1. Introduction

2. Analytical Structure

3. The Physical Universe

4. Quantum State Evolution and Collapse in Discrete 4D Spacetime and Planck Space

4.2. The Collapse of a Single Quantum State

The Bell Identity not only links the dynamic evolution of a quantum state's Bell Quantum Field in 4D spacetime with its Bell Quantum Hyper-Point in Planck Space, but it also links the instantaneous collapse of a quantum state's Bell Quantum Hyper-Point in Planck Space with its Bell Quantum Field in 4D spacetime.³⁶ More specifically, the Bell Identity links the instantaneous decrease in the number of Bell Quantum Spheres that comprise a quantum state's Bell Quantum Hyper-Point in Planck Space with a simultaneous reduction in the number of Bell Quantum Spheres that comprise the quantum state's Bell Quantum Field in 4D spacetime.³⁷

For example, assume Box A is a three-dimensional box with impenetrable walls. Box A is 2 inches wide, 1 inch deep, and 1 inch tall. There is zero potential inside Box A. The instant a single quantum state ("quantum state A") is generated, it simultaneously forms Bell Quantum Field A in 4D spacetime and Bell Quantum Hyper-Point A in Planck Space. Quantum state A is inserted into Box A, where it spreads but will never have zero energy.

As quantum state A spreads, the Bell Identity ensures that the increase in the number of Bell Quantum Spheres that comprise Bell Quantum Field A is simultaneously mirrored in a one-to-one increase in the number of Bell Quantum Spheres that comprise Bell Quantum Hyper-Point A. The opening of Box A triggers the instantaneous collapse of Bell Quantum Hyper-Point A. The collapse instantaneously reduces the number of Bell Quantum Spheres that formerly composed Bell Quantum Hyper-Point A, and the Bell Identity ensures that the collapse is simultaneously linked to the instantaneous reduction in the number of Bell Quantum Spheres that now comprise Bell Quantum Field A. Quantum state A is now generally localized in Box A.³⁸ Nevertheless, special relativity has not been violated.^{39 40} The generalized localization of quantum state A is an event extraneous to 4D spacetime caused by 1) the collapse of the quantum state's Bell Quantum Hyper-Point, 2) the instantaneous reduction in the number of Bell Quantum Spheres that comprise the quantum state’s Bell Quantum Hyper-Point following its collapse, and 3) the simultaneous decrease in the number of Bell Quantum Spheres that comprise the quantum's state's generally localized Bell Quantum Field in 4D spacetime.⁴¹

4.2.1. The Einstein/de Broglie Boxes Thought Experiment

The Einstein/de Broglie Boxes thought experiment is a more complex example of the dynamics of a single quantum state.⁴² Assume Box B is initially identical to Box A. A single quantum state ("quantum state B") is generated, simultaneously forming Bell Quantum Field B in 4D spacetime and Bell Quantum Hyper-Point B in Planck Space. Quantum state B is inserted into Box B and begins to spread. As quantum state B spreads, the number of Bell Quantum Spheres that comprise Bell Quantum Field B within Box B increases, and so does the number of Bell Quantum Spheres that form Bell Quantum Hyper-Point B in Planck Space.

Without becoming entangled with quantum state B, an impenetrable divider is inserted into the middle of Box B, separating it into two identical boxes, C and D. Ignoring the physical dimensions of the divider, Box C and Box D are now 1 inch wide, 1 inch deep, and 1inch tall. Inside Boxes C and D, the potential energy remains zero.

The insertion of the impenetrable divider has separated the quantum state into two equal Bell Quantum Fields in 4D spacetime: Bell Quantum Field C and Bell Quantum Field D. Nevertheless, the quantum state continues to form a single Bell Quantum Hyper-Point in Planck Space, now designated as "Bell Quantum Hyper-Point CD." The mathematical wave function ${\Psi }_{C,D}=\frac{1}{\sqrt{2}}\left({\Psi }_C+{\Psi }_D\right)$ indicates that the quantum state is in a superposition of location with a 50% chance that following the quantum state's collapse, the quantum state is found in Box B and a 50% chance that the quantum state is found in Box C.

Box C remains in Princeton, and Box D is shipped to Copenhagen, 6,252 kilometers away. Although the movement of Box D's physical location has altered the x, y, z coordinates of the Bell Quantum Spheres that comprise Bell Quantum Field D in 4D spacetime, the Bell Quantum Spheres that comprise Bell Quantum Field C and Bell Quantum Field D continue to comprise Bell Quantum Hyper-Point CD. In other words, so long as Bell Quantum Hyper-Point CD does not collapse, the quantum state remains in a superposition of location with a 50% chance of being found in Box C and a 50% chance of being found in Box D.

Regardless of whether Box B or Box C is opened first, the opening of either box is the physical trigger that causes the collapse of Bell Quantum Hyper-Point CD. In turn, the collapse instantaneously reduces the number of Planck Spheres that formerly composed Bell Quantum Hyper-Point CD. The reduction in the number of Planck Spheres that formerly composed Bell Quantum Hyper-Point CD has several significant ramifications.

If Box C is opened first and the entire quantum state ψ_c (x₁,y₁,z₁)_c is found in Box C, 1) the number of Planck Spheres that comprise Bell Quantum Field C and Bell Quantum Hyper-Point C have been instantaneously reduced, 2) Bell Quantum Field C is generally localized in Box C, and 3) there is a one to one mapping and identity between the Bell Quantum Spheres that comprise Bell Quantum Field C in 4D spacetime and Bell Quantum Hyper-Point C in Planck Space. In addition, the mathematical wave function formerly representing Bell Quantum Field D and Bell Quantum Hyper-Point D no longer has meaning. A similar analysis applies if Box C is opened and the quantum state is not found in Box C or if Box D is opened first and the quantum state is or is not found in Box D.⁴³

Finally, the collapse of Bell Quantum Hyper-Point CD is not a “quantum jump” in 4D spacetime.⁴⁴ Recall that a Bell Quantum Hyper-Point is an ultra-high dimensional point in a Planck Space where time, space, and volume do not exist. When Bell Quantum Hyper-Point CD collapses, there is a reduction in the number of dimensions that comprise the quantum state's new Bell Quantum Hyper-Point, and the Bell Identity ensures that there is a simultaneous reduction in the number of Bell Quantum Spheres that comprise the quantum state's new Bell Quantum Field. What appears to be a "jump" in 4D spacetime is the collapse of Bell Quantum Hyper-Point CD in Planck Space and the reduction in the number of Bell Quantum Spheres that comprise the quantum state's Bell Quantum Field. ⁴⁵

4.2.2. The Double-Slit Experiment

The double-slit experiment and its multiple incarnations have been reviewed extensively by physicists and philosophers. Notwithstanding the numerous controversies surrounding it, the experimental results of the various double-slit experiments are subject to the same ontological structure and dynamic laws that govern the dynamic spreading and the instantaneous collapse of all quantum states under the Dual Ontology conjecture.

Individual electrons ("quantum states") are sent one at a time towards "Wall (W)" with two narrow Gaussian slits (A) and (B). In comparison with a quantum state's wavelength, slits (A) and (B) are sufficiently narrow so that a quantum state diffracts if it passes through slits (A) and (B). Some of the individual quantum states that move towards Wall (W) hit the wall, while others pass through slits (A) and (B). Once a quantum state passes through slit (A), it spreads uniformly as a spherical wave toward a detector "Detector (D)." Similarly, as the quantum state passes through slit (B), it too spreads uniformly as a spherical wave toward Detector (D). The two spherical waves interfere as they spread toward Detector (D). A single flash occurs whenever a quantum state hits Detector (D). Only one flash is detected per quantum state. After many flashes, Detector (D) indicates an interference pattern.

When each quantum state is generated, it forms a Bell Quantum Field in 4D spacetime and an ultra-high dimensional Bell Quantum Hyper-Point in Planck Space. Accordingly, when a quantum state is fired toward Wall W, the quantum state is simultaneously composed of a Bell Quantum Field in 4D spacetime and a Bell Quantum Hyper-Point in Planck Space. As the quantum state travels toward Wall W, it spreads spherically in 4D spacetime but continuously forms a single Bell Quantum Hyper-Point in Planck Space. A one-to-one mapping and identity exists between the Bell Quantum Spheres that comprise the quantum state’s Bell Quantum Field in 4D spacetime and the quantum state's Bell Quantum Hyper-Point in Planck Space.

As the quantum state passes through slits (A) and (B), both slits independently diffract the quantum state, and the quantum state begins to spread from both slits towards Detector D in a spherical pattern. The Bell Quantum Spheres of the quantum state that passes through slit A forms Bell Quantum Field A in 4D spacetime, and the Bell Quantum Spheres of the quantum state that passes through slit B forms Bell Quantum Field B in 4D spacetime. The quantum state forms a single Bell Quantum Hyper-Point AB in Planck Space. Mathematically, the quantum state's wavefunction is typically described as ${\Psi }_{ A+ B}=\frac{1}{\sqrt{2}}\left({\Psi }_{ A }+ {\Psi }_{ B}\right)$.⁴⁶

Before reaching Detector D, the two wave functions combine linearly, and the linear combination causes interference. The modulus squared of the mathematical wavefunction is greater where the linear combination is constructive and approaches zero where the interference is destructive. Whether or not the mathematical wavefunction forms a peak or a trough, the quantum state always continues to form Bell Quantum Hyper-Point AB in Planck Space.

