# Spooky Action at a Temporal Distance

## Abstract

**:**

## 1. Introduction

## 2. Temporal Locality

#### 2.1. Definition

**Definition**

**1.**

**Spatial Locality:**Suppose that two observers, Alice and Bob, perform measurements on a shared physical system: Alice performs a measurement with setting a and obtains a measurement outcome A, while Bob performs a measurement with measurement setting b and obtains a measurement outcome B. Let λ be the joint state of the shared system prior to the two measurements. Then:

**Definition**

**2.**

**Temporal Locality:**Suppose that two observers, Alice and Bob, perform measurements on a shared physical system. At some time ${t}_{a}$, Alice performs a measurement with measurement setting a and at some time ${t}_{a}+\delta $ she obtains a measurement outcome A; likewise, at some time ${t}_{b}$, Bob performs a measurement with measurement setting b and at some time ${t}_{b}+\delta $ he obtains a measurement outcome B. Let $\lambda \left({t}_{a}\right)$ be the state of the world at time ${t}_{a}$ and let $\lambda \left({t}_{b}\right)$ be the state of the world at time ${t}_{b}$. Then:

#### 2.2. Motivation

## 3. Origins

#### The Pragmatic Argument

An essential aspect of this arrangement of things in physics is that they lay claim, at a certain time, to an existence independent of one another, provided these objects “are situated in different parts of space”. Unless one makes this kind of assumption about the independence of the existence (the “being-thus”) of objects which are far apart from one another in space ... physical thinking in the familiar sense would not be possible. It is also hard to see any way of formulating and testing the laws of physics unless one makes a clear distinction of this kind.

