What is a second?
A second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom, measured at a temperature of zero kelvin. That is the formal SI definition adopted by the 13th General Conference on Weights and Measures in 1967 and reaffirmed in the 2019 SI redefinition, and it is the technical foundation on which every modern timekeeping system rests. The definition has nothing to do with the Earth's rotation, nothing to do with the Sun, and nothing to do with any astronomical reference whatever. It is an intrinsic property of a single chemical element, and the choice of that element was made with care.
Caesium-133 is the only stable isotope of caesium, which removes any isotopic ambiguity. Its outermost electron sits alone in the 6s shell, and that single electron has a hyperfine interaction with the nuclear spin that produces a sharp, clean energy gap. When the electron jumps between the two hyperfine ground states, it absorbs or emits microwave radiation at a frequency that is the same for every caesium-133 atom anywhere in the universe, to the precision that has been measured. The transition is at 9.192 gigahertz, which is conveniently in a microwave band that mid-twentieth-century electronics could already handle. The number 9,192,631,770 was not arbitrarily picked. It was chosen so that the new atomic second would match the previous astronomical second derived from observations of the Earth's orbit, to the best precision then available, so that adopting the new definition would not jolt every existing astronomical table.
The authority that maintains the definition is the Bureau International des Poids et Mesures (BIPM) in Sèvres, near Paris. The BIPM does not itself operate the world's primary clocks; it collects timing data from roughly 80 metrology laboratories worldwide that run their own caesium fountain clocks and increasingly their own optical lattice clocks, weights and averages those signals using a defined statistical algorithm, and publishes the result monthly as International Atomic Time (TAI). Coordinated Universal Time (UTC) is TAI plus an integer number of leap seconds, currently 37, kept within 0.9 seconds of the Earth's actual rotational time. Every wall clock on the planet is ultimately calibrated against UTC, and UTC is ultimately calibrated against the BIPM's monthly average of caesium and optical-lattice clock readings.
The current state of the art is already pushing beyond caesium. The 2019 SI redefinition kept caesium as the formal reference for now, but the international metrology community has been preparing a redefinition based on optical-lattice clocks using strontium-87 or ytterbium-171, which are roughly a hundred times more precise than the best caesium fountains. The redefinition is expected sometime in the late 2020s or early 2030s. When it happens, the second will be redefined in terms of one of those optical transitions, the number 9,192,631,770 will be reframed as a derived constant, and the precision of timekeeping will jump by roughly two orders of magnitude in a single administrative act.
Newtonian absolute time
Isaac Newton opened the Principia in 1687 with a definition of time that framed every physics paper for the next two centuries: 'Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration.' Time in Newton's universe is a background parameter against which all motion unfolds. It ticks at the same rate everywhere, for every observer, regardless of their state of motion or the gravitational field they are in. There is a single universal clock to which all real clocks are approximations.
This conception is intuitive, mathematically tractable, and it works essentially perfectly for everything we encounter in everyday life. Cannon balls, planets, tides, and steam engines all behave as if time were absolute, because the deviations from absolute time at non-relativistic speeds and in weak gravitational fields are vanishingly small. The Newtonian framework was so successful that for two centuries no one had any reason to question its picture of time. The celestial mechanics of Laplace, the thermodynamics of Carnot and Clausius, the electrodynamics of Ampere and Faraday — all of them assumed a universal time parameter without comment.
The cracks appeared in two places. James Clerk Maxwell's 1865 unified equations of electromagnetism had a peculiar property: they predicted electromagnetic waves travelling at a specific speed c, derived from two physical constants (the permittivity and permeability of free space), and they predicted that speed regardless of the motion of either the source or the observer. This was strange, because every other wave known to physics — sound in air, ripples on a pond — travels at a speed relative to its medium, and the speed measured by an observer depends on the observer's motion relative to the medium. If electromagnetic waves obeyed the same rule, then the speed of light should depend on the motion of the observer through whatever medium light propagates in. The hypothesized medium was called the luminiferous aether, and finding it was the dominant experimental project of the late nineteenth century.
The Michelson-Morley experiment of 1887, performed at what is now Case Western Reserve University in Cleveland, tried to detect the Earth's motion through the aether by measuring the difference in the speed of light along and perpendicular to the direction of Earth's orbital motion. The expected fringe shift was within the experiment's resolution. They found nothing. The null result was confirmed by more precise repetitions over the next two decades. Either the Earth happened to be at rest in the aether at all times (implausible, since the Earth was known to be orbiting the Sun at 30 kilometres per second), or there was no aether and Maxwell's equations were telling the truth: the speed of light really is the same for every observer regardless of motion. The latter explanation is correct, and getting it right required throwing Newton's absolute time overboard.
