What Is Time? Why It Ticks Uniformly for All Observers?

"What then is time? If no one asks me, I know; if I seek to explain it, I do not," Aurelius Augustinus Hipponensis

Time is one of the most fundamental and mysterious aspects of physical reality. This thesis explores the nature of time from classical physics through relativity, quantum mechanics, and modern cosmology, aiming to illuminate what time is, where it might have “come from,” and why it appears to tick uniformly for all observers. We begin by reviewing how time is conceived in Newtonian mechanics as an absolute flowing background versus in Einstein’s relativity as part of a four-dimensional spacetime that is relative and observer-dependent. We then examine the role of time in quantum theory: as an external parameter in non-relativistic quantum mechanics, and the more subtle status of time in relativistic quantum field theory and prospective quantum gravity frameworks such as causal dynamical triangulations, loop quantum gravity, and holography. The arrow of time and the question of whether time’s flow is fundamental or emergent are analyzed through the lenses of thermodynamics (entropy increase), symmetry-breaking, and philosophical interpretations. We address the notion of time’s origin—investigating whether time began with the Big Bang or could emerge from a prior timeless state—through theories including the Hartle–Hawking no-boundary proposal, Penrose’s conformal cyclic cosmology, bouncing cosmologies, and string-based pre-Big Bang scenarios. A critical discussion is provided on the claim that “time ticks uniformly for all observers,” clarifying its meaning in relativity (the invariant nature of proper time) and the conditions under which it holds or breaks down. Throughout, known empirical facts (from relativity tests to cosmological observations) are synthesized with speculative but well-motivated ideas to assess the ontology of time. We conclude by summarizing what is established about time and highlighting the open questions—our profound known unknowns (like the resolution of time at singularities or in quantum gravity) and even potential unknown unknowns about time that future breakthroughs may uncover.

Introduction

What is the true nature of time? Few questions sit so squarely at the intersection of physics, philosophy, and human experience. Time enters physics as a parameter to order events and quantify change. In everyday life and classical physics, time is often assumed to be universal and absolute, flowing uniformly everywhere. Isaac Newton encapsulated this classical view by asserting that “absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external”. In Newton’s mechanics, time is an independent background variable ticking steadily in the same way for all observers, providing a universal stage on which dynamics unfold. This notion of an external, absolute time was long unchallenged in physics.

In the early 20th century, however, Einstein’s theories of relativity shattered the Newtonian absolute time. Special relativity (1905) revealed that measurements of time are relative – different observers moving at different velocities do not share the same “now,” and the duration between events can differ from one frame to another. Two events that appear simultaneous in one inertial frame occur at different times in another, and moving clocks are measured to tick slower (time dilation) relative to stationary ones. There is no single universal time; instead each inertial observer carries their own clock. Herman Minkowski, expanding on Einstein’s work, introduced the concept of spacetime in 1908, uniting time and space into a four-dimensional continuum. In Minkowski’s famous words: “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve independence.”. Time, in the relativistic view, is a dimension much like space, and only the unified spacetime has absolute meaning. The passage of time became path-dependent and observer-dependent, rather than a universal flow. General relativity (1915) deepened this picture by showing that gravity is not a force in the Newtonian sense but rather the manifestation of spacetime curvature. Mass-energy tells spacetime how to curve, and curved spacetime tells clocks (and all processes) how to run. Time itself is affected by gravity: the stronger the gravitational potential or the higher the relative speed, the slower a clock ticks as seen by an external observer. Yet, critically, each observer still perceives their own clock to run normally. We will explore this apparent paradox of “time ticking uniformly” in detail later. In cosmology, applying general relativity to the universe as a whole yields a model where time is often measured by the cosmic time coordinate – essentially the proper time experienced by “comoving” observers who move with the Hubble flow. This provides a kind of universal time for the standard cosmological model, starting from zero at the Big Bang, although the use of such a time assumes a specific cosmic frame (one in which the universe looks homogeneous and isotropic).

Quantum physics offers yet another perspective on time. In non-relativistic quantum mechanics, time enters as an external parameter in the Schrödinger equation, not as an observable. The wavefunction $\Psi(x,t)$ evolves in time according to $i\hbar \frac{\partial}{\partial t}\Psi = H\Psi$, but time itself is not represented by a quantum operator the way position or momentum are. (In fact, Pauli’s analysis showed that there cannot be a self-adjoint time operator conjugate to a usual Hamiltonian – essentially because having such an operator with an energy spectrum bounded below leads to contradictions.) Thus, standard quantum theory retains a Newtonian-like role for time as an independent background parameter. This approach works well for laboratory systems, but it becomes deeply problematic when we try to meld it with general relativity, where time is dynamical. In relativistic quantum field theory (QFT), space and time coordinates enter on a more equal footing in that the laws are Lorentz-invariant, yet typically QFT still assumes a fixed background spacetime (often flat Minkowski space) with a time coordinate. Fields evolve and particles propagate in that fixed spacetime. Some formulations of relativistic quantum mechanics promote time to a more explicit role (for example, treating energy and time as conjugates in a relativistic context, or considering “parametrized” time formulations), but by and large, in everyday QFT used for particle physics, time is not an operator but a parameter that labels the evolution of quantum states.

The tension between the dynamical, relative time of general relativity and the fixed, absolute time parameter of quantum mechanics is at the heart of the problem of time in quantum gravity. Candidate quantum gravity theories each offer different insights into how time might behave at the deepest level. Some approaches, like the Wheeler–DeWitt equation from canonical quantum gravity, imply a “timeless” universe where a global time parameter disappears from the fundamental equations. Other approaches like causal dynamical triangulations, loop quantum gravity, or holographic dualities strive to either recover an emergent time or embed time in a larger framework where its usual meaning might be altered. For instance, loop quantum gravity suggests that at the Planck scale the smooth flow of time might break down – time might be emergent from more primitive variables or even an illusion in a sense. In the AdS/CFT holographic correspondence, time is a shared parameter in the dual description, preserving a notion of unitary evolution, whereas in some cosmological quantum gravity models time could be a derived concept that appears only for macroscopic observers.

Beyond the realm of physics equations, there is the everyday experience of the passage of time and the unidirectional flow or arrow of time. Physical laws at the microscopic level are largely time-symmetric – they don’t care about the direction of time. Yet the second law of thermodynamics introduces an arrow: entropy (disorder) tends to increase with time in an isolated system. This thermodynamic arrow of time aligns with our psychological arrow (we remember the past, not the future) and the cosmological arrow (the universe expands and cools from an ordered Big Bang state to higher entropy states). An unsolved puzzle is explaining why the early universe had such a low entropy – essentially an extremely special initial condition – which allowed a sensible arrow of time to develop. We will delve into how entropy and cosmology set the arrow of time, and whether the arrow is fundamental or emergent from probabilistic considerations.

Finally, we confront the question of time’s origin: did time begin at the Big Bang? If so, what does it mean to talk about “before” the Big Bang? Several theoretical proposals suggest our Big Bang may not have been the absolute beginning. Stephen Hawking famously argued (in the context of the no-boundary proposal) that asking what happened before the Big Bang is like asking what’s north of the North Pole – it’s not a defined question. In the Hartle–Hawking model, the universe’s earliest “time” behaves more like a space dimension (with “imaginary time”), smoothing out the origin so there is no boundary in time. Other ideas include cyclic models like Penrose’s Conformal Cyclic Cosmology (where time is infinite and the end of one universe becomes the beginning of another in a rescaled sense), or bounce cosmologies (where a previous contracting universe collapsed and then bounced into expansion, avoiding a singular start), and string cosmology scenarios of a pre-Big Bang phase. These models raise profound issues: Is time fundamental, existing without beginning, or can time “switch on” as an emergent phenomenon after something like a quantum gravitational transition? We will review these ideas and the critiques surrounding them (including the feedback from the previous thesis and peer review on the “timeless before the Big Bang” question), building on them to develop a deeper understanding in this work.

In summary, this introduction has outlined the multifaceted concept of time across classical physics, relativity, quantum mechanics, and cosmology. In the sections that follow, we develop a comprehensive discussion of each of these domains, then synthesize insights to address the core questions: What is time? Where did it come from? And why does it tick uniformly for all observers?

Background

Philosophical and Classical Foundations of Time

Debate about the nature of time long predates modern physics. Philosophically, two broad viewpoints emerged: absolute time versus relational time. Newton’s quote above represents the absolute time view – time exists as an entity in itself, flowing uniformly regardless of the presence or happenings of material objects. In contrast, thinkers like Gottfried Leibniz and later Ernst Mach argued for a relational concept of time: time has no meaning except as the order of events and changes; it does not exist as a thing on its own. Leibniz suggested that saying “time passes” without things changing is meaningless – time is essentially a measure of change or sequence. Mach in the 19th century criticized Newton’s absolute space and time, positing that time might be defined only by the relation of events and the interval measured by actual clocks.

Classical physics (pre-1900) largely took the Newtonian paradigm for granted: time $t$ was a universal parameter in all equations (such as $F=ma$ or Maxwell’s electrodynamics), and it was assumed one could synchronize clocks in principle across the universe to a single master clock. All observers, regardless of their state of motion, would agree on the intervals between events (after accounting for signal delays). This absolute and universal time was considered self-evident; as Newton wrote, it flows equably for all and “without relation to anything external”.

The absoluteness of time also implied a clear distinction between past, present, and future that was the same everywhere – a universal present moment slicing across all of space. Philosophers call this an A-theory of time (where the “now” has objective reality and time flows), as opposed to a B-theory (where only a network of relations “earlier than/later than” exists and the flow is subjective). Newton’s view was an A-theory with an absolute now. This started to be questioned even before Einstein: for example, the development of electromagnetism and the inability to detect absolute motion (as in the Michelson–Morley experiment) hinted that perhaps nature did not provide an absolute rest frame or a preferred time. But it was Einstein’s special relativity that decisively overthrew absolute time.

