The preprint version is available on SSRN: The Observer and Spacetime: On the Existential Precondition of Physical Theory (August 18, 2026). http://dx.doi.org/10.2139/ssrn.7316678

[The Observer Series P1]

The Observer and Spacetime:
On the Existential Precondition of Physical Theory

Juliet Zhong

Independent Researcher | London, United Kingdom | August 2026

ORCID: 0009-0006-5099-3671

Abstract

This paper argues that the observer is not a peripheral element in physics but the existential precondition without which physical theory loses its empirical content. Using a series of thought experiments grounded in special relativity, the paper demonstrates that the construction of a reference frame—the foundational operation upon which all of relativistic physics depends—requires an entity capable of measurement, and that measurement, in every instance, presupposes an observing system. When this precondition is removed, the formal apparatus of special relativity—coordinate systems, the Lorentz transformation, the Minkowski metric—retains its mathematical structure but forfeits all physical referents. The paper proceeds in four stages. First, it establishes that a reference frame cannot be constructed without a measuring subject. Second, it shows that the Lorentz transformation, which connects two reference frames, becomes an operation on two empty sets when both observers are stripped of measurement capacity. Third, it demonstrates that the Minkowski metric, whose invariance is conventionally taken as proof of observer-independent reality, in fact presupposes the observer it claims to transcend. Fourth, it draws the structural parallel between this result and the measurement problem in quantum mechanics, showing that both theories independently point to the same conclusion: the empirical content of physics is not discovered by the observer but constituted by the act of observation. The paper concludes that physics has operated with an unexamined existential presupposition—the existence of a measuring observer—and that until this presupposition is formally acknowledged, no unified foundation for physics is possible.

Keywords: observer, spacetime, special relativity, reference frame, Lorentz transformation, Minkowski metric, measurement problem, philosophy of physics, existential precondition, consciousness

1. The Unexamined Presupposition

Every physical theory begins with measurement. Newtonian mechanics begins with the measurement of position, velocity, and force. Electrodynamics begins with the measurement of fields and charges. Thermodynamics begins with the measurement of temperature, pressure, and volume. Quantum mechanics begins with the measurement of observables—and it is in quantum mechanics alone that the act of measurement has become a theoretical problem rather than a silent assumption. But even in quantum mechanics, the problem is framed as an anomaly: the measurement problem is treated as something peculiar to the quantum domain, a puzzle to be solved within the formalism, not a symptom of a deeper structural issue that pervades all of physics.

This paper argues that the measurement problem is not an anomaly confined to quantum mechanics. It is the surface expression of a presupposition that runs through every physical theory without exception: the presupposition that there exists at least one entity capable of performing measurements. This entity—the observer—is never derived from the equations, never predicted by the formalism, never accounted for within the theoretical structure. It is simply assumed. The equations of physics describe what can be measured, but they never ask who or what is doing the measuring. The entire edifice of physical science rests on an existential precondition that it has never examined.

The consequences of this oversight are not merely philosophical. They are structural. If the observer is the precondition for physical theory to have empirical content, then the observer is not one element among many in the physical world—not a biological organism that happens to interact with physical systems, not an instrument that happens to register signals, not a computational process that happens to correlate inputs with outputs. The observer is the condition without which the distinction between "physical" and "mathematical" cannot be drawn. Without the observer, the equations of physics are indistinguishable from pure mathematics: they are self-consistent formal structures with no empirical referent, no connection to phenomena, no claim on reality.

This is not a new insight in philosophy. Kant argued that space and time are not features of things-in-themselves but forms of intuition—structures imposed by the knowing subject upon experience [Kant, 1781]. Berkeley argued that to be is to be perceived [Berkeley, 1710]. Husserl argued that consciousness is always consciousness of something, that the intentional structure of experience is irreducible [Husserl, 1913]. But these arguments have been conducted almost entirely within the tradition of philosophy, in a language that physicists have felt entitled to ignore. What has not been done—and what this paper undertakes to do—is to demonstrate from within the formal structure of physics itself, using the logic and language of physical theory, that the observer is the existential precondition of that theory's empirical content.

The demonstration proceeds through special relativity, chosen not because it is the most fundamental theory in physics, but because it is the theory that has done the most to shape the modern understanding of spacetime, and because it is conventionally regarded as providing the strongest evidence for an observer-independent reality. If the argument holds within special relativity—if it can be shown that even this theory, with its Lorentz invariance and its claim to geometric objectivity, cannot secure its physical content without presupposing a measuring subject—then the argument holds a fortiori for every other physical theory.

2. The Reference Frame and Its Hidden Dependency

What a reference frame requires

A reference frame, in the precise sense used in special relativity [Einstein, 1916; Minkowski, 1908], is not merely a coordinate system. It is a structured apparatus for the assignment of spatiotemporal labels to physical events. To construct a reference frame, three conditions must be satisfied simultaneously.

First, an origin must be designated. Some particular event—some here-and-now—must be singled out as the zero point from which all spatial and temporal coordinates are measured. This designation is not a mathematical operation. It is a physical act of selection [Einstein, 1922]: one particular location at one particular moment is chosen, and all other events are defined by their relation to it. The question of who or what performs this selection is usually passed over in silence, but it cannot be evaded. A coordinate origin does not designate itself. Something must do the designating.

Second, a set of measurement standards must be established. Spatial distances require a unit of length—a ruler, a wavelength, a baseline. Temporal intervals require a unit of time—a clock, an oscillation, a decay rate. These standards must be physically instantiated: they must exist as material objects or reproducible physical processes capable of generating definite, repeatable numerical outputs [Eddington, 1923]. A number is not a measurement. A measurement is the production of a number through a physical interaction [Bridgman, 1938] between a standard and a system. Without the standard, no number is produced [Reichenbach, 1928/1958].

