Foundations References

Below is a list of foundation-related references that are of particular use to our research in the Knuth Information Physics Lab (including our own papers).

Ahluwalia, D.V., Labun, L., Torrieri, G. 2015. The Unruh effect and oscillating neutrinos. Honorable mention, Gravity Research Foundation essay competition. arXiv:1505.04082 [hep-ph]

Akemann, G. 2016. Random matrix theory and quantum chromodynamics. Les Houches lecture notes, Session July 2015. arXiv:1603.06011 [math-ph]

Arnault, P.; Debbasch, F. 2016. Quantum Walks and discrete gauge theories. arXiv:1508.00038 [quant-ph]

Baez, J.C. 2016. Struggles with the continuum. arXiv:1609.01421 [math-ph]

Barcelo', C.; Carballo-Rubio, R. and Luis J. Garay. 2017. Weyl relativity: A novel approach to Weyl's ideas arXiv:1703.06355 [gr-qc]

Baierlein, R. Two myths about special relativity. Am. J. Phys. 74, 193-195.
pdf here

Bialynicki-Birula, I. 1994. Weyl, Dirac, and Maxwell equations on a lattice as unitary cellular automata. Physical Review D, 49(12), 6920. (arXiv:hep-th/9304070)

Bekenstein, J.D. 2003. Information in the holographic universe. Scientific American, 289(2), 58-65.

Bisio, A., D'Ariano, G.M., Perinotti, P. 2015. Lorentz symmetry for 3d quantum cellular automata
arXiv:1503.01017 [quant-ph]

Bock, R.D. 2015. Gauge Theory of the Gravitational-Electromagnetic Field arXiv:1505.04133 [gr-qc]

Bombelli, L., Lee, J., Meyer, D., Sorkin, R.D. 1987. Space-time as a causal set. Physical review letters, 59(5), 521.

Bondi, H. 1966. The teaching of special relativity Phys. Educ. 1, 223-227.

Bondi, H. 1980. Relativity and common sense: a new approach to Einstein. Courier Corporation.

Breit, G. 1928. An Interpretation of Dirac’s Theory of the Electron. Proceedings of the National Academy of Sciences of the United States of America, 14(7), 553–559.

Carlip, S. 2015. Dimensional reduction in causal set gravity. Class. Quantum Grav. 32 (2015) 232001. arXiv:1506.08775 [gr-qc]

Carlip, S. 2017 Dimension and Dimensional Reduction in Quantum Gravity arXiv:1705.05417 [gr-qc]

Chern, S.S. 1990. What is geometry? Am. Math. Mon. 97, 679-686.
pdf here

Caticha, A. 2011. Entropic dynamics, time and quantum theory. Journal of Physics A: Mathematical and Theoretical, 44(22), 225303. (arXiv:1005.2357 [quant-ph])

Caticha, A. 2009. From entropic dynamics to quantum theory. (arXiv:0907.4335 [quant-ph])

Caticha, A. 2000. Insufficient reason and entropy in quantum theory. Foundations of Physics, 30(2), 227-251. (arXiv:quant-ph/9810074)

Caticha, A. 1998. Consistency, amplitudes, and probabilities in quantum theory. Physical Review A, 57(3), 1572. ()

Caticha, A. 1998. Consistency and linearity in quantum theory. Physics Letters A, 244(1), 13-17. (arXiv:quant-ph/9803086)

Cavalleri, G. 1985. Schroedinger’s equation as a consequence of Zitterbewegung. Lettere Al Nuovo Cimento Series 2, 43(6), 285-291.

Chappell, J.M., Hartnett, J.G., Iannella, N., Abbott, D. 2015. Deriving time from the geometry of space arXiv:1501.04857 [physics.gen-ph]

Chiribella, G., D’Ariano, G.M., Perinotti, P. 2011. Informational derivation of quantum theory. Physical Review A, 84(1), 012311. (arXiv:1011.6451 [quant-ph])

Clawson, R. D. 2009. A zitterbewegung model of the electron. Thesis (Ph.D.)--Arizona State University, 2009.; Publication Number: AAI3391971; ISBN: 9781109570830; Source: Dissertation Abstracts International, Volume: 71-01, Section: B, page: 0378.; 226 p.

