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This version is not peerreviewed
Submitted:
07 January 2024
Posted:
09 January 2024
You are already at the latest version
This version is not peerreviewed
Submitted:
07 January 2024
Posted:
09 January 2024
You are already at the latest version
^{1}  Despite the Dual Ontology’s unique structure, “It may be that a real synthesis of quantum and relativity theories requires not just technical developments but radical conceptual renewal.” (Bell, 2004, p. 171). 
^{2}  See (Monton, 2002, 2006) regarding mixed ontologies and the problems associated with ontologies that are not based upon a onetoone identity and mapping. See also (Maudlin, 2013b). 
^{3}  In the abstract, a ((3 x N) + 3) hyperspace formed by a (3 x N) Planck Space and the three spatial dimensions of 4D spacetime appears to be an imposing physical structure. From a nontechnical perspective, however, the closed universe formed by the Dual Ontology is a combination of the 4D spacetime of everyday experience and a manydimensional Planck Space. The Planck Spheres that comprise 4D spacetime on a onetoone basis also comprise Planck Space. As a simple example, assume that there are 5 Planck Spheres in 4D spacetime, one each somewhere on Venus, Mars, the Milky Way Galaxy, the Andromeda Galaxy, and the Orion Constellation. The 5 Planck Spheres in 4D spacetime form a (3 x N) space in Planck Space where N equals five, and the number of dimensions equals 15. Unlike 4D spacetime, the Planck Spheres in Planck Space are not separated by time, space, or volume. All of the Planck Spheres in 4D spacetime and the corresponding Planck Spheres in Planck Space form a closed ((3 x N) +3) hyperspace where (3 x N) represents Planck Space and “3” represents the three spatial dimensions of 4D spacetime. 
^{4}  For a discussion regarding a mathematical (3 x N) dimensional space composed of an ordered Ntuple of ordered triples and the difference between a (3 x N) space and a 3N space, see (Lewis, 2013, pp. 116118). 
^{5}  “My own view is that…belief in the completeness of Relativity as an account of spacetime structure has been irrationally fetishized just as belief in the completeness of the quantummechanical description had been by Bohr and company.” (Maudlin, 2014, p. 24). 
^{6}  See generally (Maudlin, 2013b, 2019, pp. 3637 and 7993); (Monton, 2006); (Pusey et al., 2012). 
^{7}  (Barrow, 2002); (Grunbaum, 2009); (Holt, 2012). The existence of the SOAN turns one of the greatest philosophical questions of all time on its head. The question is not, “Why is there something rather than nothing.” Rather, the question is, “Why is there something AND nothing.” 
^{8}  See section 2.1 for a complete definition. 
^{9}  See generally (Bedingham, 2021); (Gao, 2018, pp. 248253); (Smolin, 2004). 
^{10}  The calculation assumes the diameter of a Planck Sphere equals the Planck length. The designation of a Planck Sphere as the smallest unit of space is illustrative only. The actual shape and size of the smallest unit of space may differ. 
^{11}  See (Howard, 1989, pp. 247253) for an early consideration of higher dimensional spaces. 
^{12}  See also (Albert, 1992, 2013); (Chen, 2019); (Ney, 2021) regarding the ontic nature of a wave function in higher dimensional 3N spaces. 
^{13}  See also (Genovese, 2023); (Genovese and Gramenga, 2022). 
^{14}  See Section 4.3 for a discussion on the physical triggers for quantum state collapse and Section 4.5 for a more comprehensive discussion regarding instantaneity. 
^{15}  The location of a quantum state following its collapse is unknown. Accordingly, the term “generally localized” denotes the general location of a quantum state in 4D spacetime. See Section 4.4 for a more complete discussion. 
^{16}  For a mathematical 3N notation the transition would be ∣ψ 1,2⟩→∣ψ 1⟩⊗∣ψ 2⟩. The (3 x N) notation describes the transition of an entangled state to a product state in a physical (3 x N) Planck Space in which there is a onetoone mapping and identity between a Planck Sphere in 4D spacetime and Planck Space. 
