Time
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
Time can be combined mathematically with other
physical quantities to derive other concepts such as motion, kinetic
energy and time-dependent fields.
Timekeeping
Timekeeping is a complex of
technological and scientific issues, and part of the foundation of
recordkeeping.
Contents
1 Markers of time
2 The unit of measurement of time: the second
2.1 The state of the art in timekeeping
3 Conceptions of time
3.1 Regularities in nature
3.1.1 Mechanical clocks
3.2 Galileo: the flow of time
3.3 Newton's physics: linear time
3.4 Thermodynamics and the paradox of irreversibility
3.5
Electromagnetism
Electromagnetism and the speed of light
3.6 Einstein's physics: spacetime
3.7
Time
Time in quantum mechanics
4 Dynamical systems
5 Signalling
6 Technology for timekeeping standards
7
Time
Time in cosmology
8 Reprise
9 See also
10 References
11 Further reading
Markers of time[edit]
Main article:
History
History of timekeeping devices
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
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[edit]
In the
International System of Units
International System of Units (SI), the unit of time is the
second (symbol:
s
displaystyle mathrm s
). It is a SI base unit, and it is currently defined 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.
The state of the art in timekeeping[edit]
Prerequisites
Measurement
Scientific notation
Natural units
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 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[edit]
Main article: Time
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.
Both
Galileo
Galileo and 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. 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 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
Big Bang theory time itself began
as part of the entire
Universe
Universe about 13.8 billion years ago.
Regularities in nature[edit]
Main article:
History
History of science
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[edit]
Richard of Wallingford
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
Atomic clocks can theoretically keep
accurate time for millions of years. They are appropriate for
standards and scientific use.
Galileo: the flow of time[edit]
Main article: reproducibility
In 1583,
Galileo
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
Two New Sciences (1638),
Galileo
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[edit]
Main article: classical physics
In or around 1665, when
Isaac Newton
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
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.
Prerequisites
differential equations
partial differential equations
Thermodynamics and the paradox of irreversibility[edit]
Main article: arrow of time
By 1798,
Benjamin Thompson
Benjamin Thompson (1753–1814) had discovered that work
could be transformed to heat without limit - a precursor of the
conservation of energy or
1st law of thermodynamics
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:
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 Hawking
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
Entropy is maximum in an isolated thermodynamic system, and increases.
In contrast,
Erwin Schrödinger
Erwin Schrödinger (1887–1961) pointed out that life
depends on a "negative entropy flow".[23]
Ilya Prigogine
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
Electromagnetism and the speed of light[edit]
Main article: Maxwell's equations
In 1864,
James Clerk Maxwell
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 (
∇
displaystyle nabla
) are known as
Maxwell's equations
Maxwell's equations for electromagnetism.
In free space (that is, space not containing electric charges), the
equations take the form (using SI units):[27]
Prerequisites
vector notation
partial differential equations
∇
×
E
=
−
∂
B
∂
t
displaystyle nabla times mathbf E =- frac partial mathbf B
partial t
∇
×
B
=
μ
0
ε
0
∂
E
∂
t
=
1
c
2
∂
E
∂
t
displaystyle nabla times mathbf B =mu _ 0 varepsilon _ 0 frac
partial mathbf E partial t = frac 1 c^ 2 frac partial
mathbf E partial t
∇
⋅
E
=
0
displaystyle nabla cdot mathbf E =0
∇
⋅
B
=
0
displaystyle nabla cdot mathbf B =0
where
ε0 and μ0 are the electric permittivity and the magnetic
permeability of free space;
c =
1
/
ϵ
0
μ
0
displaystyle 1/ sqrt epsilon _ 0 mu _ 0
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
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
Maxwell's equations held unmodified
in the known form.