D'Ariano, G. M., & Perinotti, P. 2013. Derivation of the Dirac equation from principles of information processing. Phys. Rev. A 90, 062106. doi:10.1103/PhysRevA.90.062106
arXiv:1306.1934 [quant-ph]

D'Ariano, G.M.; Mosco, N.; Perinotti, P.; Tosini, A. 2017. Path-sum solution of the Weyl Quantum Walk in 3+1 dimensions
arXiv:1705.08552 [quant-ph]

Davidon, W.C. 1975. Consequences of inertial equivalence of energy Found. Phys. 5, 525-542.
pdf here

Dolce, D., Perali, A. 2015. On the Compton clock and the undulatory nature of particle mass in graphene systems (arXiv:1403.7037 [physics.gen-ph])

Dyson, F.J. 1972. Missed opportunities. Bull. Am. Math. Soc. 78, 635-652.
pdf here

Earle, K. A. 2010. Notes on The Feynman Checkerboard Problem. arXiv preprint arXiv:1012.1564.

Earle, K. A. 2011. A Master Equation Approach to the 3+1 Dirac Equation.
arXiv preprint arXiv:1102.1200

Eichhorn, A.; Mizera, S. and Surya S. 2017. Echoes of Asymptotic Silence in Causal Set Quantum Gravity.
arXiv:1703.08454 [gr-qc]

Farrelly, T.C., Short, A.J. 2014. Discrete spacetime and relativistic quantum particles. Physical Review A, 89(6), 062109. arXiv:1312.2852 [quant-ph]

Feynman, R.P. 1948. Space-time approach to non-relativistic quantum mechanics. Reviews of Modern Physics, 20(2), 367. (pdf here)

Feynman, R.P., Hibbs, A.R. 1965. Quantum Mechanics and Path Integrals, McGraw-Hill Companies.

Francis, C. 2001. An intuitive approach to special and general relativity.
arXiv:physics/0110007 [physics.gen-ph]

Gersch, H.A. 1981. Feynman's relativistic chessboard as an ising model. International Journal of Theoretical Physics, 20(7), 491-501.

Goyal, P. 2012. Information physics—towards a new conception of physical reality. Information, 3(4), 567-594. (pdf from mdpi)

Goyal P., Knuth K.H. 2011. Quantum theory and probability theory: their relationship and origin in symmetry. Symmetry 3(2):171-206.'''

Goyal P., Knuth K.H., Skilling J. 2010. Origin of complex quantum amplitudes and Feynman's rules. Phys. Rev. A 81, 022109.
arXiv:0907.0909 [quant-ph]

Goyal P., Knuth K.H., Skilling L. 2009. The origin of complex quantum amplitudes. P. Goggans, C.-Y. Chan (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Oxford, MS, USA, 2009, AIP Conference Proceedings 1193, American Institute of Physics, Melville NY, 89-96.

Griffiths, R.B. 2017. What quantum measurements measure arXiv:1704.08725 [quant-ph]

Gudder, S. 2015. Inflation and Dirac in the causal set approach to discrete quantum gravity arXiv:1507.01281 [gr-qc]

Gull, S. F. 1991. Charged particles at potential steps. In The Electron (pp. 37-48). Springer Netherlands.

Haisch, B., Rueda, A., Nickisch, L. J., Mollere, J. 2002. Update on an electromagnetic basis for inertia, gravitation, the principle of equivalence, spin and particle mass ratios. arXiv preprint gr-qc/0209016. (arXiv:gr-qc/0209016)

Haouat, S., Chekireb, R. 2015. Comment on "Creation of spin 1/2 particles by an electric field in de Sitter space"
arXiv:1207.4342 [hep-th]

Hestenes, D. 2010. Zitterbewegung in quantum mechanics. Foundations of Physics, 40(1), 1-54. (pdf here)

Hestenes, D. 2008. Zitterbewegung in Quantum Mechanics–a research program. (arXiv:0802.2728 [quant-ph])

Hestenes, D. 2008. Electron time, mass and zitter. The Nature of Time Essay Contest. Foundational Questions Institute. (pdf here)

Hestenes, D. 2008. Gauge gravity and electroweak theory. (arXiv:0807.0060 [gr-qc])