Third, and most critically, there must be an agent that performs the measurement—that applies the standard to the system, registers the result, and assigns the coordinate value. In practice, this agent is either a human observer or an instrument designed, calibrated, and interpreted by a human observer. In either case, the chain of measurement terminates in an entity that can distinguish between different outcomes, record them, and relate them to one another [von Neumann, 1932].

A note on terminology is essential here. The word "observer," as used throughout this paper, does not refer exclusively to a human being or to a conscious organism. An observer is any physical system capable of entering into an information-discriminating relationship with another physical system—capable, that is, of registering distinct physical states, retaining a record of them, and thereby establishing a measurement relation. A photomultiplier tube is an observer. A CCD detector is an observer. A seismograph is an observer. What makes a system an observer is not consciousness but the capacity to differentiate and record physical states. The double-slit experiment in quantum mechanics illustrates this precisely: the interference pattern disappears not when a human watches the screen, but when any physical apparatus records which-path information [Bohr, 1928; Zurek, 2003]. The apparatus is the observer. This functional definition is not a weakening of the paper's thesis—it is a strengthening of it. If even a mindless detector counts as an observer, then the claim that physical spacetime requires an observer becomes harder, not easier, to dismiss. The question is not whether a human must be present, but whether any observing system—any system capable of physically instantiating a measurement relation—must be present. The argument of this paper is that it must. Without it, the origin is undesignated, the standards are unused, and the coordinate system is a mathematical abstraction with no physical instantiation.

Physics has always acknowledged the first two conditions in its pedagogy. Textbooks on special relativity routinely discuss the choice of coordinate origin and the synchronization of clocks. But the third condition—the existence of a measuring agent—is treated as so obvious as to require no discussion. It is precisely this obviousness that conceals the depth of the dependency. The measuring agent is not an incidental feature of the measurement process that could, in principle, be replaced by an automated procedure. It is the locus at which the formal structure of the theory makes contact with empirical reality.

The blind observer thought experiment

To see why this is so, consider the following thought experiment. A blind person—deprived of all visual perception—sits alone inside a perfectly soundproofed aircraft flying in uniform rectilinear motion. There are no instruments, no co-passengers, no announcements, no devices of any kind. The cabin is maintained at a constant temperature. The aircraft neither accelerates nor decelerates.

What can this person know about their spatiotemporal situation?

He knows he is seated. He feels the pressure of the seat against his body, the pull of gravity, the rhythm of his own breathing. He possesses an internal sense of duration—a felt passage of time—but no means of calibrating this internal sense against any external standard. He cannot determine whether he has been seated for one hour or five hours. His internal duration is real as experience but undefined as a physical quantity, because physical quantities require units, and units require standards, and standards require access to a reproducible physical process that this person does not have.

He does not know whether he is moving. This is not merely an epistemic limitation—a case of a person who lacks the information to determine their motion. It is a consequence of the Galilean principle of relativity, which Einstein elevated to a postulate of special relativity [Einstein, 1905]: uniform rectilinear motion is physically indistinguishable from rest. In the absence of any external reference, there is no experiment the person can perform—even in principle—that would distinguish between being stationary on the ground and flying at nine hundred kilometres per hour. The velocity of the aircraft is not a quantity that exists-but-is-unknown to the observer. It is a quantity that has no physical meaning within a single inertial frame considered in isolation.

He does not know where he is. Position is defined relative to an origin, and an origin requires designation, and designation requires an act of selection by a subject with access to external references. In the absence of all such access, position is not merely unknown—it is undefined.

The standard response from physics would be: the aircraft is still in motion, the pilot's instruments still register airspeed and altitude, the ground-based radar still tracks the flight path, and the global positioning system still assigns coordinates. The person's ignorance does not affect the physical facts.

But this response smuggles in precisely what the thought experiment was designed to remove. The pilot, the instruments, the radar, the GPS satellites—these are all additional observers and measuring devices. They are other reference frames populated by other measuring agents. The standard response does not refute the claim that a reference frame requires a measuring agent. It confirms it, by instinctively reaching for other measuring agents the moment the original one is removed.

The second removal

Now extend the thought experiment by asking a question that exposes the hidden structure of the standard objection. The standard response to the blind observer thought experiment—that the aircraft is "objectively" in motion regardless of the passenger's inability to perceive it—relies entirely on invoking other observers: the pilot reading instruments, the radar operator tracking the flight path, the GPS satellites assigning coordinates. But this response does not refute the argument—it confirms it, because it demonstrates that the "objectivity" of the aircraft's motion is itself the product of another observer's measurements. The aircraft is "objectively at 35,000 feet travelling at 900 kilometres per hour" only because a ground-based observer with functioning instruments has measured its altitude and velocity. Remove this second observer, and the objectivity vanishes. Suppose, then, that the ground-based observer is also blind, also alone, also sealed in a room without instruments or sensory access to the outside world. For this second person, sitting motionless in a chair, the situation is identical to that of the first: no spatial reference, no calibrated time, no means of determining position or motion. The two blind persons—one in the aircraft, one on the ground—are each enclosed in a private sensorium with no access to any external coordinate.

The logical structure is now fully exposed, and it proceeds in three steps. First: the blind person in the aircraft cannot determine their position, velocity, or the current time—not because the information is hidden, but because position, velocity, and time are quantities that require measurement for their physical instantiation, and no measurement is being performed. Second: the supposed objectivity of the aircraft's spatiotemporal location depends entirely on a second observer—someone on the ground who can see the aircraft, read a clock, and assign coordinates. The "objective" spacetime of the aircraft is not independent of observation; it is the product of a different observer's observation. Third: if the ground-based observer is also stripped of measurement capacity—if he too is blind, alone, and without instruments—then neither observer can assign coordinates to any event, neither can determine the other's existence, position, or state of motion, and the mutual spatiotemporal relationship between them (the very thing that special relativity describes) has no physical instantiation whatsoever.