Special relativity (1905)
Albert Einstein's 1905 paper Zur Elektrodynamik bewegter Körper ('On the Electrodynamics of Moving Bodies'), published in Annalen der Physik, took the speed of light's invariance as a postulate rather than a problem to explain. Combined with the principle of relativity (that the laws of physics are the same in every inertial frame), it forced a complete rethinking of time and space. The mathematical consequences were already known to Hendrik Lorentz, Henri Poincaré, and others, but Einstein was the first to articulate what they actually meant physically: time and space are not independent, absolute, universal stages. They are interwoven into a four-dimensional spacetime, and the way they mix depends on the observer's state of motion.
The headline consequence is time dilation. If a clock is moving past you at velocity v, the time it shows is dilated (stretched) by a factor of gamma, the Lorentz factor, where gamma equals one divided by the square root of one minus v squared over c squared. At everyday speeds gamma is so close to one that the effect is invisible: a car travelling at 100 kilometres per hour has a gamma of roughly 1 + 4 times 10 to the minus 15, an absolutely undetectable correction. At relativistic speeds the effect becomes enormous. At 87 per cent of the speed of light, gamma is 2, and a moving clock ticks at half the rate of a stationary one. At 99.5 per cent of the speed of light, gamma is 10, and a moving clock ticks one tenth as fast.
Einstein illustrated the effect with what is now called the light-clock thought experiment. Imagine a clock built from two mirrors with a light pulse bouncing between them. In the clock's own rest frame, the pulse travels straight up and down, and the period of the tick is twice the mirror separation divided by c. Now set the clock moving sideways relative to an outside observer. From the outside observer's frame, the light pulse follows a diagonal path (it has to keep up with the sideways motion of the clock as well as travel between the mirrors), which is longer than the up-and-down path in the clock's own frame. Because the speed of light is the same in both frames, the longer path takes longer in the outside observer's frame, so the clock ticks more slowly when viewed from outside. The effect is symmetric: each frame sees the other's clock as running slow. This is not an illusion, and it is not a measurement artifact. It is what is actually happening.
The cleanest natural demonstration is muons from cosmic rays. High-energy protons from the Sun and beyond collide with nuclei in the upper atmosphere about 15 kilometres above the Earth's surface, producing showers of secondary particles including muons. Muons are unstable, with a rest-frame mean lifetime of about 2.2 microseconds. At 15 kilometres altitude, a muon travelling at essentially the speed of light should decay long before reaching the ground: even at light speed, 15 kilometres takes 50 microseconds to traverse, which is more than 22 muon lifetimes. Yet large numbers of muons are detected at sea level every minute. The explanation is straightforward time dilation. The muons are typically moving at Lorentz factors of around 20, which stretches their effective lifetime in the ground frame to about 44 microseconds, enough time to reach the surface in detectable numbers. From the muon's own frame, the resolution is symmetric: the muon sees the 15 kilometres of atmosphere as length-contracted to about 750 metres, which it traverses well within its own internal 2.2 microsecond lifetime. Both frames agree on what the muon detector at sea level registers, but they describe the journey very differently.
General relativity (1915)
Special relativity handled inertial frames moving at constant velocity, but it said nothing about gravity. Einstein spent the next decade extending the theory to accelerated frames and gravitational fields, publishing the field equations of general relativity in 1915. The headline insight is the equivalence principle: being at rest in a uniform gravitational field is locally indistinguishable from being in a uniformly accelerating reference frame. From this principle, an enormous amount of physics follows, including a second form of time dilation quite distinct from the velocity-based effect of special relativity.
Gravitational time dilation says that clocks tick more slowly the deeper they are in a gravitational potential well. A clock at the bottom of a mountain ticks slower than a clock at the top of the mountain. A clock on the Sun's surface ticks noticeably slower than a clock far from any star. A clock just outside the event horizon of a black hole ticks vanishingly slowly compared to a clock at infinity. The mathematical factor is roughly one minus the gravitational potential divided by c squared, which makes the effect tiny in everyday gravitational fields but measurable with sufficiently precise clocks. The 1959 Pound-Rebka experiment at Harvard measured the effect over a 22.5 metre vertical drop using gamma-ray emission from iron-57, confirming the prediction to within 10 per cent. Modern optical-lattice clocks routinely measure gravitational time dilation over height differences of a few centimetres.
