Representations of Space-Time and Nonlocality
Abstract
A brief panorama of contemporary researches on the concepts of space, space-time and its relations to nonlocality is presented. In this regard, some historical aspects of the concept of space-time and quantum theory are considered under the perspective of possible connections between them. It is argued that, even though it is accepted the important role of each one for the topic, there are numerous gaps between mathematics, physics and philosophy that deserve further attention on this old theme.
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Arkani-Hamed, N., Boujaily, J., Cachazo, F., Goncharov, A., Postnikov, A., Trnka, J. (2016). Grassmannian geometry of scattering amplitudes. Cambridge: Cambridge U. P.
Ashtekar A., Pullin, J. (eds.) (2017). The Overview Chapter in Loop Quantum Gravity: The First 30 Years, en Loop Quantum Gravity. The first 30 years. World Scientific. New Jersey.
Baez, J. (ed.) (1994). Knots and Quantum Gravity. Oxford: Clarendon Press.
Barrau, A. (2017). Testing different approaches to quantum gravity with cosmology: An overview. arXiv: 1705.01597v1 [gr-qc].
Brans, C. (1994). Exotic smoothness and physics. J. Math. Phys. 35 (10).
Calcagni, G. (2017). Complex dimensions and their observability. arXiv: 1705.01619v1 [gr-qc].
Cao, C., Carroll, S., Michalakis, S. (2016). Space from Hilbert Space: Recovering Geometry from Bulk Entanglement. CALT 2016-15. arXiv: 1606.08444v3 [hep-th].
Carlip, S. (2017). Dimension and Dimensional Reduction in Quantum Gravity. arXiv: 1705.05417v1 [gr-qc].
Collins, H. (2004). Gravity’s Shadow. The Search for Gravitational Waves. Chicago: University of Chicago Press.
Connes, A. (2008). Géométrie Non Commutative. Paris. Dunod.
Connes, A. (2012). On the fine structure of spacetime. En Majid, S. (ed.), On Space and Time. Cambridge: Cambridge U. P.
Connes, A., Marcolli, M. (2008). Noncommutative Geometry, Quantum Fields and Motives. New Delhi: AMS. Hidustan Book Agency.
Dawid, R. (2013). String theory and the scientific method. Cambridge: Cambridge U. P.
De Haro, S., Mayerson, D., Butterfield, J. (2016). Conceptual Aspects of Gauge/Gravity Duality. Found Phys 46: 1381-1425.
Earman, J. (1989). World Enough and Space-Time. Cambridge, Mass: The MIT Press.
Einstein, A. (1916). Approximative Integration of the Field Equations of Gravitation. Traducido en: Engel, A., Translator; Schucking E., Consultant: The Collected Papers of Albert Einstein, Vol. 6: The Berlin Years: Writings, 1914- 1917, 1997. New Jersey: Princeton U. P.
Fearnley-Sander, D. (1979). Hermann Grassmann and the Creation of Linear Algebra. Am. Math. Monthly 86, 809-817.
Gauss, C. (1900). Werke Vol. III. Leipzig: Teubner. (carta a Bessel de 1830).
Giustina, M. (2017). On Loopholes and Experiments. En R. Bertlmann and A. Zeilinger (eds), Quantum [Un]Speakables II. Half a Century of Bell’s Theorem. The Frontiers Collection. Cham: Springer.
Grassmann, H. (1947). Teoría de la Extensión. Buenos Aires: Espasa-Calpe.
Hawking, S., Ellis, G. (1973). The large scale structure of space-time. New York: Cambridge U. P.
Hubeny, V. (2015). The AdS/CFT Correspondence. arXiv: 1501.00007v2 [gr-qc].
Hurewicz, W., Wallman, H. (1941). Dimension Theory. Princeton: Princeton Math. Series.
James, I. (ed.) (1999). History of Topology. New York: Elsevier.
Kennefick, D. (2007). Traveling at the speed of thought: Einstein and the Quest for Gravitational Waves. Princeton: Princeton U. P.
Kerszberg, P. (1989). The Invented Universe. Oxford: Clarendon Press.
Lucas, J., Hobson, P. (1990). Spacetime and electromagnetism. New York: Oxford U. P.
Maldacena, J. (1997). The Large N Limit of Superconformal field and supergravity. hep-th/9711200 HUTP-97/A097.