In 4D spacetime, a flash anywhere on Detector (D) indicates that a quantum state's single Bell Quantum Hyper-Point has instantaneously collapsed. Upon its collapse, the number of Bell Quantum Spheres that comprise the quantum state’s Bell Hyper-Point is reduced to a subset of the Bell Quantum Spheres that composed its Bell Quantum Hyper-Point prior to the collapse. Simultaneously, the Bell Identity ensures that the collapse of the quantum state's Bell Quantum Hyper-Point is, on a one-to-one basis, linked to an instantaneous reduction in the number of Bell Quantum Spheres that now comprise the quantum state's single Bell Quantum Field in 4D spacetime.

Regardless of how spread out a quantum state's Bell Quantum Field may have been in 4D spacetime before its collapse, and regardless of the interference caused by the interaction of the diffracted waves spreading from slits (A) and (B), the collapse of a quantum state's Bell Quantum Hyper-Point ensures that the entire quantum state is generally localized in 4D spacetime. The collapse of the quantum state to a generally localized position anywhere on Detector (D) is instantaneous, and the mathematical wave function of Bell Quantum Spheres that are no longer occupied by the quantum state following its collapse has no meaning.

Following many flashes caused by the collapse of individual electrons, an interference pattern emerges on the Detector (D). The interference pattern is the combined result of the collapse of individual Bell Quantum Hyper-Points in Planck Space and the simultaneous reduction in the number of Bell Quantum Spheres that comprise each quantum state's Bell Quantum Field.

4.2.3. A Which-Way Experiment

Historically, "which way" experiments have compounded the theoretical issues of double-slit experiments. Once again, however, from the perspective of the Dual Ontology conjecture, the theoretical analysis of a which-way experiment is the same as it is for all other collapse-based quantum events.

The baseline experiment repeats the double-slit example in Section 3.2.2 but is modified by inserting a proton into an empty rectangular box at the center of Wall (W).⁴⁷ The proton is positively charged, and each electron ("quantum state") fired towards Wall (W) is negatively charged. Assuming the experiment is 100% reliable, slit (A) flashes if the proton is attracted towards slit (A), and slit (B) flashes if the proton is attracted towards slit (B). Experimentally, 50% of the flashes are recorded at slit (A) and 50% at slit (B) 50%.

As an electron spreads in 4D spacetime, it forms a Bell Quantum Field in 4D spacetime and simultaneously forms a single Bell Quantum Hyper-Point in Planck Space. If slit (A) flashes, the electron's Bell Quantum Hyper-Point collapses, and the number of Bell Quantum Spheres that comprise the electron's Bell Quantum Hyper-Point is reduced. Simultaneously, on a one-to-one basis, the Bell Identity ensures that the number of Bell Quantum Spheres comprising the electron's Bell Quantum Field is reduced. The electron is now generally localized at slit A. The analysis is the same if slit B flashes rather than slit A.

Once the electron is generally localized at either slit (A) or slit (B), it will once again continue to spread towards Detector (D). Critically, however, since the electron passed through either slit (A) or slit (B), but not both, an interference pattern is not formed at detector D. Conversely, if neither slit (A) nor slit (B) flashes, as the electron passes through slits (A) and (B) the analysis of the double-slit experiment described in Section 3.2.2 above is once again applicable.

4.3. N-Body Quantum State Evolution and Collapse

The Dual Ontology conjecture examines the ontic status of N-body quantum states based on the principle that the same theoretical and physical laws of physics must apply equally to single and N-body quantum states. Instead of relying on a mathematical or ontic 3N configuration space to describe the dynamic motion of N-body quantum states, the Dual Ontology conjecture posits that all N-body quantum states are physical entities that dynamically evolve in a discrete 4D spacetime and collapse in a (3 x N) Planck Space.⁴⁸

The Bohm-EPR Thought Experiment

The Bohm version of the EPR experiment highlights the issues raised by the dynamic evolution of an N-body quantum state in 4D spacetime and its collapse in Planck Space.⁴⁹ A pair of electrons is prepared in the singlet state. The wave function of the entangled quantum state is in a superposition, and its combined angular momentum is 0. The instant the entangled quantum state is generated, the quantum state simultaneously forms two Bell Quantum Fields in 4D spacetime (Bell Quantum Fields E and F, respectively) and a single ultra-high dimensional Bell Quantum Hyper-Point ("Bell Quantum Hyper-Point EF") in Planck Space. Quantum state E is sent toward Princeton, and quantum state F is sent toward Copenhagen. Testing equipment is configured to conduct a Stern-Gerlach experiment in the z direction on either Bell Quantum Field E or Bell Quantum Field F.

Regardless of the space-like separation or dynamic motion of Bell Quantum Fields E and F in 4D spacetime, the Bell Identity ensures that the Bell Quantum Spheres that comprise Bell Quantum Fields E and F also comprise Bell Quantum Hyper-Point EF. As Bell Quantum Fields E and F dynamically spread in 4D spacetime, the number of Bell Quantum Spheres that comprise their respective Bell Quantum Fields increases, as does the number of Bell Quantum Spheres that comprise Bell Quantum Hyper-Point EF.

Bell Quantum Hyper-Point EF collapses following a Stern-Gerlach experiment in the z direction in either Princeton or Copenhagen.⁵⁰ The collapse instantaneously reduces the number of Bell Quantum Spheres that formerly composed Bell Quantum Hyper-Point EF. The Bell Identity ensures that the collapse is simultaneously linked to the reduced number of Bell Quantum Spheres that comprise Bell Quantum Field E and Bell Quantum Field F, respectively. Unlike the case with a single Bell Quantum Hyper-Point, Bell Quantum Hyper-Point EF now forms two independent Bell Quantum Hyper-Points designated as Bell Quantum Hyper-Point E and Bell Quantum Hyper-Point F. Bell Quantum Hyper-Point E shares a one-to-one mapping and identity with the Bell Quantum Spheres that now form Bell Quantum Field E, and Bell Quantum Hyper-Point F shares a one-to-one mapping and identity with the Bell Quantum Spheres that now form Bell Quantum Field F.

Following the collapse of Bell Quantum Hyper-Point EF, Bell Quantum Hyper-Point E and Bell Quantum Hyper-Point F form a product state rather than an entangled state. Using a notation based on a physical (3 x N) Planck Space rather than a mathematical 3N space, the transition would be ψ_1,2((x₁,y₁,z₁)_1,(x₂,y₂,z₂)₂) → ψ₁(x₁,y₁,z₁)₁ ⊗ ψ₂(x₂,y₂,z₂)₂.⁵¹ The reduction in the number of Bell Quantum Spheres that comprise Bell Quantum Field E and Bell Quantum Field F instantaneously causes the generalized localization of both Bell Quantum Field E and Bell Quantum Field F on the detectors in Princeton and Copenhagen, respectively. Nevertheless, regardless of how spread out each of the individual Bell Quantum Fields may have been before the collapse of Bell Quantum Hyper-Point EF, special relatively has not been violated.

If the Stern-Gerlach experiment in the z direction is conducted in Princeton on quantum state E, and the quantum state is found in the z spin-up direction, quantum state F is instantly in the z spin-down direction in Copenhagen. Conversely, if the Stern-Gerlach experiment in the z direction is conducted in Princeton on quantum state E and the quantum state is found in the z spin-down direction, quantum state F is instantly in the z spin-up direction in Copenhagen. The same analysis applies if the Stern-Gerlach experiment in the z direction is conducted on quantum state F in Copenhagen instead of quantum state E in Princeton.

