Time in physics

Time in physics is defined by its measurement: time is what a clock reads.[1] In classical, non-relativistic physics it is a scalar quantity and, like length, mass, and charge, is usually described as a fundamental quantity. Time can be combined mathematically with other physical quantities to derive other concepts such as motion, kinetic energy and time-dependent fields. Timekeeping is a complex of technological and scientific issues, and part of the foundation of recordkeeping.

Pendule de Foucault
Foucault's pendulum in the Panthéon of Paris can measure time as well as demonstrate the rotation of Earth.

Markers of time

Before there were clocks, time was measured by those physical processes[2] which were understandable to each epoch of civilization:[3]

Eventually,[9][10] it became possible to characterize the passage of time with instrumentation, using operational definitions. Simultaneously, our conception of time has evolved, as shown below.[11]

The unit of measurement of time: the second

In the International System of Units (SI), the unit of time is the second (symbol: ). It is a SI base unit, and it has been defined since 1967 as "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".[12] This definition is based on the operation of a caesium atomic clock. These clocks became practical for use as primary reference standards after about 1955 and have been in use ever since.

The state of the art in timekeeping


The UTC timestamp in use worldwide is an atomic time standard. The relative accuracy of such a time standard is currently on the order of 10−15[13] (corresponding to 1 second in approximately 30 million years). The smallest time step considered theoretically observable is called the Planck time, which is approximately 5.391×10−44 seconds - many orders of magnitude below the resolution of current time standards.

The caesium atomic clock became practical after 1950 when advances in electronics enabled reliable measurement of the microwave frequencies it generates. As further advances occurred, atomic clock research has progressed to ever-higher frequencies, which can provide higher accuracy and higher precision. Clocks based on these techniques have been developed but are not yet in use as primary reference standards.

Conceptions of time

Andromeda galaxy Ssc2005-20a1
Andromeda galaxy (M31) is two million light-years away. Thus we are viewing M31's light from two million years ago,[14] a time before humans existed on Earth.

Galileo, Newton, and most people up until the 20th century thought that time was the same for everyone everywhere. This is the basis for timelines, where time is a parameter. The modern conception of time is based on Einstein's theory of relativity, in which rates of time run differently depending on relative motion, and space and time are merged into spacetime, where we live on a world line rather than a timeline. In this view time is a coordinate. According to the prevailing cosmological model of the Big Bang theory time itself began as part of the entire Universe about 13.8 billion years ago.

Regularities in nature

In order to measure time, one can record the number of occurrences (events) of some periodic phenomenon. The regular recurrences of the seasons, the motions of the sun, moon and stars were noted and tabulated for millennia, before the laws of physics were formulated. The sun was the arbiter of the flow of time, but time was known only to the hour for millennia, hence, the use of the gnomon was known across most of the world, especially Eurasia, and at least as far southward as the jungles of Southeast Asia.[15]

In particular, the astronomical observatories maintained for religious purposes became accurate enough to ascertain the regular motions of the stars, and even some of the planets.

At first, timekeeping was done by hand by priests, and then for commerce, with watchmen to note time as part of their duties. The tabulation of the equinoxes, the sandglass, and the water clock became more and more accurate, and finally reliable. For ships at sea, boys were used to turn the sandglasses and to call the hours.

Mechanical clocks

Richard of Wallingford (1292–1336), abbot of St. Alban's abbey, famously built a mechanical clock as an astronomical orrery about 1330.[16][17]

By the time of Richard of Wallingford, the use of ratchets and gears allowed the towns of Europe to create mechanisms to display the time on their respective town clocks; by the time of the scientific revolution, the clocks became miniaturized enough for families to share a personal clock, or perhaps a pocket watch. At first, only kings could afford them. Pendulum clocks were widely used in the 18th and 19th century. They have largely been replaced in general use by quartz and digital clocks. Atomic clocks can theoretically keep accurate time for millions of years. They are appropriate for standards and scientific use.

Galileo: the flow of time

In 1583, Galileo Galilei (1564–1642) discovered that a pendulum's harmonic motion has a constant period, which he learned by timing the motion of a swaying lamp in harmonic motion at mass at the cathedral of Pisa, with his pulse.[18]

In his Two New Sciences (1638), Galileo used a water clock to measure the time taken for a bronze ball to roll a known distance down an inclined plane; this clock was

"a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for a part of its length; the water thus collected was weighed, after each descent, on a very accurate balance; the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results."[19]

Galileo's experimental setup to measure the literal flow of time, in order to describe the motion of a ball, preceded Isaac Newton's statement in his Principia:

I do not define time, space, place and motion, as being well known to all.[20]

The Galilean transformations assume that time is the same for all reference frames.

Newton's physics: linear time

In or around 1665, when Isaac Newton (1643–1727) derived the motion of objects falling under gravity, the first clear formulation for mathematical physics of a treatment of time began: linear time, conceived as a universal clock.

Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.[21]

The water clock mechanism described by Galileo was engineered to provide laminar flow of the water during the experiments, thus providing a constant flow of water for the durations of the experiments, and embodying what Newton called duration.

