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105-417: TORU has a similar layout to the controls of a Soyuz spacecraft with two joysticks which can be used to manually fly the ship. The left joystick is used to control the movement of the ship (translation) and the right joystick is used to control its orientation (rotation). The system also includes a camera mounted on the docking spacecraft and provides visual feedback when the spacecraft is remotely controlled from

210-471: A boson . To Isaac Newton , his law of universal gravitation simply expressed the gravitational force that acted between any pair of massive objects. When looking at the motion of many bodies all interacting with each other, such as the planets in the Solar System , dealing with the force between each pair of bodies separately rapidly becomes computationally inconvenient. In the eighteenth century,

315-404: A "complete standstill" by passing it through a Bose–Einstein condensate of the element rubidium . The popular description of light being "stopped" in these experiments refers only to light being stored in the excited states of atoms, then re-emitted at an arbitrarily later time, as stimulated by a second laser pulse. During the time it had "stopped", it had ceased to be light. This type of behaviour

420-524: A classical field are usually specified by the Lagrangian density in terms of the field components; the dynamics can be obtained by using the action principle . It is possible to construct simple fields without any prior knowledge of physics using only mathematics from multivariable calculus , potential theory and partial differential equations (PDEs). For example, scalar PDEs might consider quantities such as amplitude, density and pressure fields for

525-530: A classical field theory should, at least in principle, permit a recasting in quantum mechanical terms; success yields the corresponding quantum field theory . For example, quantizing classical electrodynamics gives quantum electrodynamics . Quantum electrodynamics is arguably the most successful scientific theory; experimental data confirm its predictions to a higher precision (to more significant digits ) than any other theory. The two other fundamental quantum field theories are quantum chromodynamics and

630-476: A construction of the dynamics of a field, i.e. a specification of how a field changes with time or with respect to other independent physical variables on which the field depends. Usually this is done by writing a Lagrangian or a Hamiltonian of the field, and treating it as a classical or quantum mechanical system with an infinite number of degrees of freedom . The resulting field theories are referred to as classical or quantum field theories. The dynamics of

735-412: A finite speed. Consequently, the forces on charges and currents no longer just depended on the positions and velocities of other charges and currents at the same time, but also on their positions and velocities in the past. Maxwell, at first, did not adopt the modern concept of a field as a fundamental quantity that could independently exist. Instead, he supposed that the electromagnetic field expressed

840-505: A further 4–24 minutes for commands to travel from Earth to Mars. Receiving light and other signals from distant astronomical sources takes much longer. For example, it takes 13 billion (13 × 10 ) years for light to travel to Earth from the faraway galaxies viewed in the Hubble Ultra-Deep Field images. Those photographs, taken today, capture images of the galaxies as they appeared 13 billion years ago, when

945-490: A height field. Fluid dynamics has fields of pressure , density , and flow rate that are connected by conservation laws for energy and momentum. The mass continuity equation is a continuity equation , representing the conservation of mass ∂ ρ ∂ t + ∇ ⋅ ( ρ u ) = 0 {\displaystyle {\frac {\partial \rho }{\partial t}}+\nabla \cdot (\rho \mathbf {u} )=0} and

1050-464: A light year is nearly 10 trillion kilometres or nearly 6 trillion miles. Proxima Centauri , the closest star to Earth after the Sun, is around 4.2 light-years away. Radar systems measure the distance to a target by the time it takes a radio-wave pulse to return to the radar antenna after being reflected by the target: the distance to the target is half the round-trip transit time multiplied by

1155-615: A material-dependent constant. The refractive index of air is approximately 1.0003. Denser media, such as water , glass , and diamond , have refractive indexes of around 1.3, 1.5 and 2.4, respectively, for visible light. In exotic materials like Bose–Einstein condensates near absolute zero, the effective speed of light may be only a few metres per second. However, this represents absorption and re-radiation delay between atoms, as do all slower-than- c speeds in material substances. As an extreme example of light "slowing" in matter, two independent teams of physicists claimed to bring light to

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1260-420: A new quantity was devised to simplify the bookkeeping of all these gravitational forces. This quantity, the gravitational field , gave at each point in space the total gravitational acceleration which would be felt by a small object at that point. This did not change the physics in any way: it did not matter if all the gravitational forces on an object were calculated individually and then added together, or if all

1365-410: A physical entity, making the field concept a supporting paradigm of the edifice of modern physics. Richard Feynman said, "The fact that the electromagnetic field can possess momentum and energy makes it very real, and [...] a particle makes a field, and a field acts on another particle, and the field has such familiar properties as energy content and momentum, just as particles can have." In practice,

