Time in physics
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In physics, time is defined by its measurement: time is what a clock reads.[1] In classical, non-relativistic physics, it is a scalar quantity (often denoted by the symbol ) and, like
Markers of time
Before there were clocks, time was measured by those physical processes[2] which were understandable to each epoch of civilization:[3]
- the first appearance (see: heliacal rising) of Sirius to mark the flooding of the Nile each year[3]
- the periodic succession of night and day, seemingly eternally[4]
- the position on the horizon of the first appearance of the sun at dawn[5]
- the position of the sun in the sky[6]
- the marking of the moment of noontime during the day[7]
- the length of the shadow cast by a gnomon[8]
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 has been defined since 1967 as "the duration of 9,192,631,770 [cycles] 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
The
Conceptions of time
Regularities in nature
In order to measure time, one can record the number of occurrences (events) of some
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,
Mechanical clocks
Richard of Wallingford (1292–1336), abbot of St. Albans Abbey, famously built a mechanical clock as an astronomical orrery about 1330.[16][17]
By the time of Richard of Wallingford, the use of
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:[19]
...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.
Galileo's experimental setup to measure the literal
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 engine 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.
With time, entropy increases in an isolated thermodynamic system. 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 that reminisce life. 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 equations are known as Maxwell's equations for electromagnetism; they allow for solutions in the form of electromagnetic waves and propagate at a fixed speed, 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
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,[27] which was published before Einstein's articles of 1905.
The Lorentz transformation predicted
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” 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 are universally 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"[28]
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.
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′):
where:
- 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
Einstein developed a geometric solution to Lorentz's transformation that preserves
Einstein's equations predict that time should be altered by the presence of
Where:
- 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
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:[29]
- "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
Time in quantum mechanics
There is a time parameter in the equations of quantum mechanics. The Schrödinger equation[30] is
One solution can be
- .
where is called the
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:
- where
- 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
Dynamical systems
See
One could say that time is a
Time crystals
Khemani, Moessner, and Sondhi define a time crystal as a "stable, conservative, macroscopic clock".[33]: 7
Signalling
Signalling is one application of the
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
In 19th century
That said,
Technology for timekeeping standards
The primary time standard in the U.S. is currently NIST-F1, a laser-cooled Cs fountain,[34] 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.[35] 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
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
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
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
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.)
Reprise
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,[39] as well as the arrow of time and the Big Bang.
See also
- Relativistic dynamics
- Category:systems of units
- Time in astronomy
References
- ISBN 0-07-012436-1.
- simple harmonic oscillator with his pulse.
- ^ Otto NeugebauerThe Exact Sciences in Antiquity. Princeton: Princeton University Press, 1952; 2nd edition, Brown University Press, 1957; reprint, New York: Dover publications, 1969. Page 82.
- ^ 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."
- ^ "Heliacal/Dawn Risings". Solar-center.stanford.edu. Retrieved 2012-08-17.
- ^ 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
- ^ Eratosthenes, On the measure of the Earth calculated the circumference of Earth, based on the measurement of the length of the shadow cast by a gnomon in two different places in Egypt, with an error of -2.4% to +0.8%
- ^ Fred Hoyle (1962), Astronomy: A history of man's investigation of the universe, Crescent Books, Inc., London LC 62-14108, p.31
- P. W. Bridgman defined his operational definitionin the twentieth c.
- Starry Messenger) 1610.
- ^ http://tycho.usno.navy.mil/gpstt.html http://www.phys.lsu.edu/mog/mog9/node9.html Archived 2010-07-13 at the Wayback Machine Today, automated astronomical observations from satellites and spacecraft require relativistic corrections of the reported positions.
- ^ "Unit of time (second)". SI brochure. International Bureau of Weights and Measures (BIPM). pp. Section 2.1.1.3. Retrieved 2008-06-08.
- ^ S. R. Jefferts et al., "Accuracy evaluation of NIST-F1".
- ISBN 0-684-86576-9p.35.
- ^ 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.
- ISBN 1-85285-451-0
- ^ Watson, E (1979) "The St Albans Clock of Richard of Wallingford". Antiquarian Horology 372-384.
- ISBN 0-306-45787-3p.99.
- ISBN 0-7624-1348-4
- ISBN 0-7624-1348-4
- ^ Newton 1687 page 738.
- ISBN 0-553-10374-1
- ^ Erwin Schrödinger (1945) What is Life?
- ^ G. Nicolis and I. Prigogine (1989), Exploring Complexity
- ^ R. Kapral and K. Showalter, eds. (1995), Chemical Waves and Patterns
- ^ Ilya Prigogine (1996) The End of Certainty pp. 63–71
- ^ Henri Poincaré, (1902). Science and Hypothesis Eprint Archived 2006-10-04 at the Wayback Machine
- ISBN 0-7624-1348-4
- ^ Taylor (2000). "Exploring Black Holes: Introduction to General Relativity" (PDF). Addison Wesley Longman.
- ISSN 0031-899X.
- ^ A Brief History of Atomic Clocks at NIST Archived 2009-02-14 at the Wayback Machine
- ^ Slashdot (25 Oct 2021) An Ultra-Precise Clock Shows How To Link the Quantum World With Gravity Jun Ye's work at JILA
- ^ Vedika Khemani, Roderich Moessner, and S. L. Sondhi (23 Oct 2019) A Brief History of Time Crystals
- ^ 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
- ^ 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
- ISBN 0-465-01575-1p. 41.
- cosmic microwave background radiation.
- ISBN 0-201-15142-1p. 210.
- ISBN 0-684-83705-6On pages 163 and 182.
Further reading
- Boorstein, Daniel J., The Discoverers. Vintage. February 12, 1985. ISBN 0-394-72625-1
- ISBN 978-3-540-42081-1
- ISBN 0-226-45808-3
- ISBN 0-387-98539-5
- ISBN 0-394-54204-5
- 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
- Media related to Time in physics at Wikimedia Commons