The
Michelson-Morley experiment
Michelson-Morley experiment failed to detect any difference in the
relative speed of light due to the motion of the
Earth
Earth relative to the
luminiferous aether, suggesting that
Maxwell's equations
Maxwell's equations did, in fact,
hold in all frames. In 1875,
Hendrik Lorentz
Hendrik Lorentz (1853–1928) discovered
Lorentz transformations, which left
Maxwell's equations
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
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.[citation
needed]
Einstein's physics: spacetime[edit]
Main articles:
Special relativity
Special relativity and General relativity
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
t
B
−
t
A
=
t
A
′
−
t
B
.
displaystyle t_ text B -t_ text A =t'_ text A -t_ text B
text . ,!
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" [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:
v
=
d
r
d
t
,
displaystyle mathbf v = dmathbf r over dt text ,
where r is position and t is time.
Indeed, the
Lorentz transformation
Lorentz transformation (for two reference frames in
relative motion, whose x axis is directed in the direction of the
relative velocity)
Prerequisites
algebra
trigonometry
t
′
=
γ
(
t
−
v
x
/
c
2
)
where
γ
=
1
/
1
−
v
2
/
c
2
x
′
=
γ
(
x
−
v
t
)
y
′
=
y
z
′
=
z
displaystyle begin cases t'&=gamma (t-vx/c^ 2 ) text where
gamma =1/ sqrt 1-v^ 2 /c^ 2 \x'&=gamma
(x-vt)\y'&=y\z'&=zend cases
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.
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
Lorentz transformation is a hyperbolic rotation
(
c
t
′
x
′
)
=
(
cosh
ϕ
−
sinh
ϕ
−
sinh
ϕ
cosh
ϕ
)
(
c
t
x
)
where
ϕ
=
artanh
v
c
,
displaystyle begin pmatrix ct'\x'end pmatrix = begin pmatrix
cosh phi &-sinh phi \-sinh phi &cosh phi end pmatrix begin
pmatrix ct\xend pmatrix text where phi =operatorname artanh ,
frac v c text ,
which is a change of coordinates in the four-dimensional Minkowski
space, a dimension of which is ct. (In
Euclidean space
Euclidean space an ordinary
rotation
(
x
′
y
′
)
=
(
cos
θ
−
sin
θ
sin
θ
cos
θ
)
(
x
y
)
displaystyle begin pmatrix x'\y'end pmatrix = begin pmatrix cos
theta &-sin theta \sin theta &cos theta end pmatrix begin
pmatrix x\yend pmatrix
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
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
Lorentz transformation by putting ∆x′ = 0, ∆τ = ∆t′):
Δ
t
=
Δ
τ
1
−
v
2
/
c
2
displaystyle Delta t= Delta tau over sqrt 1-v^ 2 /c^ 2
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 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:
[
(
d
x
1
)
2
+
(
d
x
2
)
2
+
(
d
x
3
)
2
−
c
(
d
t
)
2
)
]
,
displaystyle left[(dx^ 1 )^ 2 +(dx^ 2 )^ 2 +(dx^ 3 )^ 2 -c(dt)^ 2
)right],
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):
T
=
d
t
(
1
−
2
G
M
r
c
2
)
d
t
2
−
1
c
2
(
1
−
2
G
M
r
c
2
)
−
1
d
r
2
−
r
2
c
2
d
θ
2
−
r
2
c
2
sin
2
θ
d
ϕ
2
displaystyle T= frac dt sqrt left(1- frac 2GM rc^ 2
right)dt^ 2 - frac 1 c^ 2 left(1- frac 2GM rc^ 2 right)^ -1
dr^ 2 - frac r^ 2 c^ 2 dtheta ^ 2 - frac r^ 2 c^ 2 sin ^ 2
theta ;dphi ^ 2
Where:
T
displaystyle T
is the gravitational time dilation of an object at a distance of
r
displaystyle r
.
d
t
displaystyle dt
is the change in coordinate time, or the interval of coordinate time.