In this section, the relationships listed below treat time as a parameter which serves as an index to the behavior of the physical system under consideration. Because Newton's fluents treat a linear flow of time (what he called mathematical time), time could be considered to be a linearly varying parameter, an abstraction of the march of the hours on the face of a clock. Calendars and ship's logs could then be mapped to the march of the hours, days, months, years and centuries.


Thermodynamics and the paradox of irreversibility

By 1798, Benjamin Thompson (1753–1814) had discovered that work could be transformed to heat without limit - a precursor of the conservation of energy or

In 1824 Sadi Carnot (1796–1832) scientifically analyzed the steam engines with his Carnot cycle, an abstract engine. Rudolf Clausius (1822–1888) noted a measure of disorder, or entropy, which affects the continually decreasing amount of free energy which is available to a Carnot engine in the:

Thus the continual march of a thermodynamic system, from lesser to greater entropy, at any given temperature, defines an arrow of time. In particular, Stephen Hawking identifies three arrows of time:[22]

  • Psychological arrow of time - our perception of an inexorable flow.
  • Thermodynamic arrow of time - distinguished by the growth of entropy.
  • Cosmological arrow of time - distinguished by the expansion of the universe.

Entropy is maximum in an isolated thermodynamic system, and increases. In contrast, Erwin Schrödinger (1887–1961) pointed out that life depends on a "negative entropy flow".[23] Ilya Prigogine (1917–2003) stated that other thermodynamic systems which, like life, are also far from equilibrium, can also exhibit stable spatio-temporal structures. Soon afterward, the Belousov-Zhabotinsky reactions[24] were reported, which demonstrate oscillating colors in a chemical solution.[25] These nonequilibrium thermodynamic branches reach a bifurcation point, which is unstable, and another thermodynamic branch becomes stable in its stead.[26]

Electromagnetism and the speed of light

In 1864, James Clerk Maxwell (1831–1879) presented a combined theory of electricity and magnetism. He combined all the laws then known relating to those two phenomenon into four equations. These vector calculus equations which use the del operator () are known as Maxwell's equations for electromagnetism.

In free space (that is, space not containing electric charges), the equations take the form (using SI units):[27]



ε0 and μ0 are the electric permittivity and the magnetic permeability of free space;
c = is the speed of light in free space, 299 792 458 m/s;
E is the electric field;
B is the magnetic field.

These equations allow for solutions in the form of electromagnetic waves. The wave is formed by an electric field and a magnetic field oscillating together, perpendicular to each other and to the direction of propagation. These waves always propagate at the speed of light c, regardless of the velocity of the electric charge that generated them.

The fact that light is predicted to always travel at speed c would be incompatible with Galilean relativity if Maxwell's equations were assumed to hold in any inertial frame (reference frame with constant velocity), because the Galilean transformations predict the speed to decrease (or increase) in the reference frame of an observer traveling parallel (or antiparallel) to the light.

It was expected that there was one absolute reference frame, that of the luminiferous aether, in which Maxwell's equations held unmodified in the known form.

The Michelson-Morley experiment failed to detect any difference in the relative speed of light due to the motion of the Earth relative to the luminiferous aether, suggesting that Maxwell's equations did, in fact, hold in all frames. In 1875, Hendrik Lorentz (1853–1928) discovered Lorentz transformations, which left Maxwell's equations unchanged, allowing Michelson and Morley's negative result to be explained. Henri Poincaré (1854–1912) noted the importance of Lorentz's transformation and popularized it. In particular, the railroad car description can be found in Science and Hypothesis,[28] which was published before Einstein's articles of 1905.

The Lorentz transformation predicted space contraction and time dilation; until 1905, the former was interpreted as a physical contraction of objects moving with respect to the aether, due to the modification of the intermolecular forces (of electric nature), while the latter was thought to be just a mathematical stipulation.

Einstein's physics: spacetime

Albert Einstein's 1905 special relativity challenged the notion of absolute time, and could only formulate a definition of synchronization for clocks that mark a linear flow of time:

If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B.

But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an "A time" and a "B time."

We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establish by definition that the "time" required by light to travel from A to B equals the "time" it requires to travel from B to A. Let a ray of light start at the "A time" tA from A towards B, let it at the "B time" tB be reflected at B in the direction of A, and arrive again at A at the “A time” tA.

In accordance with definition the two clocks synchronize if

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:—

  1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
  2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.
    — Albert Einstein, "On the Electrodynamics of Moving Bodies" [29]

Einstein showed that if the speed of light is not changing between reference frames, space and time must be so that the moving observer will measure the same speed of light as the stationary one because velocity is defined by space and time:

where r is position and t is time.

Indeed, the Lorentz transformation (for two reference frames in relative motion, whose x axis is directed in the direction of the relative velocity)


can be said to "mix" space and time in a way similar to the way a Euclidean rotation around the z axis mixes x and y coordinates. Consequences of this include relativity of simultaneity.

Relativity of Simultaneity
Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame.