There are now two inertial frames in the mathematical description—one co-moving with the aircraft, one co-moving with the ground—but neither has been physically instantiated, because neither possesses a measuring agent capable of assigning coordinates. The "objectivity" that the standard response appeals to has been revealed as a regress: the first observer's spacetime is "objective" only relative to a second observer's measurements, and the second observer's spacetime is "objective" only relative to a third observer's measurements, and so on. When the regress is halted—when no observer anywhere in the chain possesses measurement capacity—the entire structure of "objective spacetime" collapses, not because spacetime has been destroyed, but because the conditions required for its physical constitution were never met.

What remains? The mathematical description remains. One can still write down two sets of coordinates and connect them with a Lorentz transformation. But this mathematical description describes nothing. It predicts nothing. It refers to nothing. It is a formal structure without physical content—a set of equations whose variables have no values, because no measurement has been performed, because no measurement can be performed, because no entity capable of measurement exists.

Physics typically insists at this point that the physical facts are independent of whether anyone measures them. The aircraft is still moving relative to the ground. The time dilation is still occurring. The length contraction is still in effect. These are objective features of the physical world, not products of measurement.

But this insistence is precisely the unexamined presupposition that this paper identifies. The claim that physical facts exist independently of measurement is not a conclusion derived from physical theory. It is an axiom imported into physical theory from a pre-theoretical metaphysical commitment—the commitment to realism, to the existence of a mind-independent external world. This commitment may be defensible on philosophical grounds, but it is not a theorem of physics. It cannot be derived from the equations. And it cannot be verified empirically, because every empirical verification is itself a measurement, and every measurement presupposes a measurer.

The circularity is not a minor technical point. It is the structural feature of physics that this paper brings to the surface: physics claims that reality exists independently of the observer, but it cannot provide evidence for this claim without employing an observer to gather the evidence. The observer is the condition of possibility for any evidence whatsoever, including evidence that purports to establish the observer's dispensability.

3. The Lorentz Transformation Without Observers

What the Lorentz transformation connects

The Lorentz transformation is the mathematical rule that relates the spacetime coordinates assigned to a given event by two different inertial observers moving at constant velocity relative to one another. In the standard formulation, if observer S assigns coordinates (t, x, y, z) to an event, and observer S' moves with velocity v along the x-axis relative to S, then S' assigns coordinates:

t' = gamma (t - vx/c²)

x' = gamma (x - vt)

y' = y

z' = z

where gamma = 1/sqrt(1 - v²/c²).

The physical content of this transformation is considerable. It entails time dilation: clocks in the moving frame run slower as measured from the stationary frame. It entails length contraction: objects in the moving frame are shorter along the direction of motion as measured from the stationary frame. It entails the relativity of simultaneity: events that are simultaneous in one frame are not simultaneous in another. These are not mere appearances or illusions. They are the actual results of actual measurements performed by actual observers with actual instruments.

But notice the structure of the transformation. It takes as input a set of coordinate values (t, x, y, z) assigned by observer S. It produces as output a set of coordinate values (t', x', y', z') assigned by observer S'. The transformation is a function whose domain is the set of measurements made by one observer and whose range is the set of measurements made by another observer.

The transformation applied to nothing

What happens to this function when neither observer can perform measurements?

Return to the two blind persons from the previous section: one in the aircraft, one on the ground, both without instruments, both sealed off from all sensory contact with the external world. Neither can assign coordinates to any event. The set of measurements made by observer S is empty. The set of measurements made by observer S' is empty.

The Lorentz transformation, applied to this situation, maps the empty set to the empty set. It is a function with no input and no output. It is a perfectly well-defined mathematical operation—the empty function is a legitimate object in set theory—but it has no physical content. Time dilation between the two frames is not occurring, because "occurring" is a physical predicate that requires at least one measurement to instantiate. Length contraction is not happening, because "happening" is a physical predicate that requires spatial measurements that are not being made. The relativity of simultaneity is not in effect, because simultaneity is a relation between events that have been assigned temporal coordinates, and no temporal coordinates have been assigned.

The standard objection reasserts itself: these effects are still real even though no one measures them. Time dilation is a property of spacetime geometry, not a property of measurement. The geometry is there whether anyone looks at it or not.

But this objection, examined carefully, is incoherent. What does it mean to say that time dilation is "a property of spacetime geometry"? It means that the mathematical structure of the Minkowski metric entails a specific relationship between temporal intervals measured in different inertial frames. But "temporal intervals measured in different inertial frames" is a phrase that contains the word "measured." Remove the measurement, and the phrase loses its referent. What remains is the mathematical structure—the metric, the group of transformations that leave it invariant, the algebraic relations between the components. But mathematical structure, by itself, is not physics. Physics is the discipline that connects mathematical structure to empirical phenomena. The connection is measurement. Without measurement, the connection is severed.

This is not an argument against the mathematical consistency of special relativity. The Lorentz group is a perfectly well-defined mathematical object. The Minkowski metric is a perfectly well-defined pseudo-Riemannian metric. The algebra is sound. The geometry is internally consistent. None of this is in question.

What is in question is the physical interpretation of these mathematical objects—the claim that they describe something real about the world. This claim, the paper argues, is sustainable only in the presence of a measuring observer. Without the observer, the claim cannot be made, because there is no one to make it; and it cannot be verified, because there is no one to verify it; and it cannot even be given a definite content, because the content of a physical theory just is the set of its empirical consequences, and empirical consequences are consequences for an observer.