^{17}  See also (Ney, 2021, pp. 1011). 
^{18}  This conclusion is at odds with the Born rule and its probability density interpretation of wavefunction collapse for continuous variables. Not only does the physical structure of the Dual Ontology differ from the ontology used to derive the Born Rule, but the collapse of a quantum state to a discrete subset of the Bell Quantum Spheres occupied by the quantum state prior to collapse is a probability, not a probability density. Rather than integrating a density function of the quantum state over a continuous space, the likelihood of generally locating the electron in a “discrete, constrained space” is a probability based on the square modulus of the quantum state’s wave function. OpenAI. (2023). Background information on the Born Rule. See also (Norsen, 2017, pp. 238239) regarding the use of two real functions to replace a complex wave function in 4D spacetime. 
^{19}  Note that the “Planck Energy HyperPoint” and “4D Energy Field” include dark energy and any other form of energy not yet identified. 
^{20}  For extensive information regarding the Planck data, see (Aghanim et al., 2018). 
^{21}  More technically, data from the Planck satellite and other sources indicates that the curvature parameter Ω_{k} is 0.0005 ± 0.0005, corresponding to a 4D spacetime within 0.1% of being flat. Accordingly, ρ_{4D} = $\frac{3{H}^{2}}{8\pi G}.$

^{22}  See generally (Carroll & Chen, 2004); (Penrose, 1991, 2006). 
^{23}  The CMB and related data indirectly indicate that the spatial geometry of 4D spacetime was nearly homogeneous and isotropic near t = 0. The FLRW metric supports a spatial geometry that is homogeneous and isotropic at each 3D time slice. 
^{24}  The generalized localization of 4D Spacetime at t = 0 does not involve the destruction or localization of the Planck Spheres that comprise Planck Space, nor does it affect the SOAN. Although the energy content of the 4D Energy Field and the Planck Energy HyperPoint are localized at t = 0, Planck Spheres and the SOAN continue to form an ultrahigh dimensional (3 x N) space. See Section 7. 
^{25}  See (Holt, 2012) for an extensive discussion on the issues associated with a physical state of nothingness. See also (Barrow, 2002); (Kuhn, 2013). 
^{26}  The SOAN is a difficult concept to grasp fully. For example, see (Davies, 2013, p. 126). “The concept of a true void…strikes many people as preposterous or even meaningless. If two bodies are separated by nothing, should they not be in contact? How can ‘emptiness’ keep things apart or have properties such as size or boundaries?” 
^{27}  See also, Interview with Sean Carroll, Vice Magazine On Line. What is Nothing? with Nick Rose, October 31, 2018. 
^{28}  (Bedingham, 2016); (Hagar, 2014); Hossenfelder, 2013); (Rovelli, 2017); OpenAI (2023). 
^{29}  Arguments in favor of the discretization of space have been proposed based upon mathematics, electrodynamics, quantum electrodynamics, loop quantum gravity, loop quantum cosmology, string theory, discrete lattice, asymptotic safe gravity, causal sets, spin foams, deformed special relativity, causal dynamical triangulation, quantum graphity, and black hole theory among others. (Crouse, 2016); (Crouse & Skufca, 2018); (Hagar, 2014); (Hossenfelder, 2014). 
^{30}  (Hossenfelder, 2013). 
^{31}  The nonrelativistic Schrödinger equation is based on a continuous 3D space and treats time as a separate parameter. 
^{32}  Black holes are also composed of Planck Spheres. 
^{33}  See also footnote 4. 
^{34}  (Lewis, 2013, p. 116); (Ney, 2013). Note also that a (3N + 3) hyperspace raises serious theoretical and mathematical issues. A wavefunction that describes a quantum state in a 3N space cannot simultaneously describe the same quantum state in a discrete 3D space. 
^{35}  “We first note that most authors agree that habitable universes should have only one time dimension [56, 84, 506, 507]. If spacetime had more than one temporal dimension, then closed timelike loops could be constructed. Such loops, in turn, allow for observers to revisit the “past” and thereby affect causality. In addition to violations of causality, multiple time dimensions can lead to violations of unitarity, tachyons, and ghosts [212].” (Adams, 2019, p. 158). 