Maldacena, J., Susskind L. (2013). Cool horizons for entangled black holes. arXiv: 1306.0533v2 [hep-th].
Manin, Y. (2005). The notion of dimensión in geometry and algebra. arXiv: math/0502016v1 [math.AG].
Maudlin, T. (2002). Quantum Non-Locality and Relativity. Second edition. Oxford: Blackwell Pub.
Mazur, B. (1997). Conjecture. Synthese, 111, 197-210.
Molina, J. (2011). Fragmentos de Arquíloco. México: Textofilia S.C., Colección Ión.
Musser, G. (2015). Spooky Action at a Distance. New York: Scientific American/ Farrar, Straus and Giroux.
Nagata, J. (1983). Modern Dimension Theory. Berlin: Heldermann Verlag.
Newton, I. (2004). Isaac Newton: Philosophical Writings. Ed. A. Janiak. Cambridge: Cambridge U. P.
Oriti, D. (ed.) (2009). Approaches to Quantum Gravity. Cambridge: Cambridge U. P.
Penrose, R. (1967). Twistor Algebra. J. of Math. Physics, 8 (2), 345.
Pérez, A. (2017). Black Holes in Loop Quantum Gravity. arXiv: 1703.09149v1 [gr-qc].
Rodríguez, V. (2013). El efecto Hall y sus contextos. Scientiae Studia 11(1). San Pablo, Brasil.
Rovelli, C. (2004). Quantum Gravity. Cambridge: Cambridge U. P.
Rangamani, M., Takayanagi, T. (2017). Holographic Entanglement Entropy. Cham: Springer.
Saunders, S., Brown H. (eds.) (1991). The Philosophy of Vacuum. Oxford: Clarendon Press.
Siegfried, T. (2014). Einstein was wrong about spooky quantum entanglement. ScienceNews (On line), Feb. 19.
‘t Hooft, G. (1993). Dimensional reduction in quantum gravity. THU-93/26. gr-qc/9310026.
Van Dongen, J. (2010). Einstein’s Unification. New York: Cambridge U. P.
Van Raamsdonk, M. (2016). Lectures on Gravity and Entanglement. arXiv: 1609.00026v1 [hep-th].
Weinberg, S. (2008). Cosmology. Oxford: Oxford U. P.
Yau, S.-T. (2010). The Shape of Inner Space. New York: Perseus Books Group.
Ashtekar A., Pullin, J. (eds.) (2017). The Overview Chapter in Loop Quantum Gravity: The First 30 Years, en Loop Quantum Gravity. The first 30 years. World Scientific. New Jersey.
Baez, J. (ed.) (1994). Knots and Quantum Gravity. Oxford: Clarendon Press.
Barrau, A. (2017). Testing different approaches to quantum gravity with cosmology: An overview. arXiv: 1705.01597v1 [gr-qc].
Brans, C. (1994). Exotic smoothness and physics. J. Math. Phys. 35 (10).
Calcagni, G. (2017). Complex dimensions and their observability. arXiv: 1705.01619v1 [gr-qc].
Cao, C., Carroll, S., Michalakis, S. (2016). Space from Hilbert Space: Recovering Geometry from Bulk Entanglement. CALT 2016-15. arXiv: 1606.08444v3 [hep-th].
Carlip, S. (2017). Dimension and Dimensional Reduction in Quantum Gravity. arXiv: 1705.05417v1 [gr-qc].
Collins, H. (2004). Gravity’s Shadow. The Search for Gravitational Waves. Chicago: University of Chicago Press.
Connes, A. (2008). Géométrie Non Commutative. Paris. Dunod.
Connes, A. (2012). On the fine structure of spacetime. En Majid, S. (ed.), On Space and Time. Cambridge: Cambridge U. P.
Connes, A., Marcolli, M. (2008). Noncommutative Geometry, Quantum Fields and Motives. New Delhi: AMS. Hidustan Book Agency.
Dawid, R. (2013). String theory and the scientific method. Cambridge: Cambridge U. P.
De Haro, S., Mayerson, D., Butterfield, J. (2016). Conceptual Aspects of Gauge/Gravity Duality. Found Phys 46: 1381-1425.
Earman, J. (1989). World Enough and Space-Time. Cambridge, Mass: The MIT Press.