4. The Minkowski Metric and the Illusion of Observer-Independence

The invariant interval

The Minkowski metric defines the spacetime interval between two events [Minkowski, 1908]:

ds² = -c²dt² + dx² + dy² + dz²

This interval is invariant under Lorentz transformations. That is, all inertial observers, regardless of their relative velocity, agree on the value of ds² between any two events. This invariance is conventionally taken as the strongest evidence that special relativity describes an observer-independent reality. The individual coordinates (t, x, y, z) are observer-dependent—different observers assign different values. But the interval ds² is the same for everyone. It is the objective residue that survives the passage from one observer's perspective to another's.

The philosophical weight placed on this invariance is enormous. The transition from Newtonian absolute space and absolute time to Minkowski spacetime is often presented as the discovery that spacetime is more fundamental than space or time individually—that the objective reality is the four-dimensional spacetime manifold, and that the decomposition of this manifold into space and time is a frame-dependent, observer-relative artifact. The manifold is real; the decomposition is perspectival.

This narrative is elegant, and it is mathematically grounded. But it harbours precisely the same unexamined presupposition identified in the previous sections.

The interval requires events, events require observers

The interval ds² is defined between two events. An event, in special relativity, is a point in spacetime—a location specified by four coordinates (t, x, y, z). But what determines whether something is an event [Bergmann, 1961; Komar, 1958]? In practice, an event is an occurrence that can be detected, recorded, and assigned coordinates: a flash of light, a collision of particles, the tick of a clock. Detection, recording, and coordinate assignment are all measurement operations. They all require a measuring agent.

Without a measuring agent, events are not identified. They are not located. They are not assigned coordinates. And without coordinates, the interval ds² is not computed. It is not that ds² has a value but no one knows it. It is that ds² is defined as a function of coordinate differences, and coordinate differences are defined as the results of measurements, and measurements are defined as operations performed by observers. Remove the observer, and the chain of definitions breaks at its first link [Rovelli, 1991a; Rovelli, 1991b; Rovelli, 2002]. The interval is undefined—not unknown, not hidden, not awaiting discovery, but undefined, in the strict sense that the conditions required for its definition have not been met.

Invariance without substance

Consider what Lorentz invariance actually guarantees. It guarantees that if observer S computes ds² from their measurements, and observer S' computes ds² from their measurements, the two numbers will be the same. This is a powerful constraint on the relationship between different observers' measurements. But it is a constraint on measurements. It says: if measurements are made, they will be related in this way. It does not say: if no measurements are made, something is still there.

An analogy may clarify the point. Consider the grammatical structure shared by translations of the same sentence into different languages. "The cat sat on the mat" and "Le chat s'est assis sur le tapis" share a common propositional content that is invariant under translation. But this invariance does not mean that the proposition exists independently of all languages. The proposition is expressible in many languages, and its content is preserved under translation—but it must be expressed in some language to exist as a proposition. A proposition that is expressed in no language is not a hidden proposition awaiting expression. It is not a proposition.

Similarly, the spacetime interval is expressible in many coordinate systems, and its value is preserved under Lorentz transformation—but it must be expressed in some coordinate system to exist as a physical quantity. A spacetime interval that is computed in no coordinate system is not a hidden interval awaiting computation. It is not a physical quantity.

This does not mean that nothing exists when no one is measuring. The argument is not solipsistic. It is an argument about the scope and limits of physical theory. Physical theory describes the results of measurements. When no measurements are being made, physical theory has nothing to describe. This is not a deficiency of physical theory—it is its nature. The equations do not fail. They simply have no input. A calculator does not malfunction when no one presses its keys. It simply has nothing to calculate.

The error—the error that this paper identifies as the unexamined presupposition of physics—is the slide [Earman and Norton, 1987] from "the equations are always valid" to "the equations are always describing something." Validity is a mathematical property. Description is a semantic property. The equations are always valid. But they are describing something only when there is a measurement to describe, and there is a measurement only when there is a measurer.

What Lorentz invariance actually demonstrates

If the argument of this paper is correct, then Lorentz invariance must be reinterpreted. It does not demonstrate the existence of an observer-independent reality. It demonstrates something more precise and more interesting: that different observers, performing measurements within their respective reference frames, generate spacetime descriptions that are structurally compatible with one another.

This structural compatibility is not trivial. It is a deep and remarkable feature of the physical world—or, more precisely, of the way observers generate physical worlds through measurement. But it is a relation between observer-generated descriptions, not evidence for a description-independent reality.

The analogy with translation is again instructive. The fact that a novel can be translated from English into French and back without loss of narrative structure tells us something important about the two languages and about the narrative. But it does not prove that the narrative exists independently of all languages. It proves that the two languages are structurally rich enough to encode the same information.

Similarly, Lorentz invariance proves that different observers' measurement-generated spacetime descriptions are structurally rich enough to encode the same physical information. The invariant interval is the guarantee of translatability. But translatability is not existence. Two books in different languages are not one book. Two observers' spacetime descriptions are not one spacetime.

This is the conclusion that special relativity, pursued to its logical terminus, compels: there is no single, observer-independent spacetime. There are as many spacetimes as there are observers capable of generating them through measurement. Lorentz invariance is not the signature of a unique underlying reality. It is the structural correspondence between distinct, observer-constituted realities.

5. The Structural Parallel with Quantum Mechanics

The measurement problem revisited

Quantum mechanics, unlike all other physical theories, has been forced to confront the role of the observer explicitly. The measurement problem—the fact that quantum systems appear to exist in superpositions of states until a measurement is performed, at which point the superposition collapses to a single definite outcome—has been the central interpretive puzzle of the theory since its formulation in the 1920s.

The Copenhagen interpretation, associated with Bohr and Heisenberg [Bohr, 1928; Heisenberg, 1927], holds that quantum mechanics does not describe the physical system itself but the results of measurements performed on the system. Prior to measurement, the system does not have definite properties; it has a wave function, which is a mathematical object encoding the probabilities of various outcomes. The measurement does not reveal a pre-existing property. It produces the property. The observer, in this interpretation, is not a passive recorder of facts but an active participant in the constitution of physical reality.