Time in Special Relativity: Relativity of Simultaneity and Proper Time

Einstein’s 1905 postulates – that the laws of physics are the same for all inertial observers and that the speed of light is constant in all inertial frames – lead inexorably to the conclusion that time is not absolute. Different observers have their own measures of time, related by the Lorentz transformations. A key result is the relativity of simultaneity: two events that are simultaneous in one frame (say, two flashes of light seen at the same moment by one observer) will in general occur at different times in another frame moving relative to the first. There is no objective, frame-independent meaning to “simultaneous distant events” once you relinquish absolute time. This demolished the idea of a single universal present – each observer carries their own clock and frame, and what one calls “now” may be in another’s past or future in relativity.

Time dilation is another hallmark of special relativity. A moving clock runs slower as seen from the rest frame of a stationary observer: if a clock moves at speed $v$, an interval $\Delta t_{\text{moving}}$ measured by that moving clock will correspond to a longer interval $\Delta t_{\text{stationary}} = \gamma \Delta t_{\text{moving}}$ in the stationary frame, where $\gamma = 1/\sqrt{1-v^2/c^2}$ is the Lorentz factor. This has been confirmed by many experiments, from muon decay in the atmosphere to atomic clocks flown on airplanes. Notably, in 1971 the Hafele–Keating experiment flew cesium-beam clocks around the world on commercial jets and compared them to a reference clock on the ground. The eastward-flying clock (speeding in the direction of Earth’s rotation) lost time (ticked slower relative to ground) and the westward-flying clock gained time, by amounts consistent with the predictions of special and general relativity combined. All these tests support the view that time is not absolute. However – and this is crucial – each clock, in its own rest frame, ticks at its normal rate. No matter how fast Alice is moving relative to Bob, Alice always perceives her own clock to tick normally, one second per second. It is Bob who will observe Alice’s clock ticking slow. Likewise, Alice sees Bob’s clock as slow if Bob is moving relative to her. There is symmetry in relative motion. So the notion of proper time is introduced: the proper time along an object’s worldline is the time measured by a clock traveling with that object. Proper time is an invariant in relativity – all observers will agree on the amount of proper time accumulated along a specific worldline between two events (though they coordinate it differently). Mathematically, if an object travels between two events in spacetime, the proper time $\tau$ is given by $\Delta \tau = \int \sqrt{1-\frac{v^2(t)}{c^2}},dt$ (for a piecewise inertial path) or more generally $\Delta \tau = \int \sqrt{g_{μν} dx^μ dx^ν}$ in covariant terms. Proper time is the physically meaningful time for that object – e.g. how much an astronaut ages during a journey. This is why we sometimes hear that “time flows differently for different observers,” yet each observer finds their own flow of time to be uniform. We will later dissect the statement that “time ticks uniformly for all observers” in light of this.

Minkowski’s formulation of spacetime gives a nice unification. Events are points in 4D spacetime; the separation between two events has a spacetime interval $ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2$ (in flat spacetime). For timelike separations (those that a clock can travel through), the proper time is this interval ($d\tau^2 = ds^2/c^2$). All inertial observers agree on $ds^2$ even if they slice it into space and time differently. This invariant interval is the same for all (it’s the Lorentzian analog of distance). Thus, special relativity doesn’t say “anything goes” for time; it imposes a new structure where the division between space and time depends on the observer, but the spacetime structure as a whole is absolute. We lose absolute time but gain an absolute spacetime.

Time in General Relativity: Dynamical and Gravitational Time

General relativity (GR) extends relativity to accelerated frames and incorporates gravity as curvature of spacetime. In GR, there is still no global preferred time coordinate – any coordinate time is just a label, and only invariantly defined quantities (like proper time along worldlines or the spacetime interval) carry physical meaning. However, GR introduces new ways that time can behave: through gravitational time dilation and the possibility of globally different time flows in different parts of spacetime.

Clocks located in a strong gravitational field run slow relative to clocks in a weaker field (as compared by a distant observer). For example, a clock on the surface of Earth (deeper in Earth’s gravitational well) will tick slightly more slowly than a clock on a high mountain or in orbit. This was first confirmed by the Pound–Rebka experiment measuring gravitational redshift of gamma rays in 1960, and later directly by flying clocks and even by comparing identical atomic clocks at different heights (NIST scientists showed time dilation for a height difference of just 33 cm!). In GR, this happens because what we call “time” is tied up with the geometry of spacetime, and gravity warps that geometry. In the Schwarzschild metric for a non-rotating mass like Earth, the time component of the metric is $g_{tt} = -(1-2GM/rc^2)$, which means $d\tau = \sqrt{1- \frac{2GM}{rc^2}},dt$ for a clock at rest at radius $r$. Closer to Earth (smaller $r$), the factor is smaller, so $\tau$ (proper time) accumulates more slowly relative to the far-away coordinate time $t$. As $r$ approaches the Schwarzschild radius ($2GM/c^2$), time dilation becomes extreme (time essentially “stands still” at the horizon from the external viewpoint). This leads to the dramatic effects near black holes (gravitational redshift and time slowing) often popularized in science fiction.

Despite these differences, a central principle of GR is the equivalence principle: locally (in a small region of spacetime), the laws of physics reduce to those of special relativity. An observer in free fall feels no gravity and their local clock ticks at a normal rate. They can use their wristwatch to measure proper time and it will be uniform for them. When we compare clocks between different locations or states of motion, we see differences in rates, but each clock in its own rest frame is as good as any other, with time flowing uniformly. This is an important clarification to the statement “time passes at a fixed rate for all observers: one second per second”. Locally, all observers agree that their own proper time advances uniformly. Globally, observers may not agree on the rate of each other’s clocks due to relative motion or gravitational differences – but relativity provides equations to relate these rates (via Lorentz factors or gravitational potentials).

Another feature of time in GR is that it becomes intertwined with the structure and evolution of the universe in cosmology. In the standard Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology, one can define a universal cosmic time coordinate $t$ because the universe is assumed homogeneous and isotropic. This $t$ essentially measures the proper time since the Big Bang for an observer who sees the universe as isotropic (a comoving observer). All such observers (at rest with respect to the expanding space and not moving peculiarly) will share the same $t=0$ at the singular Big Bang and age similarly as the universe expands. This is a convenient choice – it essentially uses the large-scale structure as a reference frame (defined by the Cosmic Microwave Background rest frame). Cosmic time flows uniformly for all comoving observers by symmetry. However, cosmic time would not be agreed upon by, say, a fast-moving galaxy or any observer moving relative to the Hubble flow. Those have their own proper time which would not align with cosmic $t$. Nonetheless, the concept of cosmic time is powerful: we say the universe is ~13.8 billion years old meaning about $13.8\times10^9$ years have passed for a clock that has been at rest relative to the expansion (since shortly after the Big Bang). Cosmic time gives an approximate absolute scale to the history of the universe, even though underlying GR says no single time coordinate is privileged unless we impose the cosmological principle to select it.

It’s worth noting that general relativity permits solutions that play havoc with time globally – for instance, solutions with closed timelike curves (CTCs) where time loops back on itself (as in the Gödel rotating universe solution, or certain wormhole and warp-drive spacetime solutions). These are exotic and thought to be unphysical (or ruled out by chronology protection conjectures), but they illustrate that in Einstein’s theory time need not be globally monotonic; the theory itself doesn’t forbid time travel loops except possibly by quantum gravity corrections. In standard cosmology and everyday conditions, we don’t encounter these pathologies.

Figure: Representation of how mass curves spacetime, affecting the flow of time. In Einstein’s general relativity, the presence of Earth (mass) warps the spacetime grid. Straight lines of space and time are bent by gravity, so clocks deeper in the gravitational well (closer to Earth) run slightly slower relative to clocks farther away. This visualization underscores that time is not absolute but influenced by gravity’s curvature of spacetime.

In summary, the classical and relativistic background teaches us that time went from being absolute and universal in Newtonian physics to being flexible, observer-dependent, and part of a dynamic spacetime in Einstein’s theories. Still, the notion of proper time provides a handle on why every observer perceives their own time to march uniformly – because by definition their clock measures the maximal proper time along their worldline, setting their experienced rate of one second per second. With this background in place, we now turn to time’s role in quantum theory, where a new set of conceptual challenges emerges.

Time in Quantum Mechanics and Quantum Field Theory

Quantum physics introduced a revolution in how we understand physical quantities, but it left the concept of time almost untouched in its core formalisms – with some intriguing caveats. In this section, we examine how time is treated in quantum mechanics (QM), quantum field theory (QFT), and the subtle interplay between time and measurement at microscopic scales.

Time as a Parameter in Schrödinger Mechanics

In non-relativistic quantum mechanics (the Schrödinger/Heisenberg formulation), time is an external classical parameter. The primary equation, the Schrödinger equation, $i\hbar \frac{\partial}{\partial t}\Psi(x,t) = \hat H \Psi(x,t)$, explicitly uses time $t$ as a continuous variable that parametrizes the evolution of the wavefunction. The state of a quantum system $|\psi(t)\rangle$ lives in a timeless Hilbert space; time enters only through the evolution $|\psi(t)\rangle = e^{-i\hat H t/\hbar}|\psi(0)\rangle$. Unlike position $\hat{x}$ or momentum $\hat{p}$, there is no Hermitian operator $\hat{t}$ in conventional quantum mechanics whose eigenvalues correspond to time readings. In essence, quantum theory borrows the concept of time from classical physics, treating it as a backdrop. This was pointed out early in quantum theory’s development and formalized by Wolfgang Pauli in what’s known as Pauli’s theorem: one cannot have a self-adjoint time operator conjugate to the Hamiltonian if the Hamiltonian spectrum is bounded below (like it is for energy, which has a ground state). If $\hat{T}$ were a time operator conjugate to energy ($[\hat{H},\hat{T}] = i\hbar$), then $\hat{H}$ would have to be unbounded both above and below (just as momentum being conjugate to position implies momentum’s spectrum runs from $-\infty$ to $\infty$). But physically energy is bounded below, so no such $\hat{T}$ exists in the usual sense. Thus time remains a c-number (a classical parameter) in ordinary quantum mechanics.

This approach is entirely adequate for laboratory-scale quantum experiments. One always has an external clock (ultimately provided by some macroscopic device, or the experimentalist’s wristwatch) to time the evolution of quantum systems. We prepare a state, let time $t$ elapse, then measure – all the while $t$ was a classical parameter under our control. In that sense, time in QM is much like in Newtonian physics: absolute and universal, not subject to quantum uncertainty or observer-dependence. However, this raises a concern when we consider combining quantum mechanics with relativity or gravity: if time is classical and absolute in QM but dynamical in GR, we have a conceptual mismatch.

