- Time in physics
physics, the treatment of timeis a central issue. It has been treated as a question of geometry. One can measure time and treat it as a geometrical dimension, such as length, and perform mathematical operations on it. It is a scalar quantity and, like length, mass, and charge, is usually listed in most physics books as a fundamental quantity. Time can be combined mathematically with other fundamental quantities to deriveother concepts such as motion, energyand fields. Time is largely defined by its measurement in physics. "" is a complex of technological and scientific issues, and part of the foundation of " recordkeeping".! scientific notation
partial differential equations
The unit of measurement of time: the second
International System of Units(SI), the unit of time is the second(symbol: ). It is a SI base unit, and it is currently defined as "the duration of nowrap|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." [cite web
title=Unit of time (second)
International Bureau of Weights and Measures(BIPM)]
The state of the art in timekeeping
Natural unitsThe UTC timestampin use worldwide is an atomic time standard. The relative accuracy of such a time standard is currently on the order of 10−15 [ [http://tf.nist.gov/general/pdf/1823.pdf S. R. Jefferts et al., "Accuracy evaluation of NIST-F1".] ] (corresponding to 1 second in approximately 30 million years). The smallest time step considered 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.
Conceptions of time
Galileoand Newton and most people up until the 20th century thought that time was the same for everyone everywhere. This is the basis for s, where time is a parameter. Our modern conception of time is based on Einstein's theory of relativity, in which rates of time run differently depending on relative motion, and spaceand time are merged into spacetime, where we live on a world linerather than a timeline. Thus time is part of a coordinate, in this view. Physicists believe the entire Universeand therefore time itself began about 13.7 billion years ago in the big bang. (See Time in Cosmology below) Whether it will ever come to an end is an open question. (See philosophy of physics.)
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, moonand stars were noted and tabulated for millennia, before the laws of physicswere formulated. The sun was the arbiter of the flow of time, but timewas known only to the hour, for millennia. The gnomonwas known across Eurasia, at least as far southward as the jungles of Southeast Asia. [Fred Hoyle (1955), "Frontiers of Astronomy". New York: Harper & Brothers ]
:I farm the land from which I take my food.:I watch the sun rise and sun set.:Kings can ask no more.-- as quoted by
Joseph Needham"Science and Civilisation in China"
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.
timekeepingwas 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 clockbecame more and more accurate, and finally reliable. For ships at sea, boys were used to turn the sandglasses and to call the hours.
Richard of Wallingford(1292–1336), abbot of St. Alban's abbey, famously built a mechanical clock as an astronomical orreryabout 1330. [North, J. (2004) "God's Clockmaker: Richard of Wallingford and the Invention of Time". Oxbow Books. ISBN 1-85285-451-0] [Watson, E (1979) "The St Albans Clock of Richard of Wallingford". "Antiquarian Horology" 372-384.]
By the time of Richard of Wallingford, the use of
ratchets and gears allowed the towns of Europeto 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 clockscan theoretically keep accurate time for millions of years. They are appropriate for standards and scientific use.
Galileo: the flow of time
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 motionat mass at the cathedral of Pisa, with his pulse. [Jo Ellen Barnett, "Time's Pendulum" ISBN 0-306-45787-3 p.99.]
In his "
Two New Sciences" (1638), Galileo used a water clockto 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." Galileo1638 "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]
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, placeand motion, as being well known to all."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]
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 physicsof 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."
Newton1687 page 738.] The water clockmechanism described by Galileo was engineered to provide laminar flowof 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.
partial differential equations
Lagrange (1736-1813) would aid in the formulation of a simpler version ["Dynamics is a four-dimensional geometry." --Lagrange (1796), "Thèorie des fonctions analytiques", as quoted by Ilya Prigogine (1996), "The End of Certainty" ISBN 0-684-83705-6 p.58] of Newton's equations. He started with an energy term, L, named the "Lagrangian" in his honor, and formulated "
Lagrange's equations"::The dotted quantities, denote a function which corresponds to a Newtonian fluxion, whereas denote a function which corresponds to a Newtonian fluent. But linear time is the parameter for the relationship between the and the of the physical system under consideration.Some decades later, it was found that the second order equation of Lagrange or Newton can be more easily solved or visualized by suitable transformation to sets of first order differential equations.