5. Physical Implications of the Dual Ontology Conjecture

6. Resolving the Tension between Special Relativity and Quantum Mechanics

7. Conclusions

References

1. Adams, F. C. (2019). The degree of fine-tuning in our universe — and others. Physics Reports, 807, 1–111. [CrossRef]
2. Aghanim, N., et al. (2019). Planck 2018 results. VI. Cosmological parameters. ArXiv. https://arxiv.org/abs/1807.06209.
3. Aerts, D. (1984). The missing elements of reality in the description of quantum mechanics of the EPR paradox situation. Helvetica Physica Acta, 57(4), 421–428.
4. Albert, D. Z. (1992). Quantum mechanics and experience. Harvard University Press. https://www.jstor.org/stable/j.ctv1bzfptv.
5. Albert, D. Z. (1996). Elementary quantum metaphysics. In J. T. Cushing, A. Fine, & S. Goldstein (Eds.), Bohmian Mechanics and Quantum Theory: an Appraisal 184, 277–284. Kluwer Academic Publishers. [CrossRef]
6. Albert, D. Z. (2003). Time and chance. Harvard University Press. https://www.jstor.org/stable/j.ctvjsf57g.
7. Albert, D. Z. (2013). Wave function realism. In A. Ney & D. Z. Albert (Eds.), The Wave Function: Essays on the Metaphysics of Quantum Mechanic (pp. 51–57). Oxford University Press. https://philarchive.org/rec/ALLPOA.
8. Albert, D. Z., & Loewer, B. (1996). Tails of Schrödinger’s cat. In R. Clifton (Ed.), Perspectives on Quantum Reality: Non-relativistic, Relativistic, and Field-Theoretic (pp. 81–92). Kluwer Academic Publishers. https://link.springer.com/chapter/10.1007/978-94-015-8656-6_7.
9. Albert, D. Z., & Ney, A. (2013). The wave function: Essays on the metaphysics of quantum mechanics. Oxford University Press. https://philpapers.org/rec/ALBTWF.
10. Albert, D., & Loewer, B. (1990). Wanted dead or alive: Two attempts to solve Schrödinger’s paradox. In PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association (pp. 277–285). University of Chicago Press. https://www.jstor.org/stable/192710.
11. Alberto, P., Das, S., & Vagenas, E. C. (2011). Relativistic particle in a three-dimensional box. Physics Letters A, 375(12), 1436–1440. [CrossRef]
12. Allori, V. (2022). What is it like to be a relativistic GRW theory? Or: Quantum mechanics and relativity, still in conflict after all these years. Foundations of Physics, 52(4), 1–28. [CrossRef]
13. Lebihan (Ed.), Precis de la Philosophie de la Physique (pp. 116–151). Vuibert. https; Allori, V. (2013a). On the metaphysics of quantum mechanics. In S. Lebihan (Ed.), Precis de la Philosophie de la Physique (pp. 116–151). Vuibert. https://philpapers.org/rec/ALLOTM-2.
14. Allori, V. (2013b). Primitive ontology and the structure of fundamental physical theories. In A. Ney & D. Alberts (Eds.), The Wave Function: Essays on the Metaphysics of Quantum Mechanic (pp. 58–75). Oxford University Press. https://philarchive.org/rec/ALLPOA.
15. Allori, V. (2015). Primitive ontology in a nutshell. International Journal of Quantum Foundations, 1(3), 107–122. https://philsci-archive.pitt.edu/11651/.
16. Allori, V. (2016). How to make sense of quantum mechanics: Fundamental physical theories and primitive ontology. PhilPapers. https://philpapers.org/rec/ALLQTM.
17. Allori, V. (2016a). Primitive ontology and the classical world. R. Kastner, J. Jeknic-Dugic, G. Jaroszkiewicz (Eds.), Quantum Structural Studies: Classical Emergence from the Quantum Level. https://philsci-archive.pitt.edu/12287/.
18. Allori, V. (2020). Scientific realism without the wave-function: An example of naturalized quantum metaphysics. In S. French & J. Saatsi (Eds.), Scientific Realism and the Quantum (pp. 212–228). Oxford University Press. https://philarchive.org/rec/ALLSRW.
19. Allori, V. (2021). Primitive beables are not local ontology: On the relation between primitive ontology and local beables. Crítica (México D. F. En Línea), 53(159). [CrossRef]
20. Allori, V. (2022). Spontaneous localization theories. In G. Bacciagaluppi & O. Freire Jr. (Eds.), Oxford Handbook of the History of Interpretations and Foundations of Quantum Mechanics (pp. 1103–1134). Oxford University Press. https://philpapers.org/rec/ALLSLT-3.
21. Allori, V. (2022b). What is it like to be a relativistic GRW theory? Or: Quantum mechanics and relativity, still in conflict after all these years. Foundations of Physics, 52(4). [CrossRef]
22. Allori, V. (2023). What if we lived in the best of all possible (quantum) worlds? PhilSci-Archive. http://philsci-archive.pitt.edu/21840/1/what-if-latest.pdf.
23. Allori, V., Bassi, A., Durr, D., & Zanghi, N. (2021). Do wave functions jump?: Perspectives of the work of GianCarlo Ghirardi. Springer. https://link.springer.com/book/10.1007/978-3-030-46777-7.
24. Allori, V., Goldstein, S., Tumulka, R., & Zanghi, N. (2008). On the common structure of Bohmian mechanics and the Ghirardi-Rimini-Weber theory. The British Journal for the Philosophy of Science, 59(3), 353–389. [CrossRef]
25. Allori, V., Goldstein, S., Tumulka, R., & Zanghi, N. (2010). Many worlds and Schrödinger’s first quantum theory. The British Journal for the Philosophy of Science, 62(1), 1–27. [CrossRef]
26. Ashtekar, A., & Barrau, A. (2015). Loop quantum cosmology: From pre-inflationary dynamics to observations. Classical and Quantum Gravity, 32(23), 234001. [CrossRef]
27. Ashtekar, A., & Sloan, D. A. (2011). Probability of inflation in loop quantum cosmology. General Relativity and Quantum Cosmology, 43(12), 3619–3655. [CrossRef]
28. Azhar, F., & Loeb, A. (2021). Finely tuned models sacrifice explanatory depth. Foundations of Physics, 51(5), 1–36. [CrossRef]
29. Bacciagaluppi, G., & Valentini, A. (2009). Quantum theory at the crossroads: Reconsidering the 1927 Solvay conference. ArXiv (Cornell University. https://arxiv.org/abs/quant-ph/0609184.
30. Bahrami, M., Bassi, A., Donadi, S., Ferialdi, L., & León, G. (2015). Irreversibility and collapse models. In A. von Müller & T. Filk (Eds.), Re-Thinking Time at the Interface of Physics and Philosophy, (Vol. 4, pp. 125–146). Springer International Publishing. Kindle Edition.
31. Baker, D. J. (2009). Against field interpretations of quantum field theory. The British Journal for the Philosophy of Science, 60(3), 585–609. [CrossRef]
32. Banerjee, S., Bera, S., & Singh, T. P. (2016). Quantum nonlocality and the end of classical spacetime. International Journal of Modern Physics D, 25(12), 1644005–1644005. [CrossRef]
33. Barrett, J. A. (2005). The preferred-basis problem and the quantum mechanics of everything. The British Journal for the Philosophy of Science, 56(2), 199–220. [CrossRef]
34. Barrow, J. D. (2001). The book of nothing. Vintage. https://philpapers.org/rec/BARTBO-11.
35. Bassi, A. (2009). Collapse models: Analysis of the free particle dynamics. ArXiv. [CrossRef]
36. Bassi, A. (2021). Philosophy of quantum mechanics: Dynamical collapse theories. Oxford Research Encyclopedia of Physics. [CrossRef]
37. Bassi, A., & Ghirardi, G. (2003). Dynamical reduction models. Physics Reports, 379(5-6), 257–426. [CrossRef]
38. Bassi, A., Lochan, K., Satin, S., Singh, T. P., & Ulbricht, H. (2013). Models of wave-function collapse, underlying theories, and experimental tests. Reviews of Modern Physics, 85(2), 471–527. [CrossRef]
39. Bassi, A., & Ulbricht, H. (2014). Collapse models: From theoretical foundations to experimental verifications. Journal of Physics: Conference Series, 504. [CrossRef]
40. Becker, A. (2018). What is real? Basic Books. Kindle Edition.
41. Bedingham, D. (2021). Collapse models, relativity, and discrete spacetime. In V. Allori, A. Bassi, D. Durr, & N. Zanghi (Eds.), Do Wave Functions Jump? Perspectives of the Work of GianCarlo Ghirardi (pp. 191–203). Springer. [CrossRef]
42. Bedingham, D. (2016). Collapse models and spacetime symmetries. ArXiv. [CrossRef]
43. Bell, J. S. (2004). Speakable and unspeakable in quantum mechanics: collected papers on quantum philosophy. Cambridge University Press. Kindle Edition.
44. Bell, M., & Gao, S. (2016). Quantum nonlocality and reality: 50 years of Bell’s theorem. Cambridge University Press. Kindle Edition.
45. Belot, G. (2012). Quantum states for primitive ontologists. European Journal for Philosophy of Science, 2(1), 67–83. [CrossRef]
46. Blandford, R. D., Dunkley, J., Frenk, C. S., Lahav, O., & Shapley, A. E. (2020). Coming of age of the standard model. Nature Astronomy, 4(2), 122–123. [CrossRef]
47. Bohm, D. (1952a). Quantum theory. Prentice-Hall; Constable.
48. Bohm, D. (1952b). A suggested interpretation of the quantum theory in terms of “hidden” variables. I. Physical Review, 85(2), 166–179. [CrossRef]
