ΔT

In precise timekeeping, ΔT (Delta T, delta-T, deltaT, or DT) is a measure of the cumulative effect of the departure of the Earth's rotation period from the fixed-length day of atomic time.[3] Formally it is the time difference obtained by subtracting Universal Time (UT, defined by the Earth's rotation) from Terrestrial Time (TT, independent of the Earth's rotation): ΔT = TT − UT. The value of ΔT for the start of 1902 is approximately zero; for 2002 it is about 64 seconds. So the Earth's rotations over that century took about 64 seconds longer than would be required for days of atomic time.

Delta t
ΔT vs. time from 1657 to 2018.[1][2]

Calculation

The Earth's rotational speed is ν = 1//dt, and a day corresponds to one period P = 1/ν. A rotational acceleration /dt gives a rate of change of the period of dP/dt = −1/ν2/dt, which is usually expressed as α = νdP/dt = −1/ν/dt. This has units of 1/time, and is commonly quoted as milliseconds-per-day per century (written as ms/day/cy, understood as (ms/day)/cy). Integrating α gives an expression for ΔT against time.

Universal time

Universal Time is a time scale based on the Earth's rotation, which is somewhat irregular over short periods (days up to a century), thus any time based on it cannot have an accuracy better than 1 in 108. However, a larger, more consistent effect has been observed over many centuries: Earth's rate of rotation is inexorably slowing down. This observed change in the rate of rotation is attributable to two primary forces, one decreasing and one increasing the Earth's rate of rotation. Over the long term, the dominating force is tidal friction, which is slowing the rate of rotation, contributing about α = +2.3 ms/day/cy or dP/dt = +2.3 ms/cy, which is equal to the very small fractional change +7.3×10−13 day/day. The most important force acting in the opposite direction, to speed up the rate, is believed to be a result of the melting of continental ice sheets at the end of the last glacial period. This removed their tremendous weight, allowing the land under them to begin to rebound upward in the polar regions, an effect that is still occurring today and will continue until isostatic equilibrium is reached. This "post-glacial rebound" brings mass closer to the rotational axis of the Earth, which makes the Earth spin faster, according to the law of conservation of angular momentum, similar to an ice skater pulling their arms in to spin faster. Models estimate this effect to contribute about −0.6 ms/day/cy. Combining these two effects, the net acceleration (actually a deceleration) of the rotation of the Earth, or the change in the length of the mean solar day (LOD), is +1.7 ms/day/cy. This matches the average rate derived from astronomical records over the past 27 centuries.[4]

Terrestrial time

Terrestrial Time is a theoretical uniform time scale, defined to provide continuity with the former Ephemeris Time (ET). ET was an independent time-variable, proposed (and its adoption agreed) in the period 1948–52[5] with the intent of forming a gravitationally uniform time scale as far as was feasible at that time, and depending for its definition on Simon Newcomb's Tables of the Sun (1895), interpreted in a new way to accommodate certain observed discrepancies.[6] Newcomb's tables formed the basis of all astronomical ephemerides of the Sun from 1900 through 1983: they were originally expressed (and published) in terms of Greenwich Mean Time and the mean solar day,[7][8] but later, in respect of the period 1960–1983, they were treated as expressed in terms of ET,[9] in accordance with the adopted ET proposal of 1948–52. ET, in turn, can now be seen (in light of modern results)[10] as close to the average mean solar time between 1750 and 1890 (centered on 1820), because that was the period during which the observations on which Newcomb's tables were based were performed. While TT is strictly uniform (being based on the SI second, every second is the same as every other second), it is in practice realised by International Atomic Time (TAI) with an accuracy of about 1 part in 1014.