Another interesting feature appears when considering energy–time uncertainty. There is a relation often written as $\Delta E,\Delta t \gtrsim \hbar/2$, analogous to the Heisenberg uncertainty relations for, say, position and momentum. But $\Delta t$ here is not the uncertainty of a time operator (since we have none); rather it can be interpreted as the timescale over which a system’s energy $E$ can change by amount $\Delta E$, or the duration for which one must observe a system to discern an energy to accuracy $\Delta E$. Formally, one can derive an energy-time uncertainty relation from the fact that the Hamiltonian is the generator of time translations. If a system is in a state that is a superposition of energy eigenstates, then its energy uncertainty $\Delta E$ relates to how rapidly the state’s phase evolves in time, giving a timescale for noticeable change. The absence of a time operator means this uncertainty relation has a different status from, say, $\Delta x,\Delta p$, but it still prevents one from having arbitrary precision in energy for a process happening in a finite time interval.

It’s also worth noting that in certain quantum measurements, “time of arrival” or “tunneling time” become operationally defined quantities. For instance, how long does a particle take to tunnel through a barrier? These questions can sometimes be addressed by constructing specific experimental setups (clocks coupled to the particle, or Larmor clock using spins, etc.), but there is no unique, universal definition of such times in quantum theory. These remain areas of subtlety and even controversy in quantum foundations.

Proper Time in Relativistic Quantum Mechanics and QFT

When extending quantum mechanics to be consistent with special relativity, one is led to quantum field theory. In QFT, we typically describe particles and fields in a way that is Lorentz invariant – roughly speaking, time and space indices are treated on similar footing in equations. The field $\phi(x,t)$ evolves in time $t$, but one often reformulates things in a covariant way so that time is just one coordinate in Minkowski space. Still, the standard formulation of QFT (the canonical formulation) involves quantizing fields at a given time and then evolving them. Time remains the parameter labelling the progression of the Heisenberg-picture field operators $\phi(x,t)$ or of states $|\Psi(t)\rangle$ in the Schrödinger picture. So even in QFT, one usually does not promote the coordinate $t$ to an operator.

However, one might ask: if space coordinates $x$ are like operators (in the sense that position of a particle is an observable), why isn’t time like that? One answer is: because in relativity, time is intertwined with energy (via $E=mc^2$ etc.), and since energy is the generator of time translations, having a time operator would duplicate that role. Another perspective: In relativistic quantum mechanics (as opposed to field theory), attempts were made to parameterize particle worldlines with a proper time parameter and treat $x^\mu(\tau)$ as operators. The Stueckelberg approach and others considered an invariant evolution parameter, which can lead to a notion of a “time operator” conjugate to the Hamiltonian under certain formalisms. In some advanced relativistic quantum frameworks (like certain approaches to quantum gravity or string theory), something akin to time might appear as an operator-like entity. For example, in string theory, one treats the string’s embedding in spacetime $X^\mu(\sigma,\tau)$ as dynamical variables, including $X^0$ which is essentially the time coordinate of string’s worldsheet. In that context, $X^0$ (time) is indeed an operator on the string’s Hilbert space, albeit that Hilbert space is for the string’s worldsheet theory, not a operator acting in the target spacetime of the string theory. This can be confusing: it means in the string’s 2D worldsheet CFT, the coordinate corresponding to spacetime time is like a field. But in the end, when interpreting physically, one still ends up with a picture of particles or fields moving in a classical spacetime with time as the background parameter.

Ethan Siegel, in the article discussing a “timeless” universe before the Big Bang, alluded that when we go to fully relativistic quantum theories, time “gets promoted to an operator”. This phrasing needs careful unpacking. In standard quantum field theories (like the Standard Model of particle physics), time is not literally an operator – it is part of the coordinate set. However, the treatment of time in relativistic quantum formalism becomes subtler: for example, in the Hamiltonian constraint approach of general relativity (the Wheeler–DeWitt equation), we get $H|\Psi\rangle = 0$, which is like saying the Hamiltonian (energy) acting on the “wavefunction of the universe” yields zero – an equation with no explicit time, suggestive of a timeless state. So in quantum gravity contexts, one often has to “find” time as an emergent parameter. We will talk more about that soon.

In summary, conventional QFT still respects a form of the relativity principle by treating time and space in a unified way in the equations, but operationally it requires a time coordinate to define and interpret dynamics. Some proposals in beyond-standard physics propose that spacetime coordinates might become non-commutative operators at high energies (for instance, in certain quantum gravity or Planck-scale models, $[ \hat{t}, \hat{x} ] \neq 0$ could be imagined, meaning a fundamental limit to how precisely one can define a time coordinate at very small scales). Such ideas remain speculative.

The Problem of Time in Quantum Gravity

Perhaps the deepest issue with time arises when we try to quantize gravity itself. In canonical quantum gravity (the Dirac–ADM formalism leading to the Wheeler–DeWitt equation), we treat the 3-geometry of space as a configuration variable and write a wave functional $\Psi[\text{geometry}, \text{fields}]$. The Wheeler–DeWitt equation, in simple form, is $\mathcal{H}\Psi = 0$, where $\mathcal{H}$ is the Hamiltonian constraint. This equation notably does not contain an $i\hbar \partial/\partial t$ term – because in GR, time is just a coordinate choice, and the true physical statements are those like $\mathcal{H}=0$. As a result, the equation looks like a stationary Schrödinger equation $\hat{H}\Psi = 0$, not a time-evolution equation. Julian Barbour and others have latched onto this to argue that fundamentally the universe is timeless – change is an illusion emerging from correlations between different parts of a static wavefunction. More formally, the problem of time in quantum gravity is that the “time” we experience might have to be identified with an internal degree of freedom or a clock made out of fields, since there is no external time parameter in the Wheeler–DeWitt framework.

Various strategies exist to address this. One approach is the emergent time idea: even if the fundamental equations are timeless, in suitable semi-classical limits one can recover an approximate time parameter. For instance, if the universe is large and classical in some degrees of freedom (like the scale factor of the universe), one can use that as a clock to parametrize other quantum variables – this is analogous to a WKB approximation where one part of the wavefunction oscillates rapidly and can serve as a time variable for the rest. This is seen in some formulations of quantum cosmology, where one splits the wavefunction into “heavy” (background) and “light” (perturbation) parts; the heavy part’s phase can act as a clock. Another approach is relational time: choose one observable (like the reading of some physical clock variable) and define time by it, then see how other observables change with respect to that clock. Carlo Rovelli, for example, champions a “thermal time hypothesis” in some contexts and generally a relational viewpoint: time is not fundamental; it’s a reflection of how we describe correlations in the universe.

Specific quantum gravity approaches offer different insights:

• Loop Quantum Gravity (LQG): LQG does not assume a background time; it builds spacetime from spin networks and loops. In LQG, spatial geometry is quantized, and time as an external parameter is absent in the fundamental equations. Instead, one might speak of the discrete steps in spin network evolution, or use a matter reference field to define time. Rovelli in his popular writing suggests that time as we perceive it is an emergent phenomenon from the thermodynamics of quantum gravity – essentially that at fundamental level, there is no continuous flowing time, but when many degrees of freedom entangle and behave collectively, an approximate time emerges (related to entropy increase or correlation). LQG in the cosmology context yields the Big Bounce scenario, where the classical Big Bang singularity is resolved and time can be extended through the bounce. Yet even there, what “time” means inside the quantum region is subtle – in one sense, the quantum difference equations can be stepped through something like a time iteration, but that “internal time” might be given by something like the volume of the universe (which decreases to a minimum then increases).
• Causal Dynamical Triangulations (CDT): CDT is a lattice approach to quantum gravity that, interestingly, does use a notion of time in its setup. CDT builds a spacetime from small simplex building blocks, with a fixed causal structure that distinguishes timelike and spacelike directions. In CDT simulations, one enforces a global proper time slicing – essentially putting the triangulation in layers labeled by an integer time step. This makes the path integral manageable and maintains causality. The surprising result from CDT is that a classical 4D spacetime (with one time and three space dimensions) emerges at large scales from the sum over quantum geometries. In effect, CDT suggests that if you include a notion of time causality at the fundamental level, you end up with an emergent extended time dimension macroscopically. However, there have been recent developments exploring CDT without a preferred foliation. The key takeaway is that CDT, by “treating time as an emergent concept” while still having an ordering of slices, tries to solve the problem of time by a kind of compromise: it gives time a skeleton to hang onto (the foliation), but the geometry of each slice and how slices glue can fluctuate quantum mechanically. CDT demonstrates how critical the notion of time is even in quantum gravity – getting rid of time altogether makes the theory hard to connect to our experience, whereas keeping too rigid a notion of time might prevent true quantum behavior. The success of CDT in producing a sensible universe (with an emergent de Sitter-like geometry) is an encouraging sign that causality and time might survive quantization in some form.
• Holography (AdS/CFT): The AdS/CFT correspondence posits an equivalence between a quantum gravity in an Anti-de Sitter (AdS) spacetime (with time and a radial dimension etc.) and a conformal field theory (CFT) living on the boundary of that spacetime. In this duality, the boundary theory has a time coordinate (since it’s a normal field theory in one lower dimension, often including time), and this time is essentially the same as the time coordinate in the AdS bulk (at least in standard setups). Thus, in AdS/CFT, time is not really eliminated or emergent; it’s shared. One could say the holographic principle hints that spacetime geometry is emergent from quantum degrees of freedom (like the entanglement structure of the dual CFT might encode the spatial geometry of the bulk), but the presence of a time dimension in both pictures means the flow of time and causality is preserved in the emergence. This ensures that unitarity (conservation of quantum information over time) in the boundary theory translates to causally well-behaved evolution in the bulk theory. Some researchers have speculated whether space might be emergent but time fundamental, or vice-versa. Holography so far suggests space is more readily emergent (e.g., “it from qubit” ideas where spatial connectivity relates to entanglement), while time might remain as a fundamental parameter needed for quantum evolution. That said, certain cosmological holographic scenarios (like dS/CFT for de Sitter space) struggle with defining time properly, since de Sitter space doesn’t have a time-like boundary in the same way AdS does. Those frontiers remain unsettled.