^{36}  Unlike quantum mechanics, quantum chemistry often approaches Nbody quantum states differently. See generally (Fortin et al., 2018); (Sebens, 2021). 
^{37}  For an alternative approach, see (Norsen et al., 2015). 
^{38}  The preferred basis for all observations of a quantum state is the position basis. “The second moral is that in physics the only observations we must consider are position observations, if only the positions of instrument pointers.” (Bell, 204, p. 161). See also (Maudlin, 2019, pp. 4850). 
^{39}  See section 4.3 below for additional information on “physical triggers.” 
^{40}  See section 4.4 for additional information on generalized localization. 
^{41}  (Allori, 2022); (Bricmont, 2016); (Broglie, 1964); (Norsen, 2005). 
^{42}  See generally (Allori et al., 2021). 
^{43}  Despite its metaphorical usefulness, “quantum tunneling” is neither a jump nor a tunneling process. The instantaneous collapse of a quantum state at some point after the quantum state’s leading edge has passed through a physical barrier that is classically impenetrable reflects the collapse of the quantum state’s Bell Quantum HyperPoint, not the tunneling of the entire quantum state through an otherwise impassible barrier. Following the quantum state’s collapse, its Bell Quantum Field is generally localized on the other side of the physical barrier. See generally (Castro et al., 2018). 
^{44}  The dynamic evolution and collapse of quantum states also apply to black hole information loss. See generally (Giddings, 2019); (Wallace D., 2018). 
^{45}  (Bohm, 1951, pp. 611619). 
^{46}  Although the SternGerlach experiment in the z direction is conducted in 4D spacetime on either Bell Quantum Field E in Princeton or Bell Quantum Field F in Copenhagen, the Bell Identity ensures that the experiment is simultaneously reflected on Bell Quantum HyperPoint EF in Planck Space. More generally, any quantum experiment in 4D spacetime is always reflected simultaneously on the quantum state’s Bell Quantum HyperPoint in Planck Space. 
^{47}  Doubleslit experiments describe a quantum state by its wave function rather than the considerably more amorphous terms “charge density” or “energy content.” Nevertheless, since all quantum states are real if an electron passes through slits A and B, the charge density, and the energy content of the electron, however illdefined after it has passed through slits A and B, must also do so. See (Sebens C. T., 2021). 
^{48}  The “which way” monitoring experiment is based upon the example discussed in (Maudlin, 2019). 
^{49}  (Lewis, 2016, pp. 72107). 
^{50}  In Planck Space, a single Bell Quantum HyperPoint is neither spacelike separated nor a separable system. See Sections 5.1 and 5.2 below. See also (Ney, 2021, pp. 112128); (Howard, 1985, p. 197). 
^{51}  For a detailed discussion, see (Ney, 2021). 
^{52}  The unobservable Universe is considerably larger than the observable universe and may be infinite. 
^{53}  Although decoherence extensively considers environmental triggers and the loss of coherence rather than a specific quantum collapse mechanism, the Dual Ontology conjecture supports a very specific collapse mechanism initiated exclusively by 4D spacetime Physical Interactions. 
^{54}  No assumptions are made regarding dark matter or dark energy. 
^{55}  See also (Licata & Chiatti, 2019). 
^{56}  Although physical triggers such as nuclear interactions on the sun may be statistically determinable, individual quantum state collapses are still time and locationdependent. 
^{57}  The collapse rate of individual quantum states on the sun is directly related to temperature and location. 
^{58}  Humans can, at will, use a scanning tunneling microscope (STM) to control and precisely vary the collapse rate of electrons. 
^{59}  (Bassi, et al., 2012). 
^{60}  (Ghirardi, 2004, p. 406). 
^{61}  Note that the Dual Ontology conjecture conflicts with mathematical models that describe quantum state collapse to a single dimensionless point, a Dirac delta function, or an eigenstate of position with a single discrete value. 