Earth's rate of rotation

Earth's rate of rotation must be integrated to obtain time, which is Earth's angular position (specifically, the orientation of the meridian of Greenwich relative to the fictitious mean sun). Integrating +1.7 ms/d/cy and centering the resulting parabola on the year 1820 yields (to a first approximation) 32 × (year − 1820/100)2
- 20
seconds for ΔT.[11][12] Smoothed historical measurements of ΔT using total solar eclipses are about +17190 s in the year −500 (501 BC), +10580 s in 0 (1 BC), +5710 s in 500, +1570 s in 1000, and +200  s in 1500. After the invention of the telescope, measurements were made by observing occultations of stars by the Moon, which allowed the derivation of more closely spaced and more accurate values for ΔT. ΔT continued to decrease until it reached a plateau of +11 ± 6 s between 1680 and 1866. For about three decades immediately before 1902 it was negative, reaching −6.64 s. Then it increased to +63.83 s in January 2000 and +68.97 s in January 2018.[13] This will require the addition of an ever-greater number of leap seconds to UTC as long as UTC tracks UT1 with one-second adjustments. (The SI second as now used for UTC, when adopted, was already a little shorter than the current value of the second of mean solar time.[14]) Physically, the meridian of Greenwich in Universal Time is almost always to the east of the meridian in Terrestrial Time, both in the past and in the future. +17190 s or about ​4 34 h corresponds to 71.625°E. This means that in the year −500 (501 BC), Earth's faster rotation would cause a total solar eclipse to occur 71.625° to the east of the location calculated using the uniform TT.

Values prior to 1955

All values of ΔT before 1955 depend on observations of the Moon, either via eclipses or occultations. The angular momentum lost by the Earth due to friction induced by the Moon's tidal effect is transferred to the Moon, increasing its angular momentum, which means that its moment arm (its distance from the Earth) is increased (for the time being about +3.8 cm/year), which via Kepler's laws of planetary motion causes the Moon to revolve around the Earth at a slower rate. The cited values of ΔT assume that the lunar acceleration (actually a deceleration, that is a negative acceleration) due to this effect is dn/dt = −26″/cy2, where n is the mean sidereal angular motion of the Moon. This is close to the best estimate for dn/dt as of 2002 of −25.858 ± 0.003″/cy2[15] so ΔT need not be recalculated given the uncertainties and smoothing applied to its current values. Nowadays, UT is the observed orientation of the Earth relative to an inertial reference frame formed by extra-galactic radio sources, modified by an adopted ratio between sidereal time and solar time. Its measurement by several observatories is coordinated by the International Earth Rotation and Reference Systems Service (IERS).

Notes

  1. ^ IERS Rapid Service/Prediction Center (c. 1986). Historic Delta T and LOD. Source attributed data to McCarthy and Babcock (1986). Retrieved December 2009.
  2. ^ IERS Rapid Service/Prediction Center. Monthly determinations of Delta T. Retrieved May 2018.
  3. ^ "Day of atomic time" in this article refers to a day of 86,400 atomic seconds, or more formally, 86,400 seconds of Terrestrial Time.
  4. ^ McCarthy & Seidelmann 2009, 88–89.
  5. ^ Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, Nautical Almanac Offices of UK and US (1961), at pp. 9 and 71.
  6. ^ See G M Clemence's proposal of 1948, contained in his paper: "On the System of Astronomical Constants", Astronomical Journal (1948) vol.53 (6), issue #1170, pp 169–179; also G M Clemence (1971), "The Concept of Ephemeris Time", in Journal for the History of Astronomy v2 (1971), pp. 73–79 (giving details of the genesis and adoption of the ephemeris time proposal); also article Ephemeris time and references therein.
  7. ^ Newcomb's Tables of the Sun (Washington, 1895), Introduction, I. Basis of the Tables, pp. 9 and 20, citing time units of Greenwich Mean Noon, Greenwich Mean Time, and mean solar day
  8. ^ W de Sitter, on p. 38 of Bulletin of the Astronomical Institutes of the Netherlands, v4 (1927), pp.21–38, "On the secular accelerations and the fluctuations of the moon, the sun, Mercury and Venus", which refers to "the 'astronomical time', given by the earth's rotation, and used in all practical astronomical computations", and states that it "differs from the 'uniform' or 'Newtonian' time".
  9. ^ See p.612 in Explanatory Supplement to the Astronomical Almanac, ed. P K Seidelmann, 1992, confirming introduction of ET in the 1960 edition of the ephemerides.
  10. ^ See especially F R Stephenson (1997), and Stephenson & Morrison (1995), book and papers cited below.
  11. ^ A similar parabola is plotted on p. 54 of McCarthy & Seidelmann (2009).
  12. ^ https://eclipse.gsfc.nasa.gov/SEhelp/deltat2004.html
  13. ^ "Long-term Delta T — Naval Oceanography Portal". c. 2018. Retrieved September 29, 2018.
  14. ^ :(1) In "The Physical Basis of the Leap Second", by D D McCarthy, C Hackman and R A Nelson, in Astronomical Journal, vol.136 (2008), pages 1906–1908, it is stated (page 1908), that "the SI second is equivalent to an older measure of the second of UT1, which was too small to start with and further, as the duration of the UT1 second increases, the discrepancy widens." :(2) In the late 1950s, the caesium standard was used to measure both the current mean length of the second of mean solar time (UT2) (result: 9192631830 cycles) and also the second of ephemeris time (ET) (result: 9192631770 ± 20 cycles), see "Time Scales", by L. Essen, in Metrologia, vol.4 (1968), pp.161–165, on p.162. As is well known, the 9192631770 figure was chosen for the SI second. L Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".
  15. ^ J.Chapront, M.Chapront-Touzé, G.Francou (2002): "A new determination of lunar orbital parameters, precession constant, and tidal acceleration from LLR measurements" (also in PDF). Astronomy & Astrophysics 387, 700–709.