More specifically, the Lorentz transformation is a hyperbolic rotation which is a change of coordinates in the four-dimensional Minkowski space, a dimension of which is ct. (In Euclidean space an ordinary rotation is the corresponding change of coordinates.) The speed of light c can be seen as just a conversion factor needed because we measure the dimensions of spacetime in different units; since the metre is currently defined in terms of the second, it has the exact value of 299 792 458 m/s. We would need a similar factor in Euclidean space if, for example, we measured width in nautical miles and depth in feet. In physics, sometimes units of measurement in which c = 1 are used to simplify equations.

Time in a "moving" reference frame is shown to run more slowly than in a "stationary" one by the following relation (which can be derived by the Lorentz transformation by putting ∆x′ = 0, ∆τ = ∆t′):


  • τ is the time between two events as measured in the moving reference frame in which they occur at the same place (e.g. two ticks on a moving clock); it is called the proper time between the two events;
  • t is the time between these same two events, but as measured in the stationary reference frame;
  • v is the speed of the moving reference frame relative to the stationary one;
  • c is the speed of light.

Moving objects therefore are said to show a slower passage of time. This is known as time dilation.

These transformations are only valid for two frames at constant relative velocity. Naively applying them to other situations gives rise to such paradoxes as the twin paradox.

That paradox can be resolved using for instance Einstein's General theory of relativity, which uses Riemannian geometry, geometry in accelerated, noninertial reference frames. Employing the metric tensor which describes Minkowski space:

Einstein developed a geometric solution to Lorentz's transformation that preserves Maxwell's equations. His field equations give an exact relationship between the measurements of space and time in a given region of spacetime and the energy density of that region.

Einstein's equations predict that time should be altered by the presence of gravitational fields (see the Schwarzschild metric):


is the gravitational time dilation of an object at a distance of .
is the change in coordinate time, or the interval of coordinate time.
is the gravitational constant
is the mass generating the field
is the change in proper time , or the interval of proper time.

Or one could use the following simpler approximation:

That is, the stronger the gravitational field (and, thus, the larger the acceleration), the more slowly time runs. The predictions of time dilation are confirmed by particle acceleration experiments and cosmic ray evidence, where moving particles decay more slowly than their less energetic counterparts. Gravitational time dilation gives rise to the phenomenon of gravitational redshift and Shapiro signal travel time delays near massive objects such as the sun. The Global Positioning System must also adjust signals to account for this effect.

According to Einstein's general theory of relativity, a freely moving particle traces a history in spacetime that maximises its proper time. This phenomenon is also referred to as the principle of maximal aging, and was described by Taylor and Wheeler as:[30]

"Principle of Extremal Aging: The path a free object takes between two events in spacetime is the path for which the time lapse between these events, recorded on the object's wristwatch, is an extremum."

Einstein's theory was motivated by the assumption that every point in the universe can be treated as a 'center', and that correspondingly, physics must act the same in all reference frames. His simple and elegant theory shows that time is relative to an inertial frame. In an inertial frame, Newton's first law holds; it has its own local geometry, and therefore its own measurements of space and time; there is no 'universal clock'. An act of synchronization must be performed between two systems, at the least.

Time in quantum mechanics

There is a time parameter in the equations of quantum mechanics. The Schrödinger equation[31] is


One solution can be


where is called the time evolution operator, and H is the Hamiltonian.

But the Schrödinger picture shown above is equivalent to the Heisenberg picture, which enjoys a similarity to the Poisson brackets of classical mechanics. The Poisson brackets are superseded by a nonzero commutator, say [H,A] for observable A, and Hamiltonian H:

This equation denotes an uncertainty relation in quantum physics. For example, with time (the observable A), the energy E (from the Hamiltonian H) gives:

is the uncertainty in energy
is the uncertainty in time
is Planck's constant

The more precisely one measures the duration of a sequence of events, the less precisely one can measure the energy associated with that sequence, and vice versa. This equation is different from the standard uncertainty principle, because time is not an operator in quantum mechanics.

Corresponding commutator relations also hold for momentum p and position q, which are conjugate variables of each other, along with a corresponding uncertainty principle in momentum and position, similar to the energy and time relation above.

Quantum mechanics explains the properties of the periodic table of the elements. Starting with Otto Stern's and Walter Gerlach's experiment with molecular beams in a magnetic field, Isidor Rabi (1898–1988), was able to modulate the magnetic resonance of the beam. In 1945 Rabi then suggested that this technique be the basis of a clock[32] using the resonant frequency of an atomic beam.

Dynamical systems

See dynamical systems and chaos theory, dissipative structures

One could say that time is a parameterization of a dynamical system that allows the geometry of the system to be manifested and operated on. It has been asserted that time is an implicit consequence of chaos (i.e. nonlinearity/irreversibility): the characteristic time, or rate of information entropy production, of a system. Mandelbrot introduces intrinsic time in his book Multifractals and 1/f noise.



