Bayesianism and Interaction-Based Measurement: A Unified Picture from the Perspective of Natural Quantum Theory

1. Introduction: From the “Measurement Problem” to “Evidence Updating”

In traditional quantum mechanics, the “measurement problem” has long occupied a central place in debates between physics and philosophy of science:

• Formally, we possess a complete Schrödinger evolution together with projection operators;

• Conceptually, however, it remains unclear what measurement actually is: an externally imposed rule, the intervention of conscious observation, or some mysterious “collapse”?

Meanwhile, in philosophy of science, Bayesianism has gradually become the dominant framework for understanding scientific reasoning and theory choice:

• Theories enter comparison with prior probabilities;

• Observational data serve as evidence that updates credences via Bayes’ rule;

• Scientific practice is understood as a continuous cycle of “prior → evidence → posterior.”

Natural Quantum Theory (NQT) provides a crucial bridge:

• Ontologically, measurement is simply an interaction process between system and apparatus—a part of dynamics, not an external postulate;

• Epistemologically, the observational outcome of that same interaction constitutes precisely the “evidence” invoked in Bayesianism, used to update our confidence in theories and parameters.

The core claim of this paper is:

From the NQT perspective, the Bayesian schema of “observation–update” and the physical notion of “interaction-based measurement” are fundamentally one and the same:
— Physically, the interaction reconfigures the system’s global modes;
— Epistemically, that same interaction delivers data that drives Bayesian updating of our beliefs about theories and physical quantities.

Thus, “confidence in theory–experiment agreement” and “confidence in a measured value” are structurally equivalent within a unified probabilistic framework—they differ only in their target domains: the former operates over theory space, the latter over parameter/observable space.

We now unpack this unified picture step by step.

2. Measurement in Natural Quantum Theory: Interaction and Global Mode Reconfiguration

2.1 The Physical Nature of Measurement: Local Interaction + Global Mode Change

In the NQT framework, measurement is first and foremost a physical process:

• The system and measuring device couple via a local interaction;

• This coupling, over a finite time, alters the joint electromagnetic and matter-field structure of the system–apparatus composite;

• Possible outcomes include:

• The establishment of new global modes (e.g., entangled states, resonant modes, level splittings);

• The triggering of localized events in specific channels (detector clicks, photon absorption, electron transitions).

The so-called “reading” is merely the macroscopically stable endpoint of this interaction process:

• Whether a detector pixel fires;

• Where a pointer settles on a scale;

• How much spectral intensity appears in a frequency band.

NQT emphasizes:

• Measurement is not an external interrogation of a “static wave function,” but an integral part of the system’s dynamics;

• “Wave function collapse” is merely a shorthand for encoding the consequences of such interactions within a global spectral description—not an independent physical mechanism.

2.2 The Wave Function as Spectral Representation and Knowledge Encoding

In NQT, the wave function plays a dual role:

• Physical role:
  As the spectral representation of the system under the Schrödinger equation, it encodes projections onto a set of global eigenmodes—i.e., it expresses the electromagnetic/matter field’s global mode structure under given constraints and topology.

• Epistemic role:
  It encodes the observer’s incomplete knowledge about the system’s state; different experimental inputs correspond to successive refinements of this encoding.

Thus, when a measurement interaction occurs:

• Physically, it modifies the actual field distribution and mode structure;

• Cognitively, it supplies a new data point requiring us to update our representation of the system’s state, parameters, or underlying theory.

This aligns closely with the Bayesian “observation–update” cycle:

• Bayesian view: Observation D updates prior P(T) to posterior P(T∣D);

• NQT view: The interaction produces observation D, prompting a corresponding update of our descriptive model.

3. Bayesianism: A Unified Probabilistic Framework from Theories to Parameters

3.1 Bayesian Updating at the Theory Level

In Bayesian philosophy of science, the credibility of a theory T is quantified by its posterior probability:

P(T∣D)=P(D)P(D∣T)P(T)

where:

• P(T): prior credence—the degree of belief in T before new data;

• P(D∣T): likelihood—the probability of observing data D if T is true;

• P(D): normalization factor ensuring total probability sums to 1.

A new measurement record D—the macroscopic trace of an interaction—is thus used to reweight the plausibility of competing theories. Here, “observation is evidence,” and “evidence triggers updating.”

3.2 Bayesian Updating at the Parameter/Observable Level

The same framework applies to physical quantities or parameters. For a parameter θ (e.g., particle mass, dipole moment, field strength), we have:

P(θ∣D)=P(D)P(D∣θ)P(θ)

• P(θ): prior knowledge of the “true value” (from past experiments or theoretical constraints);

• P(D∣θ): probability of obtaining data D assuming the true value is θ;

• P(θ∣D): the rational posterior distribution after the experiment.

Common experimental reports—“confidence intervals” or “error bars”—are, in Bayesian terms, summaries of P(θ∣D). For example:

“ θ = θ₀ ± δ (68% C.L.)”
means approximately 68% of the posterior probability mass lies within that interval.

4. The Dual Role of Measurement: One Event, Two Languages

With this groundwork, we can now state clearly:

The same measurement event is, physically, an interaction—and, epistemically, a trigger for Bayesian updating.