Lagrange's equations can be transformed, under a
Legendre transformation, to " Hamilton's equations"; the Hamiltonian formulation for the equations of motion of some conjugate variables p,q (for example, momentum p and position q) is: ! Operators
- ::in the
Poisson bracketnotation and clearly shows the dependence of the time variation of conjugate variables p,q on an energy expression.
This relationship, it was to be found, also has corresponding forms in
quantum mechanicsas well as in the classical mechanicsshown above. These relationships bespeak a conception of time which is reversible.
Thermodynamics and the paradox of irreversibility
Benjamin Thompson(1753-1814) had discovered that work could be transformed to heatwithout limit - a precursor of the conservation of energy or
*1st law of thermodynamics In 1824 Sadi Carnot (1796-1832) scientifically analyzed the
steam engineswith 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:
*2nd law of thermodynamics 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 Hawkingidentifies three arrows of time: pp. 182-195. Stephen Hawking1996. "The Illustrated Brief History of Time": updated and expanded edition ISBN 0-553-10374-1]
*Psychological arrow of time - our perception of an inexorable flow.
*Thermodynamic arrow of time - distinguished by the growth of
*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 lifedepends on a "negative entropy flow". [ Erwin Schrödinger(1945) "What is Life?"] 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 [G. Nicolis and I. Prigogine (1989), "Exploring Complexity"] were reported, which demonstrate oscillating colors in a chemical solution. [R. Kapral and K. Showalter, eds. (1995), "Chemical Waves and Patterns"] These nonequilibrium thermodynamic branches reach a "bifurcation point", which is unstable, and another thermodynamic branch becomes stable in its stead. [Ilya Prigogine (1996) "The End of Certainty" pp. 63-71]
Electromagnetism and the speed of light
James Clerk Maxwell(1831-1879) presented a combined theory of electricityand magnetism. He combined all the laws then known relating to those two phenomenon into four equations. These vector calculusequations which use the deloperator () are known as Maxwell's equationsfor electromagnetism. In free space (that is, space not containing electric charges), the equations take the form (using SI units):
partial differential equations:
where:"ε"0 and "μ"0 are the electric permittivity and the magnetic permeability of free space;:"c" = is the
speed of lightin 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.
Michelson-Morley experimentfailed 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' transformation and popularized it. In particular, the railroad car description can be found in "Science and Hypothesis", [Henri Poincaré, (1902). "Science and Hypothesis" [http://spartan.ac.brocku.ca/~lward/Poincare/Poincare_1905_toc.html Eprint] ] which was published before Einstein's articles of 1905.
The Lorentz transformation predicted
space contractionand 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. Fact|date=May 2008
Einstein's physics: spacetime
special relativity" (1905), " general relativity" (1915). Albert Einstein's 1905 special relativitychallenged the notion of absolute time, and could only formulate a definition of synchronizationfor clocks that mark a linear flow of time:Quote|If at the point A of space there is a clock, an observer at A can determine thetime values of events in the immediate proximity of A by finding the positionsof the hands which are simultaneous with these events. If there is at the point Bof space another clock in all respects resembling the one at A, it is possible foran 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 definedonly an "A time" and a "B time." We have not defined a common "time" forA 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" itrequires to travel from B to A. Let a ray of light start at the "A time" "t"A fromA towards B, let it at the "B time" "t"B be reflected at B in the direction of A,and arrive again at A at the “A time” "t"′A.
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 areuniversally valid:—
#If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
#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" 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] 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)!
trigonometry:can be said to "mix" space and time in a way similar to the way an Euclidean rotation around the "z" axis mixes "x" and "y" coordinates. Consequences of this include relativity of simultaneity.
thumb|Event B is simultaneous with A in the green reference frame, but it occurredbefore 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 spacean 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 metreis currently defined in terms of the second, it has the "exact" value of nowrap|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"′)::where:
*∆"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 timebetween 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
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 tensorwhich 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 spacetimeand 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 dilationof an object at a distance of .
