We are all experiencing time right now. The words on this page arrive in a sequence. Some things have already happened and cannot be changed. Others have not happened yet. The present moment feels real in a way the past and future do not. Time seems to flow from earlier to later, from cause to effect, from youth to age, at a rate that feels constant and unavoidable.
Physics has almost nothing to say about any of this.
Not because physicists have failed to think carefully about time. They have for centuries. But because the properties of time that feel most immediate and certain in experience are precisely the ones that appear nowhere in the fundamental equations of physics. The flow of time, the special status of the present moment, the difference between past and future: none of these features appear in Newton’s mechanics, Maxwell’s electrodynamics, Einstein’s relativity, or quantum mechanics. The equations of physics work equally well run forward or backward in time. They do not distinguish past from future. They contain no present moment. They describe no flow.
And when physicists attempt to construct a quantum theory of gravity, time does not merely become difficult to define. It disappears from the equations entirely.
Time in Newtonian Physics
Isaac Newton introduced a specific conception of time in his 1687 Principia Mathematica that dominated physics for more than two centuries. Newton’s time is absolute, universal, and external to the physical system it measures. It flows uniformly from past to future at the same rate everywhere in the universe, regardless of what is happening physically. It is not itself a physical quantity with dynamics. It does not curve, slow down, or interact with matter. It simply flows, uniformly and inexorably, providing a backdrop against which all physical change is measured.
In Newton’s mechanics, the fundamental equation of motion is
where F is the force acting on an object, m is its mass, and a is its acceleration. The acceleration is the second derivative of position with respect to time. Time here is a parameter, a number labelling moments, not a physical object. It is external to the system, imposed from outside, and it flows at the same rate regardless of what the system is doing.
This conception of time matches everyday experience so well that it survived unchallenged for two centuries. It was dismantled not by philosophical argument but by a specific physical fact: the speed of light.
Time in Special Relativity
Einstein’s 1905 special relativity established that the speed of light is the same for all observers in uniform motion, regardless of their relative velocity. This single fact forces a complete revision of how time works.
In special relativity, time is not absolute. Two observers in relative motion measure different amounts of time between the same pair of events. An observer moving relative to a clock measures that clock as ticking more slowly than an observer at rest relative to it. This is time dilation, and it is not an illusion. It has been confirmed in experiments ranging from the decay rates of muons produced in cosmic ray showers to atomic clocks flown on aircraft.
The relevant equation is the time dilation formula:
where is the time measured by a clock at rest, is the time measured by an observer moving at velocity v relative to the clock, and c is the speed of light. As approaches , the denominator approaches zero and grows without bound.
A clock moving close to the speed of light ticks almost infinitely slowly as seen by a stationary observer.
More fundamentally, special relativity unifies space and time into a single four-dimensional structure called spacetime. What one observer calls a purely temporal interval between two events, another observer moving relative to the first will describe as partly spatial and partly temporal. There is no privileged frame, no absolute now that all observers share.
Time in General Relativity
Einstein’s general relativity of 1915 went further. In special relativity, spacetime is a fixed background, a rigid four-dimensional arena in which physical events occur, unchanged by those events. In general relativity, spacetime is itself a dynamical entity. It curves in response to the distribution of matter and energy, and that curvature is what gravity is.
This means time is affected by gravity. A clock near a massive object ticks more slowly than a clock far from it. This gravitational time dilation is described by
where G is Newton’s gravitational constant, M is the mass of the gravitating body, r is the distance from the centre of mass, and c is the speed of light. Near a massive object, the factor inside the square root is less than one, meaning t’ is less than t.
The clock near the massive object ticks more slowly. At the event horizon of a black hole, where r equals 2GM/c², the factor reaches zero. Time stops entirely as seen from outside.
GPS satellites must correct for gravitational time dilation continuously. Their clocks tick approximately 45 microseconds per day faster than clocks on Earth’s surface due to being farther from Earth’s gravitational field. Without this correction, GPS position errors would accumulate at roughly 10 kilometres per day.
