The
variable speed of light (VSL) concept states that the
speed of lightIn physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
in a vacuum, usually denoted by
c, may not be
constantA physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...
in some cases. In most situations in
condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the...
when light is traveling through a medium, it effectively has a slower speed. Virtual photons in some calculations in
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically described by fields or of many-body systems. It is widely used in particle physics and condensed matter physics...
may also travel at a different speed for short distances; however, this doesn't imply that anything can travel faster than light. While it is usually thought that no meaning can be ascribed to a dimensional quantity such as the speed of light varying in time (as opposed to a dimensionless number such as the fine structure constant), in some controversial theories in cosmology, the speed of light also varies by changing the postulates of
special relativitySpecial relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies"...
. A fundamental change to relativity is needed if c is changing because relativity shows that space and time are equivalent.
Varying c in condensed matter physics
Due to the delay provoked by emission and reabsorption, the effective travel time of a light ray is less than
c in material media (between interactions, however, photons still move at speed
c). This leads to several important effects, such as
dispersionIn optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
(
see also refractive indexThe refractive index of a medium is a measure of how much the speed of light is reduced inside the medium. For example, typical soda-lime glass has a refractive index close to 1.5, which means that in glass, light travels at 1 / 1.5 = 2/3 the speed of light in a vacuum...
). The slow-down in
condensed matterCondensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the...
, such as
gasThis page is about the physical properties of gas as a state of matter. For the uses of gases, and other meanings, see Gas .A gas is one of four states of matter. Near absolute zero, a substance exists as a solid...
es,
liquidLiquid is one of the principal states of matter. A liquid is a fluid that has the particles loose and can freely form a distinct surface at the boundaries of its bulk material. The surface is a free surface where the liquid is not constrained by a container....
s and solids, can be considerable. The
group velocityThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
of light can be lowered to arbitrary speeds, though only for an arbitrarily slow (low bandwidth) signal (see
Slow lightSlow light is the literal slowing of the speed of light. It is the propagation of an optical pulse or other modulation of an optical carrier at a very low group velocity...
).
In certain highly unusual circumstances, it is also possible to prepare experiments in which the
groupThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
or
phase velocityThe phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...
of light exceeds
c. Since these velocities are mathematical constructs, these faster than light observations do not indicate any contradiction with
causalityCausality describes the relationship between causes and effects, is fundamental to all natural science, especially physics, and has a basis in logic. It is also studied from the perspectives of philosophy, computer science, and statistics. In physics it is useful to interpret certain terms of a...
or
special relativitySpecial relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies"...
, as no information or energy travels faster than
c.
Varying c in classical physics
The
photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic field and the basic "unit" of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
, the particle of light which mediates the
electromagnetic forceIn physics, the electromagnetic force is the force that the electromagnetic field exerts on electrically charged particles. It is the electromagnetic force that holds electrons and protons together in atoms, and which hold atoms together to make molecules. The electromagnetic force operates via...
is believed to be massless. The so-called
Proca actionIn physics, in the area of field theory, the Proca action describes a massive spin-1 field of mass m in Minkowski spacetime. The field involved is a real vector field A. The Lagrangian density is given by:...
describes a theory of a massive photon. Classically, it is possible to have a photon which is extremely light but nonetheless has a tiny mass, like the
neutrinoNeutrinos are elementary particles that often travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect. Neutrinos have a minuscule, but nonzero mass...
. These photons would propagate at less than the speed of light defined by
special relativitySpecial relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies"...
and have three directions of
polarizationPolarization is a property of waves that describes the orientation of their oscillations. This article primarily covers the polarization of electromagnetic waves such as light, although other types of wave also exhibit polarization....
. However, in
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically described by fields or of many-body systems. It is widely used in particle physics and condensed matter physics...
, the photon mass is not consistent with gauge invariance or renormalizability and so is usually ignored. However, a quantum theory of the massive photon can be considered in the Wilsonian
effective field theoryIn physics, an effective field theory is an approximate theory that includes appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, while ignoring substructure and degrees of freedom at shorter distances .-The renormalization group:Presently, effective...
approach to quantum field theory, where, depending on whether the photon mass is generated by a Higgs mechanism or is inserted in an ad hoc way in the Proca Lagrangian, the limits implied by various observations/experiments may be different.
Varying c in quantum theory
In
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically described by fields or of many-body systems. It is widely used in particle physics and condensed matter physics...
the Heisenberg uncertainty relations indicate that photons can travel at any speed for short periods. In the
Feynman diagramIn quantum field theory a Feynman diagram is an intuitive graphical representation of a contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory....
interpretation of the theory, these are known as "
virtual photonsIn physics, a virtual particle is a particle that exists for a limited time and space, introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty Principle...
", and are distinguished by propagating off the mass shell. These photons may have any velocity, including velocities greater than the speed of light. To quote
Richard FeynmanRichard Phillips Feynman was an American physicist known for the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as work in particle physics...