This interpretation has been enormously controversial, and it must be noted that not all interpretations of quantum mechanics assign the same role to the observer—decoherence, many-worlds, pilot-wave, and objective-collapse theories each treat measurement differently [Bell, 1990; Zurek, 2003], and the question of whether consciousness is required remains open within the discipline. The many-worlds interpretation, the pilot-wave theory, decoherence programs, and various collapse models have all been proposed as alternatives that would restore the observer to a passive role—that would allow physics to describe a reality that exists independently of observation. The intensity of this effort testifies to the depth of physics' commitment to observer-independence. The measurement problem is treated not as a discovery but as a scandal [Zurek, 1981; Zurek, 2009]—a failure of the theory to meet the standard of objectivity that physics demands of itself.

The same structure, independently derived

The argument of this paper reveals that the measurement problem is not a peculiarity of quantum mechanics. It is a structural feature of physical theory as such.

In quantum mechanics, the wave function describes a system's possible measurement outcomes. Without a measurement, the outcomes are indefinite. The measurement does not reveal a pre-existing state—it constitutes the state.

In special relativity, the coordinate system describes a system's spatiotemporal properties. Without a measurement, the coordinates are unassigned. The measurement does not reveal a pre-existing position in spacetime—it constitutes the position.

In quantum mechanics, different measurements (different choices of observable) yield different definite outcomes from the same wave function.

In special relativity, different observers (different inertial frames) yield different coordinate values for the same event.

In quantum mechanics, there is an invariant structure that constrains the relationships between different measurements: the commutation relations, the probability amplitudes, the unitary evolution.

In special relativity, there is an invariant structure that constrains the relationships between different observers: the Lorentz transformation, the invariant interval, the causal structure of the light cone.

In both cases, the invariant structure is often taken as evidence for an observer-independent reality underlying the observer-dependent descriptions. In quantum mechanics, this is the hope behind realist interpretations. In special relativity, this is the standard interpretation of Minkowski spacetime.

And in both cases, the argument of this paper applies with equal force: the invariant structure is a constraint on observer-generated descriptions, not evidence for a description-independent reality. The structure guarantees translatability between descriptions. It does not guarantee the existence of something that is not itself a description.

The convergence

The fact that quantum mechanics and special relativity—developed independently, addressing different domains of physical phenomena, using different mathematical formalisms—both arrive at the same structural conclusion is significant. It suggests that the conclusion is not an artifact of either theory's formalism but a feature of physical theory as such.

Both theories, when examined without the protective assumption of observer-independence, reveal the same dependency: the empirical content of the theory is not discovered by the observer but constituted by the observer's act of measurement. Both theories contain invariant structures that are naturally misread as evidence for observer-independent reality but that, on closer examination, turn out to be constraints on the relationships between observer-dependent descriptions. Both theories point, from different directions and through different formal structures, to the same philosophical terminus: the observer is the existential precondition of physical reality, not an incidental participant in it [Brukner, 2018; Frauchiger and Renner, 2018].

This convergence has a further implication. The notorious difficulty of unifying quantum mechanics and general relativity—the so-called problem of quantum gravity—may be, at least in part, a consequence of the failure to recognise the role of the observer in both theories. If both theories derive their empirical content from the observer's act of measurement, then a unified theory must begin by acknowledging this shared foundation rather than attempting to merge two formalisms that have each, in their own way, suppressed it.

6. The Third Consequence: There Is No Single Spacetime

From observer-dependence to observer-constitution

The argument thus far has established two conclusions: that the observer is the existential precondition for the physical content of special relativity, and that quantum mechanics independently arrives at the same structural insight. A third conclusion now follows—one that neither conclusion alone would license but that their conjunction compels.

If the observer does not merely measure spacetime but constitutes it through the act of measurement, then different observers do not inhabit the same spacetime. They generate distinct spacetimes.

This claim must be stated with precision to avoid misunderstanding. The standard formulation of special relativity says: there is one spacetime, and different observers slice it differently. The time axis tilts; the simultaneity surfaces rotate; the coordinate values change. But the underlying four-dimensional manifold is the same for everyone. It is the canvas. The observers are painters who depict it from different angles.

The argument of this paper inverts this picture. There is no canvas prior to the painting. Each observer's act of measurement generates a spacetime—a structured set of spatiotemporal relations between events that the observer has detected, located, and recorded. A different observer, performing different measurements from a different state of motion, generates a different structured set. The Lorentz transformation is not a rule for translating between two views of the same underlying object. It is a rule for translating between two independently constituted objects—two spacetimes—that happen to be structurally isomorphic.

The translation analogy, extended

The analogy with linguistic translation, introduced in Section 4, bears further examination. Consider two novels: one written in English, one written in Mandarin. Suppose the two novels tell the same story—the same characters, the same plot, the same sequence of events. A reader of both languages would recognise the structural correspondence immediately. A formal theory of translation could specify the rules that map sentences in one novel onto sentences in the other, preserving narrative content.

Now ask: is there a third object—the story itself—that exists independently of both novels? This is a genuine philosophical question, and reasonable people disagree about it. Platonists would say yes: the story is an abstract object that the two novels instantiate. Nominalists would say no: there are only the two novels, and the "story itself" is a useful fiction that describes their structural correspondence.

The standard interpretation of Lorentz invariance is Platonist. It holds that the invariant interval ds² points to a real, observer-independent spacetime—the story itself—of which different observers' coordinate descriptions are merely different linguistic renderings. The argument of this paper is nominalist. It holds that there are only the observer-generated descriptions, and that the invariant interval describes their structural correspondence, not a third thing underlying them both.

