Unravelling the Quantum Universe: How Different Theories Tackle Gravity and Spacetime

Have you ever wondered what happens at the absolute smallest scales of the universe? We have two incredibly successful theories describing reality: General Relativity (GR) for the large-scale structure of gravity and spacetime, and Quantum Mechanics (QM) for the microscopic world of particles and forces. But they don't play well together, especially when gravity becomes extremely strong, like near the Big Bang or inside black holes, where Einstein's smooth, continuous picture of spacetime geometry seems to break down.

The quest to unify these two pillars of modern physics into a single theory of "quantum gravity" is one of the biggest challenges in physics today. It's like needing a whole new language to describe the quantum nature of geometry. Several theoretical frameworks are vying for this ultimate prize, each taking a unique approach.

Let's break down the differences between Quantum Geometry Dynamics (QGD), Loop Quantum Gravity (LQG), and Causal Dynamical Triangulation (CDT).

These are all approaches attempting to tackle the significant challenge of unifying general relativity (GR) and quantum physics, often referred to as the problem of quantum gravity. However, they propose fundamentally different paths to achieve this.

Here's a look at each theory based on the provided sources:

Quantum-Geometry Dynamics (QGD)

QGD is presented as an axiomatic approach to physics. It aims to build the entire physical framework from a few fundamental postulates. This is framed as a response to Hilbert's call for axiomatizing physics.

• Core Axioms/Concepts:
  • Strict causality.
  • Fundamental particles called preons. Preons plus form matter and carry intrinsic kinetic energy and mass (defined as the number of preons plus). Preons minus make up space.
  • Discrete Space: Space is fundamentally discrete and granular, made of static preons (minus). Euclidean geometry is an emergent approximation at larger scales. The repulsion between prons minus is said to create quantum geometrical space itself.
  • Relational Time: Time is not fundamental but purely relational, defined by counting the recurrent states of periodic systems (clocks). This is proposed to sidestep the "problem of time" inherent in trying to combine QM and GR.
  • Fundamental Forces (p-gravity/n-gravity): Forces arise from preonic interactions. P-gravity is attractive between preons plus (matter). N-gravity is repulsive between preons minus (space).
  • Instantaneous Gravity: QGD proposes that gravitational interactions are instantaneous, directly changing the momentum of particles without delay. This is a major departure from relativity's speed limit (C).
  • Intrinsic vs. Metric Velocity: Distinguishes between a particle's frame-independent intrinsic velocity (momentum/mass) and the observer-dependent metric velocity (measured distance/time). The intrinsic velocity of light (photons, made of prons plus) is constant C.
• Key Predictions/Consequences:
  • One-Way Speed of Light: Predicts the measured one-way speed of light might not be constant or isotropic, potentially revealing absolute motion relative to the discrete space. This is a key, potentially testable difference from Special Relativity.
  • Gravity as Composite Effect: Gravity emerges from the combined effects of instantaneous pravity and nravity.
  • Repulsive Gravity: Predicts gravity becomes repulsive at large distances, potentially explaining dark energy.
  • Dark Matter: Explained as the gravitational pull of free prons plus (not bound into visible matter).
  • Alternative GW Interpretation: Signals detected by LIGO/Virgo are interpreted as intense electromagnetic or "preonic" disturbances traveling at c, rather than spacetime ripples.
  • Equivalence Principle: Predicts a potential violation of the strong equivalence principle, suggesting gravitational and non-gravitational acceleration might be subtly distinguishable.
  • Mass/Energy Relation: E=MC is a proportionality (E proportional to M), not an equivalence. Mass (preon(+) count) is distinct from energy (preon(+) kinetic energy). Nuclear reactions release bound preons(+) plus and their energy, not mass conversion.
  • Discrete Mathematics: Suggests reality might be fundamentally discrete and finite, implying continuous math is an approximation.

QGD is presented as challenging fundamental assumptions of both QM and GR (continuous spacetime, fundamental time, speed of light as universal limit/constant in all measurements, nature of gravity) and offering alternative, often particle-based, explanations for observed phenomena.

Loop Quantum Gravity (LQG)

LQG is described as a prominent candidate for quantum gravity that takes the core lesson of GR seriously: that gravity is geometry. It aims to be a background-independent quantization of general relativity. This means it does not assume a pre-existing spacetime metric.