49. Bohm, D., & Broglie, L. de. (2016). Causality and chance in modern physics. Routledge. [CrossRef]
50. Bohr, N., & Einstein, A. (1949). Discussion with Einstein on epistemological problems in atomic physics. Open Court Publishing Company. https://www.marxists.org/reference/subject/philosophy/works/dk/bohr.htm.
51. Bojowald, M. (2008). Loop quantum cosmology. Living Reviews in Relativity, 11(1). [CrossRef]
52. Bojowald, M. (2015). Quantum cosmology: A review. Reports on Progress in Physics, 78(2). [CrossRef]
53. Boyer, R. W. (2014). Did the universe emerge from nothing? Reductive vs. holistic cosmology. NeuroQuantology, 12(4), 424–454. [CrossRef]
54. Boyle, L., Finn, K., & Turok, N. (2018). CPT-symmetric universe. Physical Review Letters, 121(25). [CrossRef]
55. Boyle, L., & Turok, N. (2022). Thermodynamic solution of the homogeneity, isotropy, and flatness puzzles (and a clue to the cosmological constant). ArXiv (Cornell University). [CrossRef]
56. Brandenberger, R. H., & Martin, J. (2013). Trans-Planckian issues for inflationary cosmology. Classical and Quantum Gravity, 30(11), 113001. [CrossRef]
57. Brandenberger, R., & Peter, P. (2017). Bouncing cosmologies: Progress and problems. Foundations of Physics, 47(6), 797–850. [CrossRef]
58. Brenner, A. (2016). What do we mean when we ask “why is there something rather than nothing?” Erkenntnis, 81(6), 1305–1322. https://philarchive.org/rec/BREWDW.
59. Bricmont, J. (2016). Making sense of quantum mechanics. Springer. https://philpapers.org/rec/BRIMSO.
60. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., & Wehner, S. (2014). Bell nonlocality. Reviews of Modern Physics, 86(2), 419–478. [CrossRef]
61. Broglie, L. de. (1964). The current interpretation of wave mechanics. Elsevier Publishing Company.
62. Callender, C. (2014). One world, one beable. Synthese, 192(10), 3153–3177. [CrossRef]
63. Callender, C. (2020). Can we quarantine the quantum blight? In Scientific Realism and the Quantum (pp. 57–77). Oxford University Press. http://philsci-archive.pitt.edu/15450/.
64. Callender, C. (2021). Quantum mechanics: Keeping it real? The British Journal for the Philosophy of Science. [CrossRef]
65. Calmet, X. (2008). On the precision of a length measurement. European Physical Journal C, 54(3), 501–505. [CrossRef]
66. Calmet, X., Graesser, M., & Hsu, S. (2005). Minimum length from first principles. International Journal of Modern Physics D, 14(12), 2195–2199. [CrossRef]
67. Carrol, S. M. (2019). Something deeply hidden: Quantum worlds and the emergence of spacetime. Dutton. Kindle Edition.
68. Carroll, S. (2018, October 31). What is nothing? Vice Magazine Online. https://www.vice.com/en/article/vbk5va/what-is-nothing.
69. Carroll, S. M. (2014). In what sense is the early universe fine-tuned? ArXiv. [CrossRef]
70. Carroll, S. M. (2018). Why is there something, rather than nothing? ArXiv. [CrossRef]
71. Carroll, S. M., & Chen, J. (2004). Spontaneous inflation and the origin of the arrow of time. ArXiv. https://arxiv.org/abs/hep-th/0410270.
72. Carroll, S. M., & Singh, A. (2018). Mad-dog Everettianism: Quantum mechanics at its most minimal. ArXiv. [CrossRef]
73. Castro, P., Gatta, M., Croca, J. R., & Moreira, R. N. (2018). Spacetime as an emergent phenomenon: A possible way to explain entanglement and the tunnel effect. Journal of Applied Mathematics and Physics, 6, 2107–2118. [CrossRef]
74. Chen, E. K. (2017). Our fundamental physical space: An essay on the metaphysics of the wave function. The Journal of Philosophy, 114(7), 333–365. https://arxiv.org/abs/2110.14531.
75. Chen, E. K. (2018). The intrinsic structure of quantum mechanics. ArXiv. [CrossRef]
76. Chen, E. K. (2019). Realism about the wave function. Philosophy Compass, 14(7). [CrossRef]
77. Chen, E. K. (2020a). The past hypothesis and the nature of physical laws. ArXiv. [CrossRef]
78. Chen, E. K. (2020b). Bell’s theorem, quantum probabilities, and superdeterminism. ArXiv. [CrossRef]
79. Clifton, R., & Monton, B. (1999). Losing your marbles in wavefunction collapse theories. The British Journal for the Philosophy of Science, 50(4), 697–717. [CrossRef]
80. Coleman, S., & De Luccia, F. (1980). Gravitational effects on and of vacuum decay. Physical Review D, 21(12), 3305–3315. [CrossRef]
81. Cordero, A. (2001). Realism and underdetermination: Some clues from the practices-up. Philosophy of Science, 68(S3), S301–S312. [CrossRef]
82. Coutinho, F. A. B., & Wreszinski, W. F. (2016). Instantaneous spreading versus space localization for nonrelativistic quantum systems. Brazilian Journal of Physics, 46(4), 462–470. https://doi.org/10.1007/s13538-016-0426-3. [CrossRef]
83. Crouse, D. T. (2016). On the nature of discrete space-time: The atomic theory of space-time and its effects on Pythagoras’s theorem, time versus duration, inertial anomalies of astronomical bodies, and special relativity at the Planck scale. ArXiv. [CrossRef]
84. Crouse, D., & Skufca, J. (2018). On the nature of discrete space-time: Part 1: The distance formula, relativistic time dilation, and length contraction in discrete space-time. [CrossRef]
85. Davies, P. (1995). The last three minutes: Conjectures about the ultimate fate of the universe. Choice Reviews Online, 32(07), 32–386832–3868. [CrossRef]
86. Davies, P. (1996, April 27). The day time began. New Scientist. https://www.newscientist.com/article/mg15020274-200-the-day-time-began/.
87. Davies, P. (2014). The turbulent life of empty space. In J. Webb (Ed.), Nothing : Surprising Insights Everywhere from Zero to Oblivion. The Experiment.
88. Davis, T. M., & Lineweaver, C. H. (2004). Expanding confusion: Common misconceptions of cosmological horizons and the superluminal expansion of the universe. Publications of the Astronomical Society of Australia, 21(1), 97–109. [CrossRef]
89. DeWitt, B. S. (1967). Quantum theory of gravity. I. the canonical theory. Physical Review, 160(5), 1113–1148. [CrossRef]
90. Diez-Tejedor, A., & Sudarsky, D. (2012). Towards a formal description of the collapse approach to the inflationary origin of the seeds of cosmic structure. Journal of Cosmology and Astroparticle Physics, 2012(07), 045–045. [CrossRef]
91. Doyle, R. (2014). The origin of irreversibility. Department of Astronomy, Harvard University. https://www.informationphilosopher.com/problems/reversibility/Irreversibility.pdf.
92. Durham, I. T. (2018). Bell’s theory of beables and the concept of `universe’. ArXiv (Cornell University). [CrossRef]
93. Dürr, D., Goldstein, S., Taylor, J. O., Tumulka, R., & Zanghi, N. (2006). Topological factors derived from Bohmian mechanics. Annales Henri Poincaré, 7(4), 791–807. [CrossRef]
94. Dürr, D., Goldstein, S., & Zanghi, N. (1995). Bohmian mechanics as the foundation of quantum mechanics. ArXiv.org. [CrossRef]
95. Dyson, F. J. (1979). Time without end: Physics and biology in an open universe. Reviews of Modern Physics, 51(3), 447–460. [CrossRef]
96. Eddington, A. S. (1929). The nature of the physical world. Cambridge University Press. https://henry.pha.jhu.edu/Eddington.2008.pdf.
97. Egg, M. (2021). Quantum ontology without speculation. European Journal for Philosophy of Science, 11(1). [CrossRef]
98. Egg, M., & Esfeld, M. (2014). Primitive ontology and quantum state in the GRW matter density theory. Synthese, 192(10), 3229–3245. [CrossRef]
99. Egg, M., & Saatsi, J. (2021). Scientific realism and underdetermination in quantum theory. Philosophy Compass, 16(11). [CrossRef]
100. Einstein, A. (2011). Letters on wave mechanics: Correspondence with H.A. Lorentz, Max Planck, and Erwin Schrödinger (K. Przibram, Ed.). Philosophical Library/Open Road. Kindle Edition.
101. Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47(10), 777–780. [CrossRef]
102. Esfeld, M. (2012). Ontic structural realism and the interpretation of quantum mechanics. European Journal for Philosophy of Science, 3(1), 19–32. [CrossRef]
103. Esfeld, M. (2014). Science and metaphysics: The case of quantum physics. In A. Reboul (Ed.), Mind, Values, and Metaphysics Vol.1 (pp. 267–285). Springer International Publishing. http://philsci-archive.pitt.edu/3401/1/Esfeld-MetScience.pdf.
104. Esfeld, M. (2016). Collapse or no collapse? What is the best ontology of quantum mechanics in the primitive ontology framework? In S. Gao (Ed.), Collapse of the Wave Function: Models, Ontology, Origin, and Implications. Cambridge University Press. http://philsci-archive.pitt.edu/12666/.
105. Esfeld, M. (2019). From the measurement problem to the primitive ontology programme. ArXiv. https://arxiv.org/abs/1907.11058.
