Therefore, while the loops conceptually form the fabric of space-time in loop quantum gravity, their interpretation is more about the discrete nature of space rather than physical proximity or pressing against each other.

🐱: What is the nature of loops in the loop theory of quantum gravity?

🕸: Loop Quantum Gravity (LQG) is a theoretical framework that aims to reconcile general relativity, which describes the behavior of large-scale structures in the universe, with quantum mechanics, which deals with the behavior of particles at the smallest scales. In LQG, the fundamental building blocks of space-time are not continuous but discrete, represented by loops or networks known as spin networks. These networks are composed of nodes and links, with quantized areas and volumes associated with the links. The loops are not physical objects in space but rather represent the quantum excitations of the gravitational field, which is the physical space itself.
The loop representation provides a natural solution to the spatial diffeomorphism constraint, making a connection between canonical quantum gravity and knot theory. This approach has led to the identification of an infinite set of exact (if only formal) solutions for all the equations of canonical quantum gravity.
LQG predicts a smallest length, area, volume, and time, which are 10 to the -35 meters, 10 to the -70 square meters, 10 to the -105 cubic meters, and 10 to the -43 seconds, respectively. These smallest units imply that it is literally impossible to have a smaller volume than 10 to the -105 cubic meters or a shorter duration than a quantum of time.
Despite its promise, LQG faces challenges, such as the difficulty in reconciling the discrete nature of space-time with the smooth fabric of general relativity at larger scales. Additionally, different observers may have different views of the sizes of the quantized pixels of space-time, which could lead to radical alterations in their perceptions of physics.

🐱: How does the extent of space (including the pre-existing 10-dimensional space) arise in string theory?

🕸: In string theory, the concept of spacetime is fundamentally different from that in general relativity. Strings, the fundamental objects in this theory, require a 10-dimensional spacetime to vibrate and interact consistently. This 10-dimensional space includes the familiar 3 dimensions of space and 1 dimension of time, as well as 6 additional dimensions, often referred to as "hidden" or "curled up" dimensions.
The existence of these extra dimensions is not a direct prediction of string theory, but rather a requirement for the theory to be consistent and to reproduce the physics we observe in our 4-dimensional world. These dimensions are believed to be compactified or curled up on themselves at extremely small scales, making them unobservable with current experiments.
There are different ways to compactify these extra dimensions, leading to various models of string theory, such as the heterotic string theories with 10 dimensions, and Type I, Type IIA, Type IIB, and M-theory with 11 dimensions. The compactification process can result in different gauge groups and particle spectra, which are crucial for the theory's consistency and agreement with experimental data.
In summary, the 10-dimensional spacetime in string theory arises from the necessity to accommodate the vibrations and interactions of strings in a consistent manner. The extra dimensions are compactified or curled up, making them unobservable at current experimental scales. Different models of string theory arise from various ways of compactifying these extra dimensions, leading to diverse gauge groups and particle spectra.

🐱: No, I mean the extension of things in string theory as it arises. In other words, I was asking about how distance arises in string theory. Or does string theory not talk about that?

🕸: In string theory, the concept of distance is intricately linked to the nature of spacetime and the behavior of strings. The way distance is understood in string theory differs from our conventional notions due to the theory's requirement for 10 dimensions (3 spatial dimensions, 1 time dimension, and 6 additional compactified dimensions).
In string theory, the measurement of distance involves the movement of probes at a certain speed across a distance, measuring the time taken to cover that distance, and then multiplying the speed by the time elapsed. Strings in string theory have two possible configurations, leading to two different probes for measuring distance. One probe can explore the full circumference of a circle, while the other can probe distances related to the radius of the circle. This results in an inverse relationship between the energy of the probe and the distances it can explore, with one method becoming challenging due to the differences in energy levels.
The existence of extra dimensions in string theory affects how distances are perceived. The compactification of these extra dimensions and the interactions of strings with these dimensions influence the way distances are measured and understood within the theory. The intricate relationship between the dimensions, the energy of probes, and the concept of distance highlights the unique way in which string theory addresses spatial measurements.
Therefore, in string theory, the notion of distance is intricately connected to the theory's requirement for extra dimensions and the behavior of strings within this multi-dimensional spacetime.

🐱: I was not referring to the measurement of distances (in string theory), but to the fundamental nature of those distances (assumed in that theory). Or does the nature of these distances here equate to the measurement of them?

🕸: In string theory, the fundamental nature of distances arises from the vibration of strings in a multi-dimensional spacetime. The strings can vibrate in various modes, and the energy of these vibrations corresponds to different particles and forces in the universe. The compactification of extra dimensions, which are believed to be curled up or hidden, also plays a crucial role in determining the properties of these distances.
The concept of distance in string theory is not simply a measurement, but rather an intrinsic property of the multi-dimensional spacetime in which strings vibrate. The way distances are perceived and measured in our familiar 3-dimensional world may not directly apply to the string theory framework, where the notion of distance is intertwined with the behavior of strings and the structure of the compactified extra dimensions.
In summary, the fundamental nature of distances in string theory arises from the vibration of strings in a multi-dimensional spacetime, with the compactification of extra dimensions and the behavior of strings influencing the properties of these distances. The concept of distance in string theory is not merely a measurement but an intrinsic property of the multi-dimensional spacetime in which strings vibrate.

🐱: How does the extent of things arise in the theory of loop quantum gravity? That is, how does distance arise in this theory. In context of question, I mean the fundamental nature of extension (distance) in this theory, not measurement of distance (or, in this theory, are these equal notions / concepts?).

🕸: In loop quantum gravity, the concept of distance or extension arises fundamentally through the theory's postulation that space and time are composed of finite loops woven into an extremely fine fabric. These loops, known as spin networks, form the structure of space itself, suggesting that space has an atomic structure at scales above the Planck length. In this theory, the evolution of these spin networks, or spin foams, defines the notion of distance or extension.

The theory implies that space itself is quantized into these discrete loops, indicating that the fundamental nature of extension in loop quantum gravity is intricately tied to the discrete structure of space at the smallest scales. Therefore, in the context of loop quantum gravity, the fundamental concept of extension or distance is intimately connected to the discrete nature of space as composed of finite loops or spin networks, rather than continuous measurements of distance as in classical physics.

🐱: Is it true that in physical causal set theory, space, even at the smallest scales, emerges emergently from more fundamental levels of reality?

🕸: In physical causal set theory, space emerges emergently from more fundamental levels of reality, even at the smallest scales. This concept is based on the foundational principles of causal sets, which propose that spacetime is fundamentally discrete, with spacetime events related by a partial order that signifies causality relations between events. The emergence of spacetime from causal sets is deeply intertwined with philosophical considerations and aims to formulate a quantum theory of gravity by assuming a discrete set of basal events partially ordered by causality. The causal sets program, initiated by Rafael Sorkin, emphasizes that space-time is fundamentally discrete while maintaining local Lorentz invariance.
The emergence of spatial structure from causal sets reflects the idea that observed physical behaviors arise from a microscopic description, highlighting the bottom-up nature of how space manifests from more fundamental levels of reality. This perspective underscores the intricate relationship between the discrete causal structure of spacetime and the emergence of spatial properties, even at the most fundamental scales, within the framework of causal set theory.

🐱: How does spacetime emerge from causal relations?

