23].

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Amasya University, Amasya, 05100, Turkey

    Furkan Semih Dündar

Authors
  1. Furkan Semih Dündar
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

F.S.D. did the whole work in preparation of the manuscript. This includes writing the article, drawing plots, and numerical calculations

Corresponding author

Correspondence to Furkan Semih Dündar.

Ethics declarations

Conflict of interest

The authors have no Conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Statistics

Statistics

In this Appendix, we will provide statistics about the multiway system. Here we consider a bigger multiway system that is three steps bigger than the earlier representations, and it describes the same universe. In Table 1 we have given information on the number of all paths, physical paths and paths of maximum action, for each depth. Because we begin with the second node in the multiway system (since it is Leibnizian) the depth value begins with 3 and ends with 9.

Table 1 Number of paths as a function of depth in the multiway system. Since paths start from the second vertex, depth begins with three
Full size table

As the multiway system expands, new configurations are obtained. Hence, it is expected that the maximum value of action increases. The value of maximum action is plotted in Fig. 11.

Fig. 11
figure 11

Plot of maximum action as a function of depth in the multiway system. The values are as follows: {{3, 5}, {4, 9}, {5, 14}, {6, 20}, {7, 27}, {8, 35}, {9, 44}}. First value is depth, and the second one is maximum action. Figure drawn with Mathematica [23]

Full size image

Moreover, it is useful to plot the density of physical and maximum action paths in the space of all possible paths. It can be seen in Fig. 12.

Fig. 12
figure 12

Plot for density of physical and maximum action paths in the space of all possible paths. Figure drawn with Mathematica [23]

Full size image

We finish this part by providing how physical and maximum action paths propagate in the multiway system, as a function of depth. For that purpose we plotted the full multiway system (not layer by layer since it would be impossible to discern features in the scale of A4 paper), then by increasing the step, we highlighted physical and maximum action paths. Please see Fig. 13.

Fig. 13
figure 13

Propagation of physical and maximum action paths in the multiway system, as the depth increases. Paths colored red are physical paths, whereas the paths colored blue are of maximum action paths, which are a subset of physical paths. When color is not available, the highlighted regions are made thick. Most of the thick lines are red (physical paths). Figure drawn with Mathematica [23]

Full size image

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dündar, F.S. A Case Study for Leibnizian Ideas in Wolfram Model. Found Phys 54, 43 (2024). https://doi.org/10.1007/s10701-024-00777-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10701-024-00777-3

Keywords

Search

Navigation