Signalling is one application of the electromagnetic waves described above. In general, a signal is part of communication between parties and places. One example might be a yellow ribbon tied to a tree, or the ringing of a church bell. A signal can be part of a conversation, which involves a protocol. Another signal might be the position of the hour hand on a town clock or a railway station. An interested party might wish to view that clock, to learn the time. See: Time ball, an early form of Time signal.

Lorentz transform of world line
Evolution of a world line of an accelerated massive particle. This world line is restricted to the timelike top and bottom sections of this spacetime figure; this world line cannot cross the top (future) or the bottom (past) light cone. The left and right sections (which are outside the light cones) are spacelike.

We as observers can still signal different parties and places as long as we live within their past light cone. But we cannot receive signals from those parties and places outside our past light cone.

Along with the formulation of the equations for the electromagnetic wave, the field of telecommunication could be founded. In 19th century telegraphy, electrical circuits, some spanning continents and oceans, could transmit codes - simple dots, dashes and spaces. From this, a series of technical issues have emerged; see Category:Synchronization. But it is safe to say that our signalling systems can be only approximately synchronized, a plesiochronous condition, from which jitter need be eliminated.

That said, systems can be synchronized (at an engineering approximation), using technologies like GPS. The GPS satellites must account for the effects of gravitation and other relativistic factors in their circuitry. See: Self-clocking signal.

Technology for timekeeping standards

The primary time standard in the U.S. is currently NIST-F1, a laser-cooled Cs fountain,[33] the latest in a series of time and frequency standards, from the ammonia-based atomic clock (1949) to the caesium-based NBS-1 (1952) to NIST-7 (1993). The respective clock uncertainty declined from 10,000 nanoseconds per day to 0.5 nanoseconds per day in 5 decades.[34] In 2001 the clock uncertainty for NIST-F1 was 0.1 nanoseconds/day. Development of increasingly accurate frequency standards is underway.

In this time and frequency standard, a population of caesium atoms is laser-cooled to temperatures of one microkelvin. The atoms collect in a ball shaped by six lasers, two for each spatial dimension, vertical (up/down), horizontal (left/right), and back/forth. The vertical lasers push the caesium ball through a microwave cavity. As the ball is cooled, the caesium population cools to its ground state and emits light at its natural frequency, stated in the definition of second above. Eleven physical effects are accounted for in the emissions from the caesium population, which are then controlled for in the NIST-F1 clock. These results are reported to BIPM.

Additionally, a reference hydrogen maser is also reported to BIPM as a frequency standard for TAI (international atomic time).

The measurement of time is overseen by BIPM (Bureau International des Poids et Mesures), located in Sèvres, France, which ensures uniformity of measurements and their traceability to the International System of Units (SI) worldwide. BIPM operates under authority of the Metre Convention, a diplomatic treaty between fifty-one nations, the Member States of the Convention, through a series of Consultative Committees, whose members are the respective national metrology laboratories.

Time in cosmology

The equations of general relativity predict a non-static universe. However, Einstein accepted only a static universe, and modified the Einstein field equation to reflect this by adding the cosmological constant, which he later described as the biggest mistake of his life. But in 1927, Georges Lemaître (1894–1966) argued, on the basis of general relativity, that the universe originated in a primordial explosion. At the fifth Solvay conference, that year, Einstein brushed him off with "Vos calculs sont corrects, mais votre physique est abominable."[35] (“Your math is correct, but your physics is abominable”). In 1929, Edwin Hubble (1889–1953) announced his discovery of the expanding universe. The current generally accepted cosmological model, the Lambda-CDM model, has a positive cosmological constant and thus not only an expanding universe but an accelerating expanding universe.

If the universe were expanding, then it must have been much smaller and therefore hotter and denser in the past. George Gamow (1904–1968) hypothesized that the abundance of the elements in the Periodic Table of the Elements, might be accounted for by nuclear reactions in a hot dense universe. He was disputed by Fred Hoyle (1915–2001), who invented the term 'Big Bang' to disparage it. Fermi and others noted that this process would have stopped after only the light elements were created, and thus did not account for the abundance of heavier elements.

Gamow's prediction was a 5–10-kelvin black-body radiation temperature for the universe, after it cooled during the expansion. This was corroborated by Penzias and Wilson in 1965. Subsequent experiments arrived at a 2.7 kelvins temperature, corresponding to an age of the universe of 13.8 billion years after the Big Bang.

This dramatic result has raised issues: what happened between the singularity of the Big Bang and the Planck time, which, after all, is the smallest observable time. When might have time separated out from the spacetime foam;[37] there are only hints based on broken symmetries (see Spontaneous symmetry breaking, Timeline of the Big Bang, and the articles in Category:Physical cosmology).

General relativity gave us our modern notion of the expanding universe that started in the Big Bang. Using relativity and quantum theory we have been able to roughly reconstruct the history of the universe. In our epoch, during which electromagnetic waves can propagate without being disturbed by conductors or charges, we can see the stars, at great distances from us, in the night sky. (Before this epoch, there was a time, before the universe cooled enough for electrons and nuclei to combine into atoms about 377,000 years after the Big Bang, during which starlight would not have been visible over large distances.)