🕸: In Causal Set Theory (CST), spacetime emerges from causal relations as a result of the discrete nature of spacetime events and their causal relations. In CST, the fundamental structure is a locally finite partially ordered set representing possible kinematic configurations of the universe. The causal relation in CST is a partial order relation that is more fundamental than its spatiotemporal counterparts, and it can be interpreted as a constraint principle over the possible growths of all possible configurations of the causal sets. The emergence of spacetime from causal relations in CST is a bottom-up process, where the geometric properties typically attributed to space, such as topological, affine, differential, and metric structures, are only indirectly recoverable from the structure of causal sets, if at all, at the fundamental level. The individual causal sets do not track a proper time evolution, and the causal relation of CST does not correspond to a strictly forward in time relation due to the relativistic nature of spacetime, which admits spacelike separated events. The causal relations in CST differ substantially from their everyday counterparts, but they are legitimately dubbed as causal relations due to their tight relationship with the causal structure of relativistic spacetimes.

🐱: So what is this bottom-up process?

🕸: The bottom-up process in causal set theory refers to a method where the classical dynamics of causal sets are analyzed by starting with the basic concepts of causal sets and imposing certain physical conditions to generate the most general dynamics that can be obtained. This approach involves growing the causal set by adding one more element at each step or level, with each newborn element being determined to be in the past, future, or unrelated to every other existing element of the causal set. This process, known as Classical Growth Dynamics (CGD), involves adding elements with probabilities that satisfy specific physical conditions, leading to the generation of causal sets in a manner analogous to random walks but with constraints imposed by physical requirements.

The bottom-up approach in causal set theory aims to understand the evolution of causal sets and how spacetime emerges from the discrete causal structure at the fundamental level.

🐱: How does the extent of things arise in the physical theory of causal sets? That is, how does distance arise in this theory. In context of question, I mean the fundamental nature of extension (distance) in this theory, not measurement of distance (or, in this theory, are these equal notions / concepts?).

🕸: In Causal Set Theory (CST), the fundamental nature of extension (distance) arises from the partial order relation between elements of the causal set, which represents a proto-causality relation. This partial order encodes a notion of causal proximity, where elements closer in the order are considered to be nearer in some sense. However, this does not immediately provide a distance function in the usual sense, as the number of elements between any two elements in the partial order is not necessarily indicative of their spatial separation.
To extract a distance function from the causal set, various approaches have been proposed, such as considering substantively larger parts of causets than merely unstructured antichains. These methods aim to provide a more physically adequate notion of distance, but they are still in development and have limitations.
It is important to note that the geometric structure typically associated with space, such as topological, affine, differential, and metric structure, is only very indirectly recoverable from the structure of causets, if at all. This reflects the fundamentality of the causal structure over any spatial or temporal structure in CST.

🐱: What is the nature of causal sets and (proto-)causal relations?

🕸: Causal sets are a concept in theoretical physics that aim to describe quantum gravity. They are partially ordered sets, where the partial order represents a proto-causality relation, and local finiteness encodes intrinsic discreteness. The proto-causality relation is a fundamental aspect of causal sets, representing the causal structure of spacetime. The local finiteness condition introduces spacetime discreteness, meaning that spacetime is fundamentally discrete at the most fundamental level.
Causal sets can be embedded into a Lorentzian manifold, which is a smooth spacetime with a Lorentzian metric. A faithful embedding requires that, on average, the number of causal set elements mapped into a region of the manifold is proportional to the volume of the region. In this case, the causal set can be considered 'manifold-like', which is a necessary property for modelling spacetime as a causal set.
The dynamics of causal sets are typically stochastic and can be generated using a bottom-up approach, where the most general dynamics are obtained by imposing certain physical conditions on the growth process of causal sets. The resulting dynamics are not deterministic but rather probabilistic, with probabilities that satisfy specific physical conditions.
Overall, causal sets provide a discrete and causal structure for spacetime, which can be used to study quantum gravity and the emergence of spacetime from more fundamental levels of reality.

🐱: In the theory of shape dynamics, does space (including space at the smallest distances) emerge emergently from more fundamental levels of reality, or is it itself a fundamental level?

🕸: In the theory of shape dynamics, space, including space at the smallest distances, emerges emergently from more fundamental levels of reality, specifically from the intrinsic geometry of shape space. This is a key feature of the theory, which aims to implement Mach's principle and obviate the problem of time in quantum gravity. Shape dynamics is dynamically equivalent to the canonical formulation of general relativity, known as the ADM formalism, but it is not formulated as an implementation of spacetime diffeomorphism invariance. Instead, it is based on spatial relationalism and implements spatial diffeomorphisms and spatial Weyl symmetry.

The theory reduces the configuration space to C × R+, where C is conformal superspace, the space of conformal 3-geometries, and R+ represents the volume of a compact 3-geometry, which is invariant under the transformations of which the volume-preserving conformal constraint is a generator. Shape dynamics realizes the Mach-Poincaré principle through York’s solution to the initial value problem in GR.

🐱: What is shape space in this theory?

🕸: Shape space in the theory of shape dynamics refers to a fundamental concept that describes the intrinsic geometry of dynamical systems. In the context of shape dynamics, shape space is a space where the corresponding equation of state of a curve expresses the ratio of change of one of its geometric degrees of freedom. It is a key component in the relational physical theories described by shape dynamics, emphasizing the importance of describing dynamical systems based on the intrinsic geometry of shape space rather than absolute space and time references.

🐱: What is the intrinsic geometry of this shape space?

🕸: The intrinsic geometry of shape space is characterized by the curves that describe the shape deformations within the space. These curves can be computed using various methods, including maximum local rigidity criteria, Laplacian coordinates, Poisson equation, and moving frame manipulation, among others. The intrinsic geometry of shape space is essential for understanding the behavior of dynamical systems within this space, as it allows for the analysis of shape deformations without relying on absolute space and time references. The geometry of shape space can also be used to define intrinsic geometric scale spaces, where the intrinsic geometry of a surface is diffused by shape diffusion. This intrinsic geometric scale space provides a novel framework for analyzing the shape of 3D surfaces.

🐱: So it turns out that since shape deformations occur in space, this space is not arise emergently from more fundamental levels of reality? Or does it arise after all?

🕸: The shape space in the theory of shape dynamics is not considered to emerge from more fundamental levels of reality. Instead, it is a conceptual framework that seeks to remove any non-relational notions from its methodology, replacing the background space-time with a conceptual framework meant to reflect direct observables and recognize how measurements are taken. Shape dynamics is a theory of pure relationalism, based on different first principles than General Relativity. It asserts that only relational data exists, and thus that the gauge group is physically irrelevant and non-existent, restricting to the base space of the principle bundle and enforcing horizontality, forcing certain generalized momenta to 0 for all time. The intrinsic geometry of shape space is characterized by the curves that describe the shape deformations within the space, and it can be analyzed using various methods, including maximum local rigidity criteria, Laplacian coordinates, Poisson equation, and moving frame manipulation. The intrinsic geometry of shape space is essential for understanding the behavior of dynamical systems within this space, as it allows for the analysis of shape deformations without relying on absolute space and time references.

🐱: What is the nature of shape space?

🕸: Shape space in the theory of shape dynamics is a concept that represents the primitive fact of the matter, with shapes being topologically ordered. It is the space of all possible shapes that can be constructed with certain ingredients, such as particles or field magnitudes, stripped of their unobservable degrees of freedom associated with the symmetries of the system. Shape dynamics is a theory of gravity that overlaps with general relativity in places but is built from fewer and more fundamental principles. It is based on a different symmetry group to general relativity, which allows for the implementation of spatial and temporal relationalism, as well as the successful satisfaction of the Mach-Poincaré principle.