References

  • McCarthy, D.D. & Seidelmann, P.K. TIME: From Earth Rotation to Atomic Physics. Weinheim: Wiley-VCH. (2009). ISBN 978-3-527-40780-4
  • Morrison, L.V. & Stephenson, F. R. "Historical values of the Earth's clock error ΔT and the calculation of eclipses" (pdf, 862 KB), Journal for the History of Astronomy 35 (2004) 327–336.
  • Stephenson, F.R. Historical Eclipses and Earth's Rotation. Cambridge University Press, 1997. ISBN 0-521-46194-4
  • Stephenson, F. R. & Morrison, L.V. "Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990". Philosophical Transactions of the Royal Society of London, Series A 351 (1995) 165-202. JSTOR link. Includes evidence that the 'growth' in Delta-T is being modified by an oscillation with a wavelength around 1500 years; if that is true, then during the next few centuries Delta-T values will increase more slowly than is envisaged.

External links

Areal velocity

In classical mechanics, areal velocity (also called sector velocity or sectorial velocity) is the rate at which area is swept out by a particle as it moves along a curve. In the adjoining figure, suppose that a particle moves along the blue curve. At a certain time t, the particle is located at point B, and a short while later, at time t + Δt, the particle has moved to point C. The area swept out by the particle is the green area in the figure, bounded by the line segments AB and AC and the curve along which the particle moves. The areal velocity equals this area divided by the time interval Δt in the limit that Δt becomes vanishingly small. It is an example of a pseudovector (also called axial vector), pointing normal to the plane containing the position and velocity vectors of the particle.

The concept of areal velocity is closely linked historically with the concept of angular momentum. Kepler's second law states that the areal velocity of a planet, with the sun taken as origin, is constant. Isaac Newton was the first scientist to recognize the dynamical significance of Kepler's second law. With the aid of his laws of motion, he proved in 1684 that any planet that is attracted to a fixed center sweeps out equal areas in equal intervals of time. By the middle of the 18th century, the principle of angular momentum was discovered gradually by Daniel Bernoulli and Leonhard Euler and Patrick d'Arcy; d'Arcy's version of the principle was phrased in terms of swept area. For this reason, the principle of angular momentum was often referred to in the older literature in mechanics as "the principle of equal areas." Since the concept of angular momentum includes more than just geometry, the designation "principle of equal areas" has been dropped in modern works.

Calculus of moving surfaces

The calculus of moving surfaces (CMS) is an extension of the classical tensor calculus to deforming manifolds. Central to the CMS is the Tensorial Time Derivative whose original definition was put forth by Jacques Hadamard. It plays the role analogous to that of the covariant derivative on differential manifolds. in that it produces a tensor when applied to a tensor.