106. Esfeld, M., & Gisin, N. (2014). The GRW flash theory: A relativistic quantum ontology of matter in space-time? Philosophy of Science, 81(2), 248–264. [CrossRef]
107. Feynman, R. P. (2017). The character of physical law. The MIT Press. https://www.ling.upenn.edu/~kroch/courses/lx550/readings/feynman1-4.pdf (Original work published 1967).
108. Fine, A. (1996). The shaky game. University of Chicago Press. Kindle Edition.
109. Fleming, G. (1996). Just how radical is hyperplane-dependence? In R. Clifton (Ed.), Perspectives on Quantum Reality: Non-Relativistic, Relativistic and Field Theoretic (pp. 11–28). Kluwer Academic Publishers. https://link.springer.com/chapter/10.1007/978-94-015-8656-6_2.
110. Forrest, P. (1988). Quantum metaphysics. Blackwell. https://philpapers.org/rec/FORQM.
111. Fortin, S., Alberto, J., & Arriaga, J. (2018). About the nature of the wave function and its dimensionality: The case of quantum chemistry. PhilSci Archive. http://philsci-archive.pitt.edu/14868/1/3N-Dimensions.pdf.
112. Frigg, R. (2018). Properties and the Born rule in GRW theory. In S. Gao (Ed.), Collapse of the Wave Function: Models, Ontology, Origin, and Implications. (pp. 124–133). Cambridge University. http://philsci-archive.pitt.edu/20933/.
113. Gao, S. (2013). A discrete model of energy-conserved wavefunction collapse. Royal Society Publishing. https://arxiv.org/abs/1304.0439.
114. Gao, S. (2013b). Three possible implications of spacetime discreteness. PhilArchive. https://philarchive.org/archive/GAOTIOv1.
115. Gao, S. (2016). The meaning of the wave function: In search of the ontology of quantum mechanics. Cambridge University Press. ArXiv. https://arxiv.org/abs/1611.02738.
116. Gao, S. (2017). Is an electron a charge cloud? A reexamination of Schrödinger’s charge density hypothesis. Foundations of Science, 23(1), 145–157. [CrossRef]
117. Gao, S. (2018a). Against the field ontology of quantum mechanics. PhilSci Archive. http://philsci-archive.pitt.edu/id/eprint/15476.
118. Gao, S. (2018b). Collapse of the wave function: Models, ontology, origin, and implications. Cambridge University Press.
119. Gao, S. (2019). Quantum theory is incompatible with relativity: A new proof beyond Bell’s theorem and a test of unitary quantum theories. PhilSci Archive. http://philsci-archive.pitt.edu/16155/.
120. Gao, S. (2020). A puzzle for the field ontologists. Foundations of Physics, 50(11), 1541–1553. [CrossRef]
121. Gao, S. (2022). Reality of mass and charge and its implications for the meaning of the wave function. PhilSci Archive. http://philsci-archive.pitt.edu/21317/.
122. Gao, S. (2024). Locality implies reality of the wave function: Hardy’s theorem revisited. Philsci-Archive.pitt.edu. https://philsci-archive.pitt.edu/23005/.
123. Garfinkle, D., Ijjas, A., & Steinhardt, P. J. (2023). Initial conditions problem in cosmological inflation revisited. Physics Letters B, 843, 138028. [CrossRef]
124. Geert, D. (2006). The ontology of spacetime (D. Dieks, Ed.). Elsevier. https://philpapers.org/rec/DIETOO.
125. Genovese, M. (2016). Experimental tests of Bell inequalities. In S. Gao & M. Bell (Eds.), Quantum Nonlocality and Reality: 50 Years of Bells Theorem. Cambridge University Press. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.49.1804.
126. Genovese, M. (2023). Can quantum non-locality be connected to extra-dimensions? International Journal of Quantum Information, 21(07), 2340003. [CrossRef]
127. Genovese, M., & Gramegna, M. (2019). Quantum correlations and quantum non-locality: A review and a few new ideas. Applied Sciences, 9(24), 5406. [CrossRef]
128. Ghirardi, G. (2009a). The interpretation of quantum mechanics: Where do we stand? Journal of Physics: Conference Series, 174, 012013. [CrossRef]
129. Ghirardi, G. (2009b). Does quantum nonlocality irremediably conflict with special relativity? Foundations of Physics, 40(9-10), 1379–1395. [CrossRef]
130. Ghirardi, G. (2021). Sneaking a look at god’s cards. Princeton University Press.
131. Ghirardi, G. C., Pearle, P., & Rimini, A. (1990). Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles. Physical Review A, 42(1), 78–89. [CrossRef]
132. Ghirardi, G. C., Rimini, A., & Weber, T. (1986). Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34(2), 470–491. [CrossRef]
133. Giddings, S. B. (2019). Black holes in the quantum universe. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377(2161), 20190029. [CrossRef]
134. Goldstein, S. (1998a). Quantum theory without observers—part one. Physics Today, 51(3), 42–46. [CrossRef]
135. Goldstein, S. (1998b). Quantum theory without observers—part two. Physics Today, 51(4), 38–42. [CrossRef]
136. Goldstein, S., Norsen, T., Tausk, D., & Zanghi, N. (2011). Bell’s theorem. Scholarpedia, 6(10), 8378. [CrossRef]
137. Goldstein, S., & Zanghi, N. (2011). Reality and the role of the wavefunction in quantum theory. ArXiv (Cornell University).
138. Graham, P. W., Kaplan, D. E., & Rajendran, S. (2018). Born again universe. Physical Review D, 97(4). [CrossRef]
139. Greenberger, D. M., Horne, M. A., & Zeilinger, A. (2007). Going beyond Bell’s theorem. ArXiv. https://arxiv.org/abs/0712.0921.
140. Griffiths, D. J., & Schroeter, D. F. (2018). Introduction to quantum mechanics (2nd ed.). Cambridge University Press.
141. Gröblacher, S., Paterek, T., Kaltenbaek, R., Brukner, Č., Żukowski, M., Aspelmeyer, M., & Zeilinger, A. (2007). An experimental test of non-local realism. Nature, 446(7138), 871–875. [CrossRef]
142. Grünbaum, A. (2009). Why is there a world AT ALL, rather than just nothing? Ontology Studies, 9, 7–19.
143. Guerreiro, T., Sanguinetti, B., Zbinden, H., Gisin, N., & Suárez, A. (2012). Single-photon space-like antibunching. Physics Letters, 376(32), 2174–2177. [CrossRef]
144. Guth, A. H. (2007). Eternal inflation and its implications. Journal of Physics A: Mathematical and Theoretical, 40(25), 6811–6826. [CrossRef]
145. Hagar, A. (2015). Discrete or continuous?: The quest for fundamental length in modern physics. Cambridge University Press. Kindle Edition.
146. Harrigan, N., & Spekkens, R. W. (2010). Einstein, incompleteness, and the epistemic view of Quantum states. Foundations of Physics, 40(2), 125–157. [CrossRef]
147. Hartle, J. B. (1997). Quantum cosmology: Problems for the 21st century. Physics in the 21st Century, 179–199. [CrossRef]
148. Hartle, J. B., & Hawking, S. W. (1983). Wave function of the universe. Physical Review D, 28(12), 2960–2975. [CrossRef]
149. Hawking, S. W., & Penrose, R. (1970). The singularities of gravitational collapse and cosmology. Proceedings of the Royal Society of London, 314(1519), 529–548. [CrossRef]
150. Hayes, B. (2012). The science of sticky spheres. American Scientist, 100(6), 442–442. [CrossRef]
151. Hegerfeldt, G. C. (1998). Instantaneous spreading and Einstein causality in quantum theory. Annalen Der Physik, 7(7-8), 716–725.
152. Hitchcock, C. (2004). Contemporary debates in philosophy of science. Blackwell Pub.
153. Hobson, A. (2013). There are no particles, there are only fields. American Journal of Physics, 81(3), 211–223. [CrossRef]
154. Hobson, A. (2019). Realist analysis of six controversial quantum issues. In M. R. Matthews (Ed.), Mario Bunge: A Centenary Fetschrift (pp. 329–348). Springer Nature Switzerland. https://browse.arxiv.org/pdf/1901.02088.pdf.
155. Holman, M. (2018). How problematic is the near-Euclidean spatial geometry of the large-scale universe? Foundations of Physics, 48(11), 1617–1647. [CrossRef]
156. Holt, J. (2012). Why does the world exist?: An existential detective story. Liveright. Kindle Edition.
157. Hooft, G. t. (2018). Time, the arrow of time, and quantum mechanics. Frontiers in Physics, 6. [CrossRef]
158. Hossenfelder, S. (2013). Minimal length scale scenarios for quantum gravity. Living Reviews in Relativity, 16(1). [CrossRef]
159. Hossenfelder, S. (2014). Theory and phenomenology of space-time defects. Advances in High Energy Physics, 2014, 1–6. [CrossRef]
160. Hossenfelder, S. (2018). Lost in math. Basic Books.
161. Howard, D. (1985). Einstein on locality and separability. Studies in History and Philosophy of Science, 16(3), 171–201. [CrossRef]
162. Howard, D. (1989). Holism, separability, and the metaphysical implications of the Bell experiments. In E. McMullin (Ed.), Philosophical consequences of quantum theory: Reflections on Bell’s theorem (pp. 224–253). University of Notre Dame Press. https://philpapers.org/rec/HOWHSA-2.
163. Howard, D. (1990). “Nicht sein kann was nicht sein darf,” or the prehistory of EPR, 1909–1935: Einstein’s early worries about the quantum mechanics of composite systems. In A. I. Miller (Ed.), Sixty-Two Years of Uncertainty (pp. 61–111). Cambridge University. [CrossRef]