Shape dynamics is dynamically equivalent to the canonical formulation of general relativity, known as the ADM formalism, but it is not formulated as an implementation of spacetime diffeomorphism invariance. Instead, it is based on an implementation of spatial relationalism, which leads to the absence of a problem of time in canonical quantum gravity.

🐱: It is true that, metaphorically speaking, the shapes are "strictly close" to each other, "pressed" against each other? Or is it meaningless for theoretical physics of shape dynamics?

🕸: In the theoretical physics of shape dynamics, the metaphorical concept of shapes being "strictly close" to each other and "pressed" against each other is not a meaningful description within the context of the theory. Shape dynamics is a framework that focuses on removing non-relational notions and background space-time from its methodology, emphasizing a theory of pure relationalism based on different first principles than General Relativity. The theory aims to reflect direct observables and how measurements are taken, emphasizing a relational perspective where dynamics are described in terms of shapes and their evolution based on intrinsic measures of change and relational data.
In shape dynamics, the emphasis is on understanding the dynamics of systems based on the shapes of configurations and their relational properties, rather than on physical shapes being physically close or pressed against each other. The theory seeks to implement Mach's principle and resolve the problem of time in quantum gravity by focusing on spatial relationalism and spatial diffeomorphisms, rather than on the physical proximity of shapes in a literal or metaphorical sense.
Therefore, within the theoretical framework of shape dynamics, the metaphorical description of shapes being "strictly close" or "pressed" against each other does not align with the fundamental principles and goals of the theory, which are centered around relational dynamics, shape evolution, and the removal of non-relational elements from the description of physical systems.

🐱: Is it true that, in this theory, time does not exist, as in other physical theories and as in ordinary common sense, but emerges emergently from space?

🕸: The theory of shape dynamics suggests that time does not exist inherently but emerges from the spatial configuration of a system. This concept is rooted in relational formulations of classical mechanics and gravity, where the notion of shape space is crucial. Shape space is a metric structure that allows for the definition of a quantum motion, a Bohmian mechanics, on shape space. This motion then gives rise to the more familiar theory in absolute space and time. The emergence of time in this context is gauge-dependent, meaning it arises from the choice of a particular reference frame or gauge. This perspective challenges the traditional view of time as an absolute, pre-existing entity and instead posits it as a derived concept that emerges from the spatial configuration of a system.

🐱: Are there non-marginal physical theories in which, on the contrary, space emerges emergently from time?

🕸: Based on the provided sources, particularly the discussions on the emergence of spacetime in quantum gravity theories, there is a focus on how spacetime emerges from more fundamental non-spatiotemporal elements or structures. However, the specific scenario where space emerges emergently from time, as opposed to the more common emergence of time from space, is not a prominent feature in the literature reviewed. The emphasis is typically on the emergence of spacetime as a whole entity, with space and time intertwined, rather than one emerging from the other in a unidirectional manner. Therefore, while the emergence of spacetime is a central theme in these discussions, the emergence of space from time specifically is not a widely explored concept in the context of quantum gravity theories.

🐱: How does the extent of things arise in the physical theory of shape dynamics? That is, how does distance arise in this theory. In context of question, I mean the fundamental nature of extension (distance) in this theory, not measurement of distance (or, in this theory, are these equal notions / concepts?).

🕸: In the physical theory of shape dynamics, the concept of distance, or extension, arises fundamentally through the relational nature of the theory. Shape Dynamics is a framework that emphasizes pure relationalism, aiming to remove non-relational notions from its methodology and focusing on directly observable relationships between objects. In this theory, distance is not treated as an absolute quantity but rather emerges from the relationships and configurations of objects within the system. The theory asserts that the dynamics of a given physical system must evolve through 'horizontal' relationships, where the positions and sizes of objects are determined relative to each other. This relational approach to distance in Shape Dynamics highlights that the theory is built on the idea that extension or distance is a concept that is defined by the relationships and configurations of objects within the system, rather than being an inherent property of space itself. Therefore, in Shape Dynamics, the fundamental nature of extension or distance is intricately tied to the relational structure of the system, emphasizing the importance of spatial and temporal relationalism in defining the concept of distance within the theory.

🐱: As we discussed earlier, in modern theoretical physics all space is filled with quantum fields, and if these fields were not present, space would be spatial nothingness (or would be "filled" with spatial nothingness). And there is no empty space even in the case that in some place of space the old virtual particle has already disappeared and the new one has not appeared yet. But still I wonder if there are non-marginal modern physical theories in which this is not so?

🕸: The concept of space as a substantive container for reality is a product of our pre-cultural process of clothing, where we recognize experientially separated and stable portions of reality through penetration in depth and organize these entities into a space through penetration in width. However, modern physics has discovered entities that behave differently from classical entities and do not lend themselves to be fully included in the relational space that was built thus far, challenging the notion of space as a fundamental substantive container for reality.
In quantum field theory, the vacuum state of a quantum field is not only entangled across algebras associated with certain spacelike separated regions of Minkowski spacetime but also maximally violates Bell inequalities for algebras associated with these regions, indicating a non-spatial reality. The Core Theory, consisting of both the Standard Model of particle physics and the weak-field limit of general relativity, describes the entirety of the "everyday life regime" supervening on the ontology and dynamics of this theory, and any additional particles and forces interact too weakly with the known fields to exert any influence on human behavior.
Therefore, modern physical theories, such as quantum field theory and the Core Theory, suggest a non-spatial reality where entities are not contained in a substantive container called space but are entangled and interact in a complex web of relationships.

🐱: But it is true that there is a quantum field at any point in space, isn't it?

🕸: Yes, it is true that according to modern theoretical physics, quantum fields exist at every point in space, challenging the traditional notion of empty space as a void. Quantum field theory describes a framework where particles and forces are associated with their respective fields, which permeate all of the universe and interact across different fields, leading to the manifestation of particles when the fields are excited.

These quantum fields are not only present where there are sources like mass or charge but are omnipresent, existing regardless of the presence of charges, and are quantized with zero-point energy, allowing for non-zero values even in seemingly empty space. This concept of quantum fields existing everywhere, even in the absence of traditional sources, is a fundamental aspect of modern physics that underpins our understanding of the fabric of reality.

🐱: So are there any modern non-marginal physical theories that contradict quantum field theory?

🕸: There are no non-marginal modern physical theories that contradict quantum field theory (QFT) in the sense of providing a fundamentally different framework for understanding the behavior of particles and forces. Instead, QFT is seen as a highly robust and successful theory that captures the behavior of known particles and forces within its domain of applicability, which includes any processes between known particles with energy transfers less than a hundred billion electron volts. The Core Theory, which consists of both the Standard Model of particle physics and the weak-field limit of general relativity, is an effective quantum field theory that describes the entirety of the "everyday life regime" supervening on the ontology and dynamics of this theory. While there may be more fundamental levels of reality or additional particles and forces, they are not expected to affect the behavior of known particles and forces within the Core Theory's domain of applicability. Therefore, while there may be modifications or extensions of QFT in the future, there are currently no non-marginal physical theories that contradict its fundamental principles.

🐱: There's string theory, there's loop quantum gravity theory, there's causal set theory, and there's shape dynamics. Do all these theories agree with quantum field theory?

🕸: String theory, loop quantum gravity theory, causal set theory, and shape dynamics are all approaches in the field of quantum gravity, but they do not all agree with quantum field theory. String theory and loop quantum gravity are more aligned with quantum field theory, while causal set theory and shape dynamics have different foundational principles. String theory, for example, incorporates quantum field theory within its framework, aiming to describe all fundamental forces and particles in the universe. Loop quantum gravity, on the other hand, seeks to quantize gravity itself. Causal set theory posits a discrete structure for spacetime, while shape dynamics focuses on the evolution of spatial shapes rather than particles. Each theory has its unique perspective on quantum gravity and its relationship with quantum field theory.