"...there is also an amplitude for light to go faster (or slower) than the conventional speed of light. You found out in the last lecture that light doesn't go only in straight lines; now, you find out that it doesn't go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed,
c." These virtual photons, however, do not violate causality or special relativity, as they are not directly observable and information cannot be transmitted acausally in the theory. Feynman diagrams and virtual photons are interpreted not as a physical picture of what is actually taking place, but rather as a convenient calculation tool (which, in some cases, happen to involve faster-than-light velocity vectors).
Varying c in time
In 1937,
Paul DiracPaul Adrien Maurice Dirac, OM, FRS was a British theoretical physicist. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...
and others began investigating the consequences of natural constants changing with time. For example, Dirac proposed a change of only 5 parts in 10
11 per year of Newton's constant
G to explain the relative weakness of the gravitational force compared to other fundamental forces. This has become known as the
Dirac large numbers hypothesisThe Dirac large numbers hypothesis refers to an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of force scales. The ratios constitute very large, dimensionless numbers: some 40 orders of magnitude in the present cosmological epoch...
. However,
Richard FeynmanRichard Phillips Feynman was an American physicist known for the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as work in particle physics...
showed in his famous lectures that the
gravitational constantThe gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
most likely could not have changed this much in the past 4 billion years based on geological and solar system observations (although this may depend on assumptions about the constant not changing other constants). (See also strong equivalence principle.)
It is not clear what a variation in a dimensionful quantity actually means, since any such quantity can be changed merely by changing one's choice of units.
John BarrowJohn David Barrow FRS is an English cosmologist, theoretical physicist, and mathematician. He is currently Research Professor of Mathematical Sciences at the University of Cambridge...
wrote:
- "[An] important lesson we learn from the way that pure numbers like α define the world is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by α is a combination of the electron charge, e, the speed of light
In physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value [including the Planck massIn physics, the Planck mass is the unit of mass in the system of natural units known as Planck units. It is defined so that...
mP] you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged."
Any equation of
physical lawA physical law or scientific law is a scientific generalization based on empirical observations of physical behavior . Laws of nature are observable. Scientific laws are empirical, describing the observable laws...
can be expressed in such a manner to have all dimensional quantities normalized against like dimensioned quantities (called
nondimensionalizationNondimensionalization is the partial or full removal of units from an equation involving physical quantities by a suitable substitution of variables. This technique can simplify and parameterize problems where measured units are involved. It is closely related to dimensional analysis...
) resulting in only dimensionless quantities remaining. In fact, physicists often
choose their units so that the physical constants
c,
G,
h/(2π), and 4πε
0 take the value one, resulting in every physical quantity being normalized against its corresponding Planck unit. As such, many physicists think that specifying the evolution of a dimensionful quantity is at best meaningless and at worst inconsistent. When Planck units are used and such equations of physical law are expressed in this nondimensionalized form,
no dimensional physical constants such as
c,
G, or
h remain, only dimensionless quantities. Shorn of their anthropometric unit dependence, there simply is no
speed of lightIn physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
,
gravitational constantThe gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
, or Planck's constant, remaining in mathematical expressions of physical reality to be subject to such hypothetical variation. For example, in the case of the gravitational constant,
G, the relevant dimensionless quantities that were assumed to vary ultimately became the ratios of the
Planck massIn physics, the Planck mass is the unit of mass in the system of natural units known as Planck units. It is defined so that...
to the masses of the fundamental particles. Some key dimensionless quantities (thought to be constant) depend on the speed of light, notably the
fine-structure constantIn physics, the fine-structure constant is a fundamental physical constant, namely the coupling constant characterizing the strength of the electromagnetic interaction. The numerical value of α is the same in all systems of units, because α is a dimensionless quantity...
, would have meaningful variance and their possible variation continues to be studied.
In relativity, space-time is 4 dimensions of the same physical property of either space or time, depending on which perspective is chosen. The conversion factor of length=i*c*time is described in Appendix 2 of Einstein's
Relativity. A changing c in relativity would mean the imaginary dimension of time is changing compared to the other three real-valued spacial dimensions of space-time.