Hestenes, D. 2008. Reading the electron clock. (arXiv:0802.3227 [physics.gen-ph])

Hestenes, D. 2003. Mysteries and insights of Dirac theory. Annales de la Fondation Louis de Broglie. Fondation Louis de Broglie, 28, 367. (pdf here)

Hestenes, D. 1993. Zitterbewegung modeling. Foundations of physics, 23(3), 365-387. (pdf here)

Hestenes, D. 1993. The Kinematic Origin of Complex Wave Functions. Physics and Probability: Essays in Honor of Edwin T. Jaynes, Cambridge U. Press, Cambridge, 153-160. (pdf here)

Hestenes, D. 1991. Zitterbewegung in radiative processes. In The electron (pp. 21-36). Springer Netherlands. (pdf here)

Hestenes, D. 1990. The zitterbewegung interpretation of quantum mechanics. Foundations of Physics, 20(10), 1213-1232. (pdf here)

Hestenes, D. 1990. On decoupling probability from kinematics in quantum mechanics. In Maximum Entropy and Bayesian Methods (pp. 161-183). Springer Netherlands. (pdf here)

Hestenes, D. 1985. Quantum mechanics from self-interaction. Foundations of Physics, 15(1), 63-87. (pdf here)

Hestenes, D. 1982. Space-time structure of weak and electromagnetic interactions. Found. Physics, 12, pp. 153-168.
pdf here

Holik, F., Plastino, A., Sáenz, M. 2015. Natural information measures for contextual probabilistic models arXiv:1504.01635 [quant-ph]

Hu, Q.H. 2005. The nature of the electron arXiv:physics/0512265 [physics.gen-ph]

Huang, K. 1952. On the zitterbewegung of the Dirac electron. American Journal of Physics, 20(8), 479-484.

Jacobson, T. 1984. Spinor chain path integral for the Dirac equation. Journal of Physics A: Mathematical and General, 17(12), 2433.

Jacobson, T. 1985. Feynman's checkerboard and other games. In Non-Linear Equations in Classical and Quantum Field Theory (pp. 386-395). Springer Berlin Heidelberg.

Jacobson, T., Schulman, L. S. 1984. Quantum stochastics: the passage from a relativistic to a non-relativistic path integral. Journal of Physics A: Mathematical and General, 17(2), 375.

Johnson, D. T., & Caticha, A. 2010. Non-relativistic gravity in entropic quantum dynamics. arXiv:1010.1467 [quant-ph]

Kauffmann, L.H., Noyes, H.P. 1996. Discrete Physics and the Dirac Equation. SLAC-PUB-7115. pdf here

Knuth K.H. 2015. The problem of motion: the statistical mechanics of Zitterbewegung. Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Amboise, France, Sept 2014, AIP Conf. Proc. 1641, AIP, Melville NY, pp. 588-594.
arXiv:1411.1854 [quant-ph]

Knuth K.H. 2014. Information-based physics: an observer-centric foundation. Contemporary Physics, 55(1), 12-32, (Invited Submission).
arXiv:1310.1667 [quant-ph]

Knuth K.H. 2013. Information-based physics and the influence network. 2013 FQXi Essay Entry (
Download Essay

Knuth K.H. 2012. Inferences about interactions: Fermions and the Dirac equation. U. von Toussaint (ed.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Garching, Germany, July 2012, AIP Conference Proceedings 1553, American Institute of Physics, Melville NY.

Knuth K.H. 2010. Information physics: The new frontier. P. Bessiere, J.-F. Bercher, A. Mohammad-Djafari (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Chamonix, France, 2010, AIP Conference Proceedings 1305, American Institute of Physics, Melville NY, 3-19.
arXiv:1009.5161v1 [math-ph]

Knuth K.H. 2009. Measuring on lattices. P. Goggans, C.-Y. Chan (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Oxford, MS, USA, 2009, AIP Conference Proceedings 1193, American Institute of Physics, Melville NY, 132-144.
arXiv:0909.3684 [math.GM]

Knuth K.H. 2003. Deriving laws from ordering relations. In: G.J. Erickson, Y. Zhai (eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Jackson Hole WY 2003, AIP Conference Proceedings 707, American Institute of Physics, Melville NY, pp. 204-235.