Ilya Prigogine's reprise is "Time precedes existence". In contrast to the views of Newton, of Einstein, and of quantum physics, which offer a symmetric view of time (as discussed above), Prigogine points out that statistical and thermodynamic physics can explain irreversible phenomena,[38] as well as the arrow of time and the Big Bang.

See also


  1. ^ Considine, Douglas M.; Considine, Glenn D. (1985). Process instruments and controls handbook (3 ed.). McGraw-Hill. pp. 18–61. ISBN 0-07-012436-1.
  2. ^ For example, Galileo measured the period of a simple harmonic oscillator with his pulse.
  3. ^ a b Otto Neugebauer The Exact Sciences in Antiquity. Princeton: Princeton University Press, 1952; 2nd edition, Brown University Press, 1957; reprint, New York: Dover publications, 1969. Page 82.
  4. ^ See, for example William Shakespeare Hamlet: " ... to thine own self be true, And it must follow, as the night the day, Thou canst not then be false to any man."
  5. ^ "Heliacal/Dawn Risings". Solar-center.stanford.edu. Retrieved 2012-08-17.
  6. ^ Farmers have used the sun to mark time for thousands of years, as the most ancient method of telling time. Archived 2010-07-26 at the Wayback Machine
  7. ^ Eratosthenes used this criterion in his measurement of the circumference of Earth
  8. ^ Fred Hoyle (1962), Astronomy: A history of man's investigation of the universe, Crescent Books, Inc., London LC 62-14108, p.31
  9. ^ The Mesopotamian (modern-day Iraq) astronomers recorded astronomical observations with the naked eye, more than 3500 years ago. P. W. Bridgman defined his operational definition in the twentieth c.
  10. ^ Naked eye astronomy became obsolete in 1609 with Galileo's observations with a telescope. Galileo Galilei Linceo, Sidereus Nuncius (Starry Messenger) 1610.
  11. ^ http://tycho.usno.navy.mil/gpstt.html http://www.phys.lsu.edu/mog/mog9/node9.html Today, automated astronomical observations from satellites and spacecraft require relativistic corrections of the reported positions.
  12. ^ "Unit of time (second)". SI brochure. International Bureau of Weights and Measures (BIPM). pp. Section Retrieved 2008-06-08.
  13. ^ S. R. Jefferts et al., "Accuracy evaluation of NIST-F1".
  14. ^ Fred Adams and Greg Laughlin (1999), Five Ages of the Universe ISBN 0-684-86576-9 p.35.
  15. ^ Charles Hose and William McDougall (1912) The Pagan Tribes of Borneo, Plate 60. Kenyahs measuring the Length of the Shadow at Noon to determine the Time for sowing PADI p. 108. This photograph is reproduced as plate B in Fred Hoyle (1962), Astronomy: A history of man's investigation of the universe, Crescent Books, Inc., London LC 62-14108, p.31. The measurement process is explained by: Gene Ammarell (1997), "Astronomy in the Indo-Malay Archipelago", p.119, Encyclopaedia of the history of science, technology, and medicine in non-western cultures, Helaine Selin, ed., which describes Kenyah Tribesmen of Borneo measuring the shadow cast by a gnomon, or tukar do with a measuring scale, or aso do.
  16. ^ North, J. (2004) God's Clockmaker: Richard of Wallingford and the Invention of Time. Oxbow Books. ISBN 1-85285-451-0
  17. ^ Watson, E (1979) "The St Albans Clock of Richard of Wallingford". Antiquarian Horology 372-384.
  18. ^ Jo Ellen Barnett, Time's Pendulum ISBN 0-306-45787-3 p.99.
  19. ^ Galileo 1638 Discorsi e dimostrazioni matematiche, intorno á due nuoue scienze 213, Leida, Appresso gli Elsevirii (Louis Elsevier), or Mathematical discourses and demonstrations, relating to Two New Sciences, English translation by Henry Crew and Alfonso de Salvio 1914. Section 213 is reprinted on pages 534-535 of On the Shoulders of Giants:The Great Works of Physics and Astronomy (works by Copernicus, Kepler, Galileo, Newton, and Einstein). Stephen Hawking, ed. 2002 ISBN 0-7624-1348-4
  20. ^ Newton 1687 Philosophiae Naturalis Principia Mathematica, Londini, Jussu Societatis Regiae ac Typis J. Streater, or The Mathematical Principles of Natural Philosophy, London, English translation by Andrew Motte 1700s. From part of the Scholium, reprinted on page 737 of On the Shoulders of Giants:The Great Works of Physics and Astronomy (works by Copernicus, Kepler, Galileo, Newton, and Einstein). Stephen Hawking, ed. 2002 ISBN 0-7624-1348-4
  21. ^ Newton 1687 page 738.
  22. ^ pp. 182-195. Stephen Hawking 1996. The Illustrated Brief History of Time: updated and expanded edition ISBN 0-553-10374-1
  23. ^ Erwin Schrödinger (1945) What is Life?
  24. ^ G. Nicolis and I. Prigogine (1989), Exploring Complexity
  25. ^ R. Kapral and K. Showalter, eds. (1995), Chemical Waves and Patterns
  26. ^ Ilya Prigogine (1996) The End of Certainty pp. 63-71
  27. ^ Clemmow, P. C. (1973). An introduction to electromagnetic theory. CUP Archive. pp. 56–57. ISBN 0-521-09815-7., Extract of pages 56, 57
  28. ^ Henri Poincaré, (1902). Science and Hypothesis Eprint Archived 2006-10-04 at the Wayback Machine
  29. ^ Einstein 1905, Zur Elektrodynamik bewegter Körper [On the electrodynamics of moving bodies] reprinted 1922 in Das Relativitätsprinzip, B.G. Teubner, Leipzig. The Principles of Relativity: A Collection of Original Papers on the Special Theory of Relativity, by H.A. Lorentz, A. Einstein, H. Minkowski, and W. H. Weyl, is part of Fortschritte der mathematischen Wissenschaften in Monographien, Heft 2. The English translation is by W. Perrett and G.B. Jeffrey, reprinted on page 1169 of On the Shoulders of Giants:The Great Works of Physics and Astronomy (works by Copernicus, Kepler, Galileo, Newton, and Einstein). Stephen Hawking, ed. 2002 ISBN 0-7624-1348-4
  30. ^ Taylor (2000). "Exploring Black Holes: Introduction to General Relativity" (PDF). Addison Wesley Longman.
  31. ^ E. Schrödinger, Phys. Rev. 28 1049 (1926)
  32. ^ A Brief History of Atomic Clocks at NIST Archived 2009-02-14 at the Wayback Machine
  33. ^ D. M. Meekhof, S. R. Jefferts, M. Stepanovíc, and T. E. Parker (2001) "Accuracy Evaluation of a Cesium Fountain Primary Frequency Standard at NIST", IEEE Transactions on Instrumentation and Measurement. 50, no. 2, (April 2001) pp. 507-509
  34. ^ James Jespersen and Jane Fitz-Randolph (1999). From sundials to atomic clocks : understanding time and frequency. Washington, D.C. : U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology. 308 p. : ill. ; 28 cm. ISBN 0-16-050010-9
  35. ^ John C. Mather and John Boslough (1996), The Very First Light ISBN 0-465-01575-1 p. 41.
  36. ^ George Smoot and Keay Davidson (1993) Wrinkles in Time ISBN 0-688-12330-9 A memoir of the experiment program for detecting the predicted fluctuations in the cosmic microwave background radiation.
  37. ^ Martin Rees (1997), Before the Beginning ISBN 0-201-15142-1 p. 210.
  38. ^ Prigogine, Ilya (1996), The End of Certainty: Time, Chaos and the New Laws of Nature. ISBN 0-684-83705-6 On pages 163 and 182.