• Core Ideas/Approach:
  • Reformulates GR using the language of gauge theories.
  • Quantizes this reformulated geometry using non-perturbative techniques. This avoids starting with quantum matter on a background geometry and perturbatively incorporating gravity.
  • Constructs a theory of quantum Riemannian geometry.
  • Discreteness Emerges: A key result is that space and time are found to be granular and discrete. This discreteness is seen as emerging naturally from the quantization process, unlike in some other approaches.
  • Quantum Loops/Spin Networks: The fundamental "building blocks" of space-time are described in terms of quantum loops, or more generally, spin networks, which are like intricate lattices or polymer-like structures. Diffeomorphism invariant physical states are labeled by knots.
  • Discrete Spectra: Operators corresponding to geometrical quantities like area and volume have discrete spectra. This is interpreted as meaning physical measurements of area/volume would yield quantized results.
  • Relational Dynamics: Quantum dynamics is described relationally, often using a matter field as an internal clock.
  • Singularity Resolution: In cosmology (Loop Quantum Cosmology - LQC), singularities like the big bang are resolved, often replaced by a big bounce.
  • Dynamics (Spinfoams/Hamiltonian): There are two main approaches to quantum dynamics, Hamiltonian constraint methods (related to Dirac's work) and spinfoams (extending path integrals). The dynamics is still being developed.
• Scope: LQG is described as being more focused than string theory, concentrating solely on the quantization of gravity, not aiming for a comprehensive theory of everything (TOE) that unifies all interactions. Matter is coupled to the theory.
• Challenges: A key challenge is the treatment of dynamics and connecting the theory to the classical limit (recovering GR at large scales). LQG, like string theory, currently lacks experimental evidence to validate its ideas.

Causal Dynamical Triangulation (CDT)

CDT is described as another background independent approach to quantum gravity. It is formulated as a non-perturbative lattice theory using triangulated spacetimes.

• Core Ideas/Approach:
  • Defines the quantum theory via a path integral, but instead of integrating over continuous geometries, it sums over discrete triangulations (simplicial manifolds). This discretization is a standard regularization technique used in Quantum Field Theory (QFT).
  • Causality Constraint: A crucial feature that distinguishes CDT from other dynamical triangulation approaches is the imposition of a causality condition. This is done by assuming a global proper-time foliation, which distinguishes between time-like and space-like links in the triangulation and prevents spacetime from breaking up into "baby universes".
  • Discreteness as Regularization: Unlike LQG where discreteness is seen as fundamental and emerging from quantization, in CDT the discreteness of the triangulations is put in by hand as a regularization. The goal is to take a continuum limit where this discretization is removed.
  • Emergence of Spacetime: The process attempts to show how the spacetime fabric itself evolves from the gluing of these discrete units. At large scales, CDT simulations show the emergence of the familiar 4-dimensional spacetime. Near the Planck scale, it suggests spacetime might be 2-dimensional and have a fractal structure.
  • Geometric Approach: CDT is described as a purely geometric approach. The distance or "interval" between points in a triangulation can be calculated exactly.
• Related Theories: CDT shares similarities with spin foam formulations of LQG, both using path integrals over discrete structures, but differs in degrees of freedom and Lagrangians. It is also closely related to causal sets, both modeling spacetime with a discrete causal structure, but CDT assumes a more specific relationship between the lattice and geometry. In the continuum limit, CDT might be related to Hořava–Lifshitz gravity due to the reliance on spacetime foliation.
• Challenges: Understanding the continuum limit remains a difficult task. Like LQG, CDT currently lacks experimental evidence. Due to numerical simulation requirements, it doesn't make sense to describe CDT with just a few simplices; typically hundreds of thousands or millions are used.

Key Differences Summarized:

Based on the sources, here are some primary differences:

1. Fundamental Approach:
   • QGD: Axiomatic, building physics from fundamental particles (preons) and their interactions, from which space and forces emerge.
   • LQG: Quantization of the geometry of General Relativity using non-perturbative gauge theory methods.
   • CDT: Path integral defined by summing over discrete, causally constrained triangulations of spacetime.
2. Nature of Discreteness:
   • QGD: Space is fundamentally discrete as a starting axiom.
   • LQG: Discreteness of space emerges from the quantization of geometry. The fundamental entities are quantum loops/spin networks representing quanta of geometry.
   • CDT: Discreteness (triangulation) is primarily a regularization technique for the path integral, intended to be removed in the continuum limit.
3. Treatment of Time:
   • QGD: Time is relational, not fundamental, defined by change.
   • LQG: Employs relational time for describing dynamics.
   • CDT: Uses a fixed proper-time foliation to enforce causality.
4. Mechanism of Gravity:
   • QGD: Gravity is a composite effect of instantaneous interactions (p-gravity and n-gravity) between fundamental particles (preons).
   • LQG: Gravity is a manifestation of the quantum nature of spacetime geometry.
   • CDT: Gravity arises from the geometric sum over allowed discrete spacetime configurations, leading to the emergence of macroscopic spacetime geometry.
5. Focus and Scope:
   • QGD: Aims to provide a complete alternative framework explaining matter, forces, and cosmology from basic axioms.
   • LQG: Primarily focused on the quantization of the gravitational field and spacetime geometry, not presented as a theory of everything.
   • CDT: Focuses on constructing spacetime via a geometric path integral approach.
6. Nature of Building Blocks:
   • QGD: Starts with fundamental particles (preons) and their interactions.
   • LQG: Fundamental entities are quanta of geometry represented by loops/spin networks.
   • CDT: Fundamental entities are simplices (triangular building blocks) that form the discrete spacetime approximations.
7. Experimental Predictions:
   • QGD: Proposes specific, potentially testable differences from relativity, such as anisotropy in the one-way speed of light, details about dark matter/energy, equivalence principle violation, and reinterpretation of gravitational waves.
   • LQG: Predicts discrete spectra for area/volume (difficult to test directly) and makes predictions for cosmology in LQC. Faces general challenges with direct experimental verification.
   • CDT: Predicts the emergence of 4D spacetime at large scales and 2D fractal structure at Planck scales. Also faces significant challenges with experimental verification.