In all approaches, a common puzzle is: if time emerges from a fundamentally timeless theory, how do we recover the impressions of flowing time and the fact that we can synchronize events, etc.? Some argue that any consistent theory will have to give us an effective time in the classical limit, because that’s what we observe. But whether that time is an approximation or an exact, fundamental entity is unknown. Our best guide so far are experiments and observations: to date, we have not seen any deviations from standard time behavior – no periodic variations in fundamental constants that would hint time is discrete or cycling, no violations of Lorentz symmetry that would hint at a preferred rest frame or time. If time is emergent, it is remarkably robust and featureless at scales we can probe.

In conclusion of this section: quantum theory in its conventional form still leans on classical time, and marrying it with dynamic spacetime of GR leads to conceptual tensions. Various quantum gravity proposals offer different resolutions, from eliminating time at the fundamental level and having it emerge from correlations, to retaining a vestige of time in the formalism to keep causality manifest. This is very much an open area of research. As physicist Lee Smolin said, “Newton’s time was replaced by Einstein’s time, and now Einstein’s time must give way to a deeper concept” – we are still searching for that deeper concept of time that will seamlessly integrate quantum mechanics with gravity.

The Arrow of Time, Entropy, and the Emergence of Time’s Passage

In our everyday experience, time passes or flows in one direction: we remember the past but not the future, causes precede effects, we grow older not younger. This is the arrow of time – the directional asymmetry between past and future. Yet if one examines most fundamental physical laws (Newtonian mechanics, Maxwell’s equations, Schrödinger’s equation, Einstein’s field equations without special conditions), they are time-symmetric or nearly so. That is, the equations usually remain valid if one replaces $t$ by $-t$ (along with flipping magnetic fields in Maxwell or taking complex conjugates in quantum mechanics to account for time-reversal symmetry properly). Where, then, does time’s arrow come from?

Thermodynamic and Cosmological Arrow

The explanation currently accepted by the physics community traces the arrow of time to the second law of thermodynamics and, ultimately, to cosmology. The second law states that for an isolated system, entropy ($S$), which measures the system’s microscopic disorder or the number of accessible microstates, tends not to decrease; it either increases or stays constant (in an ideal reversible process). So as time moves forward, entropy increases (or stays the same) – this gives a direction to time: the direction of increasing entropy is what we call “future.” Indeed, “entropy is one of the few quantities in the physical sciences that require a particular direction for time, sometimes called an arrow of time”. An equivalent statement is that moving “forward” in time is the direction in which the second law holds, i.e. entropy of a closed system increases or at least doesn’t decrease.

This arrow of time is apparent in daily life: a cup of hot coffee left in a cool room will equilibrate (heat flows from hot to cold; the coffee cools down, entropy increases). But you’ll never see the reverse by itself (cold coffee spontaneously heating up while cooling the room, which would decrease entropy). Similarly, we can scramble an egg (increase entropy) but not unscramble it (which would require a conspiracy of molecules to decrease entropy). The underlying mechanical laws (molecular collisions etc.) are time-symmetric – they would allow an unscrambled egg solution, but that solution is absurdly carefully organized and essentially never occurs in practice because it represents a state of vastly lower probability given random interactions.

The deep question is why the universe (or any system) was ever in a low entropy state to begin with, so that there is room for entropy to increase. If the universe were in maximum entropy equilibrium from the start, everything would be static (in a state of heat death) and no arrow of time would be evident – every process would be thermodynamically reversible or static. The universe’s initial conditions thus hold the key. The universe began in a state of extraordinarily low entropy: imagine the entire observable universe’s matter and radiation squeezed into a hot, dense fireball (the Big Bang) – one might think that’s a high entropy state (very disordered gas), but compared to what it could be, it was highly ordered. In particular, the distribution of mass-energy was extremely uniform and gravity had not clumped matter into black holes or other high-entropy gravitating structures; also, there were strong constraints like no “white holes” (time-reversed black holes) or other acausal arrangements. Roger Penrose famously estimated the entropy of the primordial universe as ridiculously low compared to its maximum possible entropy (which would be dominated by huge black holes, etc.). This low entropy past means there was a huge entropy gradient available – entropy could increase by a colossal factor as the universe evolved. That is exactly what’s happened over the last 13.8 billion years: stars formed, burned nuclear fuel (increasing entropy), light from hot objects streamed into the cold void of space (increasing entropy by thermalizing energy), life on Earth and all processes are effectively part of this grand increase of entropy (Earth radiating waste heat to the 3K cold sky is an entropy-increasing process that enables local pockets of order to form temporarily).

The cosmological arrow of time is thus the fact that the universe is expanding and cooling from an initial hot Big Bang. This expansion provides a sense of direction: earlier times were hotter, denser, and lower entropy (for the overall universe), later times are cooler, more expanded, and higher entropy. Notably, if the universe ever were to recollapse in a “Big Crunch,” one might wonder if entropy would decrease during that phase (as some 20th-century cosmologists pondered). Hawking once thought that if the universe eventually stopped expanding and started contracting, the arrow of time might reverse (so entropy would decrease toward the crunch). He later retracted that after further analysis (and input from other physicists like Don Page), concluding that entropy would likely continue to increase even in a contracting phase unless some very exotic condition caused a time-reversal in physical laws. Thus, in all conventional scenarios, as long as the universe’s dynamics proceed from that special low-entropy Big Bang to higher entropy states, the arrow of time is well-defined and aligned with expansion.

We can summarize: The arrow of time exists because the past was highly ordered (low entropy) and the future is more disordered (high entropy). The flow of time we perceive – the fact that we can remember yesterday (a lower entropy state) but not tomorrow – is a consequence of this thermodynamic gradient. Our memories are records, which are low-entropy correlations imprinted by past conditions. One cannot record future events that haven’t happened because that would require decreasing entropy to “store” that information beforehand. Every memory or record formation increases entropy (for instance, writing data to a hard drive dissipates heat; the process is thermodynamically irreversible in a small way). Thus we remember the direction of time in which entropy was lower.

It is often said that time’s arrow is a `macroscopic’ phenomenon, not visible in fundamental equations except through the choice of initial conditions. In the micro world, processes are (mostly) reversible. Indeed, if one were shown a video of two fundamental particles scattering (assuming no weak-interaction violation for now), one couldn’t tell if it was being played forward or backward – both obey the laws of physics. But if one is shown an egg splatting on the floor, one immediately knows the direction; the time-reversed motion (egg reassembling) is essentially impossible given statistical mechanics. Arrow-of-time issues also come in quantum mechanics in subtle ways: the measurement process in QM is often treated as an irreversible process (wavefunction collapse or decoherence produces effectively classical irreversibility). The Schrödinger equation itself is time-symmetric (aside from that complex conjugation nuance which leads to the concept of T-symmetry in quantum theory). However, when we include the environment and decoherence, we see an emergent irreversibility because once a quantum system becomes entangled with many environmental degrees of freedom, effectively information is diluted and entropy increases (from the perspective of a subsystem). Thus, quantum decoherence explains why macroscopic superpositions “collapse” and yields an arrow consistent with thermodynamics – effectively the measuring apparatus and environment pick up a record of the outcome (increase in entropy), making the process irreversible.

One could ask: could the arrow of time be an illusion, and all moments of time exist equally (the so-called “block universe” view, often associated with the B-theory or with relativity’s four-dimensionalism)? In the block universe, past and future are just different directions in the 4D spacetime, and the flow of time or its arrow is not fundamental but rather a feature of how entropy and our consciousness work within that spacetime. Many physicists and philosophers subscribe to this: they say the laws of physics themselves don’t distinguish past and future (except in a few subtle cases like the weak interaction, which we’ll mention), so the arrow is emergent from initial conditions and not a basic law. In other words, the universe as a whole might be best described timelessly (as in some equations of quantum gravity), with the arrow coming out when we choose one solution of those equations that has an entropy gradient.

Time-Reversal Symmetry and its Breaking

It should be mentioned that not all fundamental laws are perfectly time-symmetric. In particular, in particle physics, the weak nuclear force (responsible for certain decays) violates a symmetry called CP (charge-parity) symmetry. By the CPT theorem of quantum field theory, any CP violation implies T (time-reversal) violation as well (because CPT as a whole is conserved in local quantum field theory). Indeed, experiments have observed direct T-violation: for example, in the neutral kaon and B-meson systems, there are processes whose time-reversed counterparts occur at different rates. This is a microscopic arrow of time of sorts – though it’s very slight and has nothing to do with the large-scale thermodynamic arrow. The observed T-violation in weak interactions is a tiny effect and doesn’t accumulate to produce macroscopic reversals; it’s more like a subtle imbalance between matter and antimatter behavior that might help explain why there’s more matter than antimatter in the universe. Aside from such intricacies, all other forces (electromagnetism, gravity, strong force) are, as far as we know, symmetric under time reversal (with appropriate adjustments). Hence, aside from the small CP-violating sectors, the fundamental equations don’t care about an arrow.

Therefore, the arrow of time in everyday terms is not coming from fundamental dynamics but from initial conditions and statistical behavior. One can encapsulate this by saying: the universe started in a low-entropy state and is headed toward higher entropy states; that’s why there is a past and a future and why we perceive time as flowing. Boltzmann, Loschmidt, and others in the late 19th century debated this. Boltzmann’s H-theorem tried to derive the second law from mechanics, but Loschmidt pointed out that if mechanics is reversible, for any trajectory that goes from low to high entropy, there’s a time-reversed trajectory from high to low – so how can irreversibility arise? The resolution is that if one assumes a random initial condition with low entropy, overwhelmingly the trajectories will have entropy increase in one direction (forward) and that same direction will correspond to what we call future. The other solution (entropy increasing toward the past) corresponds to a universe that was high entropy in the future and lower entropy in the past – essentially a crazy initial condition if we consider past to be the Big Bang and future to be now. We simply have to postulate (or explain via a deeper theory) that the Big Bang was in a special state of low entropy. This assumption is sometimes called the Past Hypothesis in philosophy of physics (a hypothesis that the universe started in a special low entropy state). It is somewhat unsatisfying because it begs the question: why was it low entropy? That’s a cosmological question possibly tied to inflation or other processes.