The most consequential everyday application is the Global Positioning System. GPS satellites orbit at an altitude of roughly 20,200 kilometres and travel at about 14,000 kilometres per hour. Both effects matter. The orbital velocity slows the satellite clocks by about 7 microseconds per day relative to ground clocks (special-relativistic time dilation). The higher altitude, putting them further out of Earth's gravity well, speeds them up by about 45 microseconds per day (gravitational time dilation). The net is plus 38 microseconds per day. Light travels about 300 metres in a microsecond, so an uncorrected 38-microsecond drift would produce position errors of about 11 kilometres per day. After a single day of uncorrected operation, the GPS system would be useless for any application requiring accuracy better than ten kilometres.
NASA's solution, when GPS launched in 1989, was to deliberately tune the satellite clock rates so that the satellites tick slow by 38 microseconds per day relative to ground clocks at sea level. From the satellite's own frame the clock is running correctly, but from the ground frame it appears to be tuned to match the ground rate exactly. The relativistic correction is baked into the hardware at the factory, before launch. Every commercial GPS receiver on Earth depends on this correction implicitly, and the system has now run continuously for over three decades without any drift attributable to relativistic errors. The NASA tests-of-general-relativity overview lists GPS as one of the most precisely confirmed predictions of the theory.
Atomic clocks
The first practical atomic clock was Louis Essen's caesium beam clock at the National Physical Laboratory in Teddington in 1955. It used a beam of caesium atoms passing through a microwave cavity tuned to the hyperfine transition frequency, with the cavity feedback locked to the atomic resonance. Its frequency stability was already better than the astronomical second, which is what motivated the 1967 SI redefinition twelve years later. Essen's clock had a fractional frequency uncertainty of about one part in ten to the tenth, meaning it would drift by about one second every 300 years.
The next generation, the caesium fountain clock, replaced the beam with a cloud of laser-cooled caesium atoms tossed vertically through a microwave cavity. The atoms are decelerated by gravity, pass through the cavity twice (once on the way up, once on the way down), and the longer interrogation time gives a sharper resonance and therefore better frequency stability. Caesium fountains have fractional frequency uncertainties of around one part in ten to the sixteenth, drifting by about one second every 100 million years. The National Institute of Standards and Technology operates the NIST-F2 caesium fountain in Boulder, Colorado, which along with similar instruments at NPL, PTB in Germany, LNE-SYRTE in Paris, and a dozen other national metrology laboratories provides the bulk of the data the BIPM uses to compute International Atomic Time.
The current frontier is optical lattice clocks using strontium-87 or ytterbium-171. Instead of microwave-frequency hyperfine transitions, these clocks use optical- frequency electronic transitions, which oscillate at hundreds of terahertz rather than gigahertz. The higher frequency means more cycles per second of natural clock signal, and therefore (with the same fractional precision) much greater absolute precision. Strontium lattice clocks at JILA in Boulder, RIKEN in Japan, NIST, and elsewhere have fractional frequency uncertainties around one part in ten to the eighteenth. Ytterbium clocks at NIST have reached similar levels. The NIST Time and Frequency Division publishes the current performance figures continuously.
What does one part in ten to the eighteenth mean? It means the clock would drift by less than one second over the entire age of the universe, which is roughly 13.8 billion years. Put another way, you could run the clock from the Big Bang to today and it would still be accurate to within a fraction of a second. This is far more precision than is required for any current human application — GPS only needs nanosecond timing, financial trading only needs microsecond timing, even deep-space navigation only needs millisecond timing — but the science enabled by this precision is substantial. Optical clocks at this precision can detect the gravitational time dilation across a one-centimetre height difference, which opens up possibilities for relativistic geodesy (mapping the Earth's gravitational potential using clock networks) and for tests of fundamental physics like whether the fine-structure constant is drifting over cosmological time.
Leap seconds
The Earth's rotation is slowing down. Tidal friction with the Moon transfers angular momentum from the Earth's rotation to the Moon's orbital motion, which is why the Moon is receding from us by about 3.8 centimetres per year and the day is lengthening by about 2.3 milliseconds per century. There are also short-term fluctuations: post-glacial rebound, fluid motion in the Earth's outer core, atmospheric mass redistribution, and major earthquakes can all change the Earth's moment of inertia and therefore its rotational rate. The net effect is that solar time (UT1, anchored to the actual rotation of the Earth) drifts behind atomic time (TAI, anchored to the caesium standard) by a few hundred milliseconds per year.