In general relativity, there is no background time. The theory is background-independent: the geometry of spacetime, including its temporal structure, is determined by the solution to Einstein’s field equations, which depend on the distribution of matter and energy. Time is not a fixed container in which physics happens. It is a participant in the physical dynamics. And this creates a deep problem when general relativity is combined with quantum mechanics.
Time in Quantum Mechanics
In quantum mechanics, time plays a completely different role from the one it plays in general relativity. The Schrödinger equation describes how the quantum state of a system evolves:
where i is the imaginary unit, ℏ is the reduced Planck constant, ψ is the wavefunction encoding the complete quantum state of the system, t is time, and Ĥ is the Hamiltonian operator representing the total energy of the system.
Time appears here as an external parameter, exactly as it does in Newton’s mechanics. It is not a quantum observable in the technical sense. There is no Hermitian operator corresponding to time, no measurement that directly extracts a time value from a quantum state. The equation tells you how the wavefunction changes from one moment to the next, but the moments themselves are given by an external clock that sits outside the quantum system being described.
This treatment of time as an external background parameter is inherited directly from Newton and works perfectly well for all particle physics experiments, where gravity is negligibly weak and spacetime can be treated as a fixed flat background. It fails when gravity is strong, because in strong gravitational fields the geometry of spacetime is itself dynamical and cannot be treated as a fixed background.
The tension between general relativity’s dynamic time and quantum mechanics’s external parametric time is the problem of time in quantum gravity.
The Problem of Time
The problem of time occurs because the time of general relativity and the time of ordinary quantum theory are mutually incompatible notions. This incompatibility creates serious problems when trying to replace these two branches of physics with a single framework in regimes in which neither quantum theory nor general relativity can be neglected, such as in black holes or in the very early universe.
The problem appears most sharply when one attempts to apply quantum mechanics directly to the universe as a whole, including its gravitational field. In ordinary quantum mechanics, the Schrödinger equation describes how a quantum state evolves over time:
When this procedure is applied to the entire universe, including gravity, the result is the Wheeler-DeWitt equation, first derived by John Wheeler and Bryce DeWitt in the 1960s.
The difference between these two equations is the entire problem of time stated in a single comparison. In the Schrödinger equation, the left-hand side contains a time derivative, . The wavefunction changes over time. In the Wheeler-DeWitt equation, there is no time derivative. The Hamiltonian operator Ĥ acts on the wavefunction of the universe (ψ), and the result is zero. The wavefunction does not evolve. It is static.
The Wheeler-DeWitt equation imposes a Hamiltonian constraint that removes explicit temporal evolution from the quantum state of the universe, producing a frozen mathematical description that conflicts with the observed dynamical nature of physics.
This is called the frozen formalism problem. The quantum state of the universe, as described by the Wheeler-DeWitt equation, does not change. Yet the universe clearly does change. Galaxies form, stars collapse, black holes evaporate. If the Wheeler-DeWitt equation is correct, these changes cannot be changes in the fundamental quantum state of the universe. They must be something else. What that something else is, and how to recover the apparent flow of time from a timeless quantum state, is the central challenge.
Does Time Flow at All?
The problem of time in quantum gravity connects to a deeper question that special and general relativity already raise.
In Newtonian physics, time flows. The present moment is special. The past is fixed and gone. The future is open and not yet real. This matches intuition so well that it feels like a description of obvious fact rather than a theoretical commitment.
Special relativity challenges this at its foundations. Because different observers in relative motion disagree about what events are simultaneous, there is no universal present moment. What one observer calls now, another observer moving relative to the first will call partly past and partly future. The present is not an objective feature of reality. It is observer-dependent.
This leads naturally to the block universe view of time. In the block universe, all moments of time exist equally. Spacetime is a four-dimensional structure in which all events are present simultaneously in the same sense that all points in space are present simultaneously. The apparent flow of time is not a feature of this four-dimensional structure. It is a feature of how observers experience it from within.