Modern cosmology adds some pieces to this puzzle: cosmic inflation (the accelerated expansion in the very early universe) is often invoked to explain why the universe was so spatially uniform and low entropy initially. By rapidly blowing up quantum fluctuations, inflation creates a vast, smooth space with tiny perturbations – a setup for stars and galaxies to eventually form, but also one that is far from thermal equilibrium (thus low entropy compared to what it could be if everything collapsed into black holes immediately). Some have argued inflation itself needs a low entropy to start, so it might not solve the arrow problem completely, but it shifts it: maybe the inflaton field’s initial state was simple (like a local vacuum state) which is low entropy.

If we consider far future, entropy will eventually max out when all available free energy is used up. Stars burn out, matter might ultimately decay or fall into black holes, black holes themselves evaporate (very slowly) increasing entropy tremendously, and one ends up with thin gas of particles at uniform temperature – the “heat death” of the universe. In such a state, if reached, the arrow of time would effectively end because no further macro changes would happen. That’s billions of years away at least (trillions for black hole evaporation, etc.), so currently we are safely in an entropy-increasing regime.

Is Time Fundamental or Emergent?

A deep question related to the arrow is whether the flow of time (the feeling that time passes) is something fundamental or a feature of emergent thermodynamics or consciousness. Many physicists suspect that flow is subjective – in the equations, time simply is, not flows. We can parametrize the worldline, but nothing in Newton’s or Einstein’s equations explicitly says “time flows at 1 second per second”; that’s a tautology. So some argue that the passage of time is an emergent illusion – each moment exists, and the sensation of flow comes from memory and causation structures in our brain (which are thermodynamically constrained). Carlo Rovelli in The Order of Time makes such arguments: that our common time variables (like temperature time, biological time, etc.) emerge from statistical mechanics, and fundamentally time might not exist in the way we think. If one takes the block universe view, then past and future are equally “there” in the 4D spacetime, and our consciousness moves or rather is located at different slices and experiences them in sequence because of entropy and memory. In this view, talking about “now” objectively is like talking about “here” – it’s perspective-dependent.

On the other hand, some philosophers and physicists (especially those in the camp of relational or process philosophy) think time or something like becoming is fundamental and not just emergent. They’d say the flow is real and maybe our theories need to account for it. This borders on metaphysics, but it informs how we search for a new theory: whether to include time (or an arrow) into the axioms or get it out as a consequence.

One potential physical handle on “is time emergent?” is to ask: are there scenarios where time could change or vary? For example, do the fundamental “constants” (like speed of light, or coupling constants) vary in time? We have looked – so far, no convincing evidence of variation over cosmological time has been found (there were some claims of slight variations in the fine-structure constant, but they are unconfirmed). If time were emergent, could it have fluctuations? Perhaps on the tiniest scales, time might not be smooth; it might come in quanta or something. There have been proposals that time could be discrete with a very tiny quantum (the Planck time ~$5.4\times10^{-44}$ s), but no evidence yet – our best experiments (like those looking at high-energy gamma-ray bursts for dispersion that could hint at a discrete time or space step) haven’t found any deviation from continuous Lorentz symmetry.

In the absence of experimental clues, the status of time (fundamental versus emergent) remains a topic of theoretical taste and interpretation. The prudent stance is that time as a parameter works exceedingly well in all tested regimes, but when we push to the limits (inside black holes, at $t=0$ of the Big Bang, or in a Theory of Everything), we may need a paradigm shift. It could be that time as we know it is an emergent phenomenon from a deeper timeless reality – much like temperature emerges from statistics of atoms, not something fundamental on its own (no single molecule has a temperature, it’s an ensemble property). Some have drawn the analogy that time might be to fundamental reality what temperature is to molecules – a coarse descriptor of something deeper.

To summarize this section: The arrow of time arises from entropy increase and low initial entropy of the universe. It gives a clear direction to “why time seems to flow.” Whether this flow is a fundamental aspect of the universe or an emergent one tied to thermodynamics is still debated. All known physics can be made consistent with a block-universe, time-symmetric underlying picture plus a special initial condition. Yet our experience of time’s passage is fundamental to us, so any “theory of time” ultimately must explain why that experience is so strong and universal. It might turn out that what we call time is an emergent approximation – but even if so, it’s as real to us as, say, a phonon (which is emergent from atomic lattice vibrations, yet can be treated as a real particle in solid-state physics). In the next section, we directly address the question posed: where did time come from, especially regarding the origin of the universe, and was there “no time” before the Big Bang?

The Origin of Time: Did Time Begin? Timelessness Before the Big Bang and Beyond

One of the grandest questions is whether time itself had a beginning. The prevailing Big Bang cosmology implies that our universe (as we know it) expanded from an extremely hot, dense initial state about 13.8 billion years ago. If we trace that timeline back, using classical general relativity, we encounter a singularity – a point of infinite density and curvatures – at $t=0$. In the classical theory, $t=0$ marks the beginning of the universe and the beginning of time; it makes no sense to ask “what happened before?” since $t<0$ isn’t part of the mathematical solution. This led to the common statement (attributed to Stephen Hawking among others) that time itself began at the Big Bang. Hawking quipped that asking what was before the Big Bang is like asking what’s north of the North Pole. In other words, it’s a category error – there is no “before” if time starts with the Big Bang, just as there’s no north once you are at the northernmost point.

However, this conclusion is drawn from general relativity (GR) applied to the ultimate extreme, where it likely breaks down (the singularity). Physicists do not trust GR at times earlier than the Planck time (~$10^{-43}$ s) after the Big Bang, because quantum effects of gravity should become important. Thus, the door is open to possibilities in which time might extend or behave differently around what we call the Big Bang. Here we discuss a few leading ideas: the no-boundary proposal, cyclic or ekpyrotic cosmologies (including Penrose’s CCC), quantum bounce cosmologies (like loop quantum cosmology), and string-inspired pre-Big Bang scenarios. Each offers a different answer to “Where did time come from?” and whether there was a “before.”

No-Boundary Proposal and Imaginary Time

Stephen Hawking and James Hartle proposed the no-boundary proposal (also called the Hartle–Hawking state) in the 1980s. In this idea, the universe can be described by a path integral over compact Euclidean geometries – effectively, the universe is finite but has no boundary in (imaginary) time, the way the Earth’s surface has no edge (no boundary in space, analogous to a 2-sphere). When “analytically continued” back to real time, this suggests that the universe “tunnels” from a timeless Euclidean regime into the normal expanding universe. In Hawking’s picturesque description, the beginning of the universe is like the South Pole: there is no point south of the South Pole; the universe doesn’t have a boundary or initial singular moment – instead, time emerges smoothly from a sort of space-like state. Near the Big Bang, time behaves more like a spatial dimension (it can be treated with imaginary values in the Euclidean solution), removing the singularity. As Wikipedia summarizes: “It proposed that prior to the Planck epoch, the universe had no boundary in space-time; before the Big Bang, time did not exist and the concept of the beginning of the universe is meaningless.”. In the no-boundary view, then, time as we know it effectively “switches on” at the Big Bang, but there isn’t a physical singular moment. There is a rounded-off beginning – a finite though extremely small “Euclidean” region. The phrase “timeless before the Big Bang” can apply here: the concept of time ceases to have its classical meaning before a certain point. Rather than a classical universe with a time coordinate going to negative values, one imagines approaching $t=0$ by turning time into an imaginary parameter – beyond that, there is no time, just a different kind of space. The Hartle–Hawking proposal thus suggests the universe is self-contained: it needs no external time or cause to start because the question is rendered moot. Hawking often stated that asking what came before the Big Bang is like asking who lit the firecracker that caused it – he’d answer that there was no firecracker, no outside agent; the universe is a closed system with no before.

It’s important to note the no-boundary idea comes from uniting quantum mechanics and cosmology – it’s not proven, but it’s an application of quantum principles to the entire universe’s origin. One consequence Hawking once deduced from it (erroneously, as it turned out) was that if the universe recollapsed, time’s arrow might reverse (we mentioned this earlier and how he retracted it). The no-boundary condition was initially formulated for a universe with positive cosmological constant that would re-collapse (a closed universe). With our current universe apparently accelerating (also a de Sitter-like state but expanding forever), the details might differ, but the essence is that time as a concept emerges from a quantum origin rather than extends eternally.

The phrase “imaginary time” often appears in this context. Hawking liked to say that in imaginary (Euclidean) time, the distinction between time and space fades, so the beginning of the universe is just like a smooth South Pole point. Imaginary time is a mathematically convenient trick – by using $\tau = it$, the metric signature flips and the path integrals converge. But some like to philosophize if maybe real time is somehow less fundamental than imaginary time. However, in the end one has to “rotate” back to real time to describe our universe, and in real time, we get a universe that starts expanding from a small size. The timeline of the universe in this picture starts at some minimum scale (not zero size, thus no singularity) and then grows. Before that minimum scale, asking “what was the time?” is like asking what’s earlier than the beginning – there’s no answer because our notion of time doesn’t extend there.

The no-boundary proposal doesn’t imply a “cyclic” or “pre-big-bang” universe; it’s more like a one-off spontaneous creation of time and space.

Cyclic and Ekpyrotic Universes

Alternative to a universe with a unique beginning are cyclic cosmologies, where time is conceived to be endless and the Big Bang is not the absolute beginning but rather a transition. One of the oldest cosmological ideas (dating to Friedmann and Tolman, etc.) is an oscillatory universe: an eternal series of expansions and contractions (big bangs followed by big crunches followed by bangs, etc.). Classic oscillatory models faced issues (like entropy buildup – each cycle would get bigger and longer due to entropy produced in the previous cycle, so it’s not truly periodic, and eventually it either diverges or requires finetuned entropy dilution). Modern versions of cyclic cosmology try to address these issues.