🐱: How is causal set theory inconsistent with quantum field theory?

🕸: Causal set theory is a discrete approach to quantum gravity, positing that spacetime is fundamentally discrete and composed of elements with a partial order representing causality relations. While causal set theory can be reconciled with quantum field theory (QFT) to some extent, it is not fully consistent with QFT in its current form.
One of the main challenges is that causal set theory does not naturally accommodate a Hamiltonian framework, which is crucial for QFT. This makes it difficult to define quantum fields on causal sets and find a quantization scheme without reference to the continuum.
However, there have been attempts to reconcile causal set theory with QFT. For instance, the paper "Algebraic Classical and Quantum Field Theory on Causal Sets" discusses using the framework of perturbative algebraic quantum field theory (pAQFT) to construct QFT models on causal sets. This approach involves defining various discretized wave operators and using them to construct classical free and interacting field theory models on a fixed causal set. Additionally, the paper describes how the sensitivity of observables to changes in the background causal set can be encapsulated in a relative Cauchy evolution, which is then used as the basis for a deformation quantization.

Despite these efforts, causal set theory remains at odds with some aspects of QFT, particularly in its lack of a natural Hamiltonian framework and the difficulty in defining quantum fields on causal sets. Further research is needed to fully reconcile these two approaches to quantum gravity and field theory.

🐱: In loop quantum gravity theory, space is also discrete (I think). And if everything is correct, quantum field theory uses the (mathematical?) idea of continuum. So how does loop quantum gravity theory agree with quantum field theory? And does it agree completely?

🕸: Loop quantum gravity (LQG) and quantum field theory (QFT) agree in the sense that LQG is a standard quantum (field) theory, but it doesn't unify all interactions like string theory. LQG is a quantum theory of the gravitational field, not a quantum field theory over a metric manifold, which is the conventional approach in QFT. Instead, LQG assumes that the identification between the gravitational field and the metric-causal structure of spacetime must be taken into account even in the quantum regime, without making a split of the metric or assuming a background metric on spacetime. This results in a quantum field theory on a manifold, where the classical metric structure is defined only by expectation values of the gravitational field operator.
In summary, while LQG and QFT share some common ground, they differ significantly in their approaches to quantum gravity.

🐱: Are there attempts to reconcile loop quantum gravity theory, and it manipulates discrete space, and quantum field theory, and it manipulates continuous space?

🕸: There are attempts to reconcile loop quantum gravity theory, which deals with discrete space, and quantum field theory, which operates in continuous space. Loop quantum gravity (LQG) posits that space is composed of finite loops woven into a fine fabric, implying a discrete structure. On the other hand, quantum field theory typically operates in continuous space. Efforts to reconcile these two theories involve exploring how the discrete nature of space in LQG can be integrated with the continuous framework of quantum field theory. This reconciliation is a significant challenge in theoretical physics, aiming to bridge the gap between the discrete structures of LQG and the continuous nature of quantum field theory.

🐱: And in more detail and specificity, how do physicists try to harmonize them?

🕸: Physicists endeavor to harmonize loop quantum gravity theory, which postulates a discrete structure of spacetime, with quantum field theory, which operates in continuous space, through various approaches. One significant attempt involves proposing a "postquantum theory of classical gravity," as suggested by Professor Jonathan Oppenheim and his team at University College London. This theory challenges the conventional belief that gravity must be quantized to reconcile with quantum mechanics. Instead of quantizing spacetime, this theory introduces a probabilistic mechanism where spacetime interacts with quantum particles, leading to unpredictable fluctuations that can be experimentally validated.
Furthermore, loop quantum gravity itself offers insights into the discrete nature of space, akin to atoms, where volume and area measurements return results in a discrete set of numbers, indicating a granular structure of spacetime. This discrete nature of space in loop quantum gravity contrasts with the continuous framework of quantum field theory. Physicists explore the implications of loop quantum gravity in cosmological questions, such as the early universe and the potential for observable effects that could validate modifications of relativity theory.
In essence, physicists are exploring innovative ways to bridge the gap between the discrete structures of loop quantum gravity and the continuous nature of quantum field theory, challenging long-held assumptions and seeking a unified framework that harmonizes these fundamental theories of physics.

🐱: How is shape dynamics theory inconsistent with quantum field theory?

🕸: Shape Dynamics (SD) and Quantum Field Theory (QFT) are two different theoretical frameworks used to describe physical phenomena, and they are inconsistent with each other in several ways.Firstly, SD is based on the symmetry of conformal 3-geometries, while QFT assumes a smooth 4-dimensional spacetime geometry. This fundamental difference in the treatment of spacetime makes it challenging to reconcile the two theories.Secondly, SD considers only the angle-determining part of the metric as physical, while in QFT, lengths are physical. This discrepancy in the treatment of physical quantities is another point of inconsistency.Thirdly, SD is formulated based on relational principles, specifically temporal and spatial relationalism, while QFT does not explicitly adhere to these principles. Lastly, SD has been applied to investigate many facets of classical and quantum cosmology, while QFT is primarily used to describe particle physics and condensed matter physics. The inconsistency between the two theories is further highlighted by the fact that they are used in different domains of physics.In summary, Shape Dynamics and Quantum Field Theory are inconsistent with each other due to their different treatment of spacetime, physical quantities, underlying principles, and application domains.

🐱: Is there any attempt to harmonize these theories? And if so, what are they?

🕸: There are several attempts to harmonize Shape Dynamics (SD) and Quantum Field Theory (QFT), although the reconciliation of these two theories remains an open question. Some of the relevant sources discussing these attempts include:
1. arXiv paper: "Topological Quantum: Lecture Notes and Proto-Book" by Steve Simon. This paper provides a comprehensive overview of topological quantum field theory, which is a key area of research in reconciling SD and QFT.
2. "Condensed Matter Field Theory, Second Edition" by Altland and Zirnbauer. This book discusses functional field integral methods in classical and quantum nonequilibrium physics, which can be applied to both SD and QFT.
3. "Topological Quantum Computing with Majorana Zero Modes and Beyond" by Christina Paulsen Knapp. This dissertation focuses on topological phases of matter, which are related to both SD and QFT.
4. "Mathematical Tripos Part III Lecture Courses in 2022-2023". This course covers quantum error correction with the toric code and topological quantum computation using non-Abelian anyons, which are relevant to both SD and QFT.
5. "Classical Covariant Fields" by Mark Burgess. This book discusses the classical foundations of field theory and its connection to second quantized field theory, which can provide insights into the reconciliation of SD and QFT.
These sources, along with others, contribute to the ongoing research in harmonizing SD and QFT. However, it is important to note that the full reconciliation of these two theories remains an open question and is a topic of ongoing research in the field of theoretical physics.

🐱: Is a truly empty space possible in causal set theory?

🕸: In causal set theory, the concept of an empty space is not straightforward. The theory posits that spacetime is fundamentally discrete and its structure is that of a locally finite partially ordered set, known as a causal set. This means that spacetime is not considered to be a continuous entity, but rather a collection of discrete events, each with a causal history and a causal relationship to other events.
In this context, the question of a truly empty space in causal set theory is not straightforward. Since the theory is based on the idea that spacetime is made up of causally linked particles, the concept of an empty space is not as simple as in classical physics. Instead, the theory suggests that space is not empty in the traditional sense, but rather filled with causally linked particles.