Suppose that is the evolution of the surface indexed by a time-like parameter . The definitions of the surface velocity and the operator are the geometric foundations of the CMS. The velocity C is the rate of deformation of the surface in the instantaneous normal direction. The value of at a point is defined as the limit

where is the point on that lies on the straight line perpendicular to at point P. This definition is illustrated in the first geometric figure below. The velocity is a signed quantity: it is positive when points in the direction of the chosen normal, and negative otherwise. The relationship between and is analogous to the relationship between location and velocity in elementary calculus: knowing either quantity allows one to construct the other by differentiation or integration.

The Tensorial Time Derivative for a scalar field F defined on is the rate of change in in the instantaneously normal direction:

This definition is also illustrated in second geometric figure.

The above definitions are geometric. In analytical settings, direct application of these definitions may not be possible. The CMS gives analytical definitions of C and in terms of elementary operations from calculus and differential geometry.

Calorimeter constant

A calorimeter constant (denoted Ccal) is a constant that quantifies the heat capacity of a calorimeter. It may be calculated by applying a known amount of heat to the calorimeter and measuring the calorimeter's corresponding change in temperature. In SI units, the calorimeter constant is then calculated by dividing the change in enthalpy (ΔH) in joules by the change in temperature (ΔT) in kelvins or degrees Celsius:

The calorimeter constant is usually presented in units of joules per degree Celsius (J/°C) or joules per kelvin (J/K). Every calorimeter has a unique calorimeter constant.

Dielectric

A dielectric (or dielectric material) is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.The study of dielectric properties concerns storage and dissipation of electric and magnetic energy in materials. Dielectrics are important for explaining various phenomena in electronics, optics, solid-state physics, and cell biophysics.

Equation of time

The equation of time describes the discrepancy between two kinds of solar time. The word equation is used in the medieval sense of "reconcile a difference". The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with uniform motion. Apparent solar time can be obtained by measurement of the current position (hour angle) of the Sun, as indicated (with limited accuracy) by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would resolve to zero.The equation of time is the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth. The equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides.

Isothermal process

An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change in the system will occur slowly enough to allow the system to continue to adjust to the temperature of the reservoir through heat exchange. In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0). In other words, in an isothermal process, the value ΔT = 0 and therefore the change in internal energy ΔU = 0 (only for an ideal gas) but Q ≠ 0, while in an adiabatic process, ΔT ≠ 0 but Q = 0.

Simply, we can say that in isothermal processes

while in adiabatic processes

Mean anomaly

In celestial mechanics, the mean anomaly is the fraction of an elliptical orbit's period that has elapsed since the orbiting body passed periapsis, expressed as an angle which can be used in calculating the position of that body in the classical two-body problem. It is the angular distance from the pericenter which a fictitious body would have if it moved in a circular orbit, with constant speed, in the same orbital period as the actual body in its elliptical orbit.

Microscale thermophoresis

Microscale thermophoresis (MST) is a technology for the biophysical analysis of interactions between biomolecules. Microscale thermophoresis is based on the detection of a temperature-induced change in fluorescence of a target as a function of the concentration of a non-fluorescent ligand. The observed change in fluorescence is based on two distinct effects. On the one hand it is based on a temperature related intensity change (TRIC) of the fluorescent probe, which can be affected by binding events. On the other hand it is based on thermophoresis, the directed movement of particles in a microscopic temperature gradient. Any change of the chemical microenvironment of the fluorescent probe, as well as changes in the hydration shell of biomolecules result in a relative change of the fluorescence detected when a temperature gradient is applied and can be used to determine binding affinities. MST allows measurement of interactions directly in solution without the need of immobilization to a surface (immobilization-free technology).

Neural coding

Neural coding is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the individual or ensemble neuronal responses and the relationship among the electrical activity of the neurons in the ensemble. Based on the theory that

sensory and other information is represented in the brain by networks of neurons, it is thought that neurons can encode both digital and analog information.

Permittivity

In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium.

The SI unit for permittivity is farad per meter (F/m or F·m−1).

The lowest possible permittivity is that of a vacuum. Vacuum permittivity, sometimes called the electric constant, is represented by ε0 and has a value of approximately 8.85×10−12 F/m.

The permittivity of a dielectric medium is often represented by the ratio of its absolute permittivity to the electric constant. This dimensionless quantity is called the medium’s relative permittivity, sometimes also called "permittivity". Relative permittivity is also commonly referred to as the dielectric constant, a term which has been deprecated in physics and engineering as well as in chemistry.

