.png)
Information Without Matter: Can Spacetime Store Information?
Author: Thamansri Varma Gadhiraju
Editor's note
This article presents Spatiotemporal Information Theory (SIT) as an exploratory interpretation of existing physics, and not a new theory with predictive power. Also, the Bekenstein entropy bound discussed in Section 5 is distinct from the holographic area bound, and Figure 3 should be treated as a qualitative illustration only.
Abstract
Information is usually thought of as something that must be stored inside a physical object: a hard drive stores information as electric charge, a book stores it as ink on paper, and a strand of DNA stores it as an ordered sequence of molecules. Modern theoretical physics, however, raises a strange and still-unresolved possibility: information may not always require ordinary matter to hold it. According to general relativity, spacetime itself is a dynamical object that bends and ripples in response to matter and energy, and these geometric changes appear to carry physical information from place to place. Black holes push this idea to its limit. The entropy of a black hole – a direct measure of the information associated with it – is proportional not to its volume, as ordinary thermodynamics would suggest, but to the surface area of its event horizon. This single fact, first proposed by Bekenstein and later placed on firm footing by Hawking, seeded an entire research program connecting gravity, geometry, and information theory, culminating in the holographic principle and the discovery (via the AdS/CFT correspondence) that a gravitational theory in a volume of spacetime can be exactly equivalent to a non-gravitational quantum theory living on its boundary. This paper surveys the chain of evidence connecting spacetime to information: general relativity and the dynamics of geometry, the no-hair theorem and the black-hole information problem, Bekenstein-Hawking entropy, Hawking radiation and the Page curve, the holographic principle and AdS/CFT, the ER = EPR conjecture linking quantum entanglement to spacetime connectivity, and the direct detection of gravitational waves by LIGO as physical carriers of information. To organize this evidence, the paper proposes Spatiotemporal Information Theory (SIT), an interpretive framework – not a new physical theory in the technical sense, but a way of stating explicitly what the surveyed results jointly imply – which holds that spacetime geometry and physical information are two expressions of a single underlying structure rather than a container and its contents. None of the evidence reviewed here proves that spacetime is literally a hard drive. It does, however, build a strong cumulative case that geometry and information are far more intertwined than classical physics ever anticipated, and that a future theory of quantum gravity may need to treat information – not matter – as the truly fundamental ingredient of reality.
Keywords: spacetime, information theory, black holes, Bekenstein-Hawking entropy, holographic principle, AdS/CFT, quantum entanglement, gravitational waves, quantum gravity, Spatiotemporal Information Theory (SIT)
Read online
Please click here to read this article online.
Download PDF
References
[1] Bekenstein, J. D. (1973). Black holes and entropy. Physical Review D, 7(8), 2333–2346.
[2] Bekenstein, J. D. (1981). Universal upper bound on the entropy-to-energy ratio for bounded systems. Physical Review D, 23(2), 287–298.
[3] Hawking, S. W. (1975). Particle creation by black holes. Communications in Mathematical Physics, 43, 199–220.
[4] Page, D. N. (1993). Information in black hole radiation. Physical Review Letters, 71(23), 3743–3746.
[5] ’t Hooft, G. (1993). Dimensional reduction in quantum gravity. arXiv preprint gr-qc/9310026.
[6] Susskind, L. (1995). The world as a hologram. Journal of Mathematical Physics, 36(11), 6377–6396.
[7] Maldacena, J. (1998). The large N limit of superconformal field theories and supergravity. Advances in Theoretical and Mathematical Physics, 2, 231–252.
[8] Ryu, S., & Takayanagi, T. (2006). Holographic derivation of entanglement entropy from AdS/CFT. Physical Review Letters, 96, 181602.
[9] Maldacena, J., & Susskind, L. (2013). Cool horizons for entangled black holes. Fortschritte der Physik, 61(9), 781–811.
[10] Abbott, B. P., et al. (LIGO Scientific Collaboration and Virgo Collaboration). (2016). Observation of gravitational waves from a binary black hole merger. Physical Review Letters, 116, 061102.
[11] Penington, G. (2020). Entanglement wedge reconstruction and the information paradox. Journal of High Energy Physics, 2020(9), 2.
[12] Almheiri, A., Engelhardt, N., Marolf, D., & Maxfield, H. (2019). The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole. Journal of High Energy Physics, 2019, 63.
[13] Israel, W. (1967). Event horizons in static vacuum spacetimes. Physical Review, 164(5), 1776–1779.
[14] Einstein, A. (1915). Die Feldgleichungen der Gravitation. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, 844–847.
[15] Einstein, A., & Rosen, N. (1935). The particle problem in the general theory of relativity. Physical Review, 48(1), 73–77.
[16] Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47(10), 777–780.
[17] Carter, B. (1971). Axisymmetric black hole has only two degrees of freedom. Physical Review Letters, 26(6), 331–333.
[18] Wheeler, J. A. (1990). Information, physics, quantum: The search for links. In Complexity, Entropy, and the Physics of Information (pp. 3–28). Addison-Wesley.
[19] Van Raamsdonk, M. (2010). Building up spacetime with quantum entanglement. General Relativity and Gravitation, 42(10), 2323–2329.
[20] Tiesinga, E., Mohr, P. J., Newell, D. B., & Taylor, B. N. (2021). CODATA recommended values of the fundamental physical constants: 2018. Reviews of Modern Physics, 93(2), 025010. Used here via the scipy.constants Python module for the numerical estimates in Section 10.
Comments