IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v27y2006i4p843-849.html
   My bibliography  Save this article

The idealized quantum two-slit gedanken experiment revisited—Criticism and reinterpretation

Author

Listed:
  • El Naschie, Mohamed Saladin

Abstract

An idealized two-slit experiment is envisaged in which the hypothetical experimental set-up is constructed in such a way as to resemble a toy model giving information about the structure of quantum space–time itself. Thus starting from a very simple equation which may be interpreted as a physical realization of Gödel’s undecidability theorem, we proceed to show that space–time is very likely to be akin to a fuzzy Kähler-like manifold on the quantum level. This remarkable manifold transforms gradually into a classical space–time as we decrease the resolution in a way reversibly analogous to the processes of recovering classical space–time from the Riemannian space of general relativity.

Suggested Citation

  • El Naschie, Mohamed Saladin, 2006. "The idealized quantum two-slit gedanken experiment revisited—Criticism and reinterpretation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 843-849.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:4:p:843-849
    DOI: 10.1016/j.chaos.2005.06.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905005679
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.06.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
    2. El Naschie, M.S., 2005. "From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 969-977.
    3. El Naschie, M.S., 2005. "Non-Euclidean spacetime structure and the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 1-6.
    4. El Naschie, M.S., 2005. "Dead or alive: Desperately seeking Schrödinger’s cat," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 673-676.
    5. El Naschie, M.S., 2006. "Hilbert space, the number of Higgs particles and the quantum two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 9-13.
    6. Van Kampen, N.G., 1988. "Ten theorems about quantum mechanical measurements," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 153(1), pages 97-113.
    7. El Naschie, M.S., 2005. "‘t Hooft ultimate building blocks and space–time as an infinite dimensional set of transfinite discrete points," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 521-524.
    8. El Naschie, M.S., 2005. "Spinorial content of the standard model, a different look at super-symmetry and fuzzy E-infinity hyper Kähler," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 303-311.
    9. El Naschie, M.S., 2005. "Einstein’s dream and fractal geometry," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 1-5.
    10. El Naschie, M.S., 2005. "Stability Analysis of the two-slit experiment with quantum particles," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 291-294.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Saadati, Reza & Razani, Abdolrahman & Adibi, H., 2007. "A common fixed point theorem in L-fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 358-363.
    2. Zorlutuna, İdris, 2008. "On strong forms of completely irresolute functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 970-979.
    3. Sedghi, Shaban & Shobe, Nabi & Žikić-Došenović, Tatjana, 2009. "A common fixed point theorem in two complete fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2590-2596.
    4. Yilmaz, Yilmaz, 2009. "Fréchet differentiation of nonlinear operators between fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 473-484.
    5. Azab Abd-Allah, M. & El-Saady, Kamal & Ghareeb, A., 2009. "(r,s)-Fuzzy F-open sets and (r,s)-fuzzy F-closed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 649-656.
    6. Zahran, A.M. & Abd-Allah, M. Azab. & Abd El-Rahman, Abd El-Nasser G., 2009. "Fuzzy weakly preopen (preclosed) function in Kubiak–Šostak fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1158-1168.
    7. Saadati, R. & Sedghi, S. & Shobe, N., 2008. "Modified intuitionistic fuzzy metric spaces and some fixed point theorems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 36-47.
    8. Shams, M. & Vaezpour, S.M., 2009. "Best approximation on probabilistic normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1661-1667.
    9. Sadeqi, I. & Solaty kia, F., 2009. "Some fixed point theorems in fuzzy reflexive Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2606-2612.
    10. Goudarzi, M. & Vaezpour, S.M. & Saadati, R., 2009. "On the intuitionistic fuzzy inner product spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1105-1112.
    11. Saadati, Reza, 2008. "Notes to the paper “Fixed points in intuitionistic fuzzy metric spaces” and its generalization to L-fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 176-180.
    12. Saadati, Reza, 2008. "On the L-fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1419-1426.
    13. Rezaiyan, R. & Cho, Y.J. & Saadati, R., 2008. "A common fixed point theorem in Menger probabilistic quasi-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1153-1157.
    14. Deschrijver, Glad & O’Regan, Donal & Saadati, Reza & Mansour Vaezpour, S., 2009. "L-Fuzzy Euclidean normed spaces and compactness," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 40-45.
    15. Saadati, Reza, 2009. "A note on “Some results on the IF-normed spaces”," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 206-213.
    16. Cho, Yeol Je & Sedghi, Shaban & Shobe, Nabi, 2009. "Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2233-2244.
    17. Mukhamedov, Alfred M., 2007. "The two-slit gedanken experiment in E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 1-4.
    18. Alimohammady, Mohsen & Esmaeli, Abdolreza & Saadati, Reza, 2009. "Completeness results in probabilistic metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 765-769.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Iovane, G., 2006. "Cantorian spacetime and Hilbert space: Part I—Foundations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 857-878.
    2. Agop, M. & Murgulet, C., 2007. "Ball lightning as a self-organizing process of a plasma–plasma interface and El Naschie’s ε(∞) space–time," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 754-769.
    3. Materassi, Massimo & Wernik, Andrzej W. & Yordanova, Emiliya, 2006. "Statistics in the p-model," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 642-655.
    4. Iovane, Gerardo & Giordano, Paola, 2007. "Wavelets and multiresolution analysis: Nature of ε(∞) Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 896-910.
    5. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
    6. Agop, M. & Craciun, P., 2006. "El Naschie’s Cantorian gravity and Einstein’s quantum gravity," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 30-40.
    7. Agop, M. & Craciun, P., 2006. "El Naschie’s ε(∞) space–time and the two slit experiment in the Weyl–Dirac theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 441-452.
    8. Iovane, G., 2007. "Hypersingular integral equations, Kähler manifolds and Thurston mirroring effect in ϵ(∞) Cantorian spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1041-1053.
    9. Agop, M. & Chicos, Liliana & Nica, P., 2009. "Transport phenomena in nanostructures and non-differentiable space–time," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 803-814.
    10. Agop, M. & Vasilica, M., 2006. "El Naschie’s supergravity by means of the gravitational instantons synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 318-323.
    11. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    12. Agop, M. & Nica, P. & Ioannou, P.D. & Malandraki, Olga & Gavanas-Pahomi, I., 2007. "El Naschie’s ε(∞) space–time, hydrodynamic model of scale relativity theory and some applications," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1704-1723.
    13. He, Ji-Huan, 2006. "Application of E-infinity theory to turbulence," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 506-511.
    14. Agop, M. & Abacioaie, D., 2007. "El Naschie’s ε(∞) space–time, interface between Weyl–Dirac bubbles and Cantorian fractal superstring," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 235-243.
    15. Buzea, C. Gh. & Agop, M. & Galusca, G. & Vizureanu, P. & Ionita, I., 2007. "El Naschie’s superconductivity in the time dependent Ginzburg–Landau model," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1060-1074.
    16. Sun, Lei & Cheng, Zhengxing & Huang, Yongdong, 2007. "Construction of trivariate biorthogonal compactly supported wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1412-1420.
    17. Yang, Ciann-Dong, 2007. "The origin and proof of quantization axiom p→pˆ=-iℏ∇ in complex spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 274-283.
    18. Falcón, Sergio & Plaza, Ángel, 2009. "The metallic ratios as limits of complex valued transformations," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 1-13.
    19. Sun, Lei & Zhang, Xiaozhong, 2009. "A note on biorthogonality of the scaling functions with arbitrary matrix dilation factor," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 711-715.
    20. Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:27:y:2006:i:4:p:843-849. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.