Conformal Cyclic Cosmology (CCC) – proposed by Roger Penrose – is a recent and notable cyclic idea. In CCC, each cosmic aeon (era) starts with a Big Bang and ends in an exponential expansion that, after infinite time, becomes so stretched and dilute that space and time can be rescaled conformally and “matched” to a new Big Bang of a next aeon. Penrose argues that if the universe empties out (all matter decays, black holes evaporate, leaving only massless particles like photons), then technically physics no longer provides any length or time scale (because massless particles don’t have a natural scale – their conformal geometry can be stretched arbitrarily). In such a scenario, one can mathematically identify the infinitely stretched end of one universe with the singular Big Bang of a new universe by a conformal mapping. So time in CCC is continuous in a sense – it goes on forever, but segmented into aeons. The “Big Bang” of each new aeon is the remnant of the remote future of a previous one. Thus there was effectively a “time before the Big Bang” – it was the aeon prior to ours. Penrose even suggested that signals from that previous aeon might be observable in our universe (for instance, as subtle patterns in the CMB caused by black hole collisions in the previous aeon, manifesting as low-variance circles, etc. – these claims are controversial and not widely accepted as confirmed).

In CCC, time is fundamental and infinite; there is no beginning, just transitions. The arrow of time in each aeon is assumed to reset – basically, since the universe reaches a cold, empty, high entropy state at the end of an aeon, and then the new Big Bang is a very low entropy state (almost all free energy again available in radiation form), CCC asserts that effectively the arrow of time “flips” or rather that each aeon’s time is separate and always increasing within that aeon. There is no global time arrow conflict because the physical fields that carry entropy (like massive particles) aren’t carried through the crossover; only conformally invariant structure carries over, and in that sense the entropy “flushes out” or is irrelevant at the crossover.

One could consider a more traditional cyclic universe: e.g., a Big Crunch leads to a Big Bang (like a bounce at high density). The ekpyrotic universe, based on brane collision in string theory (proposed by Steinhardt, Turok, et al.), is one such scenario: two 3-dimensional branes collide in a higher dimensional space; their collision is perceived as a Big Bang, then they separate (universe expands), then a slow contraction phase ensues after a long time, ending in another collision (a new bang), and so on. This provides a potentially cyclic model that doesn’t necessarily suffer from expansion of cycles because the ekpyrotic (from Greek “conflagration”) phase of slow contraction can shed entropy and homogenize the universe before the next bang. These models often have a time before what we call our Big Bang – yes, there was an earlier cycle. Time is again effectively endless in both directions (infinite past, infinite future), although defining a proper “t” that goes through the bounce is tricky if a singularity intervenes. They try to resolve that via new physics at the collision (brane physics or ghost fields, etc.).

The Big Bounce in a more general sense is any scenario where the universe had a contracting phase that reached some minimum size (or maximum density) and then rebounded into the expanding phase we see, instead of a singular beginning. Loop quantum cosmology (LQC), as mentioned earlier, predicts such a bounce due to quantum gravity effects making gravity repulsive at very high densities. In LQC, if one evolves a simple universe model backward in time, instead of $a(t)\to 0$ at some $t=0$, one finds $a(t)$ stops shrinking at some tiny but non-zero value (on the order of Planck length perhaps) and then increases – a bounce occurs. This is achieved because quantum geometry corrections provide an effective pressure that counteracts collapse. So time doesn’t end; it extends through the bounce. There was a “pre-Big-Bang” branch which was large and then contracted. When it was very dense, quantum gravity caused a bounce, yielding our expanding branch. In such models, the Big Bang is replaced by a Big Bounce that is nonsingular. The concept of time is well-defined throughout, except possibly exactly at the bounce where classical coordinates break down but one can patch solutions across. People like Bojowald have derived solutions showing a prior universe could not be identical to our post-bounce one (there’s some “cosmic forgetfulness” – certain parameters get randomized), but generally a time existed before. Some properties might pass through (maybe total volume at turnaround, etc.) but others get “forgotten.”

One might ask: if time is infinite into the past, why is the universe not in heat death already? Typically, cyclic models avoid heat death by resetting entropy or having an infinite phase to dilute it. Penrose’s CCC bypasses the question by basically reusing the cold death state as the low-entropy initial state of the next aeon (via conformal magic, he essentially discards what we normally count as entropy like infinite dilute radiation; in the conformal picture that’s reinterpreted as a new low-entropy start). Other bounce models rely on contraction somehow reducing entropy (which is counterintuitive since one would think contraction increases temperature and entropy). Some versions have a “crunch” that is not adiabatic – e.g., particle annihilation or dumping entropy into degrees of freedom that don’t make it through the bounce. It’s tricky and often such models face scrutiny about the second law.

Empirically, we have little evidence of a pre-Big-Bang phase. We look at the cosmic microwave background (CMB) and its fluctuations – so far they are consistent with inflation after the Big Bang, not clearly with a bounce, but some bounce models can mimic inflation’s predictions or incorporate inflation. There was an interesting result of LQC that some CMB anomalies might be explained by pre-Big-Bang structure imprint, but it’s not conclusive.

String Theory Pre-Big-Bang and Emergent Time Models

String theory, being a candidate fundamental theory, has offered some exotic ideas about the origin of the universe and time. One is the pre-Big-Bang scenario by Gabriele Veneziano and Maurizio Gasperini in the 1990s. In this model, the universe existed in a long quasi-static or slowly expanding dilaton phase in the “pre-big-bang” time, then underwent a super-exponential expansion (different from inflation) as the Big Bang, then rejoined standard cosmology. Essentially, string theory’s duality symmetries allow a cosmological solution where as you go to negative time, the universe was initially cold and empty (in the infinite past), then collapses (or rather, time-reversed expands) and heats up, then transitions into the hot Big Bang expansion. The scale factor behavior is like a mirror: the pre-big-bang branch is a decelerating contraction (in string frame) that leads to a high curvature, then after a high-curvature phase (stringy effects needed there), it emerges as our hot expanding universe. This scenario struggled to match some conditions (like producing a scale-invariant spectrum of fluctuations like inflation does, although there have been tweaks and claims it can produce certain spectra). The important part is it provides a time before the bang, albeit the physics there is not like our current universe – it might be a weakly coupled, empty, cold state.

Another idea from string theory context is the emergent universe from a quasi-static state: e.g., the universe “starts” from an eternal static (or oscillatory) state and then somehow transitions to expansion. There’s a model called the string gas cosmology (Brandenberger and Vafa) where in the early universe near the string scale, time may be just one of many dimensions that aren’t yet distinguished until a phase transition picks out 3 expanding spatial dimensions and 1 time dimension.

In some of these models, time might be more fundamental (string time exists always), or in others time might not be well-defined until after a certain phase.

One of the more radical proposals is that time might emerge from entanglement or some quantum information process. For example, in the AdS/CFT context, there are discussions of how space emerges from entanglement (the ER = EPR conjecture that entangled pairs relate to wormholes, etc.). Time’s emergence is trickier, but some have speculated that in a fully quantum gravity theory, time and space might both be emergent from a more abstract “Hilbert space” structure. This goes into realms like the quantum causal histories or bootstrap and fixed point approaches where one finds an effective time dimension coming out of something timeless.

If time had a beginning, that raises philosophical issues too (not the least, causal ones: can something come from nothing? If there was no time, how did anything start? The no-boundary proposal tries to answer that by using quantum tunneling ideas, but it’s admittedly a mind-bender). If time is eternal, we avoid “something from nothing,” but then we face the question “why is the universe not in a steady state or equilibrium if it’s existed forever?” – cyclic models attempt to answer that by periodic renewal.

Current observational cosmology doesn’t rule out a brief phase before our bang (like some bounce or contraction), but it strongly supports some version of inflation or something like it to explain the uniformity and flatness. Many bounce or cyclic models incorporate inflation or an inflation-like expansion anyway.

To tie back to the previous thesis and its peer review, likely there were discussions about whether it’s valid to call the pre-Big-Bang phase “timeless.” Perhaps one critique is that if time didn’t exist, how could inflation start or how could anything happen? A possible resolution is that during a quantum gravity phase, the concept of time may lose meaning (timeless in the sense of no classical time), but once the universe cools/expands, classical time emerges.

From the perspective of a comoving observer in our current universe, it might be moot whether time existed before – because any extension beyond the Big Bang is not observable (space beyond our horizon or before inflation, etc., leaves at best indirect imprints). But as truth-seekers, we attempt these extensions for consistency.

In summary, the origin of time is still speculative:

• Maybe time truly began with our universe (as in no-boundary). In that case, the universe is finite age and there was no prior time.
• Maybe time is cyclic and what we call the beginning was just the end of something else (CCC, bounce, etc.), making time effectively eternal.
• Maybe time is emergent and before the emergence, asking about “time” is like asking what’s north of the North Pole – it’s not the right category because the question presupposes a time axis that didn’t exist yet.

All these ideas need a consistent theory of quantum gravity to evaluate them, which we don’t yet fully have. Future cosmological observations (like detailed primordial gravitational wave spectra) might hint at new physics that could differentiate a bounce from simple inflation, etc.

What we do know is that within our observable universe, time as we measure it can be traced reliably back to a fraction of a second after the Big Bang (nucleosynthesis, CMB, etc.). Before that, from $10^{-36}$ seconds (inflation epoch) to $10^{-43}$ seconds (Planck scale), we have conjectures but no direct data. That’s the window where “time’s origin” is debated.

“Time Ticks Uniformly for All Observers”: Analysis under Relativity

We now return to a statement that was highlighted in the previous thesis and raised for rigorous attention: “time ticks uniformly for all observers.” This phrasing can be initially perplexing in light of relativity, which teaches that observers in relative motion or different gravitational potentials will measure each other’s clocks ticking at different rates (time dilation). So in what sense can we claim time passes at the “same rate” for everyone? Let’s clarify this with the concept of proper time and the relativity of simultaneity.

In the Ethan Siegel article that inspired this discussion, the intended meaning was: for any given observer, their own clock (which can be any physical process like a heartbeat, a second pendulum, a cesium atomic oscillation) will tick at one second per second, and every other observer will agree on that observer’s self-measured rate. This is actually a tautology when you unpack it: one second per second is the definition of the flow of time for that observer. It simply means that nobody feels their time slowing down internally. If you carry a wristwatch, you always see it advance normally. If you make a local measurement of a physical process (like how many vibrations a cesium atom does in what you call one second), it will always be the standard number (9,192,631,770 cycles for the Cs-133 hyperfine transition per SI second) because that’s how you define your second.