Einstein, A. (1916). Approximative Integration of the Field Equations of Gravitation. Traducido en: Engel, A., Translator; Schucking E., Consultant: The Collected Papers of Albert Einstein, Vol. 6: The Berlin Years: Writings, 1914- 1917, 1997. New Jersey: Princeton U. P.
Fearnley-Sander, D. (1979). Hermann Grassmann and the Creation of Linear Algebra. Am. Math. Monthly 86, 809-817.
Gauss, C. (1900). Werke Vol. III. Leipzig: Teubner. (carta a Bessel de 1830).
Giustina, M. (2017). On Loopholes and Experiments. En R. Bertlmann and A. Zeilinger (eds), Quantum [Un]Speakables II. Half a Century of Bell’s Theorem. The Frontiers Collection. Cham: Springer.
Grassmann, H. (1947). Teoría de la Extensión. Buenos Aires: Espasa-Calpe.
Hawking, S., Ellis, G. (1973). The large scale structure of space-time. New York: Cambridge U. P.
Hubeny, V. (2015). The AdS/CFT Correspondence. arXiv: 1501.00007v2 [gr-qc].
Hurewicz, W., Wallman, H. (1941). Dimension Theory. Princeton: Princeton Math. Series.
James, I. (ed.) (1999). History of Topology. New York: Elsevier.
Kennefick, D. (2007). Traveling at the speed of thought: Einstein and the Quest for Gravitational Waves. Princeton: Princeton U. P.
Kerszberg, P. (1989). The Invented Universe. Oxford: Clarendon Press.
Lucas, J., Hobson, P. (1990). Spacetime and electromagnetism. New York: Oxford U. P.
Maldacena, J. (1997). The Large N Limit of Superconformal field and supergravity. hep-th/9711200 HUTP-97/A097.
Maldacena, J., Susskind L. (2013). Cool horizons for entangled black holes. arXiv: 1306.0533v2 [hep-th].
Manin, Y. (2005). The notion of dimensión in geometry and algebra. arXiv: math/0502016v1 [math.AG].
Maudlin, T. (2002). Quantum Non-Locality and Relativity. Second edition. Oxford: Blackwell Pub.
Mazur, B. (1997). Conjecture. Synthese, 111, 197-210.
Molina, J. (2011). Fragmentos de Arquíloco. México: Textofilia S.C., Colección Ión.
Musser, G. (2015). Spooky Action at a Distance. New York: Scientific American/ Farrar, Straus and Giroux.
Nagata, J. (1983). Modern Dimension Theory. Berlin: Heldermann Verlag.
Newton, I. (2004). Isaac Newton: Philosophical Writings. Ed. A. Janiak. Cambridge: Cambridge U. P.
Oriti, D. (ed.) (2009). Approaches to Quantum Gravity. Cambridge: Cambridge U. P.
Penrose, R. (1967). Twistor Algebra. J. of Math. Physics, 8 (2), 345.
Pérez, A. (2017). Black Holes in Loop Quantum Gravity. arXiv: 1703.09149v1 [gr-qc].
Rodríguez, V. (2013). El efecto Hall y sus contextos. Scientiae Studia 11(1). San Pablo, Brasil.
Rovelli, C. (2004). Quantum Gravity. Cambridge: Cambridge U. P.
Rangamani, M., Takayanagi, T. (2017). Holographic Entanglement Entropy. Cham: Springer.
Saunders, S., Brown H. (eds.) (1991). The Philosophy of Vacuum. Oxford: Clarendon Press.
Siegfried, T. (2014). Einstein was wrong about spooky quantum entanglement. ScienceNews (On line), Feb. 19.
‘t Hooft, G. (1993). Dimensional reduction in quantum gravity. THU-93/26. gr-qc/9310026.
Van Dongen, J. (2010). Einstein’s Unification. New York: Cambridge U. P.
Van Raamsdonk, M. (2016). Lectures on Gravity and Entanglement. arXiv: 1609.00026v1 [hep-th].
Weinberg, S. (2008). Cosmology. Oxford: Oxford U. P.
Yau, S.-T. (2010). The Shape of Inner Space. New York: Perseus Books Group.
Rodríguez, V. (2018). Representations of Space-Time and Nonlocality. Artefactos. Philosophical Studies on Science and Technology, 7(2), 145–164. https://doi.org/10.14201/art201872145164
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