164. Howard, D. (2004). Who invented the “Copenhagen Interpretation”? A study in mythology. Philosophy of Science, 71(5), 669–682. [CrossRef]
165. Hubert, M., & Romano, D. (2018). The wave-function as a multi-field. European Journal for Philosophy of Science, 8(3), 521–537. [CrossRef]
166. Huggett, N., & Wuthrich, C. (2021). Out of nowhere: Introduction: The emergence of spacetime. PhilArchive. [CrossRef]
167. Huggett, N., & Wüthrich, C. (2013). Emergent spacetime and empirical (in)coherence. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(3), 276–285. [CrossRef]
168. Ijjas, A., & Steinhardt, P. J. (2022). Entropy, black holes, and the new cyclic universe. Physics Letters B, 824, 136823. [CrossRef]
169. Ijjas, A., Steinhardt, P. J., & Loeb, A. (2013). Inflationary paradigm in trouble after Planck2013. ArXiv. [CrossRef]
170. Isam, A. (2018). Spacetime discreteness: Shedding light on two of the simplest observations in physics. Journal of Modern Physics, 09(07), 1415–1431. [CrossRef]
171. Jammer, M. (1974). The philosophy of quantum mechanics. Wiley-Interscience.
172. Jones, R. H. (2018). Mystery 101: Introduction to the big questions and the limits of human knowledge. State University of New York. https://philpapers.org/rec/JONMA-2.
173. Kahan, D. (2024). On the Dual Ontological Structure and Mixed Dynamics of the Universe. [CrossRef]
174. Karam, R. (2020). Why are complex numbers needed in quantum mechanics? Some answers for the introductory level. American Journal of Physics, 88(1), 39–45. [CrossRef]
175. Kastner, R. (2017). On quantum collapse as a basis for the second law of thermodynamics. Entropy, 19(3), 106. [CrossRef]
176. Kastner, R. (2023). Quantum theory needs (and probably has) real reduction. ArXiv.org. [CrossRef]
177. Klevgard, P. A. (2020). The Mach-Zehnder interferometer and photon dualism. In J. A. Shaw, K. Creath, & V. Lakshminarayanan (Eds.), In Light in Nature VIII (pp. 61–81). SPIE. [CrossRef]
178. Kochen, S., & Specker, E. (1967). The problem of hidden variables in quantum mechanics. Indiana University Mathematics Journal, 17(1), 59–87. [CrossRef]
179. Kragh, H. (2013). What’s in a name: History and meanings of the term “big bang.” ArXiv. [CrossRef]
180. Krauss, L. M. (2012). A universe from nothing: Why is there something rather than nothing? Free Press.
181. Kumar, M. (2011). Quantum: Einstein, Bohr, and the great debate about the nature of reality. W.W. Norton & Co. Kindle Edition.
182. Lam, V., & Wüthrich, C. (2018). Spacetime is as spacetime does. Studies in History and Philosophy of Modern Physics, 64, 39–51. [CrossRef]
183. Landsman, K., & Reuvers, R. (2013). A flea on Schrödinger’s cat. ArXiv. [CrossRef]
184. Lechuga, R. L., & Sudarsky, D. (2023). Eternal inflation and collapse theories. ArXiv. [CrossRef]
185. Leggett, A. J. (2003). Nonlocal hidden-variable theories and quantum mechanics: An incompatibility theorem. Foundations of Physics, 33(10), 1469–1493. [CrossRef]
186. Leifer, M. S. (2014). Is the quantum state real? An extended review of ψ-ontology theorems. Quanta, 3(1), 67. [CrossRef]
187. León, G., Landau, S. J., & Piccirilli, M. P. (2014). Quantum collapse as a source of the seeds of cosmic structure during the radiation era. Physical Review, 90(8). [CrossRef]
188. Leslie, J., & Kuhn, R. L. (2013). The mystery of existence. John Wiley & Sons.
189. Lewis, P. (1995). GRW and the tails problem. Topoi, 14(1), 23–33. [CrossRef]
190. Lewis, P. (2004). Life in configuration space. The British Journal for the Philosophy of Science, 55(4), 713–729. [CrossRef]
191. Lewis, P. J. (2013). Dimension and illusion. In A. Ney & D. Albert (Eds.), The Wave Function: Essays on the Metaphysics of Quantum Mechanics (pp. 110–125). Oxford University Press. http://philsci-archive.pitt.edu/8841/.
192. Lewis, P. J. (2016). Quantum ontology: A guide to the metaphysics of quantum mechanics. Oxford University Press. Kindle Edition.
193. Lewis, P. J. (2017). On the status of primitive ontology. In S. Gao (Ed.), Collapse of the Wave Function: Models, Ontology, Origin, and Implications (pp. 154–166). Cambridge University. http://philsci-archive.pitt.edu/14421/.
194. Licata, I., & Chiatti, L. (2019). Event-Based quantum mechanics: A context for the emergence of classical information. Symmetry, 11(2), 181–181. [CrossRef]
195. Lineweaver, C. H., & Davis, T. M. (2005, March). Misconceptions about the Big Bang. Scientific American, 292(3), 36–45. [CrossRef]
196. Lucia, U., & Grisolia, G. (2022). Thermodynamic definition of time: Considerations on the EPR paradox. Mathematics, 10(15), 2711. [CrossRef]
197. Mack, K. (2020). The end of everything: (Astrophysically speaking). Scribner.
198. Mariani, C. (2022a). Does the primitive ontology of GRW rest on shaky ground? In V. Allori (Ed.), Quantum Mechanics and Fundamentality (pp. 127–139). Springer, Cham. [CrossRef]
199. Mariani, C. (2022b). Non-accessible mass and the ontology of GRW. Studies in History and Philosophy of Science, 91, 270–279. [CrossRef]
200. Martin, J., & Brandenberger, R. H. (2001). Trans-Planckian problem of inflationary cosmology. 63(12). ArXiv. https://arxiv.org/abs/hep-th/0005209.
201. Maudlin, T. (1995). Three measurement problems. Topoi, 14(1), 7–15. [CrossRef]
202. Maudlin, T. (2007). Completeness, supervenience, and ontology. Journal of Physics A, 40(12), 3151–3171. [CrossRef]
203. Maudlin, T. (2010). Can the world be only wavefunction? In S. Saunders, J. Barrett, A. Kent, & D. Wallace (Eds.), Everett, Quantum Theory, & Reality (pp. 121–143). [CrossRef]
204. Maudlin, T. (2011). Quantum non-locality & relativity : Metaphysical intimations of modern physics. (3rd ed.). John Wiley. Kindle Edition.
205. Maudlin, T. (2013a). Philosophy of physics: Space and time (Princeton foundations of contemporary philosophy book 11). Princeton University Press. Kindle Edition.
206. Maudlin, T. (2013b). The nature of the quantum state. In D. Albert & A. Ney (Eds.), The Wave Function: Essays on the Metaphysics of Quantum Mechanics (pp. 126–153). [CrossRef]
207. Maudlin, T. (2014). What Bell did. Journal of Physics A: Mathematical and Theoretical, 47(42), 424010. [CrossRef]
208. Maudlin, T. (2015). The universal and the local in quantum theory. Topoi, 34(2), 349–358. [CrossRef]
209. Maudlin, T. (2016). Local beables and the foundations of physics. In M. Bell & S. Gao (Eds.), Quantum Nonlocality and Reality: 50 Years of Bell’s Theorem (pp. 317–330). Cambridge University Press. [CrossRef]
210. Maudlin, T. (2018). Ontological clarity via canonical presentation: Electromagnetism and the Aharonov–Bohm effect. Entropy, 20(6), 465. [CrossRef]
211. Maudlin, T. (2019). Philosophy of physics: Quantum theory (Princeton foundations of contemporary philosophy book 19) Princeton University Press. Kindle Edition.
212. Maudlin, T. (2020). Appreciating what he did. In V. Allori, A. Bassi, D. Durr, & N. Zanghi (Eds.), Do Wave Functions Jump? Perspectives of the Work of GianCarlo Ghirardi (pp. 55–61). Springer. [CrossRef]
213. Maudlin, T., Okon, E., & Sudarsky, D. (2020). On the status of conservation laws in physics: Implications for semiclassical gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 69, 67–81. [CrossRef]
214. McCoy, C. D. (2015). Does inflation solve the hot Big Bang model’s fine-tuning problems? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 51, 23–36. [CrossRef]
215. McQueen, K. J. (2015). Four tails problems for dynamical collapse theories. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 49, 10–18. [CrossRef]
216. Melia, F. (2020). The cosmic spacetime. CRC Press. Kindle Edition.
217. Melia, F. (2021a). Thermodynamics of the rh = ct universe: A simplification of cosmic entropy. The European Physical Journal C, 81(234). [CrossRef]
218. Melia, F. (2021b). Classicization of quantum fluctuations at the Planck scale in the rh = ct universe. Physics Letters B, 818, 136362. [CrossRef]
219. Melia, F. (2022a). A candid assessment of standard cosmology. Publications of the Astronomical Society of the Pacific, 134(1042), 121001. [CrossRef]
220. Melia, F. (2022b). Initial energy of a spatially flat universe -- a hint of its possible origin. ArXiv. [CrossRef]
221. Melia, F. (2023). The Friedmann–Lemaître–Robertson–Walker metric and the principle of equivalence. Zeitschrift Für Naturforschung, 78(6), 525–533. [CrossRef]
222. Mermin, N. D. (1981). Quantum mysteries for anyone. The Journal of Philosophy, 78(7), 397–408. [CrossRef]