Where relativity comes in is comparing clocks between observers:

• In Special Relativity: Suppose Alice and Bob move relative to each other. Alice sees her clock tick normally (uniformly). Bob sees his clock tick normally. But when Alice looks at Bob’s clock (by exchanging light signals and accounting for travel time), she finds Bob’s clock ticked slower than hers if Bob was moving relative to her. Likewise Bob finds Alice’s clock was slow from his perspective. This is symmetric if they are in inertial relative motion. If Bob turns around to come back (non-inertial for a while), then the famous twin paradox occurs: Bob will actually have aged less (accumulated less proper time) than Alice when they reunite. But crucially, at the reunion event, both agree on the proper time each clock shows. They don’t agree on “simultaneous” readings during the trip (which is relative), but when in one place, they can directly compare. So, if Bob’s clock shows 5 years and Alice’s shows 10 years at meeting, then indeed Bob’s clock ran slow in an absolute sense over the journey (because Bob took a different worldline through spacetime than Alice – one that involved acceleration and was not the longest proper time between start and end). Still, at every point along his worldline, Bob felt normal aging.

Thus, “time ticks uniformly” can be understood as: each worldline has a well-defined proper time parameter that increases uniformly (at a constant rate) along that worldline. This is built into the structure of spacetime – any inertial observer can use their proper time as a coordinate (one that they measure with an ideal clock). Relativity does not dispute this – in fact it gives proper time a special status as an invariant length of the worldline.

In more physical terms, imagine a standard clock that emits a tick every second according to itself (like a light pulse every time its second hand moves). If you are at rest relative to the clock, you’ll receive those pulses at 1-second intervals (neglecting any gravitational field differences). If someone is moving relative, they might receive the pulses Doppler shifted in time (either redshifted if moving away – pulses come slower, or blueshifted if moving closer – pulses come faster). Does that contradict “uniform ticking”? Not really, because now you’re comparing different frames. From the moving frame’s perspective, the moving clock’s ticks are indeed slowed – but that’s exactly time dilation.

The statement as given in the thesis context likely raised eyebrows because it sounded like claiming an absolute time rate for all observers, which would be wrong. But the careful phrasing includes “according to their own clocks” – that caveat aligns it with proper time concept. All observers can agree on that statement because it doesn’t try to synchronize clocks across frames, it just says each observer experiences one second per second for themselves. It’s almost a trivial statement once understood: of course, one second per second is true by definition for any clock’s rest frame. The interesting part is the reconciliation: how can everyone’s own clock be “normal” yet they disagree on each other’s? Relativity’s answer: simultaneity is relative, and each pair of events separated in time for one observer is seen with a different separation by another if those events are not causally at the same location.

The gravitational scenario: If one observer is deep in a gravity well and another is far out, each again experiences time normally locally. But when they compare, say by sending signals or eventually bringing the clocks together, they find the one that stayed deep in the gravity well is behind – less time elapsed for it. A famous example: the Hafele–Keating around-the-world clocks experiment, or a simpler one: keep one precise atomic clock at sea level and another on a mountain top for a while, then bring them together. The lower clock (strong gravity) will have ticked fewer seconds (run slower) than the higher clock. This is gravitational time dilation as confirmed by many experiments (even at 1-foot elevation differences with modern atomic clocks).

But at no point did the person next to the sea-level clock notice anything odd – their coffee brewed in 5 minutes by their clock as usual, etc. The difference only becomes apparent when comparing with the mountain clock which might say e.g. 5 minutes and 5 microseconds for the same brew when reunited. So again, each ticked uniformly on its own, but not uniformly relative to each other.

So perhaps a clearer way to phrase “time ticks uniformly for all observers” is: Each observer experiences time at the same steady rate – their own proper time – and locally measured processes occur in the same way (one second per second for them). Relativity does not alter an observer’s local rate of time flow; it only describes how different observers’ time coordinates relate to each other. This is basically the principle of relativity: the laws of physics (including whatever defines a “one-second” process) are the same in any local inertial frame. An atomic clock doesn’t behave differently just because it’s on a moving spaceship; it still counts out the same number of oscillations to reach a second internally. But an outside observer will see that spaceship clock’s oscillations Doppler-shifted.

One might object: if in some absolute sense all clock rates are the same, how do we explain a faster-than-light traveler paradox or anything? The answer is we don’t need an absolute sense; it’s all relative. The statement is really about local physics: physics yields a universal conversion factor between time units and physical processes (like cesium oscillations, or pendulum lengths given gravity, etc.), and that is true everywhere (assuming the same conditions like not jostling the clock, etc.). This uniformity of local time flow is why we can have a consistent definition of a second in the SI units that’s supposed to apply anywhere in the universe: it’s defined by a hyperfine transition of Cs-133. Any observer at rest relative to a Cs atom can in principle see $9,192,631,770$ cycles in one second of their time. And any other observer would agree that in the rest frame of that atom, that many cycles happen per second of that atom’s proper time – because that’s a fixed property of nature. If the second observer is moving relative to the atom, they’ll see something else (like time dilation of that atomic process), but they can still compute and agree what the proper time for the atom was.

This leads to the concept of invariant interval and proper time again: The fact all observers can agree on an observer’s own elapsed time between two events on their worldline is because $\Delta \tau^2 = \Delta t^2 - \Delta x^2/c^2$ is invariant. If $\Delta x = 0$ (events happen to the same clock, so no spatial separation in its rest frame), then $\Delta \tau = \Delta t_{\text{clock}}$, and everyone can compute that via Lorentz transform and gets the same number. So proper time is an invariant, which underscores that it’s meaningful to talk about “the time measured by that clock between event A and B” absolutely (all observers will agree on that number, even if they slice those events differently into space and time coordinates in their own frame).

Under what conditions does “time ticks uniformly” break down? Well, if we have non-inertial effects or varying gravitational fields along the worldline, the rate at which proper time accumulates can change relative to an external coordinate. For example, if you accelerate a clock, in some coordinate frame you might say its ticking rate changes (like during acceleration it might momentarily tick faster or slower as seen externally). But locally the clock still ticks normally – the clock itself doesn’t know it accelerated except maybe vibrations or something, but an ideal clock would still count the same number of ticks per its proper time. In GR, a clock in a changing gravitational potential (say being moved from Earth’s surface to space) will change tick rate relative to Earth time – once moved, it runs faster than identical Earth clocks because it’s higher up. But at each location it ticks at a steady rate locally.

Another scenario: near a black hole horizon, an observer hovering might see their own clock normal, but an observer far away sees it tick extremely slowly (redshift). At the horizon itself, from outside view time seems frozen. But the infalling observer crossing the horizon experiences nothing special (in classical GR) and their watch is fine. So “uniform for all observers” definitely doesn’t mean “uniform across space and gravity” – it’s purely local uniformity.

Thus, we emphasize proper time = personal time. And indeed, “one second per second” is somewhat facetious – it’s like saying velocity of time = 1. But it reminds us that we can’t detect time dilation without looking outside our own frame. In fact, an ironic way to think of “one second per second” is: that is the one thing in physics that is truly absolute – the flow of time relative to itself is the same for everyone. It’s trivial but important for intuition.

From a pedagogical perspective, perhaps the previous thesis or its review pointed out that saying “fixed rate for all observers” without clarification could mislead one into thinking relativity is being violated or that a universal time exists. The uniform rate is only meant in each observer’s rest frame.

To connect with Einstein’s equivalence principle: it ensures that locally (in free fall) physics, including time flow, is the same as in special relativity (which has that property of one second per second for each inertial frame). So even in curved spacetime, at a small scale, an observer doesn’t feel time distortions – they see normal ticks. Only upon comparison across finite separations does curvature manifest in differing elapsed times.

It might be worth noting that the International Atomic Time (TAI) is a sort of coordinated proper time. We correct measured atomic clock rates for gravitational potential and motion to bring them to the rate of an imaginary clock at geoid (sea level) on Earth. That way, we have a unified time standard. Without corrections, clocks in Colorado tick faster than clocks in Paris because Colorado is higher. Indeed, GPS satellites have to account for both special relativistic time dilation (they move fast: ~14 microseconds per day time dilation causing them to fall behind Earth clocks) and gravitational time dilation (they are high up: ~45 microseconds per day faster tick than Earth clocks). Net effect: satellite clocks tick about 31 microseconds per day faster than ground clocks if no adjustment – which would ruin GPS position accuracy quickly. So they are pre-adjusted and also continuously corrected for drift. This is a direct example of “for each observer time is uniform, but not for all compared across frames” – engineers regularly manage these differences.

In summary, the claim “time ticks uniformly for all observers” is accurate only in the sense of each observer’s own proper time. All observers agree that each observer’s proper time advances at a constant rate for that observer. But if one tries to compare the rate of one observer’s clock to another’s without specifying the frame or conditions, one must use relativity equations. Proper time is a bit like each observer’s “personal time currency,” and one unit of Alice’s proper time is equivalent to one unit of Alice’s proper time – trivial – but not equivalent to one unit of Bob’s coordinate time unless Bob is in the same frame. The statement, when properly understood, reinforces that there is no “super observer” from whose perspective some clocks speed up or slow down intrinsically; rather, any slow-down is reciprocal or due to gravity differences, and every observer finds their local physics normal.