1470-407: A point in spacetime requires three numbers, the components of the gravitational field vector at that point. Moreover, within each category (scalar, vector, tensor), a field can be either a classical field or a quantum field , depending on whether it is characterized by numbers or quantum operators respectively. In this theory an equivalent representation of field is a field particle , for instance

1575-584: A result, if something were travelling faster than  c relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated. In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded, and would lead to paradoxes such as the tachyonic antitelephone . There are situations in which it may seem that matter, energy, or information-carrying signal travels at speeds greater than  c , but they do not. For example, as

1680-493: A scalar field, a vector field, a spinor field or a tensor field according to whether the represented physical quantity is a scalar , a vector , a spinor , or a tensor , respectively. A field has a consistent tensorial character wherever it is defined: i.e. a field cannot be a scalar field somewhere and a vector field somewhere else. For example, the Newtonian gravitational field is a vector field: specifying its value at

1785-412: A set of differential equations which directly relate E and B to ρ and J . Alternatively, one can describe the system in terms of its scalar and vector potentials V and A . A set of integral equations known as retarded potentials allow one to calculate V and A from ρ and J , and from there the electric and magnetic fields are determined via the relations At the end of the 19th century,

1890-417: A simplified physical model of an isolated closed system is set . They are also subject to the inverse-square law . For electromagnetic waves, there are optical fields , and terms such as near- and far-field limits for diffraction. In practice though, the field theories of optics are superseded by the electromagnetic field theory of Maxwell Gravity waves are waves in the surface of water, defined by

1995-416: A standard for the metre. As a dimensional physical constant , the numerical value of c is different for different unit systems. For example, in imperial units , the speed of light is approximately 186 282 miles per second, or roughly 1 foot per nanosecond. In branches of physics in which c appears often, such as in relativity, it is common to use systems of natural units of measurement or

2100-412: A time dilation factor of γ  = 2 occurs at a relative velocity of 86.6% of the speed of light ( v  = 0.866  c ). Similarly, a time dilation factor of γ  = 10 occurs at 99.5% the speed of light ( v  = 0.995  c ). The results of special relativity can be summarized by treating space and time as a unified structure known as spacetime (with  c relating

2205-459: A time interval of 1 ⁄ 299 792 458 of a second", fixing the value of the speed of light at 299 792 458  m/s by definition, as described below . Consequently, accurate measurements of the speed of light yield an accurate realization of the metre rather than an accurate value of c . Outer space is a convenient setting for measuring the speed of light because of its large scale and nearly perfect vacuum . Typically, one measures

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2310-520: A value for each point in space and time . An example of a scalar field is a weather map, with the surface temperature described by assigning a number to each point on the map. A surface wind map, assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field , i.e. a 1-dimensional (rank-1) tensor field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance,

2415-425: Is The electric field is conservative , and hence can be described by a scalar potential, V ( r ): A steady current I flowing along a path ℓ will create a field B, that exerts a force on nearby moving charged particles that is quantitatively different from the electric field force described above. The force exerted by I on a nearby charge q with velocity v is where B ( r ) is the magnetic field , which

2520-411: Is associated with a gravitational field g which describes its influence on other bodies with mass. The gravitational field of M at a point r in space corresponds to the ratio between force F that M exerts on a small or negligible test mass m located at r and the test mass itself: Stipulating that m is much smaller than M ensures that the presence of m has a negligible influence on

2625-424: Is described as a type of electromagnetic wave . The classical behaviour of the electromagnetic field is described by Maxwell's equations , which predict that the speed  c with which electromagnetic waves (such as light) propagate in vacuum is related to the distributed capacitance and inductance of vacuum, otherwise respectively known as the electric constant ε 0 and the magnetic constant μ 0 , by

2730-522: Is determined from I by the Biot–Savart law : The magnetic field is not conservative in general, and hence cannot usually be written in terms of a scalar potential. However, it can be written in terms of a vector potential , A ( r ): In general, in the presence of both a charge density ρ( r , t ) and current density J ( r , t ), there will be both an electric and a magnetic field, and both will vary in time. They are determined by Maxwell's equations ,

2835-421: Is discussed in the propagation of light in a medium section below, many wave velocities can exceed  c . The phase velocity of X-rays through most glasses can routinely exceed c , but phase velocity does not determine the velocity at which waves convey information. If a laser beam is swept quickly across a distant object, the spot of light can move faster than  c , although the initial movement of