^{62}  From the perspective of the Dual Ontology conjecture, "The problem is that mathematics has become too dominant in physics. We have become so focused on finding mathematical descriptions of nature that we have forgotten to ask if these descriptions are actually true. We have become so entranced by the beauty of mathematics that we have lost sight of the goal of physics, which is to understand the real world." (Hossenfelder, 2018, p. 8). “Physics is not mathematics, and mathematics is not physics.” (Feynman, 1985, p. 55). 
^{63}  (Bell, 2004, p. 171); See also (Norsen, 2011, p. 1216). 
^{64}  The terminology that describes 4D spacetime may confirm Ludwig Wittgenstein’s concern that “The limits of my language means the limits of my world.” (Wittgenstein, 1922, p. 74). 
^{65}  Although the term “nonseparable” has multiple definitions, a stronger version of that term holds that “…the nonseparability of states is the claim that spatiotemporal separation is not a sufficient condition for the individuating systems themselves, that under certain circumstances the contents of two spatiotemporally separated regions of spacetime constitute just a single system”. (Howard, 1989). For a slightly different perspective, see (Ney, 2016). Einstein’s primary concern was not with nonseparability per se but with the possibility that nonseparability implied a violation of his theory of Special Relativity. (Howard, 1985, pp. 172173); (Howard, 1989, p. 232). 
^{66}  See also (Ney, 2016, 2021). 
^{67}  The nonseparability of a Bell Quantum HyperPoint addresses a concern raised by Einstein. Einstein questioned whether spatially separated quantum states in 4D spacetime had an independent reality. (Wiseman, 2006). The existence of a single ultrahigh dimensional Bell Quantum HyperPoint would prove two points. First, spacelike quantum states separated in 4D spacetime are “real,” and second, they are not physically independent. 
^{68}  See (Maudlin, 2011, pp. 2122). 
^{69}  The ability of a Bell Quantum HyperPoint to maintain a “quantum connection” also answers the selfinterference puzzle outlined in (Gao, 2020). An electron’s Bell Quantum HyperPoint contains all of the information regarding an electron’s charge distribution regardless of whether the electron is or is not spacelike separated in 4D spacetime. The electron’s Bell Quantum HyperPoint not only contains the charge distribution of the electron, but it also quantum discriminates and is nonattenuated. In this sense, all electrons are not the same. The electron’s Bell Quantum Hyperpoint does not interfere with itself. See also (Sebens, 2021, 2022); (Wechsler S. D., 2021). 
^{70}  (Brunner et al., 2014). 
^{71}  (Goldstein et al., 2011); (Maudlin, 2014, p. 21); See also (Bell & Gao, 2016). 
^{72}  See (Maudlin, 2011, pp. 53, Note 1). 
^{73}  (Ney, 2021, p. 96). See (Allori, 2022) regarding different uses of the term “nonlocal” in Einstein/de Broglie Box experiments. 
^{74}  See Banerjee et al. 2016: “We conclude that the problem of time in quantum theory is intimately connected with the vexing issue of quantum nonlocality and acausality in entangled states. Addressing the former compels us to revise our notions of spacetime structure, which in turn provides a resolution for the latter.” 
^{75}  See also (Genovese, 2023). 
^{76}  Stated somewhat differently, Planck Space is “extra” local. 
^{77}  See also (Ney, 2021 Sections 3.7  3.8). 
^{78}  See also (Penrose, 1997, p. 137): “My own view is that, to understand quantum nonlocality, we shall require a radical new theory. This theory will not just be a slight modification of quantum mechanics but something as different from standard quantum mechanics as General Relativity is different from Newtonian gravity. It would have to be something which has a completely different conceptual framework. In this picture, quantum nonlocality would be built into the theory”. 
^{79}  (Maudlin. 2011, p. 185). 
^{80}  The mass of a body is always reference framedependent. See generally (Maudlin T., 2011, pp. 5864). 
^{81}  OpenAI (2023). Background information on Special Relativity. 
^{82}  See (Bahrami, et al., 2015); (Doyle, 2014); (Lucia & Grisolia, 2022). 