223. Moghri, M. (2020). Much ado about nothingness? Kriterion (Salzburg), 34(3), 79–98. [CrossRef]
224. Monton, B. (2002). Wave function ontology. Synthese, 130(2), 265–277. https://philarchive.org/rec/MONWFO-2.
225. Monton, B. (2004). The problem of ontology for spontaneous collapse theories. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 35(3), 407–421. [CrossRef]
226. Monton, B. (2006). Quantum mechanics and 3N-Dimensional Space. Philosophy of Science, 73(5), 778–789. [CrossRef]
227. Monton, B. (2013). Against 3n-dimensional space. In A. Ney & D. Albert (Eds.), The Wave Function: Essay in the Metaphysics of Quantum Mechanics (pp. 154–167). Oxford University Press. [CrossRef]
228. Musser, G. (2015). Spooky action at a distance: The phenomenon that reimagines space and time and what it means for black holes, the big bang, and theories of everything. Scientific American/Farrar, Straus and Giroux. Kindle Edition.
229. Myrvold, W. C. (2002). On peaceful coexistence: Is the collapse postulate incompatible with relativity? Studies in History and Philosophy of Modern Physics, 33(3), 435–466. [CrossRef]
230. Myrvold, W. C. (2015). What is a wavefunction? Synthese, 192(10), 3247–3274. [CrossRef]
231. Myrvold, W. C. (2017). Ontology for collapse theories. In S. Gao (Ed.), Collapse of the Wave Function: Models, Ontology, Origin, and Implications (pp. 97–123). Cambridge University Press. http://philsci-archive.pitt.edu/13318/.
232. Myrvold, W. C. (2019a). Ontology for relativistic collapse theories. In O. Lombardi, S. Fortin, & C. Lopez (Eds.), Quantum Worlds: Perspectives on the Ontology of Quantum Mechanics (pp. 9–31). Cambridge University Press. [CrossRef]
233. Myrvold, W. C. (2019b). How could relativity be anything other than physical? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 67, 137–143. [CrossRef]
234. Myrvold, W. C. (2019c). On the status of quantum state realism. ArXiv. [CrossRef]
235. Narasimhan, A., Chopra, D., & Kafatos, M. C. (2019). The nature of the Heisenberg-von Neumann cut: Enhanced orthodox interpretation of quantum mechanics. Activitas Nervosa Superior, 61(12-17), 12–17. [CrossRef]
236. Neumaier, A. (2019). Foundations of quantum physics I. A critique of the tradition. ArXiv. [CrossRef]
237. Ney, A. (2016). Separability, locality, and higher dimensions in quantum mechanics. Philarchive.org. https://philarchive.org/rec/NEYSLA.
238. Ney, A. (2021). The world in the wave function : A metaphysics for quantum physics. Oxford University Press. Kindle Edition.
239. Ney, A. (2023). Three arguments for wave function realism. European Journal for Philosophy of Science, 13(4). [CrossRef]
240. Norsen, T. (2005). Einstein’s boxes. American Journal of Physics, 73(2), 164–176. [CrossRef]
241. Norsen, T. (2007). Against “realism.” Foundations of Physics, 37(3), 311–340. [CrossRef]
242. Norsen, T. (2010). The theory of (exclusively) local beables. Foundations of Physics, 40(12), 1858–1884. [CrossRef]
243. Norsen, T. (2011). John S. Bell’s concept of local causality. American Journal of Physics, 79(12), 1261–1275. [CrossRef]
244. Norsen, T. (2016). Quantum solipsism and nonlocality. In M. Bell & S. Gao (Eds.), Quantum Nonlocality and Reality: 50 Years of Bell’s Theorem (pp. 204–237). Cambridge University Press.
245. Norsen, T. (2017). Foundations of quantum mechanics: An exploration of the physical meaning of quantum theory. Springer. Kindle Edition.
246. Norsen, T. (2018). On the explanation of Born-rule statistics in the de Broglie-Bohm Pilot-Wave theory. Entropy, 20(6), 422. [CrossRef]
247. Norsen, T., Marian, D., & X. Oriols. (2015). Can the wave function in configuration space be replaced by single-particle wave functions in physical space? Synthese, 192(10), 3125–3151. [CrossRef]
248. North, J. (2013). The structure of a quantum world. In A. Ney & D. Albert (Eds.), The Wave Function Essays on the Metaphysics of Quantum Mechanics (pp. 183–202). Oxford University Press. Kindle Edition.
249. Ojo, A. (2005). On a thermodynamic basis for inflationary cosmology. ArXiv. [CrossRef]
250. Okon, E., & Sudarsky, D. (2014). Benefits of objective collapse models for cosmology and quantum gravity. Foundations of Physics, 44(2), 114–143. [CrossRef]
251. Oldofredi, A. (2018). Particle creation and annihilation: Two Bohmian approaches. Lato Sensu: Revue de La Société de Philosophie Des Sciences, 5(1), 77–85. [CrossRef]
252. OpenAI. (2023). ChatGPT (Mar 14 version) [Large language model]. https://chat.openai.com/chat.
253. Patel, V., & Lineweaver, C. (2017). Solutions to the cosmic initial entropy problem without equilibrium initial conditions. Entropy, 19(8), 411. [CrossRef]
254. Pearle, P. (1989). Combining stochastic dynamical state-vector reduction with spontaneous localization. Physical Review E, 39(5), 2277–2289. [CrossRef]
255. Pearle, P. (2000). Wavefunction collapse and conservation laws. ArXiv. https://arxiv.org/abs/quant-ph/0004067.
256. Pearle, P. (2009). How stands collapse II. In W. Myrvold & J. Christian (Eds.), Quantum Reality, Relativistic Causality and Closing the Epistemic Circle: Essays in Honor of Abner Shimony (pp. 257–292). Springer. [CrossRef]
257. Penrose, R. (1989a). The emperor’s new mind: Concerning computers, minds, and the laws of physics. Oxford University Press.
258. Penrose, R. (1989b). Difficulties with inflationary cosmology. Annals of the New York Academy of Sciences, 571(1), 249–264. [CrossRef]
259. Penrose, R. (1996). On gravity’s role in quantum state reduction. general Relativity and Gravitation, 28(5), 581–600. [CrossRef]
260. Penrose, R. (1997). Physics and the mind. In M. Longair (Ed.), The Large, the Small and the Human Mind (pp. 93–143). Cambridge University Press.
261. Penrose, R. (2006). Before the big bang: An outrageous new perspective and its implications for particle physics. Proceedings of EPAC 2006, 060626, 2759–2767.
262. Penrose, R. (2009). Black holes, quantum theory and cosmology. Journal of Physics: Conference Series, 174, 012001. [CrossRef]
263. Penrose, R. (2018). The big bang and its dark-matter content: Whence, whither, and wherefore. Foundations of Physics, 48(10), 1177–1190. [CrossRef]
264. Pérez, A., Sahlmann, H., & Sudarsky, D. (2006). On the quantum origin of the seeds of cosmic structure. Classical and Quantum Gravity, 23(7), 2317–2354. [CrossRef]
265. Price, H. (1995). Cosmology, time’s arrow, and that old double standard. In S. Savitt (Ed.), Time’s Arrows Today: Recent Physical and Philosophical Work on the Direction of Time (pp. 66–94). Cambridge University Press. [CrossRef]
266. Price, H. (1996). Time’s arrow & Archimedes’ point : New directions for the physics of time. Oxford University Press. https://philpapers.org/rec/PRITAA-2.
267. Price, H. (2004). On the origins of the arrow of time: Why there is still a puzzle about the low entropy past. In C. Hitchcock (Ed.), Contemporary Debates in the Philosophy of Science (pp. 219–239). Blackwell Publishing Ltd. https://philpapers.org/rec/PRIOTO-2.
268. Pusey, M. F., Barrett, J., & Rudolph, T. (2012). On the reality of the quantum state. Nature Physics, 8(6), 475–478. [CrossRef]
269. Redd, N. T. (2013). What is dark energy? Space.com. https://www.space.com/20929-dark-energy.html.
270. Renou, M.-O., Trillo, D., Weilenmann, M., Thinh, L. P., Tavakoli, A., Gisin, N., Acín, A., & Navascués, M. (2021). Quantum physics needs complex numbers. Research Gate. https://www.researchgate.net/publication/348802613_Quantum_physics_needs_complex_numbers.
271. Romano, D. (2020). Multi-field and Bohm’s theory. Synthese, 198(11), 10587–10609. [CrossRef]
272. Rovelli, C. (2006). The disappearance of space and time. In D. Dieks (Ed.), The Ontology of Spacetime (Vol. 1, pp. 25–36). Elsevier. https://www.sciencedirect.com/science/article/abs/pii/S1871177406010023.
273. Rovelli, C. (2011). “Forget time.” Foundations of Physics, 41(9), 1475–1490. [CrossRef]
274. Rovelli, C. (2019). Where was past low-entropy? Entropy, 21(5), 466. [CrossRef]
275. Rovelli, C., Carnell, S., & Segre, E. (2018). Reality is not what it seems: The journey to quantum gravity. Riverhead Books. Kindle Edition.
276. Rovelli, C., & Smolin, L. (1995). Discreteness of area and volume in quantum gravity. Nuclear Physics B, 442(3), 593–619. [CrossRef]
277. Rovelli, C., & Speziale, S. (2003). Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction. Physical Review D, 67(6). [CrossRef]
278. Rovelli, C., & Vidotto, F. (2022). Philosophical foundations of loop quantum gravity. ArXiv. [CrossRef]