The block universe is the picture of time that follows most directly from the mathematics of special relativity. Whether it is the correct picture of physical reality or whether time genuinely flows in a way the mathematics does not capture remains one of the most contested questions at the boundary of physics and philosophy.
Why Does Time Have a Direction?
Even setting aside whether time flows, physics faces a separate and equally deep problem. Why does time have a direction at all?
The fundamental laws of physics are time-symmetric. Newton’s mechanics, Maxwell’s electrodynamics, Einstein’s general relativity, and quantum mechanics all work equally well run forward or backward in time. A film of two billiard balls colliding looks physically correct whether played forward or in reverse. The laws do not distinguish past from future.
Yet experience is overwhelmingly time-asymmetric. A glass falls and shatters. It does not spontaneously reassemble. Heat flows from hot to cold, never the reverse. The universe evolves toward greater disorder. There is a clear direction to time in the world of experience, even though the fundamental laws governing that world are symmetric.
The resolution is attributed to the second law of thermodynamics. The Boltzmann entropy formula
defines the entropy of a system, where is the Boltzmann constant and is the number of microscopic configurations of the system consistent with its macroscopic state. A gas filling a room has high entropy because there are enormously more ways for gas molecules to be distributed throughout the room than to be concentrated in one corner. Entropy increases because there are vastly more disordered states than ordered ones, so any system evolving randomly is statistically almost certain to move toward greater disorder.
The direction of increasing entropy defines the arrow of time: the direction in which processes run spontaneously, memories accumulate, causes precede effects. This explanation works only if the universe started in a state of very low entropy, and the evidence strongly suggests it did, at the Big Bang. Earlier states do not have higher entropy than present states because we make the cosmological posit that the universe began in an extremely tiny section of its available phase space.
The thermodynamic arrow of time is therefore not explained by the fundamental laws, but is imposed as an initial cosmological condition. Crucially, however, this thermodynamic arrow explains only why macroscopic events are irreversible—it does not explain the passage of time itself. Even in localized systems where entropy is artificially reversed (like a Maxwell’s demon setup*) or during cosmic inflation where entropy remained constant, clocks still relentlessly tick forward at one second-per-second. Why the universe began in such an extraordinarily low-entropy state, and how the fundamental flow of time persists completely independent of entropy changes, remains an open question connecting the problem of time to the deepest mysteries of physics.
Time Without a Background
One response to the frozen formalism problem is to reconceive what time is at the most fundamental level.
Rather than treating time as an external parameter or background structure, relational approaches propose that time is defined entirely by the relationships between physical systems. What it means for time to pass is for one physical system to change relative to another. There is no external clock ticking away in the background. There is only the correlation between physical systems.
This approach was advocated by Gottfried Leibniz in the seventeenth century as an alternative to Newton’s absolute time and has been developed in modern form within quantum gravity by Carlo Rovelli and others. In the relational picture, the physical content of a statement like “the particle is at position x at time t” is reinterpreted as “the particle is at position x when the clock reads t”. Time is a statement about correlations between subsystems, not a statement about an external parameter.
Don Page and William Wootters made this precise in 1983. They showed that even in a universe described by a static, timeless wavefunction satisfying the Wheeler-DeWitt equation, an internal observer using one subsystem as a clock will see other subsystems evolving consistently with the Schrödinger equation. Thanks to quantum entanglement, a static system may describe an evolving universe from the point of view of internal observers. Energy entanglement between a clock system and the rest of the universe can yield a stationary state for an external observer that is able to test the entanglement against abstract coordinate time. The same state will be, instead, evolving for internal observers that test the correlations between the clock and the rest.
In 2013, Ekaterina Moreva and collaborators at the Italian National Institute of Metrological Research demonstrated the Page-Wootters mechanism experimentally using entangled photons. A static, entangled state between a clock system and the rest of the universe is perceived as evolving by internal observers that test the correlations between the two subsystems. Using an entangled state of the polarisation of two photons, one of which was used as a clock to gauge the evolution of the second, an internal observer that became correlated with the clock photon saw the other system evolve, while an external observer that only observed global properties of the two photons could prove it was static.