Knuth K.H., Bahreyni N. 2014. A potential foundation for emergent space-time, Journal of Mathematical Physics, 55, 112501.
doi: 10.1063/1.4899081
arXiv:1209.0881 [math-ph]

Knuth K.H., Skilling J. 2012. Foundations of Inference. Axioms 1(1), 38-73.

Kull, A. 2002. Quantum mechanical motion of relativistic particle in non-continuous spacetime. Physics Letters A, 303(2), 147-153.

Kunjwal, R. 2016 Contextuality beyond the Kochen-Specker theorem arXiv:1612.07250 [quant-ph]

Lebed, A.G. 2016. Breakdown of the equivalence between active gravitational mass and energy for a quantum body. Journal of Physics: Conference Series, vol. 738, 012036.
arXiv:1609.06358 [gr-qc]

Levy-Leblond, J.-M. and Provost, J.-M. 1979. Additivity, rapidity, relativity Am. J. Phys. 47, 1045-1049.
pdf here

Llosa, J. 2015. An extension of the principle of relativity for one-dimensional space
arXiv:1507.01201 [gr-qc]

Lounesto, P. 1993. Clifford algebras and Hestenes spinors. Foundations of physics, 23(9), 1203-1237. (pdf here)

Lush, D.C. 2015. Similarity of the magnetic force between Dirac particles to the quantum force of Bohmian mechanics
arXiv:1409.8271 [physics.class-ph]

MacCallum, M.A.H. 2015. Spacetime invariants and their uses. In: Proceedings of the International Conference on Relativistic Astrophysics, Lahore, February 2015.
arXiv:1504.06857 [gr-qc]

Malament, D.B. 1977. The class of continuous timelike curves determines the topology of spacetime. Journal of Mathematical Physics, 18(7), 1399-1404.

Meyer, D.A. 1996. From quantum cellular automata to quantum lattice gases, J. Stat. Phys. 85 (1996) 551-574. arXiv:quant-ph/9604003

Moustos, D. 2017. Gravity as a thermodynamic phenomenon. M.Sc. Thesis. arXiv:1701.08967 [gr-qc]

Oas, G. 2005. On the abuse and use of relativistic mass arXiv:physics/0504110 [physics.ed-ph]

Ord, G. N. 1992. Classical analog of quantum phase. International journal of theoretical physics, 31(7), 1177-1195.

Ord, G.N. 1992. A reformulation of the Feynman chessboard model. Journal of statistical physics, 66(1-2), 647-659.

Ord, G.N. 1993. The Feynman chessboard in a box. Canadian journal of physics, 71(3-4), 159-161.

Ord, G. N. 1993. Quantum interference from charge conservation. Physics Letters A, 173(4), 343-346.

Ord, G. N., McKeon, D. G. C. 1993. On the Dirac equation in 3+ 1 dimensions. Annals of Physics, 222(2), 244-253.

Ord, G. N. 1996. Fractal space-time and the statistical mechanics of random walks. Chaos, Solitons & Fractals, 7(6), 821-843.

Ord, G. N. 1999. Gravity and the spiral model. Chaos, Solitons & Fractals, 10(2), 499-512.

Ord, G.N., Gualtieri, J. A. 2002. The Feynman propagator from a single path. Physical review letters, 89(25), 250403.
pdf here

Ord, G. N., Gualtieri, J. A., Mann, R. B. 2006. A discrete, deterministic construction of the phase in Feynman paths. Foundations of Physics Letters, 19(5), 471-480.

Ord, G. N., Mann, R. B., Harley, E., Harley, Z., Lin, Q. Q., Lauritzen, A. 2009. Numerical experiments in relativistic phase generation through time reversal. Advanced Studies in Theoretical Physics, 3(3), 99-130.

Ord, G. N., Mann, R. (2012). How Does an Electron Tell the Time?. International Journal of Theoretical Physics, 51(2), 652-666.

Ord, G. 2013. Spacetime and quantum Propagation From digital clocks. In The Physics of Reality: Space, Time, Matter, Cosmos (Vol. 1, pp. 111-119).