Further reading

  • Boorstein, Daniel J., The Discoverers. Vintage. February 12, 1985. ISBN 0-394-72625-1
  • Dieter Zeh, H., The physical basis of the direction of time. Springer. ISBN 978-3-540-42081-1
  • Kuhn, Thomas S., The Structure of Scientific Revolutions. ISBN 0-226-45808-3
  • Mandelbrot, Benoît, Multifractals and 1/f noise. Springer Verlag. February 1999. ISBN 0-387-98539-5
  • Prigogine, Ilya (1984), Order out of Chaos. ISBN 0-394-54204-5
  • Serres, Michel, et al., "Conversations on Science, Culture, and Time (Studies in Literature and Science)". March, 1995. ISBN 0-472-06548-3
  • Stengers, Isabelle, and Ilya Prigogine, Theory Out of Bounds. University of Minnesota Press. November 1997. ISBN 0-8166-2517-4

External links

Absolute space and time

Absolute space and time is a concept in physics and philosophy about the properties of the universe. In physics, absolute space and time may be a preferred frame.

Arrow of time

The arrow of time, or time's arrow is the concept positing the "one-way direction" or "asymmetry" of time. It was

developed in 1927 by the British astronomer Arthur Eddington, and is an unsolved general physics question. This direction, according to Eddington, could be determined by studying the organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world ("a solid block of paper").Physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time.

Characteristic time

The characteristic time is an estimate of the order of magnitude of the reaction time scale of a system. It can loosely be defined as the inverse of the reaction rate. In chemistry, the characteristic time is used to determine whether the problem needs to be solved as an equilibrium problem or a kinetic problem.

In various fields of physics and astrophysics, the characteristic time or relaxation time refers to the time needed for a system to relax under external stimuli.

The characteristic time or relaxation time (RC time constant) of a simple RC circuit is the time it would take the capacitor to discharge from 100% down to 36.8% (1/e), or charge from 0% up to 63.2% (1 − 1/e).

In dielectric spectroscopy, it is the reciprocal of the characteristic frequency.

