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