IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v38y2008i2p316-331.html
   My bibliography  Save this article

On the existence of complex spacetime in relativistic quantum mechanics

Author

Listed:
  • Yang, Ciann-Dong

Abstract

The infinite dimensional E(∞) space, when viewed at large scales, mimics the appearance of a 4-dimensional complex spacetime. The aim of this paper is to prove the existence of such a complex spacetime in our physical world and to show that what the current relativistic quantum mechanics describes is just the quantum phenomena appeared in this 4-dimensional complex spacetime. We point out that the complex spacetime is a natural consequence of including quantum effects in the relativistic mechanics, and is a bridge connecting the causality in special relativity and the non-locality in quantum mechanics. In other words, extending special relativity to the complex spacetime automatically leads us to the relativistic quantum mechanics. We will see in this paper that the Klein–Gordon equation is a special form of the Hamilton–Jacobi equation when both relativistic and quantum effects are taken into account. The solutions of the relativistic quantum Hamilton equations of motion provide us with a detailed description of the superluminal propagation in entangled states predicted by the Bell’s theorem, and give a new mass–energy relation E=mc21-2Q/(m0c2) that is reduced to the conventional one E=mc2, when the quantum potential Q is neglected.

Suggested Citation

  • Yang, Ciann-Dong, 2008. "On the existence of complex spacetime in relativistic quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 316-331.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:2:p:316-331
    DOI: 10.1016/j.chaos.2008.01.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908000301
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.01.019?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. 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.
    2. Yang, Ciann-Dong & Wei, Chia-Hung, 2007. "Parameterization of all path integral trajectories," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 118-134.
    3. Yang, Ciann-Dong, 2007. "Quantum motion in complex space," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1073-1092.
    4. Yang, Ciann-Dong, 2007. "Complex tunneling dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 312-345.
    5. Yang, Ciann-Dong, 2006. "On modeling and visualizing single-electron spin motion," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 41-50.
    Full references (including those not matched with items on IDEAS)

    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. Yang, Ciann-Dong, 2009. "Stability and quantization of complex-valued nonlinear quantum systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 711-723.
    2. Yang, Ciann-Dong, 2009. "Complex spin and anti-spin dynamics: A generalization of de Broglie–Bohm theory to complex space," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 317-333.
    3. Yang, Ciann-Dong & Weng, Hung-Jen, 2012. "Nonlinear quantum dynamics in diatomic molecules: Vibration, rotation and spin," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 402-415.
    4. Yang, Ciann-Dong & Wei, Chia-Hung, 2007. "Parameterization of all path integral trajectories," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 118-134.
    5. Yang, Ciann-Dong, 2009. "A new hydrodynamic formulation of complex-valued quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 453-468.
    6. Mukhamedov, A.M., 2009. "Meso-structures of dynamical chaos and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1930-1938.
    7. Yang, Ciann-Dong, 2007. "Complex tunneling dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 312-345.
    8. Yang, Ciann-Dong & Weng, Hung- Jen, 2008. "Complex dynamics in diatomic molecules. Part II: Quantum trajectories," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 16-35.
    9. Yang, Ciann-Dong & Wei, Chia-Hung, 2008. "Strong chaos in one-dimensional quantum system," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 988-1001.

    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:38:y:2008:i:2:p:316-331. 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.