Real Observers in Physics and Engineering

• Real observers are defined as physically instantiated measurement entities with operational frames, finite memory, and backreaction properties, distinguishing them from idealized observers.
• They feature in diverse fields such as relativity, quantum foundations, and control theory, employing geometric, thermodynamic, and informational methodologies.
• This concept bridges physics and engineering by highlighting practical implications for state estimation, gravitational effects, and the integration of human observational data.

“Real observers” denotes a family of non-idealized observer concepts that recur across relativity, quantum foundations, gravity, control theory, and empirical human-subject research. In these literatures, the term marks a shift away from treating an observer as a mere coordinate label, abstract measurement placeholder, or unspecified external witness. Instead, the observer is modeled as a physically instantiated worldline with a frame, a finite information-processing system with memory and recognition structure, a gravitationally backreacting sector, a state estimator or monitoring construction, or a human annotator whose physiological and behavioral traces become data streams in their own right (Wang et al., 1 Jun 2026, Mashhoon, 2012, Maldacena, 2024, Stoica, 2023, Ashwin et al., 2023).

1. Geometric and operational observers in relativity

In relativistic theory, a real observer is first a kinematical object rather than a coordinate chart. One formulation defines an elementary observer as a timelike worldline together with an orthonormal tetrad,

$$O=\big(\tau: x^\mu(\tau), \lambda^\mu{}_{(\alpha)}(\tau)\big),$$

with

$$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$

so that the observer’s state contains not only position in spacetime but also a local frame for resolving tensorial or spinorial components (Mashhoon, 2012). The frame evolves by

$$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$

where the antisymmetric acceleration tensor $\Phi_{(\alpha)(\beta)}$ encodes translational acceleration and frame rotation. On this account, inertial observers are limiting cases; actual observers are generally accelerated (Mashhoon, 2012).

A complementary relativistic review defines an observer as a timelike worldline equipped with a comoving local frame and extends this to a family of observers, or congruence, whose tangent field defines a reference frame (Wang et al., 1 Jun 2026). The associated temporal and spatial projectors,

$$P_{\mu\nu}(n)=\epsilon n_\mu n_\nu,\qquad \Delta_{\mu\nu}(n)=g_{\mu\nu}-\epsilon n_\mu n_\nu,$$

supply the observer-dependent split of spacetime into time and local rest space. For unit timelike $Z^\mu$, $\Delta_{\mu\nu}(Z)=g_{\mu\nu}+Z_\mu Z_\nu$ is the standard spatial projector. The Frobenius condition

$Z_{[\mu}\nabla_\nu Z_{\rho]}=0$

determines whether a congruence is hypersurface-orthogonal and hence locally synchronizable (Wang et al., 1 Jun 2026).

This framework is used to correct a recurrent historical conflation of coordinates with reference frames. Early relativity often attached physical meaning directly to coordinate systems, but the underlying results remained valid because the real objects were geometric: worldlines, frames, projectors, and covariant tensor fields (Wang et al., 1 Jun 2026). A recurring implication is that observer dependence is not an accidental nuisance added on top of covariance; it is part of the physical content of relativistic description.

Mashhoon’s nonlocal formulation pushes this point further for field measurement. The hypothesis of locality is retained only as an approximation, valid in the ray limit $\lambda/\mathcal L\to 0$, while actual accelerated observers measure fields through a causal memory integral over their past worldline,

$$\mathcal{F}_{(\alpha)(\beta)}(\tau)=F'_{(\alpha)(\beta)}(\tau) +u(\tau-\tau_0)\int_{\tau_0}^{\tau} K_{(\alpha)(\beta)}{}^{(\gamma)(\delta)}(\tau,\tau')\,F'_{(\gamma)(\delta)}(\tau')\,d\tau' .$$

In this sense, real observers are intrinsically nonlocal for fields: their measurements depend on past acceleration history, not only on instantaneous state (Mashhoon, 2012).

2. Congruence-dependent thermodynamics and the general-relativistic “problem of observers”

A more radical observer dependence appears in relativistic fluid dynamics. In this setting, the same spacetime metric and the same energy-momentum tensor can support inequivalent physical descriptions because hydrodynamical variables are defined relative to a chosen timelike congruence (Herrera, 2018). For comoving observers one may have

$$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$0

so the source is dust with no heat flux or pressure. Relative to a tilted congruence $$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$1, the same tensor must be decomposed as

$$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$2

Heat flux, anisotropy, vorticity, acceleration, and even the electric/magnetic splitting of the Weyl tensor then become congruence-dependent (Herrera, 2018).