2940-427: Is frame-independent, because it is impossible to measure the one-way speed of light (for example, from a source to a distant detector) without some convention as to how clocks at the source and at the detector should be synchronized. By adopting Einstein synchronization for the clocks, the one-way speed of light becomes equal to the two-way speed of light by definition. The special theory of relativity explores

3045-511: Is from the distant past, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes , it can take minutes to hours for signals to travel. In computing , the speed of light fixes the ultimate minimum communication delay . The speed of light can be used in time of flight measurements to measure large distances to extremely high precision. Ole Rømer first demonstrated in 1676 that light does not travel instantaneously by studying

3150-459: Is generally microscopically true of all transparent media which "slow" the speed of light. In transparent materials, the refractive index generally is greater than 1, meaning that the phase velocity is less than c . In other materials, it is possible for the refractive index to become smaller than   1 for some frequencies; in some exotic materials it is even possible for the index of refraction to become negative. The requirement that causality

3255-505: Is important in determining how a light wave travels through a material or from one material to another. It is often represented in terms of a refractive index . The refractive index of a material is defined as the ratio of c to the phase velocity  v p in the material: larger indices of refraction indicate lower speeds. The refractive index of a material may depend on the light's frequency, intensity, polarization , or direction of propagation; in many cases, though, it can be treated as

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3360-486: Is impossible for signals or energy to travel faster than  c . One argument for this follows from the counter-intuitive implication of special relativity known as the relativity of simultaneity . If the spatial distance between two events A and B is greater than the time interval between them multiplied by  c then there are frames of reference in which A precedes B, others in which B precedes A, and others in which they are simultaneous. As

3465-422: Is independent of the motion of the light source. He explored the consequences of that postulate by deriving the theory of relativity and, in doing so, showed that the parameter c had relevance outside of the context of light and electromagnetism. Massless particles and field perturbations, such as gravitational waves , also travel at speed c in vacuum. Such particles and waves travel at c regardless of

3570-500: Is known as the Lorentz factor and is given by γ = (1 − v / c ) , where v is the speed of the object. The difference of γ from   1 is negligible for speeds much slower than  c , such as most everyday speeds – in which case special relativity is closely approximated by Galilean relativity  – but it increases at relativistic speeds and diverges to infinity as v approaches c . For example,

3675-491: Is not violated implies that the real and imaginary parts of the dielectric constant of any material, corresponding respectively to the index of refraction and to the attenuation coefficient , are linked by the Kramers–Kronig relations . In practical terms, this means that in a material with refractive index less than 1, the wave will be absorbed quickly. A pulse with different group and phase velocities (which occurs if

3780-559: Is observed, so information cannot be transmitted in this manner. Another quantum effect that predicts the occurrence of faster-than-light speeds is called the Hartman effect : under certain conditions the time needed for a virtual particle to tunnel through a barrier is constant, regardless of the thickness of the barrier. This could result in a virtual particle crossing a large gap faster than light. However, no information can be sent using this effect. So-called superluminal motion

3885-473: Is possible for a particle to travel through a medium faster than the phase velocity of light in that medium (but still slower than c ). When a charged particle does that in a dielectric material, the electromagnetic equivalent of a shock wave , known as Cherenkov radiation , is emitted. The speed of light is of relevance to telecommunications : the one-way and round-trip delay time are greater than zero. This applies from small to astronomical scales. On

3990-712: Is possible to approach their quantum counterparts from a purely mathematical view using similar techniques as before. The equations governing the quantum fields are in fact PDEs (specifically, relativistic wave equations (RWEs)). Thus one can speak of Yang–Mills , Dirac , Klein–Gordon and Schrödinger fields as being solutions to their respective equations. A possible problem is that these RWEs can deal with complicated mathematical objects with exotic algebraic properties (e.g. spinors are not tensors , so may need calculus for spinor fields ), but these in theory can still be subjected to analytical methods given appropriate mathematical generalization . Field theory usually refers to

4095-401: Is seen in certain astronomical objects, such as the relativistic jets of radio galaxies and quasars . However, these jets are not moving at speeds in excess of the speed of light: the apparent superluminal motion is a projection effect caused by objects moving near the speed of light and approaching Earth at a small angle to the line of sight: since the light which was emitted when the jet

4200-496: Is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information ) can travel through space . All forms of electromagnetic radiation , including visible light , travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects. Much starlight viewed on Earth