Coordinated Universal Time (UTC), the civil time standard that most of the world uses, was introduced in 1972 as a compromise. It runs at the same rate as TAI (constant atomic seconds, never drifts) but periodically adds a leap second to keep within 0.9 seconds of UT1. The decision to add a leap second is made by the International Earth Rotation and Reference Systems Service (IERS) in Paris, which announces the insertion roughly six months in advance through Bulletin C. Leap seconds are always inserted at the end of either 30 June or 31 December UTC, appearing as 23:59:60 followed by 00:00:00 of the next day.
Twenty-seven leap seconds have been added since 1972, the most recent on 31 December 2016. The cadence has not been steady, because the Earth's rotation rate is not steady. The 1970s and 1980s saw frequent additions (roughly one every eighteen months), the 1990s and 2000s saw fewer, and from around 2020 the Earth has actually been rotating slightly faster than the atomic standard, which has raised the unprecedented possibility of a negative leap second. None has yet been inserted, but the possibility has been discussed seriously in the metrology community.
Leap seconds wreak havoc on computer systems. Modern infrastructure assumes time is monotonic and continuous, but a leap second either inserts a duplicate second (the same second twice in sequence) or stretches the previous second over two seconds of real time (the 'leap smear' approach Google adopted). Either interpretation has caused outages. In June 2012 a leap second crashed Reddit, Mozilla's bug tracker, the Qantas airline reservation system, and several large Linux server fleets. The 2015 leap second caused similar damage. Many large operators have since adopted leap smearing rather than inserting the leap second discretely, but the underlying ambiguity remains.
In November 2022 the 27th General Conference on Weights and Measures voted to phase out leap seconds by or before 2035, allowing UTC to drift away from UT1 by a much larger margin before any correction is applied. The likely replacement is a single leap minute every century or so, which would be much less disruptive because most systems do not need to handle minute-scale alignment with solar time. The decision was politically contested — Russia in particular argued that GLONASS, its GPS equivalent, relies on the current UTC definition — but the proposal passed and the implementation details are being worked out through the International Telecommunication Union. The era of leap seconds will end before 2035.
The arrow of time
The fundamental laws of physics are almost entirely time-reversal symmetric. If you ran the equations of Newtonian mechanics, electrodynamics, or general relativity backwards in time, they would still describe valid physical processes: planets would orbit the Sun in retrograde, charged particles would emit radiation in reverse, and the equations would not complain. The only known fundamental violation of time-reversal symmetry is in certain rare weak-force decays involving neutral kaons and B mesons, and these effects are minute and only matter at particle-physics energies.
But macroscopically, time has an obvious direction. Eggs scramble; they do not unscramble. Glasses shatter; they do not reassemble. Coffee mixes with cream and does not unmix. Hot things cool down and equilibrate with their environment; cold things do not spontaneously heat up. We remember the past, not the future. The universe at large scales is expanding away from a hot, dense state in the past, not collapsing toward one in the future. All of these phenomena point in the same direction, and that direction is what we mean by 'the future'. This is what philosophers and physicists call the arrow of time, and explaining why it exists given the time-symmetry of the underlying laws is one of the deeper unsolved problems in physics.
The dominant explanation is thermodynamic. The second law of thermodynamics states that the entropy of a closed system tends to increase over time, where entropy is roughly a measure of disorder or, more precisely, of the number of microstates consistent with a given macrostate. An unbroken egg is a low-entropy state because there are relatively few ways to arrange the molecules to produce that specific configuration; a scrambled egg is high entropy because there are astronomically many arrangements of the same molecules that look 'scrambled'. Going from low to high entropy is overwhelmingly likely, simply by counting states. Going from high to low entropy is not forbidden but is so improbable that it never happens at macroscopic scales.
This is the thermodynamic arrow, and it sets the direction in which the universe is heading: toward heat death, when all the universe's energy has been converted to uniformly distributed low-grade heat with no further gradients to extract work from. The puzzle is not why entropy increases (that is statistical) but why the universe started in such an extraordinarily low-entropy state. The early universe immediately after the Big Bang was hot and dense, which sounds high-entropy, but in fact it was extremely low-entropy in the relevant gravitational sense, because all the matter was almost perfectly evenly distributed. Roger Penrose has estimated the entropy of the early universe at roughly one part in ten to the ten to the one hundred and twenty-third — a number so small it almost defies comprehension. Why the initial condition of the universe was so far from typical is the deep open question.