^{83}  (Albert D. Z., 2000, pp. 150162); (Doyle, 2014). 
^{84}  See generally (Price, 2004). 
^{85}  See also (Snyder, 2000) Footnote 1: “Generally, this irreversibility means that it is highly unlikely that the physical interaction that is the measurement could occur in the opposite direction of time to the one in which it is occurring or has occurred.” 
^{86}  Moreover, the Bell Identity does not support path reversibility. Instead, it simply posits that the Bell Quantum Spheres comprising the Bell Quantum HyperPoint z_{1} in Planck Space are identical to those comprising Bell Quantum Field z_{1} on Mars and the Bell Quantum Spheres comprising Bell Quantum HyperPoint z_{2} in Planck Space are identical to those comprising Bell Quantum Field z_{2} on Earth. 
^{87}  For a general introduction to quantum cosmology, see (Bojowald, 2015). 
^{88}  Including Type Ia Supernovae Observations, Hubble's Law and Redshift Observations, Baryon Acoustic Oscillations, Galaxy Redshift Surveys, Stellar Evolution Models, and Globular Cluster Age Estimates. 
^{89}  See generally (Davies, 1994); (Aghanim, 2018); Background source. OpenAI (2023). 
^{90}  The FLRW metric also assumes a homogeneous and isometric spatial structure. 
^{91}  “The Planck satellite data reported in 2013 … shows with high precision that we live in a remarkably simple universe. The measured spatial curvature is small; the spectrum of fluctuations is nearly scaleinvariant; there is a small spectral tilt, consistent with there having been a simple dynamical mechanism that caused the smoothing and flattening; and the fluctuations are nearly Gaussian, eliminating exotic and complicated dynamical possibilities, such as inflationary models with noncanonical kinetic energy and multiple fields.” (Ijjas et al., 2013). 
^{92}  OpenAI (2023). Background on 4D spacetime’s heat death. 
^{93}  Changes may still occur at the microstate level. 
^{94}  Note that the terms “spatial curvature” and “spatial isometry” do not apply to an ultrahigh dimensional Planck Space without space, volume, or distance. 
^{95}  See section 4.3 above. 
^{96}  The collapse of the Planck Energy HyperPoint and the reduction in the number of Planck Spheres that comprise the new 4D Energy Field does not involve the destruction or localization of the Planck Spheres that comprise Planck Space, nor does it affect the SOAN. Although the energy content of the 4D Energy Field and the Planck Energy HyperPoint are localized at t = 0, Planck Spheres and the SOAN continue forming an ultrahigh dimensional (3 x N) space. 
^{97}  The collapse of the Planck Energy HyperPoint and the generalized localization of 4D spacetime at t = 0 differs in two important respects from the collapse of a single or Nbody quantum state. First, the collapse includes all of the energy content of the Planck Energy HyperPoint, including, without limitation, dark energy. Second, the collapse generally localizes all of 4D spacetime without regard to a specific subset of Planck Spheres. 
^{98}  See (Melia, 2023) regarding the cosmological principle and the constant expansion rate of 4D spacetime. 
^{99}  The Dual Ontology conjecture also posits that the ubiquity of quantum state collapse plays a central role in the existence of the anisotropies and inhomogeneities at the last scattering of the CMB and the formation of the largescale structure of 4D spacetime. See generally (Le´on et al., 2014); (Perez et al., 2006); (Sudarsky, 2010). 
^{100}  The theory of General Relativity regards the expansion of spacetime as an intrinsic process rather than an extrinsic expansion. Although the vast majority of the Planck Spheres that comprise all of Planck Space at t =0 are extrinsic to 4D spacetime, the existence of an ultrahigh dimensional Planck Space composed of Planck Spheres does not appear to violate General Relativity. 
^{101}  See (Azhar & Loeb, 2021) regarding explanatory depth. (Adams, 2019); (Wolf & Thebault, 2022). 
^{102}  (Wald, 2005): “[T]he presently observed universe should not merely be a (highly unlikely) possibility that is allowed in the model but rather should be a prediction of the model.” 
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