G
displaystyle G
is the gravitational constant
M
displaystyle M
is the mass generating the field
(
1
−
2
G
M
r
c
2
)
d
t
2
−
1
c
2
(
1
−
2
G
M
r
c
2
)
−
1
d
r
2
−
r
2
c
2
d
θ
2
−
r
2
c
2
sin
2
θ
d
ϕ
2
displaystyle sqrt left(1- frac 2GM rc^ 2 right)dt^ 2 - frac
1 c^ 2 left(1- frac 2GM rc^ 2 right)^ -1 dr^ 2 - frac r^ 2
c^ 2 dtheta ^ 2 - frac r^ 2 c^ 2 sin ^ 2 theta ;dphi ^ 2
is the change in proper time
d
τ
displaystyle dtau
, or the interval of proper time.
Or one could use the following simpler approximation:
d
t
d
τ
=
1
1
−
(
2
G
M
r
c
2
)
.
displaystyle frac dt dtau = frac 1 sqrt 1-left( frac 2GM
rc^ 2 right) .
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
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
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
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
Time in quantum mechanics[edit]
See also: quantum mechanics
There is a time parameter in the equations of quantum mechanics. The
Schrödinger equation[31] is
Prerequisites
physics
quantum mechanics
H
(
t
)
ψ
(
t
)
⟩
=
i
ℏ
∂
∂
t
ψ
(
t
)
⟩
displaystyle H(t)leftpsi (t)rightrangle =ihbar partial over
partial t leftpsi (t)rightrangle
One solution can be
ψ
e
(
t
)
⟩
=
e
−
i
H
t
/
ℏ
ψ
e
(
0
)
⟩
displaystyle psi _ e (t)rangle =e^ -iHt/hbar psi _ e (0)rangle
.
where
e
−
i
H
t
/
ℏ
displaystyle e^ -iHt/hbar
is called the time evolution operator, and H is the Hamiltonian.
But the
Schrödinger picture
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:
d
d
t
A
=
(
i
ℏ
)
−
1
[
A
,
H
]
+
(
∂
A
∂
t
)
c
l
a
s
s
i
c
a
l
.
displaystyle frac d dt A=(ihbar )^ -1 [A,H]+left( frac
partial A partial t right)_ mathrm classical .
This equation denotes an uncertainty relation in quantum physics. For
example, with time (the observable A), the energy E (from the
Hamiltonian H) gives:
Δ
E
Δ
T
≥
ℏ
2
displaystyle Delta EDelta Tgeq frac hbar 2
where
Δ
E
displaystyle Delta E
is the uncertainty in energy
Δ
T
displaystyle Delta T
is the uncertainty in time
ℏ
displaystyle hbar
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
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
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[edit]
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[edit]
Prerequisites
electrical engineering
signal processing
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
Time ball, an
early form of
Time
Time signal.
Evolution
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
GPS satellites must
account for the effects of gravitation and other relativistic factors
in their circuitry. See: Self-clocking signal.
Technology for timekeeping standards[edit]
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
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
BIPM as a
frequency standard for TAI (international atomic time).
The measurement of time is overseen by
BIPM
BIPM (Bureau International des
Poids et Mesures), located in Sèvres, France, which ensures
uniformity of measurements and their traceability to the International
System
System of Units (SI) worldwide.
BIPM
BIPM operates under authority of the
Metre
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
Time in cosmology[edit]
Main article: physical 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
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
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.
WMAP
WMAP fluctuations of the cosmic microwave background radiation.[36]
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 kelvin 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
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
Timeline of the Big
Bang, and the articles in Category:Physical cosmology).
General relativity
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, 300,000 years after the big bang, during which starlight
would not have been visible.)
Reprise[edit]
Ilya Prigogine's reprise is "
Time
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[edit]
Relativistic dynamics
Category:systems of units
References[edit]
^ Considine, Douglas M.; Considine, Glenn D. (1985). Process
instruments and controls handbook (3 ed.). McGraw-Hill.
pp. 18–61. ISBN 0-07-012436-1.
^ For example,
Galileo
Galileo measured the period of a simple harmonic
oscillator with his pulse.
^ 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.
^ See, for example
William Shakespeare
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.