The nominalist reading has an advantage that the Platonist reading lacks: it does not require the existence of an entity (observer-independent spacetime) that is, by the argument of this paper, empirically inaccessible. The Platonist reading posits a reality that no observer can ever access directly—since every access is mediated by measurement, and measurement produces an observer-dependent description, not the underlying reality itself. The nominalist reading posits only what is empirically available: observer-generated descriptions and the structural relations between them.

The multiplicity of spacetimes

If this reading is correct, then the number of spacetimes is not one. It is equal to the number of observers capable of generating them. Each observer, through their measurements, constitutes a spacetime—a structured domain of spatiotemporal relations. These domains are not fragments of a larger whole. They are complete in themselves, each one containing all the physical information available to the observer who generated it. The Lorentz transformation is the bridge between domains—the guarantee that information constituted by one observer can be translated, without loss, into the terms of another.

This is a radical claim, but it is not an arbitrary one. It follows deductively from the premises established in the earlier sections:

Premise 1: A reference frame requires a measuring observer for its physical instantiation.

Premise 2: The Lorentz transformation relates the measurement outputs of two observers; without measurements, it relates nothing.

Premise 3: The Minkowski metric's physical content depends on events being located by observers.

Conclusion: Spacetime, as a physical (not merely mathematical) structure, exists only where and when an observer constitutes it through measurement. Multiple observers constitute multiple spacetimes. Lorentz invariance guarantees their mutual translatability but not their identity.

This conclusion dissolves the apparent paradox of the "block universe"—the interpretation of Minkowski spacetime in which past, present, and future all exist equally, and the flow of time is an illusion. If spacetime is observer-constituted, then the block universe is not a discovery about the nature of reality. It is an artifact of the mathematical formalism—a consequence of treating the observer-independent manifold as physically real rather than as a mathematical convenience that derives its physical meaning from the measurements of actual observers. The flow of time is not an illusion; it is a feature of the observer's constitutive activity, no less real than the spacetime it generates.

7. Objections and Responses

"You are confusing epistemology with ontology"

The most immediate objection to the argument of this paper is that it conflates what we can know (epistemology) with what exists (ontology). The blind observer in the aircraft cannot know their velocity, but this does not mean they have no velocity. The inability to measure a quantity does not entail the nonexistence of the quantity.

This objection assumes precisely what is in question: that there is a clear and defensible distinction between what exists and what can be known to exist. This distinction is the metaphysical commitment to realism—the commitment to a mind-independent reality that exists whether or not it is observed, measured, or known. The argument of this paper does not deny that this commitment is philosophically respectable. It denies that this commitment is a conclusion of physics.

Physics is an empirical science. Its claims are grounded in measurement. Its predictions are tested by observation. Its content just is the set of its empirical consequences. To claim that physics also describes features of reality that are in principle inaccessible to measurement is to make a metaphysical claim that goes beyond anything physics can support. Physics can tell you what happens when you measure. It cannot tell you what happens when you do not measure, because by definition it has no empirical access to that situation.

The distinction between epistemology and ontology, in the context of physics, is not a solution to the problem raised in this paper. It is a restatement of the problem. Physics claims ontological reach—claims to describe what exists. But its only access to existence is through epistemology—through measurement, observation, and knowledge. The gap between these two claims is the gap that this paper identifies.

"Instruments can replace observers"

A second objection holds that human observers are not necessary for measurement. Instruments—thermometers, clocks, particle detectors, gravitational wave observatories—can perform measurements autonomously, without any conscious observer being present. Therefore, the argument continues, the observer in physics is nothing more than a measuring instrument, and instruments are purely physical systems governed by the same laws they are used to test.

This objection does not refute the argument of this paper. It confirms it. As defined in Section 2, an observer is any physical system capable of entering into an information-discriminating relationship with another physical system—capable of registering distinct states and retaining a record. By this definition, an autonomous instrument is an observer. A particle detector that records a track is performing an observation. A clock that registers the passage of intervals is performing an observation. The objection assumes that "observer" means "human," and then triumphantly points out that humans are not necessary. But the argument of this paper has never claimed that humans are necessary. It has claimed that some observing system is necessary—some physical system capable of instantiating a measurement relation, discriminating between states, and generating a record that can bear physical meaning.

The real question, therefore, is not whether instruments can replace human observers—they can, and they do. The real question is what happens when all observing systems are removed: no instruments, no detectors, no clocks, no information-processing systems of any kind. In that situation, no measurement relation is instantiated, no physical state is discriminated, no record is generated, and no coordinate is assigned. The formal apparatus of physics—its equations, its symmetries, its mathematical structures—remains intact. But it describes nothing, predicts nothing, and refers to nothing, because the condition required for it to make contact with physical reality—the existence of at least one observing system—has not been met.

"The universe existed before conscious observers evolved"

A third objection points to cosmology: the universe existed for approximately 13.8 billion years before conscious observers evolved on Earth. Stars formed, galaxies coalesced, heavy elements were synthesized in supernovae, planets condensed from protoplanetary disks—all without any conscious observer present. If the observer is a precondition for physical reality, does this mean the pre-biological universe did not exist?

This objection rests on a subtle equivocation, and it can be dismantled on two independent grounds—one epistemological, one drawn from special relativity itself. The argument of this paper does not claim that nothing exists without an observer. It claims that physical theory—the formal, mathematical, empirically grounded enterprise of physics—has no empirical content without an observer. These are different claims.

The epistemological ground is straightforward: the pre-biological universe may well have existed. But the claim that it existed is not a conclusion of physics. It is a retroductive inference made by present-day observers on the basis of present-day measurements (the cosmic microwave background, the abundance of light elements, the redshift of distant galaxies). These measurements are performed now, by observers who exist now. The statement "the universe existed 13.8 billion years ago" is a statement made by a present observer, based on present evidence, within a theoretical framework constructed by present minds. It may be true. But its truth is established through the very act of observation that the objection claims to be unnecessary.