In December 2025, Tommaso Favalli and collaborators at the University of Naples extended the Page-Wootters framework further. Building upon the established Page and Wootters mechanism, the team demonstrated that entanglement between subsystems can effectively generate a sense of temporal order and spatial relationships, even in a universe initially devoid of both. They extended the Page-Wootters framework, originally designed to describe the emergence of time, to incorporate spatial dimensions, resulting in a model of a 3+1 dimensional spacetime arising from entanglement between subsystems in a fundamentally timeless and positionless universe.
These results do not prove that time is emergent from quantum entanglement in the physical universe. They demonstrate that the mathematical mechanism by which time could emerge from a timeless quantum state is physically realisable and experimentally testable at small scales. Whether the same mechanism operates at the cosmological level, generating the time we experience from a fundamentally timeless Wheeler-DeWitt universe, remains an open question.
Is Time Fundamental or Emergent?
A theme has recurred throughout the three approaches to quantum gravity examined in Group 2. In loop quantum gravity, smooth spacetime emerges from the discrete structure of spin networks. In string theory, spacetime geometry emerges from the dynamics of strings and branes. In asymptotic safety, smooth four-dimensional spacetime emerges from a scale-invariant fixed point of the renormalisation group. In the holographic principle examined in Article IX, the geometry of three-dimensional space emerges from a two-dimensional boundary theory.
In each of these frameworks, time is treated as emergent rather than fundamental. It is not built into the foundations. It arises, along with space and geometry, from something more fundamental that does not itself contain time in any obvious sense.
The convergence of independent theoretical frameworks on the emergent character of time, now supported by experimental demonstrations of the Page-Wootters mechanism, suggests that the question “what is time?” may not be answerable within physics as currently formulated. The correct answer may require a new framework in which time, like space and geometry, is derived from structures that are themselves timeless.
Whether those structures are the quantum entanglement correlations of the Page-Wootters mechanism, the spin network geometry of loop quantum gravity, the string dynamics of M-theory, or something not yet conceived, is not known.
So, What is Time?
Time is built into every physical theory, yet no theory explains what time is. Newton treated it as an absolute external parameter. Special relativity made it relative to observers. General relativity made it dynamic and curved. Quantum mechanics treats it as an external background that cannot be quantised. The Wheeler-DeWitt equation, which is what results when general relativity and quantum mechanics are combined at the level of the universe as a whole, eliminates time from the equations entirely.
The frozen formalism problem is the mathematical expression of a genuine physical question: if the correct quantum state of the universe is timeless, where does time come from? The Page-Wootters mechanism and its experimental realisations show that time can emerge from quantum entanglement between subsystems of a timeless whole. Whether this is the correct description of time in our universe is not established.
Whether time is fundamental or emergent, whether it genuinely flows or whether its apparent flow is a feature of how observers experience a four-dimensional block universe from within, whether the arrow of time requires explanation beyond the past hypothesis: these questions remain open. They are not open because physicists have failed to address them. They are open because the answers require a complete theory of quantum gravity that does not yet exist.
Further Readings:
- https://plato.stanford.edu/entries/quantum-gravity/
- https://www.space.com/29859-the-illusion-of-time.html
- https://www.sciencefocus.com/science/the-closer-we-look-at-time-the-stranger-it-gets
- https://brightside.me/articles/time-and-space-change-places-in-a-black-hole-but-why-815517/
- https://www.forbes.com/sites/startswithabang/2017/01/28/ask-ethan-what-is-spacetime/
- https://news.itmo.ru/en/science/photonics/news/12761/
- https://cosym.org/2024/05/19/trip-to-the-past/
- https://cosym.org/2025/01/21/is-time-real-or-just-an-illusion/
This is Article XI of The Geometry of Reality, and the first article of Group 4.
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