Three other arrows reinforce the thermodynamic one. The cosmological arrow points in the direction of cosmic expansion: the universe is getting larger and less dense over time, not smaller and denser. The cosmological arrow is probably connected to the thermodynamic arrow but the connection is subtle and still debated. The radiative arrow is that electromagnetic radiation consistently propagates outward from sources in expanding spherical waves rather than converging inward from infinity onto sinks — even though Maxwell's equations admit both solutions equally. The psychological arrow is that we remember the past but not the future, a fact that probably reduces to the thermodynamic arrow at the level of brain processes, since memory formation involves creating new low-entropy structures in neural tissue that mirror the low-entropy states of past events. All four arrows point the same way, which is itself a clue that they share a common origin in the low-entropy initial state of the universe.
Block universe vs presentism
There is a philosophical debate, going back to at least Parmenides and Heraclitus, about whether the past and future are real in the same sense the present is. The two main positions are presentism (only the present moment is real; the past has ceased to exist and the future does not yet exist) and the block universe view (all of spacetime exists timelessly as a four-dimensional structure, with past, present, and future equally real and the 'flow' of time being a feature of our subjective experience rather than of reality itself). Special relativity has implications for this debate.
Relativity tells us that simultaneity is relative. Two events that happen at the same time according to one observer happen at different times according to another observer moving relative to the first. There is no observer-independent 'now' that picks out a single hyperplane of present events. The mathematician Hilary Putnam argued in 1967 that this fact is essentially fatal to presentism: if there is no privileged 'now' across all of spacetime, then there is no principled basis for saying that what is now real is fundamentally different from what was real yesterday or what will be real tomorrow. Different observers will disagree about which events are 'now real', and the only consistent way to handle this is to say that all events in spacetime are real, period. This is the block universe.
The Putnam argument is not universally accepted. Presentists have replied that the relativity of simultaneity tells us something about the structure of relations between events, not about the ontological status of those events. Various 'growing block' theories have been proposed, in which the past and present are real but the future is not (so the block grows over time as new presents become past). These have their own technical problems with relativity: in particular, if which events count as 'past' depends on the observer's frame, then the block does not have a consistent shape, and you have to either pick a privileged frame (which violates the principle of relativity) or accept that the growing-block picture only makes sense locally.
The honest answer is that the question is currently undecided. Physics is consistent with the block universe interpretation, and many physicists (notably Einstein himself) have endorsed it. But physics does not actually require the block universe; it only constrains how presentism can be formulated. The phenomenology of conscious experience — the subjective feeling that there is a moving present and that the future is open while the past is settled — is consistent with both views. Whether the 'flow' of time is a feature of reality or a feature of our subjective experience of reality is a question that physics alone probably cannot settle, and it remains alive in contemporary philosophy of physics.
What's the smallest unit of time?
The Planck time is approximately 5.39 times ten to the minus 44 seconds. It is constructed by combining the three fundamental constants of physics that have dimensions of length, mass, and time — the gravitational constant G, the reduced Planck constant h-bar, and the speed of light c — into the unique product with units of time. The formula is the square root of (h-bar G over c to the fifth). The number is unimaginably small. There are more Planck times in one second than there are atoms in the observable universe by several orders of magnitude.
What the Planck time actually means is not that time is quantized in discrete tick-tick-tick steps of one Planck time each — we have no direct evidence for that — but rather that the Planck time marks the scale at which our current physical theories stop being self-consistent. Both general relativity and quantum field theory work superbly in their own domains. They start to interfere with each other when we consider regions of spacetime smaller than the Planck length (about ten to the minus 35 metres) or durations shorter than the Planck time. At these scales, the gravitational effects of quantum fluctuations become comparable to the energy scales involved, and we need a theory of quantum gravity to describe what is happening. We do not have one.