More concretely:

• Physical perspective (NQT):
  An interaction occurs → local and global field modes are reconfigured → a macroscopic reading stabilizes.

• Epistemic perspective (Bayesianism):
  The recorded reading is treated as data D → used to update either:
  – P(T∣D): confidence in a theory T, or
  – P(θ∣D): confidence in a parameter θ.

In this sense, “interaction-based measurement” in NQT and “observation–update” in Bayesianism are two projections of the same underlying reality:

• One describes the world’s dynamical behavior;

• The other describes how we rationally adjust our beliefs in light of evidence.

This also explains why, in NQT, the wave function is both a physical spectral expression and a carrier of incomplete knowledge:

• Physically: it encodes the system’s global field-mode structure;

• Epistemically: it functions as a parameterized belief state, updated as new interaction-generated data arrive.

5. Confidence in Theory–Experiment Agreement vs. Confidence in Measured Values: Same Probabilistic Grammar

NQT highlights a deeper equivalence:

“Confidence in theory–experiment agreement” and “confidence in a measured value”
are instances of the same probabilistic syntax applied to different domains.

5.1 Confidence in Theory–Experiment Agreement

When we say “a theory agrees well with experiment,” precision requires statements like:

• High likelihood P(D∣T): under theory T, data D is probable; or

• High posterior P(T∣D): among candidate theories {Ti}, T receives the greatest weight given D.

Thus, “agreement confidence” is essentially a probability distribution (or relative weighting) over theory space.

5.2 Confidence in Measured Values

When we report “x=x0±δ at 95% confidence,” we are:

• Providing a posterior distribution P(x∣D) over parameter space;

• Extracting an interval containing 95% of its probability mass.

Structurally, this is identical to Bayesian theory updating—only the object has shifted from “theory” to “parameter/physical quantity.”

5.3 Unified Expression

In a unified probabilistic language:

• Object space: may be a set of theories, a parameter space, or even initial-condition space;

• Probability distribution: represents rational credence over these objects, conditioned on all known data D;

• New data: arise from new interaction-based measurements, further refining the distribution.

Hence:

Both “how well a theory matches experiment” and “how credible a numerical interval is”
are mathematically posterior probability statements over their respective object spaces.

NQT’s interpretive contribution is to anchor this unified probabilistic grammar in real field interactions and spectral structures:

• Probability and credence are not manifestations of ontological randomness;

• They are statistical encodings of real structures, constrained by limited information and the inherent limitations of spectral representation.

6. Returning to the Measurement Problem: The Joint Advantage of NQT + Bayesianism

Many traditional confusions in quantum philosophy stem from conflating three distinct layers:

1. Ontological dynamics: how fields evolve via local PDEs and boundary conditions;

2. Mathematical limits of spectral representation: uncertainty relations, non-commuting operators, global wave functions;

3. Belief updating under limited data: theory selection, parameter estimation, error analysis.

The combination of NQT and Bayesianism draws clearer boundaries among these layers:

• Layer 1 is handled by NQT’s ontology of continuous fields, topological structures, and local interactions;

• Layer 2 is explained by quantum mechanics as the spectral representation of classical fields—its constraints are mathematical, not ontological;

• Layer 3 is governed by Bayesian evidence-updating, telling us how to revise our representations of Layers 1 and 2 in light of data.

In this picture:

• “Measurement” is not mysterious:
  – Physically: an ordinary interaction that may generate or reconfigure global modes;
  – Epistemically: a data point that updates prior distributions to posteriors.

• “Probability” is not fundamental randomness:
  – It is a rational, statistical encoding of real structures under informational and spectral constraints;
  – It informs judgments about both which theory is more credible and which parameter value is more plausible.

This unification allows traditional topics—uncertainty principle, wave function collapse, theory–experiment fit—to be reconceived transparently:

• Uncertainty: a mathematical limitation of spectral methods, not an ontological prohibition;

• Collapse: the combined effect of physical interaction and information update, not a standalone mechanism;

• Fit: a quantitative expression of posterior probability, not a vague “seems to match.”

7. Conclusion: One Event, Two Perspectives

Starting from NQT’s notion of “interaction-based measurement,” this paper has precisely aligned it with Bayesianism in philosophy of science, yielding several key insights:

1. Measurement = Interaction + Evidence Update

• Physically: a local system–apparatus interaction that may reconfigure global modes;

• Epistemically: the same process yields data that serve as Bayesian evidence for updating credences.

2. Equivalence of Theory and Parameter Confidence

• Both are posterior distributions within a unified probabilistic framework;

• “Good theory–experiment agreement” and “credible numerical intervals” share the same mathematical grammar.

3. Demystification of Probability and the Wave Function

• Probability reflects rational encoding under limited information and spectral constraints—not ontological chance;

• The wave function unifies physical spectral expression and epistemic belief state naturally within the NQT + Bayesian picture.

4. Dimensionality Reduction of the Measurement Problem

• Traditional philosophical puzzles arise from blurring dynamics, ontology, and belief updating;

• The NQT–Bayesian synthesis cleanly separates—and systematically connects—these layers, eliminating the need for mysterious collapse or fundamental randomness.

In summary, quantum measurement becomes intelligible once we recognize it as a natural physical interaction whose outcomes rationally inform our evolving understanding of the world—no metaphysics required.