^
Eratosthenes
Eratosthenes used this criterion in his measurement of the
circumference of Earth
^
Fred Hoyle
Fred Hoyle (1962), Astronomy: A history of man's investigation of
the universe, Crescent Books, Inc.,
London
London LC 62-14108, p.31
^ 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.
^ Naked eye astronomy became obsolete in 1609 with Galileo's
observations with a telescope.
Galileo
Galileo Galilei Linceo, Sidereus
Nuncius (Starry Messenger) 1610.
^ 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.
^ "
Unit of time
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".
^ Fred Adams and Greg Laughlin (1999), Five Ages of the Universe
ISBN 0-684-86576-9 p.35.
^ Charles Hose and William McDougall (1912) The Pagan Tribes of
Borneo, Plate 60. Kenyahs measuring the
Length
Length of the Shadow at Noon
to determine the
Time
Time for sowing PADI p. 108. This photograph is
reproduced as plate B in
Fred Hoyle
Fred Hoyle (1962), Astronomy: A history of
man's investigation of the universe, Crescent Books, Inc.,
London
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.
^ North, J. (2004) God's Clockmaker:
Richard of Wallingford
Richard of Wallingford and the
Invention of Time. Oxbow Books. ISBN 1-85285-451-0
^ Watson, E (1979) "The St Albans
Clock
Clock of Richard of Wallingford".
Antiquarian
Horology
Horology 372-384.
^ Jo Ellen Barnett, Time's Pendulum ISBN 0-306-45787-3 p.99.
^
Galileo
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
Physics and Astronomy (works by Copernicus,
Kepler, Galileo, Newton, and Einstein). Stephen Hawking, ed. 2002
ISBN 0-7624-1348-4
^ 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
Physics and Astronomy
(works by Copernicus, Kepler, Galileo, Newton, and Einstein). Stephen
Hawking, ed. 2002 ISBN 0-7624-1348-4
^ Newton 1687 page 738.
^ pp. 182-195.
Stephen Hawking
Stephen Hawking 1996. The Illustrated Brief
History
History of
Time: updated and expanded edition ISBN 0-553-10374-1
^
Erwin Schrödinger
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
Ilya Prigogine (1996) The End of Certainty pp. 63-71
^ Clemmow, P. C. (1973). An introduction to electromagnetic theory.
CUP Archive. pp. 56–57. ISBN 0-521-09815-7. , Extract
of pages 56, 57
^ Henri Poincaré, (1902).
Science and Hypothesis
Science and Hypothesis Eprint
^ 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
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
Physics and Astronomy (works by Copernicus, Kepler,
Galileo, Newton, and Einstein). Stephen Hawking, ed. 2002
ISBN 0-7624-1348-4
^ Taylor (2000). "Exploring Black Holes: Introduction to General
Relativity" (PDF). Addison Wesley Longman.
^ E. Schrödinger,
Phys. Rev. 28 1049 (1926)
^ A Brief
History
History of Atomic Clocks at NIST
^ 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
^ John C. Mather and John Boslough (1996), The Very First Light
ISBN 0-465-01575-1 p.41.
^
George Smoot
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
^
Martin Rees
Martin Rees (1997), Before the Beginning ISBN 0-201-15142-1
p.210
^ 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[edit]
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
v
t
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Time
Key concepts
Past
history
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Futures studies
Far future in religion
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Timeline
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Measurement
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standards
Chronometry
UTC
UT
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Unit of time
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Time
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Causality
Duration
Endurantism
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Temporal finitism
Temporal parts
The Unreality of Time
Human
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and use of time
Accounting period
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Fiscal year
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Music
Procrastination
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Term
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Time
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Time-tracking software
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Time
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Yesterday – Today – Tomorrow
Time
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Time
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gravitational
Time
Time domain
Time
Time translation symmetry
Time
Time reversal symmetry
other subject
areas
Chronological dating
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Dating methodologies in archaeology
Time
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Related topics
Carpe diem
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Tempus fugit
Time
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Time
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Time
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Time
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Time
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Category
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Time
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Metrology
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UT
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