Several candidate theories have been proposed. Loop quantum gravity attempts to quantize spacetime itself, treating it as a discrete network of interconnected loops at the Planck scale. In this picture, time really is quantized: there are discrete 'Planck moments', and durations shorter than the Planck time are simply not physically meaningful. String theory takes a different approach: spacetime remains continuous, but the fundamental particles are one-dimensional strings rather than point particles, with a characteristic length scale of about the Planck length. Below the Planck scale, the geometric picture of spacetime breaks down and is replaced by something describable only in terms of the string degrees of freedom. Causal set theory takes yet another approach, treating spacetime as a discrete set of events with a causal partial ordering, and recovering the continuous geometry only as an emergent large-scale approximation.
Direct experimental probes of the Planck scale are essentially impossible with current or foreseeable technology. The Planck energy, which is the energy associated with a Planck-length-sized region or a Planck-time duration, is about 19 gigajoules — a respectable but unremarkable amount of energy, comparable to a modest lightning strike. The problem is that you need to concentrate that energy into a region of size one Planck length, which is roughly one quadrillion times smaller than the diameter of a proton. The Large Hadron Collider, currently the most powerful particle accelerator ever built, reaches energies of about 14 tera- electronvolts, which is fifteen orders of magnitude below the Planck scale. Building an accelerator that could reach Planck energies, scaled naively, would require a ring with a circumference roughly the size of the solar system. We are not going to do this. Quantum gravity is probably going to have to be tested through indirect signatures (in cosmology, in black hole astrophysics, or in precision low-energy experiments) rather than by directly probing the Planck scale.
What this means for time as a concept is that the very notion of duration breaks down at the Planck scale. Asking what happens in less than one Planck time is like asking what is north of the North Pole. The question may not have a meaningful answer, not because of an experimental limitation but because the concept of 'time' as we use it might simply not apply. Whatever the correct theory of quantum gravity turns out to be, it will almost certainly not describe Planck-scale physics in terms of times and durations the way classical physics does. Something more fundamental will replace the concept of time at the deepest level, and the time we measure with atomic clocks will turn out to be an emergent property of that deeper structure.
Tools Zeitful ships for this
Everything above is the physics of time at the fundamental level. The practical tools that Zeitful publishes operate at the level of the wall clock, and relativistic corrections do not matter for any of them — the latency in a phone call across the Atlantic is dominated by network routing, not by the few nanoseconds of gravitational and special-relativistic time dilation between London and New York. But the connection to the underlying physics is real, and a few of our tools are direct manifestations of the concepts in this guide.
The time zone converter is built on UTC, which (as discussed above) is International Atomic Time offset by the current integer number of leap seconds. Every time-zone conversion you perform on the site is ultimately a calculation against the BIPM's monthly atomic-clock average. The world clock displays the current UTC time for every city, sourced from your browser's system clock which is usually synced to a Network Time Protocol (NTP) server, which itself traces back to one of the national atomic-clock standards. The age calculator counts the number of solar days between two dates, with no relativistic correction; if you have been travelling on commercial aircraft frequently, your biological age is technically a few microseconds younger than your earthbound twin, but the effect is far smaller than the noise in counting your birthday.
We do not currently ship any tools that actually compute relativistic corrections. A relativistic time dilation calculator for high-velocity travel or for travel near massive objects would be an interesting future addition. So would a GPS-style relativistic timing simulator that demonstrates the 38-microsecond- per-day combined correction. So would a black-hole proper-time calculator that shows how time elapses near the event horizon. These tools would be educational rather than practical, since nobody actually needs them for daily life, but they would round out the physics-of-time corner of the site. If you would find them useful, let us know.
For the practical history of how we got from astronomical time to the modern second, the calendar reform history guide is the companion piece on the civil and religious half of the same story. The time zones primer covers the practical infrastructure built on top of UTC, including the IANA time zone database, DST rules, and the engineering decisions that ripple out of the metrology choices described above. The JavaScript date and time guide is the developer-reference companion for handling all of this in code. The time format style guide covers the actual string encodings (ISO 8601, RFC 3339, Unix epoch) that applications use to serialize all of this.
Further reading on the physics: the BIPM's SI base units page is the formal source for the definition of the second. The NIST Time and Frequency Division publishes the current performance figures for the best atomic clocks. The Fourmilab translation of Einstein's 1905 paper is a public-domain English version of the original special-relativity paper. The NASA tests-of-general-relativity overview covers GPS, Gravity Probe B, and the other principal confirmations of the theory. For a longer popular treatment of the arrow of time, Sean Carroll's From Eternity to Here (Dutton, 2010) is the most accessible book-length presentation, and Roger Penrose's The Road to Reality (Knopf, 2004) is the more demanding technical overview that covers the same ground and much more.