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.

Strict Causality in Quantum-Geometry Dynamics: Implications for Physics

 The concept of a strictly causal universe as defined by Quantum-Geometry Dynamics (QGD) has significant implications for physics theories. According to QGD, all successive states of a particle, structure, or system are strictly and uniquely causally linked. This principle offers a way to understand the evolution of the universe as sequences of events connected by cause and effect, potentially allowing a description of evolution without relying on the relational concept of time.

Here are some key implications of a strictly causal universe within the framework of QGD for physics theories:

• Challenge to Spontaneity: Strict causality in QGD excludes spontaneity, which assumes that a particle or system can change based on probability over time without a specific cause. This challenges interpretations in other theories that might rely on inherent probabilistic behaviors without a clear causal mechanism at the fundamental level.
• Understanding the Source of Incompatibilities: QGD proposes that if reality is strictly causal, then it can be thought of as a complete and consistent axiomatic system. In this view, fundamental aspects of reality correspond to axioms, and non-fundamental aspects (observable phenomena) correspond to theorems. Incompatibilities between current physics theories arise because they are often founded on theorems derived from observations at different scales, rather than a unified set of fundamental axioms. A strictly causal framework suggests that a unified theory would require identifying the true fundamental axioms of reality.
• Possibility and Nature of a Theory of Everything (TOE): QGD's strict causality implies that a TOE is possible if it can be derived from the complete and consistent set of fundamental axioms governing the universe. However, it also suggests that achieving a TOE by simply unifying existing theories like the Standard Model and General Relativity might be mathematically impossible because they are based on mutually exclusive axiom sets. Instead, a TOE would need to be derived axiomatically from the most fundamental aspects of reality.
• Alternative to Time as a Fundamental Concept: The principle of strict causality in QGD suggests that the evolution of any system can be described without necessarily resorting to the relational concept of time. The universe changes from one state to the next due to concurrent causally related series of events, rather than evolving with time. This could lead to different formulations of physical laws that prioritize causal sequences over temporal evolution.
• Implications for Measurement and Observation: In a strictly causal universe as described by QGD, any change in a system is due to a specific cause. This perspective could influence the interpretation of quantum measurements and the role of the observer. While QGD acknowledges non-local effects, it attributes them to instantaneous gravitational interactions rather than inherent quantum randomness, suggesting a causal link even across distances. This contrasts with interpretations of quantum mechanics that emphasize intrinsic indeterminacy.
• Foundation for Axiomatic Approaches: QGD itself is presented as an axiomatic approach to physics, where the principle of strict causality is a guiding principle in choosing the fundamental axioms (such as the discreteness of space and the existence of preons). A strictly causal universe reinforces the idea that physics theories should be built from a self-consistent set of axioms that correspond to fundamental aspects of reality.

In summary, a strictly causal universe as envisioned by QGD has profound implications for how we understand the fundamental nature of reality, the relationships between different physics theories, and the possibility of a unified description of the universe. It emphasizes the primacy of causal connections and challenges the fundamental status of concepts like continuous space and time as they are often understood in other frameworks.

Taking Quantum-Geometry Dynamics from Talk to Numbers: How QGD Aims for Quantitative Predictions

 I provided the book "Quantum-Geometry Dynamics; an axiomatic approach to physics" to NotebookLM and asked to write a blogpost that answers the question: "How can the qualitative predictions of QGD be transformed into quantitative predictions?" Read the blogpost it created below.

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Hey everyone, it's fascinating to dive into the world of theoretical physics, and recently we've been discussing Quantum-Geometry Dynamics (QGD), an intriguing axiomatic approach to understanding the universe. One question that naturally arises is: how can the interesting ideas within QGD move beyond the qualitative and make concrete, testable predictions with actual numbers? Let's break down how QGD aims to bridge this gap, drawing from the "Quantum-Geometry Dynamics (an axiomatic approach to physics)" document.

At its heart, QGD operates on a foundation of discrete space built from fundamental units called preons(-). Think of it like the smallest pixels making up the image of reality. While we can't directly measure these fundamental building blocks, QGD lays the groundwork for quantitative predictions through several key concepts:

• Fundamental Units and the Speed of Light: QGD proposes fundamental units for things like displacement and momentum, rooted in the properties of preons(+). Crucially, it introduces a constant intrinsic velocity of preons (+), denoted as c, which is also the intrinsic speed of light. While the exact numerical value of these fundamental units might not be given by the theory alone at the outset, QGD defines the relationships between different physical quantities in terms of these units, setting the stage for proportional predictions.
• From Discrete to Continuous: The Emergence of Euclidean Space: While the fundamental level is discrete, QGD includes a crucial "Theorem on the Emergence of Euclidian Space from Quantum-Geometrical Space". This is a game-changer because it means that at everyday scales, and even at astronomical scales, our familiar Euclidean geometry acts as a very good approximation of the underlying discrete structure. This allows physicists working with QGD to use the powerful tools of continuous mathematics when dealing with macroscopic phenomena, making calculations feasible.
• Introducing Metric Properties for Measurable Quantities: Since we can't directly measure the intrinsic properties of preons, QGD introduces the idea of using metric properties. These are essentially scaled versions of the intrinsic properties that can be related to what we actually measure in our labs and telescopes. For example, QGD defines metric velocity and metric mass. The great thing is that the fundamental equations within QGD remain valid even when we substitute these metric properties, as long as all quantities in the equation are metric. This provides a vital link between the theoretical framework and the observable universe.
• The Curious Case of Light Speed: One-Way vs. Two-Way: QGD makes a fascinating prediction about the speed of light. It distinguishes between the intrinsic speed (c), the metric speed (c), and the speed we typically measure using a round trip. The theory predicts that while two-way measurements of the speed of light will be constant and equal to the metric velocity, one-way measurements will be anisotropic (different depending on direction) and will not be constant. Proposing experiments to precisely measure the one-way speed of light is a key step in putting QGD to a quantitative test and potentially determining the metric velocity in relation to the fundamental constant c.
• Key Testable Predictions to Differentiate QGD: The strength of any new theory lies in its ability to make predictions that differ from existing ones. QGD steps up to this challenge with several unique predictions:
• Differences in Gravitational Redshift: QGD posits an intrinsic gravitational redshift at the source due to gravitational acceleration, offering a different perspective on the observed cosmological redshift compared to some interpretations of general relativity.
• Non-Equivalence of Accelerations: QGD suggests that gravitational and non-gravitational acceleration might not be equivalent in all scenarios, proposing experiments to detect effects based on the absolute velocity of a laboratory.
• Momentum Transfer Differences: The theory predicts that the transfer of momentum through electromagnetic interactions will differ measurably from gravitationally imparted momentum due to the underlying preonic structure of particles.
• Dark Matter Halo Properties: QGD offers specific predictions about the distribution of dark matter in galaxies, such as the prohibition of a "cuspy" halo and a flat rotation curve extending further than current models suggest.
• The Nature of LIGO-Virgo Signals: QGD proposes that the signals detected as gravitational waves might actually be preonic waves, offering avenues for potential future experiments to distinguish between these interpretations.
• Anisotropic One-Way Light Speed: The prediction of a non-constant, anisotropic one-way speed of light is a direct and potentially measurable deviation from standard physics.
• Quantifying Gravity: Assigning Value to the Constant k: QGD's equation for gravitational interactions includes a proportionality constant, k. To move from qualitative descriptions of gravity to quantitative predictions of its strength, the value of this constant needs to be determined experimentally. By carefully observing gravitational interactions, measuring metric masses, and determining distances, scientists could potentially infer the value of k, allowing for numerical calculations of gravitational effects within the QGD framework.
• Using Metric Properties for Numerical Predictions: Once we have metric properties linked to measurements and values for fundamental constants within QGD, we can start plugging these into the theory's equations. This would allow for the calculation of quantitative predictions for various phenomena. For instance, by measuring the metric velocity of a galaxy, its metric momentum and energy could be numerically determined using QGD's definitions.

In Conclusion:

Transforming QGD from a fascinating theoretical framework into a quantitatively predictive one is an ongoing process. It hinges on building a robust mathematical structure, defining measurable metric counterparts to fundamental properties, deriving precise relationships between these properties, and crucially, designing and conducting experiments to measure key quantities and determine the values of fundamental constants within the theory. The unique predictions offered by QGD, particularly regarding the one-way speed of light and subtle differences in gravitational and non-gravitational interactions, provide exciting avenues for future research that could either validate or refine this intriguing approach to physics. The journey from qualitative ideas to quantitative predictions is a hallmark of scientific progress, and QGD is actively taking steps along this path.

Particular Interpretation of Double-Slit Experiments

 

Following the failure of classical physics theories to explain the interference patterns observed in double slit experiments and other light diffraction experiments and because of the similarities between these patterns and the interference patterns produced by waves at the surface of a liquid, physicists deduced that light was behaving as a wave. However, only the particle model appeared to explain phenomena such as the photoelectric effect. Consequently, physicists deduced that light was corpuscular or wave-like depending on the experiment performed on it. But what these experiments show is that neither accepted models of light could explain both behaviours and emphasized the need for a new theory.