## 4. Relativity

#### 4.1. Special Relativity

#### 4.2. General Relativity

#### 4.2.1. Objection: The Independence of Dynamics and Kinematics

#### 4.2.2. Objection: Modality

#### 4.3. Objection: Spacetimes That Are Not Globally Hyperbolic

## 5. Three Options for Temporal Nonlocality

#### 5.1. Non-Markovian Laws

#### 5.2. Retrocausality

#### 5.3. Atemporal Laws

#### 5.3.1. The Lagrangian Schema

#### 5.3.2. New Models

## 6. Dynamics and Kinematics

#### 6.1. Spekkens on Dynamics vs. Kinematics

#### 6.2. Example: Causal Set Theory

## 7. Temporal Bell Inequalities and Entanglement in Time

#### The Problem of Records

## 8. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

- Bell, J.S. Free variables and local causality. In Speakable and Unspeakable in Quantum Mechanics; Cambridge University Press: Cambridge, UK, 1987. [Google Scholar]
- Bell, J.S. La Nouvelle Cuisine. In Speakable and Unspeakable in Quantum Mechanics; Cambridge University Press: Cambridge, UK, 2004; pp. 232–248. [Google Scholar]
- Jarrett, J.P. On the Physical Significance of the Locality Conditions in the Bell Arguments. Noûs
**1984**, 18, 569–589. [Google Scholar] [CrossRef] - Spekkens, R.W. Contextuality for preparations, transformations, and unsharp measurements. Phys. Rev. A
**2005**, 71, 052108. [Google Scholar] [CrossRef] - Leifer, M.S. Is the quantum state real? An extended review of ψ-ontology theorems. Quanta
**2014**, 3, 67–155. [Google Scholar] [CrossRef] - Spekkens, R.W.; Perimeter Institute, Waterloo, Canada. Private communication, 2013.
- Leifer, M.S.; Pusey, M.F. Is a time symmetric interpretation of quantum theory possible without retrocausality? Proc. R. Soc. Lond. A Math. Phys. Eng. Sci.
**2017**, 473, 20160607. [Google Scholar] [CrossRef] [PubMed] - Colbeck, R.; Renner, R. The Completeness of Quantum Theory for Predicting Measurement Outcomes. In Quantum Theory: Informational Foundations and Foils; Springer: Berlin/Heidelberg, Germany, 2016; pp. 497–528. [Google Scholar]
- Hardy, L. Are quantum states real? Int. J. Mod. Phys. B
**2013**, 27, 1345012. [Google Scholar] [CrossRef] - Pusey, M.F.; Barrett, J.; Rudolph, T. On the reality of the quantum state. Nat. Phys.
**2012**, 8, 475–478. [Google Scholar] [CrossRef] - Harrigan, N.; Spekkens, R.W. Einstein, incompleteness, and the epistemic view of quantum states. Found. Phys.
**2010**, 40, 125–157. [Google Scholar] [CrossRef] - Wigner, E.P. Events, Laws of Nature, and Invariance Principles. Science
**1964**, 145, 995–999. [Google Scholar] [CrossRef] [PubMed] - Bigelow, J. Presentism and properties. Philos. Perspect.
**1996**, 10, 35–52. [Google Scholar] [CrossRef] - Tallant, J.; Ingram, D. Nefarious presentism. Philos. Q.
**2015**, 65, 355–371. [Google Scholar] [CrossRef] - Deasy, D. What is presentism? Noûs
**2017**, 51, 378–397. [Google Scholar] [CrossRef] - Saunders, S. How Relativity Contradicts Presentism. R. Inst. Philos. Suppl.
**2002**, 50, 277–292. [Google Scholar] [CrossRef] - Putnam, H. Time and Physical Geometry. J. Philos.
**1967**, 64, 240–247. [Google Scholar] [CrossRef] - Savitt, S.F. There’s No Time Like the Present (in Minkowski Spacetime). Philos. Sci.
**2000**, 67, 574. [Google Scholar] [CrossRef] - Hinchliff, M. The Puzzle of Change. Philos. Perspect.
**1996**, 10, 119–136. [Google Scholar] [CrossRef] - Einstein, A. Quantum Mechanics and Reality. Dialectica
**1948**, 2, 320–324. [Google Scholar] [CrossRef] - Einstein, A. Relativity: The Special and General Theory; Henry Holt: New York, NK, USA, 1920. [Google Scholar]
- Goldstein, S. Bohmian Mechanics. In The Stanford Encyclopedia of Philosophy; Zalta, E.N., Ed.; Metaphysics Research Lab, Stanford University: Stanford, CA, USA, 2016. [Google Scholar]
- Tumulka, R. A Relativistic Version of the Ghirardi Rimini Weber Model. J. Stat. Phys.
**2006**, 125, 821–840. [Google Scholar] [CrossRef] - Bell, J.S.; Aspect, A. Are there quantum jumps? In Speakable and Unspeakable in Quantum Mechanics, 2nd ed.; Cambridge Books Online; Cambridge University Press: Cambridge, UK, 2004; pp. 201–212. [Google Scholar]
- Esfeld, M.; Gisin, N. The GRW flash theory: A relativistic quantum ontology of matter in space-time? Philos. Sci.
**2014**, 81, 248–264. [Google Scholar] [CrossRef] - Wald, R. General Relativity; University of Chicago Press: Chicago, IL, USA, 2010. [Google Scholar]
- Ringström, H. The Cauchy Problem in General Relativity; European Mathematical Society: Zurich, Switzerland, 2009. [Google Scholar]
- Foures-Bruhat, Y. Théorème d’existence pour certains systèmes d’équations aux dérivées partielles non linéaires. Acta Math.
**1952**, 88, 141–225. (In French) [Google Scholar] [CrossRef] - Wharton, K. The Universe is not a Computer. In Questioning the Foundations of Physics; Aguirre, A.F.B., Merali, G., Eds.; Springer: Berlin/Heidelberg, Germany, 2015; pp. 177–190. [Google Scholar]
- Bingham, G.P. A Note on Dynamics and Kinematics. Haskins Lab. Stat. Rep. Speech Res.