4305-559: The Deep Space Network determine distances to the Moon, planets and spacecraft, respectively, by measuring round-trip transit times. There are different ways to determine the value of c . One way is to measure the actual speed at which light waves propagate, which can be done in various astronomical and Earth-based setups. It is also possible to determine c from other physical laws where it appears, for example, by determining

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4410-650: The Navier–Stokes equations represent the conservation of momentum in the fluid, found from Newton's laws applied to the fluid, ∂ ∂ t ( ρ u ) + ∇ ⋅ ( ρ u ⊗ u + p I ) = ∇ ⋅ τ + ρ b {\displaystyle {\frac {\partial }{\partial t}}(\rho \mathbf {u} )+\nabla \cdot (\rho \mathbf {u} \otimes \mathbf {u} +p\mathbf {I} )=\nabla \cdot {\boldsymbol {\tau }}+\rho \mathbf {b} } if

4515-483: The Russian Federation is a stub . You can help Misplaced Pages by expanding it . Speed of light The speed of light in vacuum , commonly denoted c , is a universal physical constant that is exactly equal to 299,792,458 metres per second (approximately 300,000 kilometres per second; 186,000 miles per second; 671 million miles per hour). According to the special theory of relativity , c

4620-470: The electric field is another rank-1 tensor field, while electrodynamics can be formulated in terms of two interacting vector fields at each point in spacetime, or as a single-rank 2-tensor field. In the modern framework of the quantum field theory , even without referring to a test particle, a field occupies space, contains energy, and its presence precludes a classical "true vacuum". This has led physicists to consider electromagnetic fields to be

4725-548: The electromagnetic field was understood as a collection of two vector fields in space. Nowadays, one recognizes this as a single antisymmetric 2nd-rank tensor field in spacetime. Einstein's theory of gravity, called general relativity , is another example of a field theory. Here the principal field is the metric tensor , a symmetric 2nd-rank tensor field in spacetime . This replaces Newton's law of universal gravitation . Waves can be constructed as physical fields, due to their finite propagation speed and causal nature when

4830-583: The electroweak theory . In quantum chromodynamics, the color field lines are coupled at short distances by gluons , which are polarized by the field and line up with it. This effect increases within a short distance (around 1 fm from the vicinity of the quarks) making the color force increase within a short distance, confining the quarks within hadrons . As the field lines are pulled together tightly by gluons, they do not "bow" outwards as much as an electric field between electric charges. These three quantum field theories can all be derived as special cases of

4935-400: The geometrized unit system where c = 1 . Using these units, c does not appear explicitly because multiplication or division by   1 does not affect the result. Its unit of light-second per second is still relevant, even if omitted. The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of

5040-459: The local speed of light is constant and equal to  c , but the speed of light can differ from  c when measured from a remote frame of reference, depending on how measurements are extrapolated to the region. It is generally assumed that fundamental constants such as  c have the same value throughout spacetime, meaning that they do not depend on location and do not vary with time. However, it has been suggested in various theories that

5145-430: The printed circuit board refracts and slows down signals. Processors must therefore be placed close to each other, as well as memory chips, to minimize communication latencies, and care must be exercised when routing wires between them to ensure signal integrity . If clock frequencies continue to increase, the speed of light may eventually become a limiting factor for the internal design of single chips . Given that

5250-400: The quantum states of two particles that can be entangled . Until either of the particles is observed, they exist in a superposition of two quantum states. If the particles are separated and one particle's quantum state is observed, the other particle's quantum state is determined instantaneously. However, it is impossible to control which quantum state the first particle will take on when it

5355-414: The speed of light may have changed over time . No conclusive evidence for such changes has been found, but they remain the subject of ongoing research. It is generally assumed that the two-way speed of light is isotropic , meaning that it has the same value regardless of the direction in which it is measured. Observations of the emissions from nuclear energy levels as a function of the orientation of

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5460-493: The temperature gradient is a vector field defined as ∇ T {\displaystyle \nabla T} . In thermal conduction , the temperature field appears in Fourier's law, where q is the heat flux field and k the thermal conductivity. Temperature and pressure gradients are also important for meteorology. It is now believed that quantum mechanics should underlie all physical phenomena, so that

5565-551: The Earth with speeds proportional to their distances. Beyond a boundary called the Hubble sphere , the rate at which their distance from Earth increases becomes greater than the speed of light. These recession rates, defined as the increase in proper distance per cosmological time , are not velocities in a relativistic sense. Faster-than-light cosmological recession speeds are only a coordinate artifact. In classical physics , light