Chronology protection conjecture

The chronology protection conjecture is a conjecture first proposed by Stephen Hawking which hypothesizes that the laws of physics are such as to prevent time travel on all but submicroscopic scales. The permissibility of time travel is represented mathematically by the existence of closed timelike curves in some exact solutions to General Relativity. The chronology protection conjecture should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the causal violation (also known as chronology violation).

Galilean transformation

In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. These transformations together with spatial rotations and translations in space and time form the inhomogeneous Galilean group (assumed throughout below). Without the translations in space and time the group is the homogeneous Galilean group. The Galilean group is the group of motions of Galilean relativity acting on the four dimensions of space and time, forming the Galilean geometry. This is the passive transformation point of view. The equations below, although apparently obvious, are valid only at speeds much less than the speed of light. In special relativity the Galilean transformations are replaced by Poincaré transformations; conversely, the group contraction in the classical limit c → ∞ of Poincaré transformations yields Galilean transformations.

Galileo formulated these concepts in his description of uniform motion.

The topic was motivated by his description of the motion of a ball rolling down a ramp, by which he measured the numerical value for the acceleration of gravity near the surface of the Earth.

Jerk (physics)

In physics, jerk is the rate of change of acceleration; that is, the time derivative of acceleration, and as such the second derivative of velocity, or the third time derivative of position. According to the result of dimensional analysis of jerk, [length/time3], the SI units for its magnitude are m/s3 (or m⋅s−3); this can also be expressed in standard gravity per second (g/s).

Jerk is a vector, and (as with acceleration) there is no distinct term to denote its scalar magnitude (more precisely, its norm, as, e.g., there is "speed" for the norm of the velocity vector).


In physics, jounce, also known as snap, is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. Equivalently, it is the second derivative of acceleration or the third derivative of velocity. Jounce is defined by any of the following equivalent expressions:

The following equations are used for constant jounce:


is constant jounce,
is initial jerk,
is final jerk,
is initial acceleration,
is final acceleration,
is initial velocity,
is final velocity,
is initial position,
is final position,
is time between initial and final states.

The notation (used by Visser) is not to be confused with the displacement vector commonly denoted similarly.

The dimensions of jounce are distance per fourth power of time. In SI units, this is "metres per second to the fourth", m/s4, m⋅s−4, or 100 gal per second squared in CGS units.

Jounce and the fifth and sixth derivatives of position as a function of time are "sometimes somewhat facetiously" referred to as snap, crackle, and pop respectively. However, time derivatives of position of higher order than four appear rarely.

Metric tensor (general relativity)

In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational potential of Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separating the future and the past.

Proper time

In relativity, proper time along a timelike world line is defined as the time as measured by a clock following that line. It is thus independent of coordinates, and a Lorentz scalar. The proper time interval between two events on a world line is the change in proper time. This interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line. The proper time interval between two events depends not only on the events but also the world line connecting them, and hence on the motion of the clock between the events. It is expressed as an integral over the world line. An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated (inertial) clock between the same two events. The twin paradox is an example of this effect.

In terms of four-dimensional spacetime, proper time is analogous to arc length in three-dimensional (Euclidean) space. By convention, proper time is usually represented by the Greek letter τ (tau) to distinguish it from coordinate time represented by t.

By contrast, coordinate time is the time between two events as measured by an observer using that observer's own method of assigning a time to an event. In the special case of an inertial observer in special relativity, the time is measured using the observer's clock and the observer's definition of simultaneity.

The concept of proper time was introduced by Hermann Minkowski in 1908, and is a feature of Minkowski diagrams.

Relaxation (physics)

In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium.

Each relaxation process can be categorized

by a relaxation time τ. The simplest theoretical description of relaxation as function of time t is an exponential law exp(-t/τ) (exponential decay).


Simultaneity is the relation between two events assumed to be happening at the same time in a given frame of reference. According to Einstein's theory of relativity, simultaneity is not an absolute relation between events; what is simultaneous in one frame of reference will not necessarily be simultaneous in another (see Relativity of simultaneity). For inertial frames moving relative to one another at low speeds compared to the speed of light, this effect is small and can for practical matters be ignored, allowing simultaneity to be treated as an absolute relation.

The word is derived from the Latin simul, meaning at the same time (see sem-1 in Indo-European Roots), plus the suffix -taneous, abstracted from spontaneous, which in turn comes directly from Latin.

Spatial scale

In sciences such as physics, geography, astronomy, meteorology and statistics, the term scale or spatial scale is used for describing or classifying with large approximation the extent or size of a length, distance or area studied or described. For instance, in physics an object or phenomenon can be called microscopic if too small to be visible. In climatology, a micro-climate is a climate which might occur in a mountain, valley or near a lake shore, whereas in statistics a megatrend is a political, social, economical, environmental or technological trend which involves the whole planet or is supposed to last a very large amount of time.

In physics, the concept of scale is closely related to the more accurate concept of order of magnitude.

These divisions are somewhat arbitrary; where, on this table, mega- is assigned global scope, it may only apply continentally or even regionally in other contexts. The interpretations of meso- and macro- must then be adjusted accordingly.