: is the change in coordinate time, or the interval of coordinate time.
: is the
: is the
massgenerating the field
: is the change in
proper time, or the interval of proper time.
Or one could use the following simpler approximation:
Time runs slower the stronger the gravitational field, and hence
acceleration, is. The predictions of time dilation are confirmed by particle acceleration experiments and cosmic rayevidence, where moving particles decay slower than their less energetic counterparts. Gravitational time dilation gives rise to the phenomenon of gravitational redshiftand delays in signal travel time near massive objects such as the sun. The Global Positioning Systemmust also adjust signals to account for this effect.
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 lawholds; 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 equationE. Schrödinger, Phys. Rev.28 1049 (1926)] is
quantum mechanics:One solution can be:.where is a Wick rotation(in the complex plane), and "H" is the scalar Hamiltonian.
Schrödinger pictureshown 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 observableA, 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:
::where: is the uncertainty in energy: is the uncertainty in time: is
Planck's constantThe 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 operatorin quantum mechanics.
commutatorrelations also hold for momentum "p" and position "q", which are conjugate variablesof 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 tableof 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 modulatethe magnetic resonanceof the beam. In 1945 Rabi then suggested that this technique be the basis of a clock [ [http://tf.nist.gov/timefreq/cesium/atomichistory.htm A Brief History of Atomic Clocks at NIST] ] using the resonant frequencyof an atomic beam.
John Cramer [http://seattlepi.nwsource.com/local/292378_timeguy15.html is preparing an experiment] to determine whether
quantum entanglementis also nonlocal in timeas it is in space. This can also be stated as 'sending a signal back in time'. Cramer has recently published an [http://faculty.washington.edu/jcramer/Nonlocal_2007.pdf update] indicating that the final experiment will take more time to prepare.
dynamical systems and chaos theory, dissipative structures
One could say that time is a
parameterizationof a dynamical systemthat 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 entropyproduction, of a system. Mandelbrotintroduces intrinsic timein his book "Multifractals and 1/f noise".
Signalling is one application of the
electromagnetic waves described above. In general, a signal is part of communicationbetween parties and places. One example might be a yellow ribbontied 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.
world lineof an accelerated massive particle. This worldline is restricted to the timeliketop and bottom sections of this spacetimefigure and can not cross the top ( future) nor the bottom ( past) light cone. The left and right sections, 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
telecommunicationcould 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 . But it is safe to say that our signalling systems can be only approximately synchronized, a plesiochronouscondition, from which jitterneed be eliminated.
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
primary time standardin the U.S.is currently NIST-F1, a laser-cooled Cs fountain, [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] 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/day to 0.5 nanoseconds/day in 5 decades. [ 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] 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-millionth
Kelvin. 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) world-wide. BIPM operates under authority of the " Convention du Metre", 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 " _fr. Vos calculs sont corrects, mais votre physique est abominable." [John C. Mather and John Boslough (1996), "The Very First Light" ISBN 0-465-01575-1 p.41. ] 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 radiationtemperature 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 kelvin temperature, corresponding to an age of the universeof 13.7 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; [ Martin Rees(1997), "Before the Beginning" ISBN 0-201-15142-1 p.210] there are only hints based on broken symmetries (see Spontaneous symmetry breaking, Timeline of the Big Bang, and the articles in ). General relativitygave 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, 300,000 years after the big bang, during which starlight would not have been visible.)
Ilya Prigogine's reprise is " Timeprecedes existence". He contrasts the views of Newton, Einstein and quantum physics which offer a symmetric view of time (as discussed above) with his own views, which point out that statistical and thermodynamic physics can explain irreversible phenomena [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. ] as well as the arrow of timeand the Big Bang.
* Boorstein, Daniel J., "The Discoverers". Vintage. February 12, 1985. ISBN 0-394-72625-1
* 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
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