Discussion

Through the course of this thesis, we have surveyed the nature of time across physics – from Newton’s absolute time, through the relational and dynamic time of relativity, to the peculiar role of time in quantum theory and the frontier ideas in cosmology about time’s beginning or eternity. Several key themes emerge from this exploration:

• Time as a Coordinate vs Time as an Experience: In theoretical physics, time is often treated as a coordinate (one parameter in equations, part of spacetime manifold). But our experience of time – the flow, the distinction of past/future – is not explicitly in those equations. We find that the experience is linked to thermodynamic irreversibility and memory. The equations themselves (apart from subtle CP violation) are reversible and don’t pick a preferred direction. This dichotomy suggests that what we call “time” actually has multiple layers: a geometric layer (time coordinate in relativity), a physical layer (thermodynamic/causal ordering), and a psychological layer (our perception). They usually align in one direction for us (increasing entropy aligns with psychological arrow and with forward coordinate time in an expanding universe), but they can be conceptually separated.
• Fundamental vs Emergent: We repeatedly asked if time could be non-fundamental. In classical mechanics and relativity, time seems fundamental (though in GR it is malleable). In canonical quantum gravity, time might not appear – hinting at emergence. If time is emergent, it may be a state-dependent notion (the universe’s quantum state might give rise to an approximate time for semi-classical observers within it). If it’s fundamental, it should appear in the ultimate equations in some form (perhaps as part of a bigger symmetry or structure). The jury is still out. What’s clear is that time as we know it is remarkably featureless – it has no identified substructure (unlike space which can have curvature, topology, etc., time is usually assumed simply connected and one-dimensional monotonic). If time has microstructure (like “chronons,” quanta of time), we have no evidence yet. Many physicists suspect there is a minimal length (Planck length), but minimal time is trickier since you can always boost to make a short time in one frame correspond to a longer time in another frame (unless Lorentz symmetry is violated at some scale).
• Symmetry and Breaking: Time-translation symmetry is central in physics (Noether’s theorem: it leads to energy conservation). If time were not fundamental, how do we get energy conservation? Perhaps energy conservation only holds in regimes where time emergence approximates a symmetry. If the universe’s laws changed with time (violating time symmetry), we’d see energy non-conservation or varying constants. As noted, no convincing evidence of that yet. This implies that at least as an effective symmetry, time-translation invariance is real. It could be that emergent time inherits a symmetry from deeper laws (like an approximate symmetry in a phase of the system). Also, CPT symmetry suggests that even if each of C, P, T are broken individually (like T broken in weak interactions), the combination CPT is exact if we assume the usual quantum field theory structure. That means there is still a consistency that overall doesn’t single out an “end of time” or such in the laws.
• Causality: Time is intimately connected to causality – the cause-effect relation. In relativity, time order of causally connected events is invariant (all observers agree on cause preceding effect if a signal can go from one to the other). This causal structure gives time a partial order in spacetime (a light cone structure). Any theory of time’s origin must also deal with causality’s origin. For instance, if time began, did causality begin? If something “caused” the Big Bang, that cause would lie outside our time, which sounds acausal in our context. Many proposals avoid that by making the Big Bang uncaused (no cause needed, it’s spontaneous or quantum). Cyclic models preserve causality through cycles. The concern for emergent time is whether a theory without fundamental time can still produce a reliable causal sequence (most think yes, via something like a Hamiltonian constraint, but it’s delicate).
• Known Unknowns: We identified some known unknowns: what is the resolution of the Big Bang singularity? Does a complete quantum gravity theory eliminate it (via bounce or something) or is it replaced by a “no-boundary” smooth cap? Are there observable relics (like gravitational waves background) from before the Big Bang if it existed? Also, is time quantized or continuous? Do we have experimental means in the future to probe Planck-scale time intervals (maybe via high energy physics or cosmology)? Another unknown: how exactly does the arrow of time emerge from quantum mechanics – can we derive the second law from unitary quantum dynamics plus a special initial state? We think so, but a rigorous derivation (reconciling the reversible micro-laws with irreversible macro-laws) is a continuing effort in statistical mechanics and quantum decoherence theory.
• Unknown Unknowns: Could time have entirely unexpected properties? One could speculate about parallel timelines (like branching universes in the Many Worlds Interpretation of quantum mechanics – does each branch have its own time or is there a higher time in which branching occurs?). Or perhaps there’s a second time dimension (two-dimensional time has been considered in some exotic theories, but it breaks our usual notion of causality severely, so it’s not popular). Another wild idea: maybe the flow of time is related to consciousness in a way we don’t understand – some have wondered if quantum collapse (with a built-in direction) is tied to conscious observation, though that veers into speculative philosophy.

At our current state of knowledge, time remains a pervasive mystery. We can measure it extremely accurately (atomic clocks to better than $10^{-15}$ precision), use it in every theory, but when we push the question “what is time?” we often answer operationally (it’s what a clock reads) rather than giving an ontological explanation. Augustine’s famous quote still resonates: “What then is time? If no one asks me, I know; if I seek to explain it, I do not.” Our exploration here explains time in pieces – in physics contexts – but does not fully unify these pieces into one crystal-clear picture. Perhaps the ultimate theory (if there is one) will treat time in a completely new way, just as Einstein’s relativity was a completely new way compared to Newton’s.

Yet, one thing appears certain: any future theory must explain why at the scales we live and experiment, time behaves exactly as we observe – relentless, one-directional (macro-scale), and linking cause to effect. This is non-negotiable, as it’s so thoroughly tested. The differences will come in extreme conditions or domains we haven’t accessed: maybe then time will show a new face.

Conclusion

We set out to write a thesis-level inquiry into the nature of time, and in doing so we traversed the landscape of modern physics and cosmology. Let’s summarize our findings and perspectives:

• In classical physics, time is absolute and external. Newton’s view of time as an ever-flowing uniform background set the stage for centuries of scientific work. But that view, while intuitive, turned out to be an approximation – a limiting case of more comprehensive laws.
• Relativity revolutionized time, merging it with space and making it relative to the observer. No longer could one speak of the universal tick of time; one had to specify “whose clock?” and how observers move relative to each other. Still, relativity provides a robust framework where each observer’s proper time is well-defined and agreed upon by all to be the physically meaningful time along that observer’s path. The seeming paradox – that everyone’s own clock ticks normally while others’ may not – is resolved by understanding that simultaneity and time comparisons depend on one’s frame. We illustrated this by examining how relativity and equivalence principle ensure that locally time is uniform for all, while globally it can differ between observers after reunions or comparisons.
• In quantum mechanics, time stands out as the parameter we don’t quantize. This split hints at a fundamental incompatibility between the way we treat time and the way we treat other observables. The open problem of unifying quantum mechanics with general relativity’s dynamical time remains one of the biggest in theoretical physics. Various approaches either eliminate time at the fundamental level (leading to a “frozen” formalism that must recover time later) or modify our notion of time (multiverses, parallel histories, etc.). None has been experimentally validated yet.
• Cosmology forced us to confront the question of time’s beginning. While classical GR suggests a beginning of time at the Big Bang, quantum and speculative theories allow alternatives: maybe time extends before in a different form (a quantum phase, another universe, etc.), or maybe our universe is one cycle in an endless history. These theories are being sharpened and tested against cosmological data (for instance, searching for imprints of a bounce or previous cycle in the cosmic microwave background). So far, inflationary Big Bang cosmology – which doesn’t require a pre-time phase (though it doesn’t rule it out either) – is extremely successful in matching observations. But it leaves the t=0 moment and “before” as an extrapolation rather than an observation. Therefore, it is in the domain of theoretical consistency and philosophical preference whether one assumes time truly began or not. The Hartle–Hawking no-boundary idea provides one elegant, if difficult, picture of a beginning without a boundary (hence without a prior), whereas bounce and cyclic models provide an infinite canvas of time where our beginning is not the ultimate beginning.
• The flow and arrow of time emerge not from the local laws (which are reversible) but from the global condition of low entropy in the past. We found that the second law of thermodynamics is the quantitative core of the arrow of time. Entropy increase both explains why we can’t remember the future and also provides an arrow that matches cosmic expansion. In a sense, the Big Bang’s legacy is not only the matter and radiation filling the universe, but also the entropic arrow that drives every physical process towards equilibrium and gives time a direction. This is a profound link between cosmology and everyday physics: the reason eggs break but don’t unbreak lies in the conditions of the early universe.
• Uniform time for all – in their own frame is a reaffirmation of the principle of relativity: no experiment completely within your own frame can tell you if you are moving or in a gravitational field (to first order) because your time flow and physical laws are standard. Differences in time flow appear only when comparing between frames, leading to the rich effects of relativity. We clarified the meaning of that statement and thus addressed the critique, showing that it is consistent with relativity when properly interpreted.

In closing, what do we know and what do we not know about time? We know how to measure time with astonishing precision and how to predict its effects in normal and relativistic situations to high accuracy. We know that time inextricably links with space in any deep description (there is no separate absolute time). We know that the universe had a hot, dense origin in which our familiar time ties to the expansion parameter. We know that any new theory must reduce to our current understanding of time in regimes we’ve tested (this constrains possibilities sharply).

We don’t know if time is an illusion, an emergent approximation out of something more complex, or a fundamental aspect of reality. We don’t know whether it makes sense to talk about “before the Big Bang” – it might, if there was a bounce or prior phase, or it might not, if time truly began. We don’t know the full resolution of combining quantum mechanics with time’s dynamic nature – that awaits a working theory of quantum gravity. We don’t know whether the flow of time can be reversed or stopped in any physical scenario (closed timelike curves hint at logical issues, and so far nature has protected causality, but wormholes and such remain theoretical possibilities that could, in principle, allow “effective” time travel under exotic conditions). And we don’t know the fate of time in the far future – will it go on eternally as the universe expands forever? If the universe approaches a heat death, time becomes almost irrelevant (nothing changes). If cyclic, time might literally repeat or continue beyond “our” eon.

Perhaps most intriguingly, there may be unknown unknowns – aspects of time we haven’t even thought to question. For instance, if a future theory suggests multiple time dimensions or a granular time, that would revolutionize things as much as relativity did.

The quest to understand time is as much a philosophical journey as a scientific one. By building on critiques and ideas from prior work (such as the notion of a timeless phase before the Big Bang), we aimed to deepen the analysis and ground it in known physics while acknowledging speculation. In doing so, we hope to have painted a comprehensive picture of the problem of time that is intellectually honest about uncertainties while celebrating what we have learned so far.

In summary, time remains the great enigma at the heart of physics: it is the parameter in every equation, yet possibly the key to something deeper beyond our current equations. As physicists continue to probe black holes, quantum entanglement, and the early universe, they are effectively probing the question of time’s nature. Whatever the ultimate truth, the uniform ticking of seconds that we all experience is our window into any new reality – it is both mundane and profound that all we ever directly know is time’s steady beat, while all we deeply seek to know is what lies behind that beat.

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What Is Time? Where It Came From? Why It Ticks Uniformly for All Observers?

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I’m thinking through the use of "ds" as proper time while considering if it typically refers to the interval between events on the same worldline, especially in FRW models.

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