5670-434: The advantage which radio waves travelling at near to the speed of light through air have over comparatively slower fibre optic signals. Similarly, communications between the Earth and spacecraft are not instantaneous. There is a brief delay from the source to the receiver, which becomes more noticeable as distances increase. This delay was significant for communications between ground control and Apollo 8 when it became

5775-413: The apparent motion of Jupiter 's moon Io . Progressively more accurate measurements of its speed came over the following centuries. In a paper published in 1865, James Clerk Maxwell proposed that light was an electromagnetic wave and, therefore, travelled at speed c . In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame of reference is a constant and

5880-418: The appearance of certain high-speed astronomical objects , and particular quantum effects ). The expansion of the universe is understood to exceed the speed of light beyond a certain boundary . The speed at which light propagates through transparent materials , such as glass or air, is less than c ; similarly, the speed of electromagnetic waves in wire cables is slower than c . The ratio between c and

5985-469: The behavior of M . According to Newton's law of universal gravitation , F ( r ) is given by where r ^ {\displaystyle {\hat {\mathbf {r} }}} is a unit vector lying along the line joining M and m and pointing from M to m . Therefore, the gravitational field of M is The experimental observation that inertial mass and gravitational mass are equal to an unprecedented level of accuracy leads to

6090-525: The components of the 3x3 infinitesimal strain and L i j k l {\displaystyle L_{ijkl}} is the elasticity tensor , a fourth-rank tensor with 81 components (usually 21 independent components). Assuming that the temperature T is an intensive quantity , i.e., a single-valued, continuous and differentiable function of three-dimensional space (a scalar field ), i.e., that T = T ( r ) {\displaystyle T=T(\mathbf {r} )} , then

6195-587: The consequences of this invariance of c with the assumption that the laws of physics are the same in all inertial frames of reference. One consequence is that c is the speed at which all massless particles and waves, including light, must travel in vacuum. Special relativity has many counterintuitive and experimentally verified implications. These include the equivalence of mass and energy ( E = mc ) , length contraction (moving objects shorten), and time dilation (moving clocks run more slowly). The factor  γ by which lengths contract and times dilate

6300-495: The contributions were first added together as a gravitational field and then applied to an object. The development of the independent concept of a field truly began in the nineteenth century with the development of the theory of electromagnetism . In the early stages, André-Marie Ampère and Charles-Augustin de Coulomb could manage with Newton-style laws that expressed the forces between pairs of electric charges or electric currents . However, it became much more natural to take

6405-476: The deformation of some underlying medium—the luminiferous aether —much like the tension in a rubber membrane. If that were the case, the observed velocity of the electromagnetic waves should depend upon the velocity of the observer with respect to the aether. Despite much effort, no experimental evidence of such an effect was ever found; the situation was resolved by the introduction of the special theory of relativity by Albert Einstein in 1905. This theory changed

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6510-505: The density ρ , pressure p , deviatoric stress tensor τ of the fluid, as well as external body forces b , are all given. The flow velocity u is the vector field to solve for. Linear elasticity is defined in terms of constitutive equations between tensor fields, where σ i j {\displaystyle \sigma _{ij}} are the components of the 3x3 Cauchy stress tensor , ε i j {\displaystyle \varepsilon _{ij}}

6615-454: The distance between two objects in a frame of reference with respect to which both are moving (their closing speed ) may have a value in excess of  c . However, this does not represent the speed of any single object as measured in a single inertial frame. Certain quantum effects appear to be transmitted instantaneously and therefore faster than c , as in the EPR paradox . An example involves

6720-479: The emitting nuclei in a magnetic field (see Hughes–Drever experiment ), and of rotating optical resonators (see Resonator experiments ) have put stringent limits on the possible two-way anisotropy . According to special relativity, the energy of an object with rest mass m and speed v is given by γmc , where γ is the Lorentz factor defined above. When v is zero, γ is equal to one, giving rise to

6825-418: The equation In modern quantum physics , the electromagnetic field is described by the theory of quantum electrodynamics (QED). In this theory, light is described by the fundamental excitations (or quanta) of the electromagnetic field, called photons . In QED, photons are massless particles and thus, according to special relativity, they travel at the speed of light in vacuum. Extensions of QED in which