**1988**, 93, 247. [Google Scholar] - McCauley, J. Classical Mechanics: Transformations, Flows, Integrable and Chaotic Dynamics; Cambridge University Press: Cambridge, UK, 1997. [Google Scholar]
- Norton, J.D. ‘Nature is the Realisation of the Simplest Conceivable Mathematical Ideas’: Einstein and the Canon of Mathematical Simplicity. Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys.
**2000**, 31, 135–170. [Google Scholar] [CrossRef] - Norton, J.D. Eliminative Induction as a Method of Discovery: Einstein’s Discovery of General Relativity. In The Creation of Ideas in Physics: Studies for a Methodology of Theory Construction; Leplin, J., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1995; pp. 29–69. [Google Scholar]
- Gödel, K. An Example of a New Type of Cosmological Solutions of Einstein’s Field Equations of Gravitation. Rev. Mod. Phys.
**1949**, 21, 447–450. [Google Scholar] [CrossRef] - Earman, J. Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes; Oxford University Press: Oxford, UK, 1995. [Google Scholar]
- Smeenk, C.; Wuthrich, C. Time Travel and Time Machines. In The Oxford Handbook of Time; Callender, C., Ed.; Oxford University Press: Oxford, UK, 2009. [Google Scholar]
- Friedman, J.L. The Cauchy Problem on Spacetimes That Are Not Globally Hyperbolic. In The Einstein Equations and the Large Scale Behavior of Gravitational Fields; Chruściel, P.T., Friedrich, H., Eds.; Birkhäuser Verlag: Basel, Switzerland, 2004; p. 331. [Google Scholar]
- Friedman, J.; Morris, M.S.; Novikov, I.D.; Echeverria, F.; Klinkhammer, G.; Thorne, K.S.; Yurtsever, U. Cauchy problem in spacetimes with closed timelike curves. Phys. Rev. D
**1990**, 42, 1915–1930. [Google Scholar] [CrossRef] - Gillespie, D. Markov Processes: An Introduction for Physical Scientists; Elsevier: Amsterdam, The Netherlands, 1991. [Google Scholar]
- Montina, A. Exponential complexity and ontological theories of quantum mechanics. Phys. Rev. A
**2008**, 77, 022104. [Google Scholar] [CrossRef] - Timpson, C. Quantum Information Theory and the Foundations of Quantum Mechanics; Oxford University Press: Oxford, UK, 2013. [Google Scholar]
- Healey, R. The Philosophy of Quantum Mechanics: An Interactive Interpretation; Cambridge University Press: Cambridge, UK, 1991. [Google Scholar]
- Morganti, M. A New Look at Relational Holism in Quantum Mechanics. Philos. Sci.
**2009**, 76, 1027–1038. [Google Scholar] [CrossRef] - Price, H. Does time-symmetry imply retrocausality? How the quantum world says “Maybe”? Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys.
**2012**, 43, 75–83. [Google Scholar] [CrossRef] - Sutherland, R.I. Causally symmetric Bohm model. Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys.
**2008**, 39, 782–805. [Google Scholar] [CrossRef] - Wharton, K.B. A Novel Interpretation of the Klein-Gordon Equation. In Quantum Theory: Reconsideration of Foundations-4; Adenier, G., Khrennikov, A.Y., Lahti, P., Man’ko, V.I., Eds.; American Institute of Physics: College Park, MD, USA, 2007; pp. 339–343. [Google Scholar]
- Price, H. Toy models for retrocausality. Stud. Hist. Philos. Mod. Phys.
**2008**, 39, 752–761. [Google Scholar] [CrossRef] - Wharton, K. Quantum states as ordinary information. Information
**2014**, 5, 190–208. [Google Scholar] [CrossRef] - Aharonov, Y.; Vaidman, L. The Two-State Vector Formalism of Quantum Mechanics. In Time in Quantum Mechanics; Muga, J.G., Mayato, R.S., Egusquiza, I.L., Eds.; Springer: Berlin/Heidelberg, Germany, 2002; pp. 369–412. [Google Scholar]
- Smolin, L. The unique universe. Phys. World
**2009**, 22, 21. [Google Scholar] [CrossRef] - Brizard, A. An Introduction to Lagrangian Mechanics; World Scientific: Singapore, 2008. [Google Scholar]
- Hartle, J.B. The spacetime approach to quantum mechanics. Vistas Astron.
**1993**, 37, 569–583. [Google Scholar] [CrossRef][Green Version] - Sorkin, R.D. Quantum dynamics without the wavefunction. J. Phys. A Math. Gen.
**2007**, 40, 3207–3221. [Google Scholar] [CrossRef] - Butterfield, J. Some Aspects of Modality in Analytical Mechanics. In Formal Teleology and Causality; Stöltzner, M., Weingartner, P., Eds.; Mentis: Paderborn, Germany, 2004. [Google Scholar]
- Papastavridis, J. Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems: For Engineers, Physicists, and Mathematicians; Oxford University Press: Oxford, UK, 2002. [Google Scholar]
- Lanczos, C. The Variational Principles of Mechanics; Mathematical Expositions, University of Toronto Press: Toronto, ON, Canada, 1949. [Google Scholar]
- Ostrogradsky, M. Mémoire sur les equations différentielles relative au problème des Isopérimètres. Mem. Acad. St. Petersbourg