This is not a sceptical argument against cosmology. It is a clarification of what cosmological claims actually are: they are inferences drawn by present observers from present data. They are not reports from a time when no observers existed. They cannot be, because there was no one there to report.

The second ground is more devastating, because it uses special relativity's own logic to undermine the claim that the universe has a single, observer-independent age. According to special relativity, temporal intervals are not absolute—they depend on the observer's state of motion. The 13.8-billion-year figure is the cosmic time measured in a specific reference frame: the comoving frame, in which the cosmic microwave background radiation is isotropic and the large-scale expansion of the universe appears uniform. But this is one frame among infinitely many. An observer moving at a different velocity relative to the comoving frame would measure a different cosmic age. The 13.8-billion-year history is not a fact about the universe—it is a fact about the universe as measured from a particular observational standpoint.

The dependence runs deeper than the choice of frame. The comoving frame itself is defined by a measurement: it is the frame in which the CMB appears isotropic. An observer in a different state of motion would measure an anisotropic CMB, and the universe described by that observer's measurements would not be homogeneous or isotropic—the FLRW model would not apply. The standard cosmological model, including its claim that the universe has no spatial centre and is expanding uniformly, is not a description of the universe as it is in itself. It is a description of the universe as it appears to a particular class of observers—comoving observers—who have been singled out not by the universe but by the convention of cosmological practice. Even the statement "the universe has no centre" is a statement made within a model whose applicability depends on the observer's state of motion.

This is not speculative metaphysics. It is a direct application of the principle of relativity: if there is no privileged reference frame, then there is no privileged cosmic history. The 13.8-billion-year narrative is one observer's narrative—the narrative of an observer at rest relative to the cosmic microwave background, equipped with telescopes and clocks and the general theory of relativity. Remove this observer, and the narrative is not "still true but unknown." It is one of infinitely many possible narratives, none of which has a stronger claim to objectivity than any other, because objectivity, in physics, just is the intersubjective agreement of observers—and without observers, there is no intersubjectivity and no agreement.

"This is just idealism"

A fourth objection categorizes the argument as a form of philosophical idealism—the position that reality is fundamentally mental—and dismisses it on the grounds that idealism has been refuted, or at least abandoned, by serious philosophy and science.

The argument of this paper is not idealism. Idealism is an ontological thesis: it claims that only minds and their contents exist, and that the physical world is a construction of the mind. The argument of this paper is not an ontological thesis. It is a thesis about the scope and limits of physical theory. It claims that physical theory, as a formal and empirical enterprise, derives its empirical content from the act of measurement, and that measurement presupposes a measurer. This is a claim about the structure of physics, not a claim about the ultimate nature of reality.

The paper is deliberately agnostic about what exists when no one is measuring. The agnosticism concerns a possible measurement-independent substrate; it does not extend to physical spacetime itself, which the paper has shown to be observer-constituted—these are two different levels, and the argument asserts the second while suspending judgment on the first. It does not claim that nothing exists. It does not claim that consciousness creates reality. It claims something more modest and more precise: that physics, as currently constituted, cannot tell us what exists when no one is measuring, because its entire empirical apparatus is measurement-dependent. Whether something exists independently of measurement is a question that physics cannot answer—not because the question is meaningless, but because physics lacks the resources to address it.

If anything, the argument is closer to Kant's transcendental idealism than to Berkeley's subjective idealism. Kant did not deny the existence of things-in-themselves. He denied that we have cognitive access to things-in-themselves. Similarly, this paper does not deny the existence of a measurement-independent reality. It denies that physics has empirical access to such a reality.

8. The Fork in the Road

The argument of this paper, if accepted, places physics at a fork in the road. Two paths open up, and the choice between them will determine the future trajectory of foundational physics.

Path one: Acknowledge and formalise

The first path is to acknowledge the observer as the existential precondition of physical theory and to incorporate this acknowledgment into the formal structure of physics. This would require a reformulation of physical theory in which the observer is not an external user of the formalism but an element within it—not as a physical system described by the equations (which would lead to infinite regress) but as a structural condition that the formalism explicitly recognises as necessary for its own physical interpretation.

What would such a reformulation look like? At minimum, it would require a formal distinction between the mathematical content of a theory (its equations, symmetries, and mathematical structures) and its empirical content (the set of measurement outcomes the theory predicts). The mathematical content would be acknowledged as observer-independent—the Lorentz group does not need an observer to be a well-defined mathematical object. But the empirical content would be explicitly indexed to an observer: every physical prediction would carry, as part of its formal structure, a specification of who or what is performing the measurement that gives the prediction its physical meaning.

This is not as radical as it may sound. Quantum mechanics already does something like this in the formalism of quantum information theory, where the observer's knowledge is encoded in the quantum state and updated by measurement. Relational quantum mechanics, proposed by Rovelli [Rovelli, 1996], goes further, defining all physical quantities as relational—as properties that a system has relative to another system, with no system-independent "absolute" properties. The argument of this paper suggests that relational quantum mechanics has identified the right structural insight but has not pushed it far enough: it is not only quantum properties that are relational, but all physical properties, including the spatiotemporal properties described by special and general relativity.

Path two: Confront the deeper question

The second path is more radical. If the observer is the precondition for physical reality—if spacetime, physical quantities, and the empirical content of all physical theories are constituted by the act of measurement, and measurement requires a discriminating, record-generating subject—then the deepest question in physics is not "what are the fundamental laws?" but "what is the observer?"

Physics has never asked this question. Biology asks what organisms are. Neuroscience asks what brains are. Psychology asks what minds are. But no science asks what the observer is—not the observer as a biological system or a neurological process or a psychological subject, but the observer as the entity whose existence is the precondition for any science, including biology, neuroscience, and psychology, to have empirical content.