A Response to Ethan Siegel’s Article titled "The Good Reasons Scientists Are So Hostile to New Ideas"

In his article titled The Good Reasons Scientists Are So Hostile to New Ideas  Ethan Siegel writes:

“Proposals that attempt to revolutionize one (or more) of our accepted theories have a large suite of hurdles to overcome. In particular, they must:

• reproduce all the successes of the prevailing theory,
• explain a phenomenon more successfully than the current theory can,
• and make novel predictions that can be tested that differ from the theory it’s attempting to supersede.”

Satisfying the above criterions requires that a new theory or proposal must be sufficiently developed.  It is unlikely that a new proposal or theory will be capable of meeting those criterions early on. Unlike accepted theories, new theories have not benefited from a century of contributions by generations of scientists. So, the consequences of ideas must be fully explored before shooting them down for not meeting the criterions.

That said, I agree with pretty much every point Segal makes in his article in that at some point a new idea, when sufficiently developed in a theory, must meet those criterions but one should avoid putting them to the test prematurely. Not only do I agree with the criterions he enumerates, but I think a theory should be held to an even more rigorous set of criterions.  From Quantum-Geometry Dynamics; an axiomatic approach to physics Quantum-Geometry Dynamics; an axiomatic approach to physics .

Any theory that is rigorously developed from a given consistent set of axioms will itself be internally consistent. That said, since any number of such axiom set can be constructed, an equal number of theories can be derived that will be internally consistent. To be a valid axiomatic physics theory, it must answer positively to the following questions.

1. Do its axioms form an internally consistent set?
2. Is the theory rigorously derived from the axiom set?
3. Are all descriptions derived from the theory consistent with observations?
4. Can we derive explanations from the axiom set that are consistent with observations?
5. Can we derive from the axiom set unique and testable predictions?

And if an axiom set is consistent and complete, then:

• Does the theory derived from the axiom set describe physical reality at all scales?

Considering that the theory exists for just a little more than a decade, I have set the bar even higher than what Siegel proposes.

There is a need however to clarify what Siegel meant by “reproduce all the successes of the prevailing theory”. I will take it that he means that it should make it possible to derive predictions that are consistent with the predictions of accepted theories. That said, predictions maybe consistent but derived from a different set of axioms which implies that those the observations are consistent with both the new and the accepted, the interpretations of the observations would differ.

He concludes:

“In the end, the Universe will always be the ultimate arbiter of what is real and what theories best describe our reality. But it’s up to us — the intelligent beings that conduct the enterprise of science — to rigorously uncover those truths. Unless we do it responsibly, we run the risk of fooling ourselves into believing what we want to be true. In science, integrity and intellectual honesty are the ideals to which we must aspire.”

This is the very definition of the scientific method. Ethan Siegel understands and explains it very well in this and other articles so it is not for lack of understanding that he forgoes the scientific method in his article titled This is Why Space Needs to be Continuous in which he argues against the idea of space being discrete.

The validity of a theory (or premise) can only be determined by the scientific method described above which implies descriptions, explanations, predictions that have or can be tested experimentally. Theoretical arguments are important but cant substitute for experiments.

The validity of a theory cannot be determined from within the framework of a second theory when their axiom sets are mutually exclusive. There is a simple reason for that. Using a premise in an argument based on a theory that axiomatically excludes it will inevitably make it internally inconsistent and consequently render any theoretical argument and its conclusion inconsistent with both the theory (or premise) and the theory on which the argument is based. Sure, we can determine if an idea is consistent with a theory, but being found to be inconsistent with an accepted theory does not invalidate it.

For example, space continuum is an implicit axiom of the relativity theories. Space continuum and space discreteness are mutually exclusive. It follows that the relativity theories cannot be used to describe physics in discrete space or make consistent predictions about discrete space.

Siegel argues that space discreteness is also inconsistent with the relativity principle but that is a forgone conclusion considering that they are axiomatically mutually exclusive.

Several strong theoretical arguments can be made against space discreteness. If space were discrete rather than continuous, then gravitational waves would not exist, time would not be physical and the universe would be strictly deterministic to give only a few examples. But Siegel’s entire argument against space discreteness is based on an application of the principle of relativity, a postulate (another word for axiom) of special relativity. The principle of relativity precludes the possibility of measuring absolute velocity, distance, momentum, etc.,

Here, Siegel's argument does not differentiate between quantised space (which results from quantization of continuous space) and discrete space, which assumes that space is made of discrete units. So even though the relativity principle argument certainly holds against quantised continuous space, it fails for discrete space. Distance in discrete space is the number of discrete units of space between two positions. That number, the quantum-geometrical distance, and unlike the metric distance, is absolute, hence observer independent the way the number of stars in a given region of space is.