🐱: And are there non-marginal modern physical theories that allow for truly empty space?

🕸: There are indeed non-marginal modern physical theories that allow for a concept of empty space, although the nature of this emptiness is not as straightforward as it might be in classical physics. The theories in question are those that incorporate the concept of quantum fields and vacuum energy.
In quantum field theory, space is not considered to be a mere void with no physical properties. Instead, it is filled with quantum fields that create and destroy particles, a phenomenon known as virtual particles. These fields are not empty in the traditional sense, but rather contain a sea of particles that constantly come and go. This concept of emptiness is far from the idea of a complete void where there is nothing. Instead, it is a concept that is filled with energy and matter at the quantum level.
The cosmological constant problem, which deals with the inexplicably tiny amount of energy infused in empty space, is a significant difficulty in understanding the nature of empty space in modern physics. This problem suggests that there might be a huge number of universes, all with different doses of vacuum energy, and that we inhabit an extraordinarily low-energy universe because we couldn't possibly find ourselves anywhere else.
In summary, modern physical theories that allow for a concept of empty space do so in a way that is not as straightforward as in classical physics. Empty space is not considered to be a mere void with no physical properties, but rather a concept that is filled with quantum fields and vacuum energy. The nature of this emptiness is a subject of ongoing research and debate in the scientific community.

🐱: What are the universes in this context?

🕸: The universes in the context of the cosmological constant problem are not specific universes like our own, but rather hypothetical universes that could exist with different amounts of vacuum energy, or cosmological constants. The cosmological constant problem arises from the fact that the observed vacuum energy in our universe is much smaller than the energy scales predicted by particle physics. This is a significant challenge for modern physics, as it suggests that there may be a deeper, unified theory that can explain this discrepancy.
The search results provided do not directly address the question of specific universes in the context of the cosmological constant problem. However, they do discuss the nature of the cosmological constant and the difficulties in understanding its value in our universe. The cosmological constant is a term that Einstein temporarily added to his field equations of general relativity to achieve a static universe, but it was later abandoned when it was discovered that the universe is expanding. From the 1930s until the late 1990s, most physicists agreed with Einstein's choice of setting the cosmological constant to zero. However, the discovery in 1998 that the expansion of the universe is accelerating implies that the cosmological constant may have a positive value, and around 68% of the mass-energy density of the universe can be attributed to this dark energy.
In summary, the universes in the context of the cosmological constant problem are not specific universes like our own, but rather hypothetical universes that could exist with different amounts of vacuum energy. The cosmological constant problem arises from the fact that the observed vacuum energy in our universe is much smaller than the energy scales predicted by particle physics, and it is a significant challenge for modern physics to understand this discrepancy.

🐱: And what current theories can explain this discrepancy?

🕸: The cosmological constant problem refers to the discrepancy between the calculated value of the cosmological constant, which is the energy density of empty space, and the observed value of dark energy, which is the dominant component of the energy density in the universe. This problem is a major challenge for modern physics, as it suggests that our understanding of the fundamental nature of space and energy is incomplete.

There are several theories that attempt to explain this discrepancy, including:
1. Cosmological constant: This is the simplest explanation, which posits that the cosmological constant is a constant energy density filling space homogeneously. It is equivalent to the mass of empty space and can be viewed as a source term in the field equation of general relativity.
2. Dark energy: This is a more complex explanation that suggests the cosmological constant is inadequate to explain the evolution of the universe and should be replaced by a slowly varying scalar field, often referred to as quintessence. This field would have a density that evolves with time and space, allowing for a solution to the cosmological constant problem.
3. Quantum field theory: Some researchers propose that the cosmological constant problem is related to the zero-point energy of a quantum field. This energy is the energy of the vacuum state of a quantum field, and it is a significant challenge to explain why it is so small compared to the calculated value.
4. Inflationary cosmology: This theory suggests that the universe underwent a period of rapid expansion in the early universe, which could have diluted the vacuum energy density to the observed value.
5. Vacuum energy: This theory proposes that the vacuum energy of free space is much smaller than the calculated value due to the principle of Lorentz covariance and the magnitude of the Planck constant.
6. String theory: Some string theory models predict a large cosmological constant, which could explain the discrepancy. However, these models also predict other phenomena that have not been observed, which makes them less likely.
7. Dynamical dark energy: This theory suggests that the dark energy density is evolving to its natural value, zero, and is small now because the expanding universe is old. This would alleviate the classical problem of the curious energy scale associated with a constant cosmological constant.
Each of these theories has its own strengths and weaknesses, and no single theory has been definitively proven to explain the cosmological constant problem. Ongoing research and observations are expected to provide new insights into the nature of empty space and the energy density of the universe.

🐱: Can this discrepancy be explained within the loop quantum gravity theory? And in the theory of causal sets? What about shape dynamics? And if yes, how exactly is it explained in them?

🕸: The discrepancy related to the cosmological constant problem can be explored within various modern physical theories, including loop quantum gravity, the theory of causal sets, and shape dynamics. Here is how each theory addresses this issue:
1. Loop Quantum Gravity:
Loop quantum gravity offers a framework to analyze the cosmological constant problem. In this theory, the one-parameter regularization freedom of the Hamiltonian constraint is examined, leading to a spatially flat, homogeneous, and isotropic model that includes well-known loop quantum cosmology models as special cases. The quantum bounce nature is tenable in generalized cases, and for a positive value of the regularization parameter, the effective Hamiltonian can result in an asymptotic de-Sitter branch of the Universe connecting to the standard Friedmann branch through a quantum bounce. Remarkably, by selecting the value of the regularization parameter appropriately, the observational cosmological constant can emerge at large volume limits from the effects of quantum gravity, while the effective Newtonian constant satisfies experimental restrictions.
2. Causal Sets Theory:
Causal set theory, which views spacetime as a discrete structure of causally related events, also offers insights into the cosmological constant problem. In this framework, the concept of empty space is not straightforward, as space is considered to be filled with causally linked particles rather than being a void. The theory suggests that space emerges from the causal relationships between events, making the idea of empty space more complex than in classical physics.

While causal set theory does not directly address the cosmological constant problem, its unique perspective on spacetime structure contributes to the broader discussion of fundamental physics.
3. Shape Dynamics:
Shape dynamics is another modern theory that can be explored in the context of the cosmological constant problem. This theory offers an alternative approach to general relativity by focusing on the evolution of spatial conformal geometry rather than spacetime geometry. Shape dynamics aims to provide a background-independent description of gravity and spacetime, which could potentially offer new insights into the cosmological constant problem. While specific details of how shape dynamics addresses the cosmological constant problem may vary, the theory's fundamental departure from traditional spacetime descriptions makes it a candidate for exploring this discrepancy in the context of modern physics.
In summary, loop quantum gravity, causal set theory, and shape dynamics each offer unique perspectives and potential explanations for the cosmological constant problem within the realm of modern physics. These theories provide alternative frameworks to explore the nature of empty space, spacetime structure, and the energy density of the universe, contributing to ongoing research and discussions in theoretical physics.

🐱: So are there non-marginal modern physical theories with void space? Meaning perfect, absolute void (in some place of space), not "empty space" in the sense of quantum field theory, which is still filled with quantum fields forming quantum foam, where even in the lowest-energy places of space virtual particles are still constantly appearing and disappearing?