In essence, QGD is an axiomatic, particle-based approach postulating fundamental discreteness and instantaneous interactions. LQG is a non-perturbative quantization of GR focusing on emergent discrete quantum geometry. CDT is a path integral approach using discrete, causally constrained geometric building blocks as a regularization. While all are background-independent approaches to quantum gravity, their starting points, fundamental concepts, and the way discreteness is handled are quite different.

 This episode of The Discrete Universe podcast, provides a summary of QGD's main ideas and concepts and their consequences.

Recent Cosmological Observations and QGD (audio podcast)

 

A Lopsided Universe? QGD and the Andromeda Satellite Problem

Distinguishing Quantum-Geometry Dynamics from Quantum Mechanics via Double-Slit Experiments

Could Quantum-Geometry Dynamics Shed Light on Anomalous Ionization in the Galactic Centre?

Quantum-Geometry Dynamics: A Deterministic View of Measurement

Quantum-Geometry Dynamics; an axiomatic approach to physics does not explicitly dedicate a section solely to the "measurement problem" as it is known in quantum mechanics. However, QGD's fundamental principles and its critique of quantum mechanics offer a perspective that implicitly addresses the issues at the heart of this problem.

Here's how QGD approaches the challenges raised by the measurement problem:

• Strict Causality and Determinism: QGD is founded on the principle of strict causality, which asserts that every successive state of a particle, structure, or system is strictly and uniquely causally linked to the preceding one. This deterministic view stands in contrast to the standard interpretation of quantum mechanics where measurement outcomes are probabilistic. From a QGD perspective, the apparent randomness of quantum measurements is likely not fundamental but rather a consequence of an incomplete description at the quantum level.

• Discrete Nature of Reality: QGD posits that space and matter are fundamentally discrete. This discreteness implies that the evolution of systems occurs through discrete steps governed by strict causal laws at the level of preons. What appears as a probabilistic "collapse" of a superposition upon measurement in quantum mechanics might be explained in QGD as a deterministic transition between discrete states that is currently not fully understood or accessible by continuous mathematical models.

• Rejection of the Uncertainty Principle as Fundamental: QGD considers the uncertainty principle a consequence of quantum mechanics' assumption of continuous space, rather than a fundamental limitation of reality itself. In a discrete and strictly causal framework, the simultaneous and certain measurement of conjugate properties should, in principle, be possible. This suggests that the limitations imposed by the uncertainty principle in quantum mechanics, which contribute to the puzzle of measurement, are not inherent in the underlying reality as described by QGD.

• Instantaneous Gravitational Interactions: QGD proposes that gravitational interactions are instantaneous. This non-local aspect of QGD could be relevant to how measurement on one part of a system seemingly instantaneously affects another, as seen in entanglement. QGD suggests that observed violations of Bell's inequalities might be due to these instantaneous classical (gravitational) effects rather than quantum non-locality. This could imply that the act of measurement involves instantaneous gravitational interactions that determine the outcome in a strictly causal way.

• Incompleteness of Quantum Mechanics: QGD implicitly suggests that quantum mechanics is an incomplete theory. The need for probabilistic interpretations and the difficulties associated with the measurement problem might indicate that quantum mechanics does not fully capture the underlying deterministic and discrete reality. QGD aims to provide a more fundamental axiomatic basis that can explain these phenomena through strictly causal mechanisms at the preonic level, potentially resolving the measurement problem by providing a deterministic account of what happens during a measurement.

In summary, while QGD does not offer a specific "solution" to the measurement problem as a distinct topic, its core tenets of strict causality, the discrete nature of reality, the view of the uncertainty principle as non-fundamental, and instantaneous gravitational interactions provide a framework that inherently challenges the probabilistic interpretation of quantum measurement. QGD would likely argue that what appears as the "collapse" of a wave function is a deterministic process governed by underlying causal laws at the preonic level, and that a more complete theory based on its axioms would ultimately provide a strictly causal explanation for measurement outcomes.