This is the basis of the general-relativistic “problem of observers.” In the Lemaître–Tolman–Bondi and Szekeres models, comoving observers see geodesic, non-dissipative dust with vanishing magnetic Weyl tensor, whereas tilted observers see dissipative anisotropic fluids with entropy production; in the Szekeres case the tilted congruence also has vorticity (Herrera, 2018). In the shear-free axially symmetric model, the contrast is sharper: comoving observers see a geodesic, shear-free, non-dissipative, vorticity-free fluid with vanishing magnetic Weyl tensor, while tilted observers generally detect nonzero 4-acceleration, shear, vorticity, heat flux, magnetic Weyl components, and super-Poynting flux interpreted partly as gravitational radiation (Herrera, 2018).

The paper’s distinctive move is to interpret this discrepancy through information theory. Passing from the comoving description, in which the fluid’s 3-velocity vanishes, to the tilted description is treated as erasing the information “the fluid is locally at rest.” By analogy with Bennett’s treatment of Maxwell’s demon and Landauer’s principle,

$$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$3

the loss of that information carries an entropic cost (Herrera, 2018). The claim is not that entropy changes under a coordinate transformation, but that entropy production is tied to the informational content associated with the chosen congruence.

A plausible implication is that relativistic thermodynamics is not fully congruence-free. More precisely, the scalar statement that a matter configuration is dissipative is not intrinsic unless the observer field is specified. This does not make the theory arbitrary; it makes the observer part of the system’s physical interpretation (Herrera, 2018).

3. Embedded, structural, and dispensable observers in quantum and informational debates

In quantum-foundational and information-theoretic work, “real observer” often means an observer with finite physical implementation, memory, recognition machinery, and restricted access to the world. One proposal replaces the “Galilean” observer—an informationally impoverished placeholder—with a minimal observer that encodes sufficient prior information to identify systems, recognize selector settings, and record outcomes in finite memory (Fields, 2011). In that framework, observers are finite physical devices implementing collections of POVMs and a control structure; the observer is described as a classical virtual machine rather than as a bare quantum system. Quantum features such as restricted observables, contextuality, Bell-type nonseparability, Born-rule probabilities, and complex amplitudes are then argued to arise from finite observer architecture plus the physicality of information (Fields, 2011).

A related black-box approach builds the observer into the system by insisting that observers are finite, embodied systems coupled to the rest of the world through a finite classical information channel (Fields, 2014). Its decisive theorem states: if the observable world contains a black box, it is a black box. From that premise the paper derives no-boundary, no-communication, no-external-reference, and observer-box equivalence corollaries, and argues that identifying macroscopic objects or other observers always requires internal reference frames (Fields, 2014). One consequence is that superposition is presented not only as a quantum postulate but as the appropriate representation of classical observational ambiguity when finite observations underdetermine what system produced the outcomes.

A different argument asks whether observers are reducible to structure. It concludes that they are not: if every observer-like structure in every parametrization counted as an observer, then memories of the external world would be no better than random guess, because structurally identical observer-like systems in different parametrizations would identify different observables with physical properties (Stoica, 2023). On that basis, the paper infers that there must be more to observers than their structure alone and that the correspondence between observables and physical properties is unique and becomes manifest through real observers (Stoica, 2023).

Not all foundational programs assign observers this weight. A process-theoretic reformulation of quantum mechanics explicitly seeks a realist account without fundamental observers, treating observers as emergent macroscopic physical systems generated by the same lower-level ontology as everything else (Sulis, 2013). In that account, measurement is a process interaction between emergent systems, not an observer-centered primitive.

Still other programs expand the observer concept in speculative directions. The Observer Class Hypothesis treats observers as gauge-invariant informational structures that dominate the space of information because they selectively absorb other information, summarized by

$$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$4

(Garrett, 2011). Another speculative proposal interprets repeated acts of observation as embedded in a “deep technological aspect” of nature and extends observerhood to “developed observers” and purposive agencies (Josephson, 2015). These proposals are not mutually compatible, but together they show that “real observer” functions as a fault line between reduction to formal structure, embodiment in information-processing architecture, and attempts either to elevate or to eliminate the observer from fundamental theory.