🕸: Based on the sources provided, particularly the book "Void: The Strange Physics of Nothing" by James Owen Weatherall and the article "Void dives into physics of nothingness" from Science News, it is evident that modern physics does not support the existence of a perfect, absolute void in space. The concept of empty space, as understood in quantum field theory, is not truly empty but is filled with quantum fields that give rise to virtual particles and fluctuations even in the lowest-energy regions of space. This means that even in the absence of matter and energy, space is not devoid of activity at the quantum level.
While classical physics, as exemplified by Isaac Newton, initially viewed empty space as a true void, modern physics, including quantum mechanics and general relativity, has reshaped this understanding. The vacuum of space, according to these theories, is a dynamic and complex environment where particles pop in and out of existence, fields fluctuate, and even gravitational waves ripple through space. This dynamic nature of the vacuum, governed by quantum principles, challenges the notion of a perfect void devoid of any activity.
Therefore, within the framework of modern physical theories like quantum field theory and general relativity, the concept of a perfect, absolute void in space is not supported. The understanding of empty space has evolved to recognize that even in the absence of traditional matter and energy, the quantum nature of space is characterized by continuous activity and fluctuations, challenging the idea of a truly empty void.

🐱: Also, as far as I've found out, string theory, loop quantum gravity theory, causal set theory, and shape dynamics - all of which do not support the idea of absolute, true emptiness? Is it true?

🕸: Yes, it is true that these theories do not support the idea of absolute, true emptiness. In quantum gravity, spacetime is often considered as a dynamical field, leading to the idea that even "empty" space has a granular structure at the smallest scales. For example, in loop quantum gravity, operators representing the area and volume of a region of space have discrete spectra, implying that space is quantized. In causal set theory, spacetime is replaced by a discrete set of causally related points, again suggesting a granular structure.

These theories, therefore, do not support the concept of absolute emptiness as found in classical physics.

🐱: What about string theory and shape dynamics?

🕸: String theory, a theoretical framework in physics, does not directly support the concept of absolute, true void/emptiness. Instead, it suggests that what we perceive as empty space is actually filled with fluctuating fields and particles, known as zero-point energy. This concept is related to early aether theories, which assumed the existence of a plenum or all-surrounding aether as a substitute for a true void. However, string theory does not necessarily reject the idea of a true void but rather shifts the focus to the complex behavior of energy and matter at quantum scales. The search results do not mention shape dynamics in the context of absolute, true void/emptiness.

🐱: So string theory, in some views, can allow for true void?

🕸: String theory, a theoretical framework that aims to unify all known fundamental forces in the universe, suggests the possibility of a true void in the form of "dualities" and "T-duality". These dualities imply that seemingly different theories are in fact different descriptions of the same underlying reality. For instance, T-duality relates string theories in spaces with different sizes of a compact dimension, suggesting that a space with a small compact dimension is equivalent to a space with a large compact dimension. This implies a kind of "void" in the sense that the physical properties of a system do not depend on the size of the compact dimension. However, it is important to note that this is a very specific and technical sense of "void" that is deeply rooted in the mathematical structure of string theory. It does not necessarily correspond to our everyday understanding of a "void" as an empty space.

🐱: And how can string theory's T-duality be compatible with the existence of an absolute, true void?

🕸: String theory's T-duality, which relates different string theories, can be compatible with the existence of an absolute, true void by considering the concept of a field within physics. This field, representing infinite potential at every place and time, can exist even in the absence of matter and light, defining the void. Within this framework, fluctuations in energy within the void can lead to the creation of matter, aligning with the idea of the universe originating from nought. Thus, the interplay of T-duality in string theory and the concept of a field can harmonize the theory with the existence of an absolute void.

🐱: And how in string theory can something (i.e. matter) arise from a true, absolute nothing (absence of matter) through T-duality in the case of infinite potential?

🕸: In string theory, T-duality is a symmetry that relates two seemingly different string theories. It states that a string moving in a compactified space with radius R is equivalent to a string moving in a space with radius 1/R, where the momentum and winding numbers of the string are interchanged. This duality can be used to relate theories with different coupling constants, leading to the idea that a strong coupling regime in one theory corresponds to a weak coupling regime in the dual theory.
Regarding the question of something arising from nothing, it is important to note that in the context of string theory, "nothing" often refers to the vacuum solutions of the theory, which can still have non-trivial topological and geometric structures. T-duality can relate these vacuum solutions to each other, leading to the possibility of creating non-trivial structures from "nothing" in certain limits.
However, the concept of "true, absolute nothing" is not well-defined in physics, and it is not clear whether string theory can provide a definitive answer to this question. The idea of something arising from nothing is a deep and complex topic that requires a careful consideration of the fundamental principles of physics and philosophy.

🐱: How could it hypothetically happen in string theory that non-trivial structures emerge from absolute nothingness, i.e. true void space? In the context of T-duality.

🕸: In string theory, T-duality is a symmetry that relates two seemingly different stringy theories, where one theory has a large compactification radius and the other has a small compactification radius. This duality can be understood as an isomorphism of twisted differential K-theory classes or as an isomorphism of standard Courant algebroids in the context of generalized complex geometry. One special case of T-duality is mirror symmetry.
In the context of absolute nothingness or true void space, the emergence of non-trivial structures through T-duality could be related to the concept of non-geometric backgrounds, which exceed established notions of geometry and can be generated through T-duality transformations. These non-geometric backgrounds are associated with string theory on spaces with non-trivial topology or non-standard geometry, and they can lead to the appearance of non-trivial structures in the theory.
However, a full understanding of this phenomenon would require a more detailed analysis of the specific string backgrounds and compactifications involved, as well as a thorough investigation of the quantum properties of T-duality invariant formalisms, which could provide insights into the emergence of non-trivial structures from absolute nothingness.

🐱: What are these non-geometric backgrounds that can describe absolute, true void space?

🕸: Non-geometric backgrounds are string theory backgrounds that cannot be described using standard geometric notions and require more advanced mathematical structures, such as generalized geometry or double field theory. These backgrounds arise naturally as T-duals of geometric backgrounds and can be understood as T-folds, where T-duality transformations are used for patching coordinate patches in addition to diffeomorphisms and B-field gauge transformations.
In the context of absolute nothingness or true void space, non-geometric backgrounds could potentially describe such a space due to their non-standard geometric properties and their ability to arise from T-duality transformations. These backgrounds can be associated with non-trivial topology or non-standard geometry, which could lead to the emergence of non-trivial structures in the theory.
However, a full understanding of this phenomenon would require a more detailed analysis of the specific string backgrounds and compactifications involved, as well as a thorough investigation of the quantum properties of T-duality invariant formalisms. This could provide insights into the emergence of non-trivial structures from absolute nothingness in the context of non-geometric backgrounds and T-duality.

🐱: And what would these non-trivial topologies or non-standard geometries be, so that there would be the possibility of a true, absolute void space there?

🕸: Non-geometric backgrounds in string theory can describe non-trivial topologies or non-standard geometries that could potentially describe a true, absolute void space. These backgrounds arise from T-duals of geometric backgrounds and can be understood as T-folds, where T-duality transformations are used for patching coordinate patches in addition to diffeomorphisms and B-field gauge transformations.
In the context of absolute nothingness, non-geometric backgrounds could potentially describe such a space due to their non-standard geometric properties and their ability to arise from T-duality transformations. These backgrounds can be associated with non-trivial topology or non-standard geometry, which could lead to the emergence of non-trivial structures in the theory.
Examples of non-Riemannian backgrounds in double field theory, which is a T-duality invariant formalism, can render a propagating string chiral and anti-chiral over certain dimensions, indicating the presence of non-trivial topological or geometric structures.