6930-512: The equatorial circumference of the Earth is about 40 075  km and that c is about 300 000  km/s , the theoretical shortest time for a piece of information to travel half the globe along the surface is about 67 milliseconds. When light is traveling in optical fibre (a transparent material ) the actual transit time is longer, in part because the speed of light is slower by about 35% in optical fibre, depending on its refractive index n . Straight lines are rare in global communications and

7035-495: The famous E = mc formula for mass–energy equivalence. The γ factor approaches infinity as v approaches  c , and it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with positive rest mass, and individual photons cannot travel faster than the speed of light. This is experimentally established in many tests of relativistic energy and momentum . More generally, it

7140-405: The field approach and express these laws in terms of electric and magnetic fields ; in 1845 Michael Faraday became the first to coin the term "magnetic field". And Lord Kelvin provided a formal definition for a field in 1851. The independent nature of the field became more apparent with James Clerk Maxwell 's discovery that waves in these fields, called electromagnetic waves , propagated at

7245-560: The first crewed spacecraft to orbit the Moon : for every question, the ground control station had to wait at least three seconds for the answer to arrive. The communications delay between Earth and Mars can vary between five and twenty minutes depending upon the relative positions of the two planets. As a consequence of this, if a robot on the surface of Mars were to encounter a problem, its human controllers would not be aware of it until approximately 4–24 minutes later. It would then take

7350-416: The group velocity to become infinite or negative, with pulses travelling instantaneously or backwards in time. None of these options allow information to be transmitted faster than c . It is impossible to transmit information with a light pulse any faster than the speed of the earliest part of the pulse (the front velocity). It can be shown that this is (under certain assumptions) always equal to c . It

7455-426: The identity that gravitational field strength is identical to the acceleration experienced by a particle. This is the starting point of the equivalence principle , which leads to general relativity . Because the gravitational force F is conservative , the gravitational field g can be rewritten in terms of the gradient of a scalar function, the gravitational potential Φ( r ): Michael Faraday first realized

7560-406: The importance of a field as a physical quantity, during his investigations into magnetism . He realized that electric and magnetic fields are not only fields of force which dictate the motion of particles, but also have an independent physical reality because they carry energy. These ideas eventually led to the creation, by James Clerk Maxwell , of the first unified field theory in physics with

7665-429: The individual crests and troughs of a plane wave (a wave filling the whole space, with only one frequency ) propagate is called the phase velocity   v p . A physical signal with a finite extent (a pulse of light) travels at a different speed. The overall envelope of the pulse travels at the group velocity   v g , and its earliest part travels at the front velocity   v f . The phase velocity

7770-403: The introduction of equations for the electromagnetic field . The modern versions of these equations are called Maxwell's equations . A charged test particle with charge q experiences a force F based solely on its charge. We can similarly describe the electric field E so that F = q E . Using this and Coulomb's law tells us that the electric field due to a single charged particle

7875-502: The massive photon is described by Proca theory , the experimental upper bound for its mass is about 10 grams ; if photon mass is generated by a Higgs mechanism , the experimental upper limit is less sharp, m ≤ 10   eV/ c   (roughly 2 × 10  g). Another reason for the speed of light to vary with its frequency would be the failure of special relativity to apply to arbitrarily small scales, as predicted by some proposed theories of quantum gravity . In 2009,

7980-484: The motion of the source or the inertial reference frame of the observer . Particles with nonzero rest mass can be accelerated to approach c but can never reach it, regardless of the frame of reference in which their speed is measured. In the theory of relativity , c interrelates space and time and appears in the famous mass–energy equivalence , E = mc . In some cases, objects or waves may appear to travel faster than light (e.g., phase velocities of waves,

8085-521: The new rules of quantum mechanics were first applied to the electromagnetic field. In 1927, Paul Dirac used quantum fields to successfully explain how the decay of an atom to a lower quantum state led to the spontaneous emission of a photon , the quantum of the electromagnetic field. This was soon followed by the realization (following the work of Pascual Jordan , Eugene Wigner , Werner Heisenberg , and Wolfgang Pauli ) that all particles, including electrons and protons , could be understood as

8190-499: The observation of gamma-ray burst GRB 090510 found no evidence for a dependence of photon speed on energy, supporting tight constraints in specific models of spacetime quantization on how this speed is affected by photon energy for energies approaching the Planck scale . In a medium, light usually does not propagate at a speed equal to c ; further, different types of light wave will travel at different speeds. The speed at which

8295-421: The observer. This invariance of the speed of light was postulated by Einstein in 1905, after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for motion against the luminiferous aether . It has since been consistently confirmed by many experiments. It is only possible to verify experimentally that the two-way speed of light (for example, from a source to a mirror and back again)