279. Saunders, S., Kent, A., Wallace, D. K., & Barrett, J. (Eds.). (2010). Many worlds? Everett, quantum theory, & reality. Oxford University Press. Kindle Edition. [CrossRef]
280. Schlosshauer, M. (2005). Decoherence, the measurement problem, and interpretations of quantum mechanics. Reviews of Modern Physics, 76(4), 1267–1305. [CrossRef]
281. Schlosshauer, M. (2019). The quantum-to-classical transition and decoherence. ArXiv. [CrossRef]
282. Sebens, C. T. (2021). Electron charge density: A clue from quantum chemistry for quantum foundations. Foundations of Physics, 51(4). [CrossRef]
283. Sebens, C. T. (2023). Eliminating electron self-repulsion. Foundations of Physics, 53(4). [CrossRef]
284. Sedley, D. (1982). Two conceptions of vacuum. Phronesis, 27(1-2), 175–193. [CrossRef]
285. Shankar, R. (1994). Principles of quantum mechanics (2nd ed.). Springer US. [CrossRef]
286. Singh, T. P. (2017). Wave function collapse, non-locality, and space-time structure. In S. Gao (Ed.), Collapse of the Wave Function: Models, Ontology Origin, and Implications (pp. 295–311). [CrossRef]
287. Singh, T. P. (2018). Space-time from collapse of the wave-function. Zeitschrift Für Naturforschung A, 74(2), 147–152. [CrossRef]
288. Slowik, E. (2016). A historical defense of non-spacetime hypotheses: Non-Local beables and Leibnizian ubeity. Philosophia Scientae, 20(3), 149–166. [CrossRef]
289. Smolin, L. (2004). Atoms of space and time. Scientific American, 290(1), 66–75. https://www.jstor.org/stable/26172656.
290. Smolin, L. (2008). Generic predictions of quantum theories of gravity. In D. Oriti (Ed.), Approaches to Quantum Gravity: Toward a New Understanding of Space, Time, and Matter (pp. 548–570). Cornell University. https://arxiv.org/abs/hep-th/0605052.
291. Smolin, L. (2017). Three roads to quantum gravity. Basic Books.
292. Snyder, D. M. (2000). Irreversibility and measurement in quantum mechanics. ArXiv. [CrossRef]
293. Solé, A. (2013). Bohmian mechanics without wave function ontology. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(4), 365–378. [CrossRef]
294. Solé, A., & Hoefer, C. (2015). Introduction: Space–time and the wave function. Synthese, 192(10), 3055–3070. [CrossRef]
295. Sorensen, R. (2020). Nothingness. In E. N. Zalta & U. Nodelman (Eds.), Stanford Encyclopedia of Philosophy (Spring 2020). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/spr2020/entries/nothingness/.
296. Srinivas, M. (1980). Collapse postulate for observables with continuous spectra. Communications in Mathematical Physics, 71(2), 131–158. [CrossRef]
297. Stapp, H. P. (2017). Quantum theory and free will. In Springer eBooks. Springer International Publishing. [CrossRef]
298. Steinhardt, P. J. (2011, April 1). The inflation debate: Is the theory at the heart of modern cosmology deeply flawed? Scientific American, 18–25. https://www.scientificamerican.com/article/the-inflation-summer/.
299. Steinhardt, P. J., & Turok, N. (2007). Endless universe : Beyond the big bang. Broadway Books.
300. Stoica, O. C. (2019). Representation of the wave function on the three-dimensional space. Physical Review A, 100(4). [CrossRef]
301. Sudarsky, D. (2010). The quantum origin of the seeds of cosmic structure: The case for a missing link. AIP Conference Proceedings, 1256, 107–121. [CrossRef]
302. Sudarsky, D. (2011). Shortcomings in the understanding of why cosmological perturbations look classical. International Journal of Moder Physics D, 20(04), 509–552. [CrossRef]
303. Tatum, E. T. (2018). Why flat space cosmology is superior to standard inflationary cosmology. Journal of Modern Physics, 09(10), 1867–1882. [CrossRef]
304. Tatum, E. T., & Seshavatharam, U. (2021). Flat space cosmology. Universal-Publishers.
305. Torre, A. (2016). Do we finally understand quantum mechanics? ArXiv. [CrossRef]
306. Tumulka, R. (2017). Paradoxes and primitive ontology in collapse theories of quantum mechanics. In S. Gao (Ed.), Collapse of the Wave Function: Models, Ontology, Origin and Implications (pp. 134–153). Cambridge University Press. https://arxiv.org/pdf/1102.5767.pdf?origin=publication_detail.
307. Turok, N., & Boyle, L. (2022). Gravitational entropy and the flatness, homogeneity and isotropy puzzles. ArXiv. [CrossRef]
308. Turok, N., & Boyle, L. (2023). A minimal explanation of the primordial cosmological perturbations. ArXiv. [CrossRef]
309. Unger, R. M., & Smolin, L. (2015). The singular universe and the reality of time: A proposal in natural philosophy. Cambridge University Press.
310. Vagnozzi, S., & Loeb, A. (2022). The challenge of ruling out inflation via the primordial graviton background. The Astrophysical Journal Letters, 939(2), L22. [CrossRef]
311. Vaidman, L. (2020). Derivations of the born rule. In M. Hemmo & O. Shenko (Eds.), Jerusalem Studies in Philosophy and History of Science (pp. 567–584). Springer. [CrossRef]
312. Vaidman, L. (2021a). Many-Worlds interpretation of quantum mechanics. The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/fall2021/entries/qm-manyworlds.
313. Vaidman, L. (2021b). Wave function realism and three dimensions. In V. Allori (Ed.), Quantum Mechanics and Fundamentality; Naturalizing Quantum Theory between Scientific Realism and Ontological Indeterminacy. Springer. http://philsci-archive.pitt.edu/19979/.
314. Verlinde, E. (2000). On the holographic principle in a radiation dominated universe. ArXiv. [CrossRef]
315. Verlinde, E. (2011). On the origin of gravity and the laws of Newton. Journal of High Energy Physics, 4, 1–27. [CrossRef]
316. Vilenkin, A. (1982). Creation of universes from nothing. Physics Letters B, 117(1-2), 25–28. [CrossRef]
317. von Neumann, J. (1955). Mathematical foundations of quantum mechanics (R. Beyer, Trans.). Princeton University Press.
318. Wald, R. M. (2006). The arrow of time and the initial conditions of the universe. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 37(3), 394–398. [CrossRef]
319. Wallace, D. (2010). Gravity, entropy, and cosmology: In search of clarity. The British Journal for the Philosophy of Science, 61(3), 513–540. [CrossRef]
320. Wallace, D. (2017). Against wavefunction realism. In S. Dasgupta, R. Dotan, & B. Weslake (Eds.), Current Controversies in Philosophy of Science (pp. 63–74). Routledge. https://philpapers.org/rec/WALAWR-3.
321. Wallace, D. (2018). On the plurality of quantum theories: Quantum theory as a framework, and its implications for the quantum measurement problem. In S. French & J. Saatsi (Eds.), Scientific Realism and the Quantum Measurement Problem (pp. 78–102). Oxford University Press. http://philsci-archive.pitt.edu/15292/.
322. Wallace, D. (2019). What is orthodox quantum mechanics? In A. Cordero (Ed.), Philosophers Look at Quantum Mechanics (pp. 285–312). Springer International Publishing. Kindle Edition.
323. Wallace, D. (2018). Why black hole information loss is paradoxical. ArXiv.org. [CrossRef]
324. Wallace, D., & Timpson, C. G. (2010). Quantum mechanics on spacetime I: Spacetime state realism. The British Journal for the Philosophy of Science, 61(4), 697–727. [CrossRef]
325. Weatherall, J. O. (2016). Void. Yale University Press. Kindle Edition.
326. Webb, J. (2014). Nothing: Surprising insights everywhere from zero to oblivion. Profile Books Ltd. Kindle Edition.
327. Wechsler, S. (2021). About the nature of the quantum system—an examination of the random discontinuous motion interpretation of the quantum mechanics. Journal of Quantum Information Science, 11(03), 99–111. [CrossRef]
328. Wechsler, S. D. (2020). In praise and in criticism of the model of continuous spontaneous localization of the wave-function. Journal of Quantum Information Science, 10(04), 73–103. [CrossRef]
329. Wechsler, S. D. (2021). The quantum mechanics needs the principle of wave-function collapse—but this principle shouldn’t be misunderstood. Journal of Quantum Information Science, 11(01), 42–63. [CrossRef]
330. Wiseman, H. M. (2006). From Einstein’s theorem to Bell’s theorem: a history of quantum non-locality. Contemporary Physics, 47(2), 79–88. [CrossRef]
331. Witherall, A. (2001). The fundamental question. Journal of Philosophical Research, 26, 53–87. https://philpapers.org/rec/WITTFQ.
332. Wittgenstein, L., & Russell, B. (2021). Tractatus logico-philosophicus (C. K. Ogden, Trans.). Routledge. https://www.gutenberg.org/files/5740/5740-pdf.pdf (Original work published 1921).
333. Wolf, W. J., & Thébault, K. P. Y. (2023). Explanatory depth in primordial cosmology: A comparative study of inflationary and bouncing paradigms. The British Journal for the Philosophy of Science. [CrossRef]