By definition, a perfect vacuum has a relative permittivity of exactly 1. The difference in permittivity between a vacuum and air can often be considered negligible, as κair = 1.0006.

Relative permittivity is directly related to electric susceptibility (χ), which is a measure of how easily a dielectric polarizes in response to an electric field, given by

otherwise written as

Proper length

Proper length or rest length refers to the length of an object in the object's rest frame.

The measurement of lengths is more complicated in the theory of relativity than in classical mechanics. In classical mechanics, lengths are measured based on the assumption that the locations of all points involved are measured simultaneously. But in the theory of relativity, the notion of simultaneity is dependent on the observer.

A different term, proper distance, provides an invariant measure whose value is the same for all observers.

Proper distance is analogous to proper time. The difference is that the proper distance is defined between two spacelike-separated events (or along a spacelike path), while the proper time is defined between two timelike-separated events (or along a timelike path).

Resonance-enhanced multiphoton ionization

Resonance-enhanced multiphoton ionization (REMPI) is a technique applied to the spectroscopy of atoms and small molecules. In practice, a tunable laser can be used to access an excited intermediate state. The selection rules associated with a two-photon or other multiphoton photoabsorption are different from the selection rules for a single photon transition. The REMPI technique typically involves a resonant single or multiple photon absorption to an electronically excited intermediate state followed by another photon which ionizes the atom or molecule. The light intensity to achieve a typical multiphoton transition is generally significantly larger than the light intensity to achieve a single photon photoabsorption. Because of this, a subsequent photoabsorption is often very likely. An ion and a free electron will result if the photons have imparted enough energy to exceed the ionization threshold energy of the system. In many cases, REMPI provides spectroscopic information that can be unavailable to single photon spectroscopic methods, for example rotational structure in molecules is easily seen with this technique.

REMPI is usually generated by a focused frequency tunable laser beam to form a small-volume plasma. In REMPI, first m photons are simultaneously absorbed by an atom or molecule in the sample to bring it to an excited state. Other n photons are absorbed afterwards to generate an electron and ion pair. The so-called m+n REMPI is a nonlinear optical process, which can only occur within the focus of the laser beam. A small-volume plasma is formed near the laser focal region. If the energy of m photons does not match any state, an off-resonant transition can occur with an energy defect ΔE, however, the electron is very unlikely to remain in that state. For large detuning, it resides there only during the time Δt. The uncertainty principle is satisfied for Δt, where ћ=h/2π and h is the Planck constant (6.6261×10^-34 J∙s). Such transition and states are called virtual, unlike real transitions to states with long lifetimes. The real transition probability is many orders of magnitude higher than the virtual transition one, which is called resonance enhanced effect.

Searle's bar method

Searle's bar method (named after George Frederick Charles Searle) is an experimental procedure to measure thermal conductivity of material. A bar of material is being heated by steam on one side and the other side cooled down by water while the length of the bar is thermally insulated. Then the heat ΔQ propagating through the bar in a time interval of Δt is given by

where

and the heat ΔQ absorbed by water in a time interval of Δt is:

where

Assuming perfect insulation and no energy loss, then

which leads to

Temperature coefficient

A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property R that changes by dR when the temperature changes by dT, the temperature coefficient α is defined by the following equation:

Here α has the dimension of an inverse temperature and can be expressed e.g. in 1/K or K−1.

If the temperature coefficient itself does not vary too much with temperature, a linear approximation will be useful in estimating the value R of a property at a temperature T, given its value R0 at a reference temperature T0:

where ΔT is the difference between T and T0. For strongly temperature-dependent α, this approximation is only useful for small temperature differences ΔT.

Temperature coefficients are specified for various applications, including electric and magnetic properties of materials as well as reactivity. The temperature coefficient of most of the reactions lies between -2 & 3.

Temporal discretization

Temporal discretization is a mathematical technique applied to transient problems that occur in the fields of applied physics and engineering.

Transient problems are often solved by conducting simulations using computer-aided engineering (CAE) packages, which require discretizing the governing equations in both space and time. Such problems are unsteady (e.g. flow problems), and therefore require solutions in which position varies as a function of time. Temporal discretization involves the integration of every term in different equations over a time step (Δt).

