مقالۀ پژوهشی: تاثیر اصل عدم قطعیت تعمیم یافته با طول بیشینه براندازه کوتوله های سفید

نوع مقاله : مقاله پژوهشی

نویسنده

استادیار، گروه فیزیک، واحد کرمانشاه، دانشگاه آزاد اسلامی، کرمانشاه، ایران

چکیده

چالش در توسعه نظریه گرانش کوانتومی ناشی از روش‌های اساسی متفاوتی است که این دو نظریه برای شرح سامانه‌های فیزیکی به کار می‌برند. مکانیک کوانتومی بر اساس اصول گسسته و احتمالی عمل می‌کند، در حالی که نسبیت عام یک نظریه پیوسته و قطعی است. اصل عدم‌قطعیت تعمیم‌یافته یک نسخه اصلاح‌شده از اصل عدم‌قطعیت هایزنبرگ است که اصلاحات گرانشی کوانتومی را در سامانه‌هایی با گرانش قوی اعمال می‌کند. نمونه بارزی از این سامانه‌ها کوتوله‌های سفید هستند. در کوتوله‌های سفید فشارتبهگنی پشتیبانی لازم را در برابر فروپاشی گرانشی فراهم می‌کند. با این وجود، نشان داده شده است که اصل عدم‌قطعیت تعمیم‌یافته در حضور طول کمینه، حد چاندراسخار را نفی می‌کند و به کوتوله‌های سفید اجازه می‌دهد تا به هر اندازه نامحدودی  بزرگ شوند، که این خود در تضاد با مشاهدات اختر فیزیکی می‌باشد. این مقاله رابطه بین فشار تبهگنی و چگالی در کوتوله‌های سفید را با استفاده از یک شکل جایگزین از اصل عدم‌قطعیت که بیشینه طول را در برمی‌گیرد، اصلاح می‌کند. ما نشان می‌دهیم که این فرمالیزم جدید حد چاندراسخار را بازیابی می‌کند و اختلاف بین نظریه و مشاهده را برطرف می‌کند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Research Paper: The Effect of the Generalized Uncertainty Principle with Maximum Length on the Size of White Dwarfs

نویسنده [English]

  • Sajad Parsamehr
Assistant Professor,Department of Physics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
چکیده [English]

The challenge in developing a theory of quantum gravity stems from the fundamentally different ways the two theories describe physical systems. Quantum mechanics operates on discrete, probabilistic principles, while general relativity is a continuous, deterministic theory. The generalized uncertainty principle is a modified version of Heisenberg's uncertainty principle that applies quantum gravitational corrections to systems with strong gravity. As a clear example of these systems, white dwarfs can be mentioned. In white dwarfs, the gravitational pressure provides the necessary support against gravitational collapse, however, the generalized uncertainty principle has been shown to negate the Chandrasekhar limit in the presence of a minimum length, allowing white dwarfs to grow to any size, even infinitely large, which is in contradiction with physical astrophysical observations. This paper modifies the relationship between degeneracy pressure and density in white dwarfs using an alternative form of the uncertainty principle that incorporates a maximum length. We demonstrate that this new formalism recovers the Chandrasekhar limit and resolves the discrepancy between theory and observation.

کلیدواژه‌ها [English]

  • Generalized Uncertainty Principle
  • Quantum Gravity
  • Chandrasekhar Limit
  • White Dwarfs
  • Maximum Length