4. Gravitational observers in Euclidean de Sitter theory

In recent Euclidean de Sitter gravity, “real observer” acquires a highly specialized meaning. The starting problem is that the sphere partition function carries the universal one-loop phase

$$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$5

which obstructs a naive state-counting interpretation (Maldacena, 2024). A proposed resolution includes an observer explicitly in the path integral, modeled as a massive particle tracing a worldline together with an internal clock. The observer-inclusive quantity is

$$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$6

with $$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$7 and $$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$8, so that the phase largely cancels: $$g_{\mu\nu}\lambda^\mu{}_{(\alpha)}\lambda^\mu{}_{(\beta)}=\eta_{(\alpha)(\beta)},$$9 After rotating the proper-length contour to impose the Hamiltonian constraint, the proposed state-counting quantity is

$$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$0

which is argued to be real and positive (Maldacena, 2024).

Subsequent work sharply narrows what kind of observer can play this role. A worldline or information-bearing clock is necessary but insufficient. A real observer, in this context, is a gravitational observer: a localized subsystem whose action couples strongly enough to metric fluctuations to alter the unstable conformal-mode structure of the Euclidean saddle (Ali, 18 Mar 2026). The central distinction is between gravitational observers and topological spectators. If a sector’s infrared effective action is metric independent at the de Sitter saddle, then the path integral factorizes,

$$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$1

and the spectator sector cannot remove the universal phase (Ali, 18 Mar 2026). Confining $$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$2 in its gapped regime and topological orders are presented as examples of information-bearing but spectatorial sectors (Ali, 18 Mar 2026).

A further refinement asks which such observer sectors are semiclassically admissible before any phase-cancellation argument is attempted. After gauge fixing and projection, the observer’s quadratic effect is governed by a Schur complement,

$$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$3

or, at the level of forms,

$$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$4

The admissibility criterion requires bounded metric-coupled infrared susceptibility. On a stable channel with coercive form $$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$5, the Gaussian saddle remains controlled whenever

$$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$6

Gapped observer sectors can satisfy this; metric-coupled soft modes produce corrections growing as $$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$7 and become infrared-singular (Espíndola et al., 28 May 2026).

In this literature, then, “real observer” means gravitationally real rather than merely informationally real. The observer must be localized, clock-bearing, and sufficiently backreacting to participate in the same unstable sector as the geometry itself (Ali, 18 Mar 2026, Espíndola et al., 28 May 2026).

5. Observer constructions in control, estimation, and formal verification

In systems and control theory, “observer” is used in a different sense: not as an epistemic subject, but as a dynamical construction for estimation, realization, or monitoring. A real-time moving-horizon observer study isolates the measurement inclusion rate as an online design variable. Because the optimizer is truncated, including every new measurement immediately is not automatically optimal; the observer must trade off responsiveness to fresh data against time spent reducing the current cost (Alamir, 2013). The paper introduces a self-adaptation law for the iteration count $$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$8, hence for the update period $$\frac{dx^\mu}{d\tau}=\lambda^\mu{}_{(0)},\qquad \frac{d\lambda^\mu{}_{(\alpha)}}{d\tau}=\Phi_{(\alpha)}{}^{(\beta)}\lambda^\mu{}_{(\beta)},$$9, using a decomposition of successive costs into an optimizer-efficiency term and a disturbance/horizon-shift term (Alamir, 2013).

A geometric estimation paper develops continuous observers for invariant kinematic systems on real finite-dimensional matrix Lie groups. The plant evolves as

$\Phi_{(\alpha)(\beta)}$0

with biased velocity measurement $\Phi_{(\alpha)(\beta)}$1, and the observer estimates both the group state and an unknown constant bias from landmark/vector measurements (Chang, 2019). Its main device is Euclidean embedding: one estimates a matrix-valued output in ambient Euclidean space and reconstructs the Lie-group state algebraically, yielding globally exponentially convergent continuous observers for simultaneous state and bias estimation (Chang, 2019).