This question cannot be answered within physics as currently constituted, because physics presupposes the observer. You cannot use a tool to investigate the condition that makes the tool possible. A microscope cannot examine the eye that looks through it. Physics cannot investigate the observer whose existence it requires in order to investigate anything.

This does not mean the question is unanswerable. It means the question requires a framework that is broader than physics—a framework in which consciousness is not a phenomenon to be explained by physical theory but a foundational element from which physical theory (along with all other empirical knowledge) is derived. What such a framework would look like, and whether it can be constructed with the intellectual resources currently available, is a question that lies beyond the scope of this paper [Adlam, 2025]. But the argument of this paper establishes that the question must be asked—that physics cannot continue to rely on a presupposition it refuses to examine, and that the examination, when it comes, will require physics to expand beyond its current self-understanding.

9. Conclusion

Every physical theory presupposes the existence of an observer. This presupposition has never been denied—it has never needed to be denied, because it has never been examined. It operates in the background of every equation, every measurement, every prediction, every experimental test, as silently and as indispensably as the act of breathing operates in the background of speech. One does not notice one's breathing until it stops. Physics has not noticed its dependence on the observer because it has never tried to do physics without one.

This paper has tried. Using a thought experiment grounded in the logic of special relativity—the theory most often cited as evidence for observer-independent reality—the paper has shown that reference frames cannot be constructed without a measuring subject; that the Lorentz transformation, without measurements to transform, maps nothing to nothing; that the Minkowski metric, without events located by observers, has no physical content; and that the invariance of the spacetime interval, far from proving the existence of an observer-independent reality, proves only that different observers' measurement-generated realities are structurally compatible with one another.

The paper has shown further that this result is not unique to special relativity. Quantum mechanics, through its measurement problem, arrives at the same structural conclusion by a completely independent route: the empirical content of the theory is constituted by the act of measurement, not discovered by it. The convergence of these two results—from two theories developed independently, in different domains, with different formalisms—suggests that the observer-dependence of physical content is not an artifact of any particular theory but a feature of physical theory as such.

This is not an argument against physics. It is an argument for taking physics more seriously than physics takes itself. Physics claims to describe reality. This paper asks: whose reality? The answer, invariably, is: an observer's reality. There is no other kind of reality available to physics. There may be other kinds of reality available to metaphysics, to theology, to contemplative practice. But physics—empirical, mathematical, measurement-based physics—can speak only of the reality that appears to a measuring subject. To pretend otherwise is not realism. It is an article of faith dressed in the language of equations.

The observer is not in spacetime. Spacetime is rendered by the observer.

This final sentence is not a metaphor. It is the logical terminus of the argument. If spacetime is constituted by the observer's act of measurement, then the observer cannot be located within spacetime, because spacetime is the product of the observer's activity, not its container. To say that the observer is "in" spacetime is to place the cause inside its own effect, the author inside their own text, the dreamer inside their own dream. It is a category error—the most consequential category error in the history of physics, and the one that has remained invisible for the longest, precisely because it is built into the grammar of every physical description.

Correcting this error will not be easy. It will require physics to relinquish the comforting picture of a universe that exists independently of anyone's knowledge of it—a universe that was there before anyone looked and will be there after everyone stops looking. This picture may be true. But physics cannot establish its truth, because every attempt to do so employs the very observer whose dispensability it is trying to prove. The most physics can honestly say is: when we measure, we find this. What exists when we do not measure is not a question physics is equipped to answer.

This is not a diminishment of physics. It is a clarification. Physics is the most powerful instrument of knowledge ever devised by the human mind. But like every instrument, it has a scope and a limit [Poincaré, 1902]. The scope of physics is the domain of measurement. The limit of physics is the observer. To recognise this limit is not to weaken physics but to understand, for the first time, exactly what it is and what it does. Physics does not describe reality [Eddington, 1916]. Physics describes what reality looks like to a measuring observer. The difference between these two statements is the difference between a physics that knows itself and a physics that does not.

A final clarification is necessary regarding the word "existence." Physics uses this word constantly—spacetime exists, fields exist, particles exist—but it has never defined what it means. When physics says "spacetime exists," it means: our measurements are consistent with a mathematical structure, and we therefore declare that this mathematical structure corresponds to a physical reality. But "corresponds to a physical reality" is not a measurement result. It is not an output of any equation. It is not a prediction that any experiment can test. It is an ontological judgment. And an ontological judgment requires a judging subject. "Existence" is not a self-executing predicate. It requires someone to assert it. On a planet with nothing but soil—no organisms, no instruments, no information-processing systems of any kind—nothing is saying "I exist," nothing is saying "mathematics exists," nothing is saying "spacetime exists." Physical processes may be occurring, but the judgment "this exists" does not spontaneously emerge from physical processes. Existence must be declared, and declaration requires a declarer. This is not idealism. It is a recognition that "existence," as used in physics, is not a property of the world but an act performed by an observer upon the world. Without the observer, the world may or may not persist—but "exists" is not a word that applies to it, because there is no one left to apply it.

Acknowledgements

The author acknowledges the use of AI tools—Claude, ChatGPT, and Gemini—in the preparation of this manuscript. These tools were employed as supportive instruments for language refinement, structural organisation, and clarity improvement of the technical exposition. All scientific ideas, modelling choices, and interpretations presented in this work are the sole responsibility of the author. The use of AI did not involve any generation of experimental data or alteration of underlying physical assumptions, and all content was reviewed and validated by the author prior to submission.

Declarations

Funding: This research received no external funding.

Conflicts of interest: The author declares no conflicts of interest.

Data availability: No new observational data were generated or analysed in this study. All referenced datasets are publicly available from the sources cited.

Author contributions: Juliet Zhong: conceptualisation, formal analysis, writing.

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