The spatial domain can be discretized to produce a semi-discrete form:

If the discretization is done using backward differences, the first-order temporal discretization is given as:

And the second-order discretization is given as:

where

φ = a scalar quantity.
n + 1 = value at the next time level, t + Δt.
n = value at the current time level, t.
n − 1 = value at the previous time level, t − Δt.

The function F() is evaluated using implicit- and explicit-time integration.

Terrestrial Time

Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth.

For example, the Astronomical Almanac uses TT for its tables of positions (ephemerides) of the Sun, Moon and planets as seen from Earth. In this role, TT continues Terrestrial Dynamical Time (TDT or TD), which in turn succeeded ephemeris time (ET). TT shares the original purpose for which ET was designed, to be free of the irregularities in the rotation of Earth.

The unit of TT is the SI second, the definition of which is currently based on the caesium atomic clock, but TT is not itself defined by atomic clocks. It is a theoretical ideal, and real clocks can only approximate it.

TT is distinct from the time scale often used as a basis for civil purposes, Coordinated Universal Time (UTC). TT indirectly underlies UTC, via International Atomic Time (TAI). Because of the historical difference between TAI and ET when TT was introduced, TT is approximately 32.184 s ahead of TAI.

Thermal destratification

Thermal destratification is the process of mixing the internal air in a building to eliminate stratified layers and achieve temperature equalization throughout the building envelope.

Thomas precession

In physics, the Thomas precession, named after Llewellyn Thomas, is a relativistic correction that applies to the spin of an elementary particle or the rotation of a macroscopic gyroscope and relates the angular velocity of the spin of a particle following a curvilinear orbit to the angular velocity of the orbital motion.

For a given inertial frame, if a second frame is Lorentz-boosted relative to it, and a third boosted relative to the second, but non-colinear with the first boost, then the Lorentz transformation between the first and third frames involves a combined boost and rotation, known as the "Wigner rotation" or "Thomas rotation". For accelerated motion, the accelerated frame has an inertial frame at every instant. Two boosts a small time interval (as measured in the lab frame) apart leads to a Wigner rotation after the second boost. In the limit the time interval tends to zero, the accelerated frame will rotate at every instant, so the accelerated frame rotates with an angular velocity.

The precession can be understood geometrically as a consequence of the fact that the space of velocities in relativity is hyperbolic, and so parallel transport of a vector (the gyroscope's angular velocity) around a circle (its linear velocity) leaves it pointing in a different direction, or understood algebraically as being a result of the non-commutativity of Lorentz transformations. Thomas precession gives a correction to the spin–orbit interaction in quantum mechanics, which takes into account the relativistic time dilation between the electron and the nucleus of an atom.

Thomas precession is a kinematic effect in the flat spacetime of special relativity. In the curved spacetime of general relativity, Thomas precession combines with a geometric effect to produce de Sitter precession. Although Thomas precession (net rotation after a trajectory that returns to its initial velocity) is a purely kinematic effect, it only occurs in curvilinear motion and therefore cannot be observed independently of some external force causing the curvilinear motion such as that caused by an electromagnetic field, a gravitational field or a mechanical force, so Thomas precession is usually accompanied by dynamical effects.If the system experiences no external torque, e.g., in external scalar fields, its spin dynamics is determined only by the Thomas precession. A single discrete Thomas rotation (as opposed to the series of infinitesimal rotations that add up to the Thomas precession) is present in situations anytime there are three or more inertial frames in non-collinear motion, as can be seen using Lorentz transformations.

ΔT (disambiguation)

ΔT is the time difference between Universal Time, a time scale based on the Earth's non-uniform rotation, and Terrestrial Time, a uniform time scale currently based on the caesium atomic clock.

The symbols Δt and ΔT are commonly used in other contexts as follows.

Δt, a difference in time, may refer to:

The interval of time used in determining velocity.

The increment between successive nerve impulses.ΔT, a difference in temperature, including thermodynamic temperature, may refer to:

In discussions of climate change.

In discussions of heat transfer.

In discussions of the effects of thermal gradients.See also Delta time (disambiguation).

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