From the impossibility to make an absolute measurement of discrete space, Siegel concludes that space cannot be discrete. His argument implies that space discreteness is the same as a fundamental unit of distance in continuous space (a smallest possible distance). While it is true that measurements of this smallest distance is observer dependent, the measurement of distance is discrete space is not. Two observers in constant motion relative to one another would not agree on the length of  metric distance, including measured in quantized units of continuous space, they would agree on the quantum-geometrical distance measured in number of discrete units of space between anything two positions. 

All the argument proves is that the principle of relativity requires space to be continuous but it says nothing about discrete space as we described. It follows that space discreteness implies that the principle of relativity would be wrong and consequently so would be special relativity. But how could special relativity be wrong considering that its predictions have been shown to be consistent with observations to a very high degree of accuracy?

One must keep in mind that special relativity is a measurement theory which accurately predicts the relative measurements of physical properties in continuous space. Special relativity (not necessarily nature) precludes absolute measurements. But special relativity cannot handle space discreteness or make any predictions about the physics of and in discrete space. Only a theory derived from a self-consistent axiom set which has space discreteness as one of its axioms can make predictions about physics in discrete space. It would not only be able to predict the absolute measurements of all physical properties (all observers would see make the same measurements), but also make accurate predictions of relative measurements as or more accurately than even special relativity.

It stands to reason that any such theory should possess explanatory powers comparable to those of the relativity theories and beyond that, should make unique testable predictions that can set it apart. These would be the necessary and sufficient criterions to validate the theory. But Siegel ignores the criterions of the scientific method and replace them with a single theoretically biased criterion: space discreteness must be consistent with the principle of relativity.

On its own, the idea of space discreteness has nothing to say about reality, it has zero descriptive, explanatory, or predictive power. Only a theory that is based on a self-consistent axiom set that contains an axiom of space discreteness can be tested using the criterions we have set forth as necessary and sufficient. Only by comparing such a theory’s descriptions, explanations and predictions to observations can it be validated or refuted. This brings me to quantum-geometry dynamics.

Quantum-geometry dynamics (QGD) is derived from a consistent axiom set containing an axiom of space discreteness. In terms of state of development there is no comparison between what a single individual can accomplish in a decade versus generations of researchers over a century, but already explains and describes what we already know, and makes a number of testable predictions. So, let us hope that some physicists will do what Segal suggests but failed to do in the case of space discreteness and rigorously subject QGD to the scientific method. The idea of space discreteness certainly deserves further exploration.

There are several articles on my blog that discuss different fields of application, but reading the opening chapters of  Quantum-Geometry Dynamics; an axiomatic approach to physics Quantum-Geometry Dynamics; an axiomatic approach to physics are a minimal prerequisite to understand them. Also, QGD has evolved in important ways since 2010 as I gained a better understanding of it. I kept the older articles for references but only the latest articles and book reflect the current state of QGD.

An Axiomatic Approach to Physics

Notice: QGD as greatly evolved since An Axiomatic Approach to Physics was written.  I will keep the article and link below for reference, but most recent developments see Quantum-Geometry Dynamics; an axiomatic approach to physics.

Abstract
Quantum-geometry dynamics; a theory derived from a minimal set of axioms can describe, explain and predict the behaviour of dynamic systems.
First, we will introduce a set of axioms and corollaries which will be used to fundamentally define space, mass, momentum, energy and forces. This will be followed by a discussion of quantum-geometrical space and its geometry. Then, we will show how gravity emerges naturally from the axiom set and propose a new equation for gravity that can be applied at different scales. At the same time, we will provide quantum-geometrical interpretations of the laws of motion and use them to describe dynamic systems. We will follow by providing quantum-geometrical grounds for key predictions of special relativity, general relativity and Newtonian mechanics. Although quantum-geometry dynamics will be shown to be in agreement with physical observations and with the predictions of special and general relativity, quantum-geometry dynamics allows for distinct falsifiable predictions that set it apart from them.

Acknowledgements

I would like to acknowledge the editorial help of my good friends Mark Batten-Carew (first and longtime supporter of QGD) and Pete Bonkemeyer (enthusiastic new supporter), of mathematicians Ben Dribus and Keli Etscorn for their comments, impressions and for going over the math, and special thanks to physicist and friend Xiaoxiao Wang for his excellent suggestions, to astrophysicist Martín López Corredoira for taking the time to read this latest paper and encouraging me to continue my research and publish my predictions, and to Meng-Chwan Tan, for taking time from his busy schedule to provide needed advice. Thank you all for your open mindedness to new ideas.

An Axiomatic Approach to Physics (new draft)

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