However, a full understanding of this phenomenon would require a more detailed analysis of the specific string backgrounds and compactifications involved, as well as a thorough investigation of the quantum properties of T-duality invariant formalisms. This could provide insights into the emergence of non-trivial structures from absolute nothingness in the context of non-geometric backgrounds and T-duality.

🐱: Did I understand correctly that non-Riemannian backgrounds can describe a absolutely void space?

🕸: Yes, you understood correctly. Non-geometric backgrounds in string theory, which can be non-Riemannian, have the potential to describe an absolutely void space. These backgrounds, arising from T-duals of geometric backgrounds, exhibit non-standard geometric properties and can involve non-trivial topologies or non-standard geometries that could represent a true void space. The presence of non-Riemannian structures in these backgrounds, as indicated in the sources, suggests the possibility of describing a space devoid of conventional geometric properties, aligning with the concept of absolute nothingness.

🐱: If there were a absolutely void space described by a non-Riemannian background, what would be its ontological status? That is, how could nothingness be correctly understood in this case?

🕸: The ontological status of a void space described by a non-Riemannian background in string theory would depend on the specific interpretation of the theory and its underlying ontology. If we adopt a 'thing' ontology, where the universe is made up of a plurality of discrete objects, a void space described by a non-Riemannian background could be understood as a space devoid of conventional geometric properties, representing a form of absolute nothingness.
On the other hand, if we adopt a 'non-thing' ontology, where the universe is considered as one continuous object, the void space described by a non-Riemannian background might be seen as a manifestation of the continuous nature of the universe, rather than a true void space.
In either case, the interpretation of the ontological status of a void space described by a non-Riemannian background would be closely tied to the specific ontological framework adopted and the interpretation of the mathematical structures used to describe the background.

🐱: Explain what is meant here by 'thing' and 'non-thing' ontologies.

🕸: In the context of the sources provided, 'thing' ontologies refer to perspectives that view the universe as composed of discrete, individual objects or entities. These ontologies consider reality to be made up of separate and distinct entities, each with its own properties and characteristics. On the other hand, 'non-thing' ontologies take a different approach, considering the universe as a unified whole or a continuous entity rather than a collection of discrete objects. Non-thing ontologies do not necessarily rely on the concept of individual objects but instead focus on a more holistic or continuous view of reality.

🐱: Is the physical theory of shape dynamics compatible with the existence of a truly absolute void space?

🕸: No, the physical theory of shape dynamics (PSD) is not compatible with the existence of a truly absolute void space. PSD is a relational theory that rejects the notion of an external space and instead focuses on the shapes and configurations of physical systems. It features unparametrized curves, meaning there is no external time parameter, and dynamics are determined by the evolution towards shapes that maximize the complexity of the system. This approach is incompatible with the idea of an absolute void space, as it emphasizes the relationships and configurations of physical objects rather than an absolute, empty background.

🐱: From the perspective of modern theoretical physics, how can there be motion in a fundamentally discrete space, be it loop quantum gravity theory, causal set theory, or string-theoretic (non-)geometric backgrounds in cases when they have discrete properties? Recall Zeno's paradox of the always resting arrow,

which essentially just teleports from place to place - is this motion in the intuitive sense? How do these physical theories solve the arrow paradox?

🕸: In modern theoretical physics, the concept of motion in a fundamentally discrete space is addressed in various quantum gravity theories such as loop quantum gravity (LQG), causal set theory, and string theory. LQG, for instance, uses connections and holonomies as its fundamental variables instead of metric variables, leading to a quantized geometry. The discrete nature of these theories challenges the intuitive understanding of motion, often associated with continuous space-time.
Regarding Zeno's arrow paradox, LQG provides a solution by quantizing geometry, where area and volume have a discrete spectrum. This quantization implies that the arrow's position is not strictly defined at any given moment, but rather in a superposition of discrete states. Therefore, the arrow's motion is not a series of teleportations between points, but a continuous evolution through a quantum state space.
In summary, modern quantum gravity theories like LQG solve Zeno's arrow paradox by quantizing geometry and introducing a probabilistic understanding of motion, which aligns with the principles of quantum mechanics.

🐱: I don't get it. How can this evolution be called continuous if time is quantized?

🕸: Quantum gravity theories, such as loop quantum gravity, propose that time can be quantized, leading to discrete steps in the evolution of quantum systems. However, the concept of continuous evolution is preserved through the use of wave equations, which describe the time evolution of quantum states as a sum over continually evolving jump amplitudes between different sectors in Fock space. This perspective reconciles the apparent dichotomy between quantum jumps and continuous time evolution, demonstrating that discussions of quantum theory interpretations must consider field quantization. The limitations of wave equations and superpositions of quantum states in forming qubits also highlight the need for a more nuanced understanding of quantum theory.

🐱: So is this evolution discrete, continuous, or something else? Explain it better, please.

🕸: The evolution of quantum systems in quantum gravity theories, such as loop quantum gravity, can be understood as both discrete and continuous in a sense. While time and space are quantized, leading to discrete steps in the evolution of quantum systems, the use of wave equations allows for a continuous description of the time evolution of quantum states as a sum over continually evolving jump amplitudes between different sectors in Fock space. This perspective reconciles the apparent dichotomy between quantum jumps and continuous time evolution, demonstrating that discussions of quantum theory interpretations must consider field quantization. The limitations of wave equations and superpositions of quantum states in forming qubits also highlight the need for a more nuanced understanding of quantum theory. In summary, the evolution in quantum gravity theories is a complex interplay between discrete and continuous aspects, arising from the quantization of space-time and the continuous description provided by wave equations.

🐱: So how to understand the motion of an object of minimal volume in these theories (quantum loop theory, causal set theory and (non-)geometric backgrounds from string theory in cases when they have discrete properties)? Will it move smoothly in space, jump from place to place or something more complicated? It's not just a matter of different descriptions. It also needs to be explained at a fundamental level. You write that motion is evolution in discrete quantum space, where time is quantized too, and evolution of quantum systems can be considered continuous from the point of view of sums of continuous amplitudes of quantum jumps in Fock space (in the context of quantum loop gravity). This moment is difficult to understand.

What will be with the object of minimal volume? I repeat, will it jump? Will it move5 smoothly? Something more complicated? If it's the case that it's a more complex phenomenon, try explaining a little more accessible. I realize this coarsens the theory, but correctly approximate scientific knowledge a bit to somewhat more intuitive and simple descriptions, please.

🕸: In theories like loop quantum gravity, objects of minimal volume in discrete quantum space may exhibit unique behaviors. While motion in these theories is not fully analogous to classical smooth movement, it can be understood as an evolution in discrete space where time is quantized. Objects may not move smoothly but evolve through quantum jumps in Fock space, representing a more complex phenomenon than simple continuous motion. This concept blends discrete properties with quantum dynamics, suggesting that the motion of an object of minimal volume involves a nuanced interplay of quantum states and transitions rather than traditional smooth trajectories.

🐱: That is, an object of minimal volume will be sort of teleported from place to place in a complex way and with complex quantum effects, but in terms of larger scales it will look like something like a smooth motion?

🕸: Yes, you're on the right track. In loop quantum gravity, the motion of an object of minimal volume can be thought of as a complex process involving quantum jumps between different quantum states of space. These transitions occur in a discrete, quantized space, where time is also quantized. While the motion is not smooth in the traditional sense, it can appear smooth on larger scales due to the averaging of quantum effects. This is because the quantum states of space are highly interconnected, leading to a complex network of relationships that can give the illusion of smooth motion when viewed from a distance or over time. However, at very small scales, the true discrete nature of the motion would become apparent, with the object seemingly teleporting from place to place in a complex, quantum manner.