8400-408: The other hand, some techniques depend on the finite speed of light, for example in distance measurements. In computers , the speed of light imposes a limit on how quickly data can be sent between processors . If a processor operates at 1   gigahertz , a signal can travel only a maximum of about 30 centimetres (1 ft) in a single clock cycle – in practice, this distance is even shorter since

8505-420: The parameter  c is ubiquitous in modern physics, appearing in many contexts that are unrelated to light. For example, general relativity predicts that  c is also the speed of gravity and of gravitational waves , and observations of gravitational waves have been consistent with this prediction. In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames ),

8610-403: The phase velocity is not the same for all the frequencies of the pulse) smears out over time, a process known as dispersion . Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called slow light . The opposite, group velocities exceeding c , was proposed theoretically in 1993 and achieved experimentally in 2000. It should even be possible for

8715-412: The photon has a mass have been considered. In such a theory, its speed would depend on its frequency, and the invariant speed  c of special relativity would then be the upper limit of the speed of light in vacuum. No variation of the speed of light with frequency has been observed in rigorous testing, putting stringent limits on the mass of the photon. The limit obtained depends on the model used: if

8820-649: The quanta of some quantum field, elevating fields to the status of the most fundamental objects in nature. That said, John Wheeler and Richard Feynman seriously considered Newton's pre-field concept of action at a distance (although they set it aside because of the ongoing utility of the field concept for research in general relativity and quantum electrodynamics ). There are several examples of classical fields . Classical field theories remain useful wherever quantum properties do not arise, and can be active areas of research. Elasticity of materials, fluid dynamics and Maxwell's equations are cases in point. Some of

8925-431: The simplest physical fields are vector force fields. Historically, the first time that fields were taken seriously was with Faraday's lines of force when describing the electric field . The gravitational field was then similarly described. A classical field theory describing gravity is Newtonian gravitation , which describes the gravitational force as a mutual interaction between two masses . Any body with mass M

9030-589: The so-called standard model of particle physics . General relativity , the Einsteinian field theory of gravity, has yet to be successfully quantized. However an extension, thermal field theory , deals with quantum field theory at finite temperatures , something seldom considered in quantum field theory. In BRST theory one deals with odd fields, e.g. Faddeev–Popov ghosts . There are different descriptions of odd classical fields both on graded manifolds and supermanifolds . As above with classical fields, it

9135-417: The speed v at which light travels in a material is called the refractive index n of the material ( n = ⁠ c / v ⁠ ). For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at ⁠ c / 1.5 ⁠ ≈ 200 000  km/s ( 124 000  mi/s) ; the refractive index of air for visible light is about 1.0003, so

9240-470: The speed of light in air is about 90 km/s (56 mi/s) slower than c . The speed of light in vacuum is usually denoted by a lowercase c , for "constant" or the Latin celeritas (meaning 'swiftness, celerity'). In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant that was later shown to equal √ 2 times the speed of light in vacuum. Historically,

9345-479: The speed of light in vacuum. Since 1983, the constant c has been defined in the International System of Units (SI) as exactly 299 792 458  m/s ; this relationship is used to define the metre as exactly the distance that light travels in vacuum in 1 ⁄ 299 792 458 of a second. By using the value of c , as well as an accurate measurement of the second, one can thus establish

9450-470: The speed of light. A Global Positioning System (GPS) receiver measures its distance to GPS satellites based on how long it takes for a radio signal to arrive from each satellite, and from these distances calculates the receiver's position. Because light travels about 300 000  kilometres ( 186 000  miles ) in one second, these measurements of small fractions of a second must be very precise. The Lunar Laser Ranging experiment , radar astronomy and

9555-439: The speed of waves in any material medium, and c 0 for the speed of light in vacuum. This subscripted notation, which is endorsed in official SI literature, has the same form as related electromagnetic constants: namely, μ 0 for the vacuum permeability or magnetic constant, ε 0 for the vacuum permittivity or electric constant, and Z 0 for the impedance of free space . This article uses c exclusively for

9660-509: The spot is delayed because of the time it takes light to get to the distant object at the speed  c . However, the only physical entities that are moving are the laser and its emitted light, which travels at the speed  c from the laser to the various positions of the spot. Similarly, a shadow projected onto a distant object can be made to move faster than  c , after a delay in time. In neither case does any matter, energy, or information travel faster than light. The rate of change in