مراجع

[1] Snyder, H.S., "Quantized space-time", Physical Review 71(1), 38, 1947. https://link.aps.org/doi/10.1103/PhysRev.71.38.
[2] Mead, C.A., "Possible connection between gravitation and fundamental length", Physical Review 135(3B), B849, 1964. https://doi.org/10.1103/PhysRev.135.B849.
[3] Amati, D., Ciafaloni, M. and Veneziano, G., "Superstring collisions at Planckian energies", Physics Letters B 197(1-2), 81-88, 1987. https://doi.org/10.1016/0370-2693(87)90346-7.
[4] Capozziello, S., Lambiase, G. and Scarpetta, G., "Generalized uncertainty principle from quantum geometry", Int. J. Theor. Phys., 39, 15–22, 2000. https://doi.org/10.1023/A:1003634814685.
[5] Maggiore, M., "A generalized uncertainty principle in quantum gravity", Physics Letters B 304(1-2), 65-69, 1993. https://doi.org/10.1016/0370-2693(93)91401-8.
[6] Kempf, A., Mangano, G. and Mann, R.B., "Hilbert space representation of the minimal length uncertainty relation", Physical Review D 52(2), 1108, 1995. https://link.aps.org/doi/10.1103/PhysRevD.52.1108.
[7] Scardigli, F., "Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment", Physics Letters B 452(1-2), 39-44, 1999. https://doi.org/10.1016/S0370-2693(99)00167-7.
[8] Scardigli, F. and Casadio, R., "Generalized uncertainty principle, extra dimensions and holography", Classical and Quantum Gravity 20(18), 3915, 2003. https://dx.doi.org/10.1088/0264-9381/20/18/305.
[9] Bizet, N.C., Obregón, O. and Yupanqui, W., "Modified entropies as the origin of generalized uncertainty principles", Physics Letters B 836, 137636, 2023. https://doi.org/10.1016/j.physletb.2022.137636.
[10] Ali, A.F. and Wojnar, A., "A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound", Classical and Quantum Gravity 41(10), 105001, 2024. https://dx.doi.org/10.1088/1361-6382/ad3ac7.
[11] Bishop, M., Lee, J. and Singleton, D., "Modified commutators are not sufficient to determine a quantum gravity minimal length scale", Physics Letters B 802, 135209, 2020. https://doi.org/10.1016/j.physletb.2020.135209.
[12] Contreras, E. and Bargueño, P., "Scale-dependent Hayward black hole and the generalized uncertainty principle", Modern Physics Letters A 33(32), 1850184, 2018. http://dx.doi.org/10.1142/S0217732318501845.
[13] Pedram, P., "A higher order GUP with minimal length uncertainty and maximal momentum II: Applications", Physics Letters B 718(2), 638-645, 2012. http://dx.doi.org/10.1016/j.physletb.2012.07.005.
[14] Bouaziz, D. and Ferkous, N., "Hydrogen atom in momentum space with a minimal length", Physical Review A—Atomic, Molecular, and Optical Physics 82(2), 022105, 2010. http://dx.doi.org/10.1103/PhysRevA.82.022105.
[15] Brau, F. and Buisseret, F., "Minimal length uncertainty relation and gravitational quantum well", Physical Review D—Particles, Fields, Gravitation, and Cosmology 74(3), 036002, 2006. http://dx.doi.org/10.1103/PhysRevD.74.036002.
[16] Nozari, K. and Etemadi, A., "Minimal length, maximal momentum, and Hilbert space representation<? format?> of quantum mechanics", Physical Review D—Particles, Fields, Gravitation, and Cosmology 85(10), 104029, 2012. http://dx.doi.org/10.1103/PhysRevD.85.104029.
[17] Yu, B. and Long, Z.W., "Black hole evaporation and its remnants with the generalized uncertainty principle including a linear term", Communications in Theoretical Physics 76(2), 025404, 2024. https://iopscience.iop.org/article/10.1088/1572-9494/ad1b49.
[18] Benhadjira, A., Benkrane, A., Bentouila, O., Benzair, H. and Aiadi, K.E., "One dimensional Bose–Einstein condensate under the effect of the extended uncertainty principle", Physica Scripta 99(5), 055224, 2024. https://iopscience.iop.org/article/10.1088/1402-4896/ad3864.
[19] Baradaran, M., Nieto, L.M. and Zarrinkamar, S., "On some quantum correction to the Coulomb potential in generalized uncertainty principle approach", Physics Letters B 852, 138603, 2024. https://doi.org/10.1016/j.physletb.2024.138603.
[20] Tang, M., "Weak cosmic censorship conjecture and black hole shadow for black hole with generalized uncertainty principle", The European Physical Journal C 84(4), 396, 2024. https://doi.org/10.1140/epjc/s10052-024-12641-9.
[21] Ong, Y.C., "A critique on some aspects of GUP effective metric", The European Physical Journal C 83(3), 209, 2023. https://doi.org/10.1140/epjc/s10052-023-11360-x.
[22] Perivolaropoulos, L., "Cosmological horizons, uncertainty principle, and maximum length quantum mechanics", Physical Review D 95(10), 103523, 2017. https://link.aps.org/doi/10.1103/PhysRevD.95.103523.
[23] Skara, F. and Perivolaropoulos, L., "Primordial power spectra of cosmological fluctuations with generalized uncertainty principle and maximum length quantum mechanics", Physical Review D 100(12), 123527, 2019. https://link.aps.org/doi/10.1103/PhysRevD.100.123527.
[24] Mureika, J.R., "Extended uncertainty principle black holes", Physics Letters B 789, 88-92, 2019. https://doi.org/10.1016/j.physletb.2018.12.009.
[25] Bensalem, S. and Bouaziz, D., "On the thermodynamics of relativistic ideal gases in the presence of a maximal length", Physics Letters A 384(36), 126911, 2020. https://doi.org/10.1016/j.physleta.2020.126911.
[26] Bensalem, S. and Bouaziz, D., "Statistical description of an ideal gas in maximum length quantum mechanics", Physica A: Statistical Mechanics and its Applications 523, 583-592, 2019. https://doi.org/10.1016/j.physa.2019.02.033.
[27] Ong, Y.C., "Generalized uncertainty principle, black holes, and white dwarfs: a tale of two infinities", Journal of Cosmology and Astroparticle Physics 2018(09), 015, 2018. https://dx.doi.org/10.1088/1475-7516/2018/09/015.
[28] Low, A.M., "Space-time is doomed! Introducing Planck scale physics in the classroom", Physics Education 59(1), 015013, 2023. https://dx.doi.org/10.1088/1361-6552/acfe54.
[29] Griffiths, D.J. and Schroeter, D.F., Introduction to quantum mechanics. Cambridge university press, 2019.
[30] Schürmann, T., "Uncertainty principle on 3-dimensional manifolds of constant curvature", Foundations of Physics 48, 716-725, 2018. https://doi.org/10.1007/s10701-018-0173-0.
[31] Pachoł, A., "Generalized Extended Uncertainty Principles, Liouville theorem and density of states: Snyder-de Sitter and Yang models", Nuclear Physics B, 116771, 2024. https://doi.org/10.48550/arXiv.2409.05110
[32] Ahmadi, S., Yusofi, E. and Ramzanpour, M.A., "Incorporating the cosmological constant in a modified uncertainty principle", Modern Physics Letters A 39(27n28), 2450125, 2024. https://doi.org/10.1142/S0217732324501256
[33] Ong, Y.C., "Schwinger pair production and the extended uncertainty principle: can heuristic derivations be trusted?", The European Physical Journal C 80(8), 777, 2020. https://doi.org/10.1140/epjc/s10052-020-8363-2

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  • تاریخ دریافت: 20 مهر 1403
  • تاریخ بازنگری: 13 دی 1403
  • تاریخ پذیرش: 23 دی 1403

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