T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal:

T-symmetry implies the conservation of entropy. Since the second law of thermodynamics means that entropy increases as time flows toward the future, the macroscopic universe does not in general show symmetry under time reversal. In other words, time is said to be non-symmetric, or asymmetric, except for special equilibrium states when the second law of thermodynamics predicts the time symmetry to hold. However, quantum noninvasive measurements are predicted to violate time symmetry even in equilibrium, contrary to their classical counterparts, although this has not yet been experimentally confirmed.

Time asymmetries are generally distinguished as among those...


Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past, through the present, to the future. Time is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions.Time has long been an important subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without circularity has consistently eluded scholars.

Nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems.Time in physics is unambiguously operationally defined as "what a clock reads". See Units of Time. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities. Time is used to define other quantities – such as velocity – so defining time in terms of such quantities would result in circularity of definition. An operational definition of time, wherein one says that observing a certain number of repetitions of one or another standard cyclical event (such as the passage of a free-swinging pendulum) constitutes one standard unit such as the second, is highly useful in the conduct of both advanced experiments and everyday affairs of life. The operational definition leaves aside the question whether there is something called time, apart from the counting activity just mentioned, that flows and that can be measured. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy.

Temporal measurement has occupied scientists and technologists, and was a prime motivation in navigation and astronomy. Periodic events and periodic motion have long served as standards for units of time. Examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the international unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms (see below). Time is also of significant social importance, having economic value ("time is money") as well as personal value, due to an awareness of the limited time in each day and in human life spans.

Time dilation

According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other, or by being differently situated relative to a gravitational field. As a result of the nature of spacetime, a clock that is moving relative to an observer will be measured to tick slower than a clock that is at rest in the observer's own frame of reference. A clock that is under the influence of a stronger gravitational field than an observer's will also be measured to tick slower than the observer's own clock.

Such time dilation has been repeatedly demonstrated, for instance by small disparities in a pair of atomic clocks after one of them is sent on a space trip, or by clocks on the Space Shuttle running slightly slower than reference clocks on Earth, or clocks on GPS and Galileo satellites running slightly faster. Time dilation has also been the subject of science fiction works, as it technically provides the means for forward time travel.

Time translation symmetry

Time translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a common interval. Time translation symmetry is the hypothesis that the laws of physics are unchanged, (i.e. invariant) under such a transformation. Time translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time translation symmetry is closely connected, via the Noether theorem, to conservation of energy. In mathematics, the set of all time translations on a given system form a Lie group.

There are many symmetries in nature besides time translation, such as spatial translation or rotational symmetries. These symmetries can be broken and explain diverse phenomena such as crystals, superconductivity, and the Higgs mechanism. However, it was thought until very recently that time translation symmetry could not be broken. Time crystals, a state of matter first observed in 2017, break time translation symmetry.

Twin paradox

In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as moving, and so, according to an incorrect and naive application of time dilation and the principle of relativity, each should paradoxically find the other to have aged less. However, this scenario can be resolved within the standard framework of special relativity: the travelling twin's trajectory involves two different inertial frames, one for the outbound journey and one for the inbound journey, and so there is no symmetry between the spacetime paths of the twins. Therefore, the twin paradox is not a paradox in the sense of a logical contradiction.

Starting with Paul Langevin in 1911, there have been various explanations of this paradox. These explanations "can be grouped into those that focus on the effect of different standards of simultaneity in different frames, and those that designate the acceleration [experienced by the travelling twin] as the main reason". Max von Laue argued in 1913 that since the traveling twin must be in two separate inertial frames, one on the way out and another on the way back, this frame switch is the reason for the aging difference, not the acceleration per se. Explanations put forth by Albert Einstein and Max Born invoked gravitational time dilation to explain the aging as a direct effect of acceleration. General relativity is not necessary to explain the twin paradox; special relativity alone can explain the phenomenon.Time dilation has been verified experimentally by precise measurements of atomic clocks flown in aircraft and satellites. For example, gravitational time dilation and special relativity together have been used to explain the Hafele–Keating experiment. It was also confirmed in particle accelerators by measuring the time dilation of circulating particle beams.

William G. Tifft

William G. Tifft is Emeritus Professor/Astronomer at the University of Arizona. His main interests are in galaxies, superclusters and what Tifft calls redshift problems (see redshift quantization). He was influential in the development of the first redshift surveys [1] and was an early proponent of manned space astronomy, conducted at a proposed moon base for example. In retirement, he is a principal scientist with The Scientific Association for the Study of Time in Physics and Cosmology (SASTPC).[2]

He has an A.B. in Astronomy from Harvard University (1954), and Ph.D. in Astronomy from the California Institute of Technology (1958) where he wrote his dissertation on photoelectric photometry, a copy of which is available online.

Yesterday (time)

Yesterday is a temporal construct of the relative past; literally of the day before the current day (today), or figuratively of earlier periods or times, often but not always within living memory.

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