9765-420: The station to which it is docking. TORU also transfers sounds from the spacecraft that may provide indirect information about the docking process. While ships are sufficiently close when docking to make signal travel delay insignificant, cosmonauts claim that TORU has a certain delay when operating the ship from the space station remotely. Some radio amateurs think they have observed TORU docking signals. TORU

9870-461: The strength of most fields diminishes with distance, eventually becoming undetectable. For instance the strength of many relevant classical fields, such as the gravitational field in Newton's theory of gravity or the electrostatic field in classical electromagnetism, is inversely proportional to the square of the distance from the source (i.e. they follow Gauss's law ). A field can be classified as

9975-407: The symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c , which by then had become the standard symbol for the speed of light. Sometimes c is used for

10080-541: The term tensor , derived from the Latin word for stretch), complex fluid flows or anisotropic diffusion , which are framed as matrix-tensor PDEs, and then require matrices or tensor fields, hence matrix or tensor calculus . The scalars (and hence the vectors, matrices and tensors) can be real or complex as both are fields in the abstract-algebraic/ ring-theoretic sense. In a general setting, classical fields are described by sections of fiber bundles and their dynamics

10185-486: The time needed for light to traverse some reference distance in the Solar System , such as the radius of the Earth's orbit. Historically, such measurements could be made fairly accurately, compared to how accurately the length of the reference distance is known in Earth-based units. Field (physics) In science , a field is a physical quantity , represented by a scalar , vector , or tensor , that has

10290-471: The travel time increases when signals pass through electronic switches or signal regenerators. Although this distance is largely irrelevant for most applications, latency becomes important in fields such as high-frequency trading , where traders seek to gain minute advantages by delivering their trades to exchanges fractions of a second ahead of other traders. For example, traders have been switching to microwave communications between trading hubs, because of

10395-475: The units of space and time), and requiring that physical theories satisfy a special symmetry called Lorentz invariance , whose mathematical formulation contains the parameter  c . Lorentz invariance is an almost universal assumption for modern physical theories, such as quantum electrodynamics , quantum chromodynamics , the Standard Model of particle physics , and general relativity . As such,

10500-529: The universe was less than a billion years old. The fact that more distant objects appear to be younger, due to the finite speed of light, allows astronomers to infer the evolution of stars , of galaxies , and of the universe itself. Astronomical distances are sometimes expressed in light-years , especially in popular science publications and media. A light-year is the distance light travels in one Julian year , around 9461 billion kilometres, 5879 billion miles, or 0.3066 parsecs . In round figures,

10605-436: The values of the electromagnetic constants ε 0 and μ 0 and using their relation to c . Historically, the most accurate results have been obtained by separately determining the frequency and wavelength of a light beam, with their product equalling c . This is described in more detail in the "Interferometry" section below. In 1983 the metre was defined as "the length of the path travelled by light in vacuum during

10710-667: The wave equation and fluid dynamics ; temperature/concentration fields for the heat / diffusion equations . Outside of physics proper (e.g., radiometry and computer graphics), there are even light fields . All these previous examples are scalar fields . Similarly for vectors, there are vector PDEs for displacement, velocity and vorticity fields in (applied mathematical) fluid dynamics, but vector calculus may now be needed in addition, being calculus for vector fields (as are these three quantities, and those for vector PDEs in general). More generally problems in continuum mechanics may involve for example, directional elasticity (from which comes

10815-454: The way the viewpoints of moving observers were related to each other. They became related to each other in such a way that velocity of electromagnetic waves in Maxwell's theory would be the same for all observers. By doing away with the need for a background medium, this development opened the way for physicists to start thinking about fields as truly independent entities. In the late 1920s,

10920-498: Was farther away took longer to reach the Earth, the time between two successive observations corresponds to a longer time between the instants at which the light rays were emitted. A 2011 experiment where neutrinos were observed to travel faster than light turned out to be due to experimental error. In models of the expanding universe , the farther galaxies are from each other, the faster they drift apart. For example, galaxies far away from Earth are inferred to be moving away from

11025-465: Was first tested in 1993 ( Progress M-15 ) and actually used next year to dock Progress M-24 (after two unsuccessful attempts to dock automatically). Despite the 1997 M-34 collision, it was used again to dock the next Progress spacecraft, Progress M-35 , after Mir ’s onboard computer failed. TORU was also used in many later missions ( Progress M-53 , Progress M-67 , Progress M1-4 and possibly others). This article about one or more spacecraft of

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