Ord, G. N. 2013. Spacetime and the missing uncertainty. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, Vol. 3, No. 1, pp. 50-58
pdf here

Orefice, A.; Giovanelli, R.; Ditto, D. 2015. Is wave mechanics consistent with classical logic?
arXiv:1506.08016 [quant-ph]

Peng, L. 2017. Symmetries, conservation laws and Noether's theorem for differential-difference equations arXiv:1607.00752 [math-ph]

Puentes, G.; Santillán, O. 2015. Zak phase in discrete-time quantum walks
arXiv:1506.08100 [quant-ph]

Robb, A.A. 1936. Geometry of Time and Space. Cambridge University Press, Cambridge.

Serras Jr., W.A., Vaz Jr., J., Recami, E., Salesi, E. 1993. About Zitterbewegung and electron structure (pp. 397-404). Springer Netherlands. (pdf here)

Schweber, S.S. 1986. Feynman and the visualization of space-time processes. Rev. Mod. Phys. 58, 449.

Silagadze, Z.K. 2008. Relativity without tears. Acta Phys, Polon, B39, 811-885. arXiv:0708.0929 [physics.ed-ph]
(In addition to being a good paper, there are a lot of excellent references)

Singh, D., Mobed, N. 2009. Effects of spacetime curvature on spin-1/2 particle zitterbewegung. Classical and Quantum Gravity, 26(18), 185007. (arXiv:0903.1346 [gr-qc])

Smith, F.T. 1997. '''From sets to quarks. arXiv preprint hep-ph/9708379.

Sobczyk, G. 2015. Part II: Spacetime Algebra of Dirac Spinors arXiv:1507.06609 [math-ph]

Sorkin, R.D. 1990. Spacetime and causal sets. Relativity and gravitation: Classical and quantum, 150-173.
pdf here

Sorkin, R.D. 2005. Causal sets: Discrete gravity. In Lectures on quantum gravity. Springer US, pp. 305-327.

Sorkin, R.D. 2017. From Green Function to Quantum Field. arXiv:1703.00610 [gr-qc]

Stoica, O.C. 2015. Causal structure and spacetime singularities.
arXiv:1504.07110 [gr-qc]

Su, D.; Ralph, T.C. 2016. Spacetime diamonds, Phys. Rev. D 93, 044023(2016). arXiv:1507.00423 [quant-ph]

Tikochinsky, Y. 1988. Feynman rules for probability amplitudes. International journal of theoretical physics, 27(5), 543-549.

Tikochinsky, Y., Gull, S.F. (2000). Consistency, amplitudes and probabilities in quantum theory. Journal of Physics A: Mathematical and General, 33(31), 5615.

Todd, S.L.; Menicucci, N.C. 2016. Sound clocks and sonic relativity arXiv:1612.06870 [physics.class-ph]

Trzetrzelewski, M. 2015. On the equivalence principle and electrodynamics of moving bodies arXiv:1503.05577 [hep-th]

Tseng, C. Y., Caticha, A. 2001. Yet another resolution of the Gibbs paradox: an information theory approach. (arXiv:cond-mat/0109324 [cond-mat.stat-mech])

Walsh J.L., Knuth K.H. 2015. Information-based physics, influence and forces. Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Amboise, France, Sept 2014, AIP Conf. Proc. 1641, AIP, Melville NY, pp. 538-547
arXiv:1411.2163 [quant-ph]

Weatherall, J.O. 2017. Conservation, Inertia, and Spacetime Geometry arXiv:1702.01642 [physics.hist-ph]

Wheeler, J.A., Feynman, R.P. 1949. Classical electrodynamics in terms of direct interparticle action. Reviews of Modern Physics, 21(3), 425. (pdf here)

Wheeler, J.A., Feynman, R.P. 1945. Interaction with the absorber as the mechanism of radiation, Reviews of Modern Physics, 17(2-3), 157. (pdf here)

Wootters, W.K. 2003. Why things fall. Foundations of Physics, 33(10), 1549-1557. (pdf here)

Vaz, J., Rodriguez, W.A. 1993. Zitterbewegung and the electromagnetic field of the electron. Physics Letters B, 319(1), 203-208.

Visser, M. 2017. Quantum mechanix plus Newtonian gravity violates the universality of free fall arXiv:1705.05493 [gr-qc]

Zeeman, E.C. 1964. Causality implies the Lorentz group. J. Math. Phys. 5, 490-493.
pdf here