**1850**, 6, 385–571. (In French) [Google Scholar] - Spekkens, R.W. The paradigm of kinematics and dynamics must yield to causal structure. In Questioning the Foundations of Physics; Springer: Berlin/Heidelberg, Germany, 2015; pp. 5–16. [Google Scholar]
- Quine, W.V. Main Trends in Recent Philosophy: Two Dogmas of Empiricism. Philos. Rev.
**1951**, 60, 20–43. [Google Scholar] [CrossRef] - Schnädelbach, H. Two Dogmas of Empiricism. Fifty Years After. Grazer Philos. Stud.
**2003**, 66, 7–12. [Google Scholar] - Rideout, D.P.; Sorkin, R.D. Classical sequential growth dynamics for causal sets. Phys. Rev. D
**2000**, 61, 024002. [Google Scholar] [CrossRef] - Sorkin, R.D. Relativity Theory Does Not Imply that the Future Already Exists: A Counterexample. In Relativity and the Dimensionality of the World; Petkov, V., Ed.; Springer: Berlin/Heidelberg, Germany, 2007; p. 153. [Google Scholar]
- Smart, J.J.C. The River of Time. Mind
**1949**, 58, 483–494. [Google Scholar] [CrossRef] [PubMed] - Sorkin, R. Geometry from Order: Causal Sets. Available online: http://www.einstein-online.info/en/spotlights/causal_sets/ (accessed on 9 January 2018).
- Arageorgis, A. Spacetime as a Causal Set: Universe as a Growing Block? Belgrad. Philos. Annu.
**2016**, 29, 33–55. [Google Scholar] [CrossRef] - Wüthrich, C.; Callender, C. What Becomes of a Causal Set? Br. J. Philos. Sci.
**2017**, 68, 907–925. [Google Scholar] [CrossRef] - Bell, J.S. On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys.
**1966**, 38, 447. [Google Scholar] [CrossRef] - Aspect, A.; Grangier, P.; Roger, G. Experimental Tests of Realistic Local Theories via Bell’s Theorem. Phys. Rev. Lett.
**1981**, 47, 460–463. [Google Scholar] [CrossRef] - Kielpinski, D.; Meyer, V.; Sackett, C.A.; Itano, W.M.; Monroe, C.; Wineland, D.J. Experimental violation of a Bell’s inequality with efficient detection. Nature
**2001**, 409, 791–794. [Google Scholar] - Hensen, B.; Bernien, H.; Dréau, A.E.; Reiserer, A.; Kalb, N.; Blok, M.S.; Ruitenberg, J.; Vermeulen, R.F.L.; Schouten, R.N.; Abellán, C.; et al. Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km. Nature
**2015**, 526, 682–686. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hossenfelder, S. Testing superdeterministic conspiracy. J. Phys. Conf. Ser.
**2014**, 504, 012018. [Google Scholar] [CrossRef] - Timpson, C.; Maroney, O. Quantum-vs. macro-realism: What does the Leggett-Garg inequality actually test? The British Journal for the Philosophy of Science. 2013. Available online: https://ora.ox.ac.uk/objects/uuid:c2c31bfa-f9d3-4bc6-9853-79fcd79917f7/datastreams/ATTACHMENT1 (accessed on 9 January 2018).
- Brukner, C.; Taylor, S.; Cheung, S.; Vedral, V. Quantum Entanglement in Time. arXiv, 2004; arXiv:quant-ph/0402127. [Google Scholar]
- Brierley, S.; Kosowski, A.; Markiewicz, M.; Paterek, T.; Przysiężna, A. Nonclassicality of temporal correlations. Phys. Rev. Lett.
**2015**, 115, 120404. [Google Scholar] [CrossRef] [PubMed] - Price, H.; Wharton, K. A Live Alternative to Quantum Spooks. arXiv, 2015; arXiv:1510.06712. [Google Scholar]
- Almada, D.; Ch’ng, K.; Kintner, S.; Morrison, B.; Wharton, K.B. Are Retrocausal Accounts of Entanglement Unnaturally Fine-Tuned? Int. J. Quantum Found.
**2015**, 2, 1–16. [Google Scholar] - Price, H.; Wharton, K. Disentangling the Quantum World. Entropy
**2015**, 17, 7752–7767. [Google Scholar] [CrossRef] - Dowker, F.; Kent, A. On the consistent histories approach to quantum mechanics. J. Stat. Phys.
**1996**, 82, 1575–1646. [Google Scholar] [CrossRef] - Halliwell, J.J. A Review of the Decoherent Histories Approach to Quantum Mechanics. In Fundamental Problems in Quantum Theory; Greenberger, D.M., Zelinger, A., Eds.; New York Academy of Sciences: New York, NY, USA, 1995; p. 726. [Google Scholar]
- Okon, E.; Sudarsky, D. On the Consistency of the Consistent Histories Approach to Quantum Mechanics. Found. Phys.
**2014**, 44, 19–33. [Google Scholar] [CrossRef] - Aharonov, Y.; Popescu, S.; Tollaksen, J. Each Instant of Time a New Universe. In Quantum Theory: A Two-Time Success Story; Struppa, D.C., Tollaksen, J.M., Eds.; Springer: Berlin/Heidelberg, Germany, 2014; p. 21. ISBN 978-88-470-5216-1. [Google Scholar]
- Kent, A. Solution to the Lorentzian quantum reality problem. Phys. Rev. A
**2014**, 90, 012107. [Google Scholar] [CrossRef]

© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Adlam, E.
Spooky Action at a Temporal Distance. *Entropy* **2018**, *20*, 41.
https://doi.org/10.3390/e20010041

**AMA Style**

Adlam E.
Spooky Action at a Temporal Distance. *Entropy*. 2018; 20(1):41.
https://doi.org/10.3390/e20010041

**Chicago/Turabian Style**

Adlam, Emily.
2018. "Spooky Action at a Temporal Distance" *Entropy* 20, no. 1: 41.
https://doi.org/10.3390/e20010041