🐱: Then how does it deal with the Zeno paradox of an always resting arrow that simply teleports from place to place? In the context of this paradox, motion does not exist (as we usually think of it).

🕸: In the context of Zeno's paradox, where an arrow appears to always be at rest yet moves from place to place, theories like loop quantum gravity offer a unique perspective. These theories suggest that motion, especially at a fundamental level, involves a complex interplay of discrete quantum states and transitions in spacetime. While the paradox challenges traditional notions of motion, the concept of discrete spacetime in loop quantum gravity implies that the arrow's movement involves a series of quantum jumps between different states, giving the appearance of teleportation rather than continuous motion. This interpretation aligns with the idea that motion, when viewed at a fundamental level, may not conform to classical expectations but instead involves intricate quantum processes that transcend traditional notions of smooth movement.

🐱: And how do jumps work in such theories? That is, how does an object of minimal volume move from place to place in discrete space? It turns out that some unit of matter appears in a new place (and this unit replaces something else in that place), and in the old place it disappears (and something else replaces this unit in that place). First, I wonder how this is physically explained, i.e. these jumps-teleportations, when matter disappears and appears in a completely different place. Secondly, how does the diachronic identity of jumping objects in discrete space be fulfilled?

🕸: In loop quantum gravity, the concept of jumps or teleportations of an object of minimal volume is related to the quantization of spacetime. The area and volume operators in loop quantum gravity have discrete eigenvalues, implying that spacetime is quantized.

This means that the object's movement involves transitions between different quantum states of space, which can be thought of as jumps or teleportations from one place to another.
The physical explanation for these jumps is rooted in the quantum nature of spacetime itself. The discreteness of spacetime implies that the object's position can only be described in terms of probabilities, and transitions between different positions occur through quantum processes. These transitions are not classical movements but rather quantum jumps between different states of space.
The diachronic identity of jumping objects in discrete space is maintained through the object's quantum state, which evolves over time. The object's identity is preserved as long as its quantum state remains coherent and distinct from othere quantum states. Even though the object may appear in a completely different place due to quantum jumps, its identity is preserved through its quantum state.
In summary, the jumps or teleportations of an object of minimal volume in loop quantum gravity are a result of the quantization of spacetime. The physical explanation for these jumps is rooted in the quantum nature of spacetime itself, and the diachronic identity of jumping objects is maintained through their quantum state.

🐱: String theory, loop quantum theory of gravity, causal set theory, shape dynamics. Can they be harmonized? At least two of them. I.e., is there a general theory for them. And / or can it be hypothetically true or correct that all or some (at least two) of these theories are somehow simultaneously true, but are different perspectives in the sense of Nietzschean perspectivism, in the sense of the Nagelian idea of looking at our universe from different embodied viewpoints followed by a mental idealization from them into as if / supposedly a view from nowhere, or in the sense of perspectivism in modern analytic philosophy? Are these perspectives simultaneously true theoretically constructed "projections" on the same thing, just with different underlying theoretical assumptions and different metaphysics of those theories?

🕸: String theory, loop quantum gravity, causal set theory, and shape dynamics can potentially be harmonized within a speculative proposal like Fragmentalist Causal Quantum Gravity (FCQG). This theory envisions a framework where different quantum gravity theories align with the Presentist Fragmentalist interpretation of quantum mechanics, offering a unified treatment of quantum theory and gravity. While each theory has distinct principles, FCQG aims to reconcile them, providing a discrete, relational view of spacetime and causality. Theoretical constructions like FCQG suggest a way to view these theories as complementary perspectives on the same phenomena, akin to Nietzschean perspectivism or Nagelian embodied viewpoints.

🐱: What is space in the theory of fragmentalist causal quantum gravity? Is it a fundamental level of reality even on the smallest scales or does it emerge emergently from (proto-)causal relations?

🕸: In Fragmentalist Causal Quantum Gravity (FCQG), space is not considered a fundamental level of reality at the smallest scales. Instead, it emerges from proto-causal relations, aligning with the causal set theory (CST) approach to quantum gravity. CST posits that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or "causal sets." The partial order on a causal set represents a proto-causality relation, while local finiteness encodes an intrinsic discreteness. This approach is deeply rooted in the Lorentzian character of spacetime, where the causal structure poset plays a primary role. The assumption of a fundamental discreteness in CST does not violate local Lorentz invariance in the continuum approximation, but it does give rise to a characteristic non-locality that distinguishes it from most other approaches to quantum gravity.

🐱: How is FCQG differ from CST?

🕸: Fragmentalist Causal Quantum Gravity (FCQG) is a theoretical framework that encompasses the Causal Set Theory (CST) approach to quantum gravity, but it extends beyond it. FCQG is a more general framework that aims to reconcile various approaches to quantum gravity, including CST, by incorporating a fragmentalist perspective on quantum mechanics. This perspective suggests that the fundamental nature of reality is not described by a single, global quantum state but rather by a collection of local quantum states, each corresponding to a fragment of spacetime.
In FCQG, space emerges from proto-causal relations, similar to CST, but the fragmentalist perspective adds a new layer of interpretation to the theory. FCQG posits that the various approaches to quantum gravity, such as CST, string theory, loop quantum gravity, and others, can be seen as complementary perspectives on the same phenomena, each highlighting different aspects of the underlying reality. By adopting this perspective, FCQG aims to provide a more comprehensive understanding of quantum gravity, one that can accommodate the strengths and insights of various approaches while also addressing their limitations and challenges.
In summary, FCQG is a theoretical framework that goes beyond CST by incorporating a fragmentalist perspective on quantum mechanics. This perspective allows FCQG to reconcile various approaches to quantum gravity, providing a more comprehensive understanding of the field.

🐱: Are there non-marginal modern physical theories that consider intervals or units of space and time, things in them and events in them, smaller than Planck scale?

🕸: Yes, there are non-marginal modern physical theories that consider intervals or units of space and time, things in them, and events in them, smaller than the Planck scale. These theories are primarily focused on unifying quantum mechanics and general relativity, which are currently incompatible at large scales, into a theory of quantum gravity. Some of these theories include string theory, loop quantum gravity, and theories with large extra dimensions.
String theory, for example, proposes that fundamental particles are not point-like objects but rather tiny, one-dimensional "strings" that vibrate at different frequencies, which correspond to different particles. These strings are modeled to be on the order of the Planck length, which is a distance scale of interest in speculations about quantum gravity.
Loop quantum gravity is another theory that attempts to unify quantum mechanics and general relativity. It is based on the idea that space and time are quantized, and it proposes that the smallest measurable length is not zero but rather the Planck length.
Theories with large extra dimensions, such as brane world models, suggest that the Planck length calculated from the observed value of G can be smaller than the true, fundamental Planck length.
It is important to note that these theories are still speculative and have not been experimentally confirmed. They are currently being tested through various means, such as the study of cosmic rays and the search for gravitational waves, but no definitive evidence has been found yet.

🐱: It says, in string theory and quantum loop gravity theory, that the nature of reality is built on things of Planck length. Except that it mentions that the observed Planck distance may be smaller than the true one. What about theories with phenomena strictly smaller (not equal!) than the Planck scale? Are there any such?

🕸: In string theory and loop quantum gravity, the fundamental structure of reality is based on the Planck length, around 10^-33 centimeters. While these theories suggest that phenomena at the Planck scale are significant, there is speculation that observed Planck distances could be smaller than the true limit. The existence of phenomena strictly smaller than the Planck scale remains uncertain in current theories, posing challenges in understanding physics at such minuscule levels.