A separate realization theory defines observer-based realization directly on selected measured functions $\Phi_{(\alpha)(\beta)}$2 rather than on the hidden state $\Phi_{(\alpha)(\beta)}$3 (Cheng et al., 2024). For the linear system $\Phi_{(\alpha)(\beta)}$4, $\Phi_{(\alpha)(\beta)}$5, the associated observer dynamics close exactly iff the row space of $\Phi_{(\alpha)(\beta)}$6 is $\Phi_{(\alpha)(\beta)}$7-invariant, equivalently iff there exists $\Phi_{(\alpha)(\beta)}$8 such that

$\Phi_{(\alpha)(\beta)}$9

When this fails, the paper constructs an extended OR-system by enlarging the observer set to the smallest $$P_{\mu\nu}(n)=\epsilon n_\mu n_\nu,\qquad \Delta_{\mu\nu}(n)=g_{\mu\nu}-\epsilon n_\mu n_\nu,$$0-invariant or $$P_{\mu\nu}(n)=\epsilon n_\mu n_\nu,\qquad \Delta_{\mu\nu}(n)=g_{\mu\nu}-\epsilon n_\mu n_\nu,$$1-invariant closure, thereby preserving the original observers as part of the state of a new realization (Cheng et al., 2024).

Formal verification uses “observer” yet differently again. In AGREE/Lustre, observers are auxiliary pieces of logic used to implement real-time specification patterns by monitoring trigger events, elapsed time, and pass/fail conditions (Backes et al., 2016). The paper shows that observers are effective for proving global timed properties as invariants, but exact trace-defining constraints are subtle when overlapping trigger obligations occur. The resulting distinction between observer-as-property-monitor and observer-as-exact-language-constraint is one of the paper’s main technical points (Backes et al., 2016).

Across these engineering usages, the common feature is not perception but operational closure: an observer is a device, realization, or monitor that makes hidden dynamics tractable from available signals.

6. Human observers as physiological sensors and annotation agents

Some recent empirical work returns the term to literal human observers. A pupillometry study asks whether smile authenticity can be inferred not from the smiler’s face, but from the observer’s involuntary physiological response (Chen et al., 2021). Twenty-five volunteers were recruited and 24 retained after signal-quality exclusion; pupil diameter was recorded at 60 Hz with an Eye Tribe tracker while observers viewed real and posed smiles from the UvA-NEMO database under paired-video, paired-image, single-video, and single-image conditions (Chen et al., 2021). After cubic spline interpolation, Hampel filtering, baseline normalization using the median of 100 pre-stimulus samples, moving-average smoothing, and resampling to 5 s, the strongest separation appeared in the paired-video condition: the normalized pupil traces diverged from about 1.5 s onward, the KS test gave $$P_{\mu\nu}(n)=\epsilon n_\mu n_\nu,\qquad \Delta_{\mu\nu}(n)=g_{\mu\nu}-\epsilon n_\mu n_\nu,$$2, and ANOVA reported significance only for paired videos with $$P_{\mu\nu}(n)=\epsilon n_\mu n_\nu,\qquad \Delta_{\mu\nu}(n)=g_{\mu\nu}-\epsilon n_\mu n_\nu,$$3 (Chen et al., 2021). In this setting, human observers are treated as biological sensors of emotional authenticity.

A complementary educational-systems paper treats human observers as trained real-time annotators whose judgments remain indispensable even in adaptive intelligent systems (Ashwin et al., 2023). Its open-source Data Logging and Organizational Tool (DLOT) supports customizable labels, customizable time intervals, radio-button and checklist selection modes, timestamped logging, Android/iOS operation, and export in xlsx or docx (Ashwin et al., 2023). The tool was validated in two studies: one observing 30 students in each class for affective-state annotation, and one observing 38 participants individually for multimodal dataset construction (Ashwin et al., 2023). The usability result was an average SUS score of 93, and the paper emphasizes that DLOT does not replace human observers; it reduces timing and logging burden while preserving the need for training, coding guidelines, and inter-rater reliability (Ashwin et al., 2023).

These empirical uses show a different but convergent sense of realism. The observer is neither an abstract epistemic idealization nor a purely formal monitoring automaton, but an embodied human whose physiology, attention, coding decisions, and practical tooling become part of the measurement process itself.

Across these literatures, “real observer” is not a single doctrine but a family of anti-idealizing moves. In relativity it means a timelike worldline or congruence with a frame and finite operational structure; in general-relativistic thermodynamics it means a congruence that changes the physical decomposition of matter; in quantum and philosophical work it marks the contrast between embedded finite observers, merely structural observer-like systems, and programs that deny fundamental observerhood; in Euclidean de Sitter theory it means an observer sector that is gravitationally real; and in engineering and empirical research it denotes estimators, monitors, or human agents whose concrete implementation matters to the dynamics under study. The unifying theme is that observation is treated as a physically structured relation, not as a view from nowhere.