Specifically regarding VSL, if the
SISi, si, or SI may refer to :- Places :* Mount Si, a mountain in state of Washington* Si County, county in Anhui, China* Si River, a river in China* Slovenia, a European nation Si, si, or SI may refer to (all SI unless otherwise stated):- Places :* Mount Si, a mountain in state of Washington* Si...
meter definition was reverted to its pre-1960 definition as a length on a
prototypeA prototype is an original type, form, or instance of something serving as a typical example, basis, or standard for other things of the same category...
bar (making it possible for the measure of
c to change), then a conceivable change in
c (the reciprocal of the amount of time taken for light to travel this prototype length) could be more fundamentally interpreted as a change in the dimensionless ratio of the meter prototype to the
Planck lengthIn physics, the Planck length, denoted ℓP, is a unit of length, equal to . It is a base unit in the system of Planck units. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, Planck's constant, and the gravitational constant...
or as the dimensionless ratio of the SI
secondThe second , sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units base unit of time...
to the
Planck timeIn physics, the Planck time, , is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length...
or a change in both. If the number of atoms making up the meter prototype remains unchanged (as it should for a stable prototype), then a perceived change in the value of
c would be the consequence of the more fundamental change in the dimensionless ratio of the Planck length to the sizes of atoms or to the
Bohr radiusIn the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy...
or, alternatively, as the dimensionless ratio of the Planck time to the
periodFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
of a particular
caesiumCaesium or cesium is the chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-gold alkali metal with a melting point of , which makes it one of only five metals that are liquid at or near room temperature...
-133
radiationAn atomic clock is a type of clock that uses an atomic resonance frequency standard as its timekeeping element. They are the most accurate time and frequency standards known, and are used as primary standards for international time distribution services, and to control the frequency of television...
or both.
One group, studying distant quasars, has claimed to detect a variation of the fine structure constant at the level in one part in 10
5. Other authors dispute these results. Other groups studying quasars claim no detectable variation at much higher sensitivities. Moreover, even more stringent constraints, placed by study of certain
isotopicIsotopes are different types of atoms of the same chemical element, each having a different number of neutrons. Correspondingly, isotopes differ in mass number but not in atomic number. The difference in the number of nucleons comes from a difference how many neutrons are in the atomic nucleus...
abundances in the
OkloOklo is a region near the town of Franceville, in the Haut-Ogooué province of the Central African state of Gabon.The discovery in September 1972 of several natural nuclear fission reactors in the uranium mines situated there has fired the imagination and aroused the curiosity of...
natural nuclear fission reactorA natural nuclear fission reactor is a uranium deposit where analysis of isotope ratios has shown that self-sustaining nuclear chain reactions have occurred. The existence of this phenomenon was discovered in 1972 by French physicist Francis Perrin. The conditions under which a natural nuclear...
, seem to indicate no variation is present.
Paul DaviesPaul Charles William Davies AM is an English physicist, writer and broadcaster, currently a professor at Arizona State University as well as the Director of BEYOND: Center for Fundamental Concepts in Science...
and collaborators have suggested that it is in principle possible to disentangle which of the dimensionful constants (the
elementary chargeThe elementary charge, usually denoted e, is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. This is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called the "elementary positive...
, Planck's constant, and the
speed of lightIn physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
) of which the fine-structure constant is composed is responsible for the variation. However, this has been disputed by others and is not generally accepted.
The varying speed of light cosmology
The varying speed of light cosmology has been proposed independently by
Jean-Pierre PetitJean-Pierre Petit is a French scientist, senior researcher at National Center for Scientific Research , now retired. His main working fields are fluid mechanics, kinetic theory of gases, plasma physics, magnetohydrodynamics power generation and propulsion, astrophysics and topology...
from 1988
and then John Moffat in 1992
and the two-man team of Andreas Albrecht and
João MagueijoJoão Magueijo is a Portuguese cosmologist and professor in Theoretical Physics at Imperial College London. He is a pioneer of the varying speed of light theory.- Career :...
in 1998
to explain the
horizon problemThe horizon problem is a problem with the standard cosmological model of the Big Bang which was identified in the 1970s. It points out that different regions of the universe have not "contacted" each other due to the great distances between them, but nevertheless they have the same temperature and...
of
cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of our universe and is concerned with fundamental questions about its formation and evolution. Cosmology involves itself with studying the motions of the celestial bodies and the first cause....
and propose an alternative to
cosmic inflationIn physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized exponential expansion of the universe at the end of the grand unification epoch, 10
−36 seconds after the Big Bang, driven by a negative-pressure vacuum energy density...
.
In Petit's VSL model, the variation of
c accompanies the joint variations of all
physical constantsA physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...
combined to space and time
scale factorsThe scale factor or cosmic scale factor parameter of the Friedmann equations is a function of time which represents the relative expansion of the universe. It is sometimes called the Robertson-Walker scale factor...
changes, so that all equations and measurements of these constants remain unchanged through the evolution of the universe. The
Einstein field equationsThe Einstein field equations or Einstein's equations are a set of ten equations in Einstein's theory of general relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
remain invariant through convenient joint variations of
c and
G in
Einstein's constantEinstein's constant or Einstein's gravitational constant, denoted κ , is the coupling constant appearing in the Einstein field equation which can be written:
...
. Late-model restricts the variation of constants to the higher
energy densityEnergy density is a term used for the amount of energy stored in a given system or region of space per unit volume, or per unit mass, depending on the context. The latter is more formally known as specific energy...
of the early universe, at the very beginning of the
Radiation-Dominated EraThe Radiation-Dominated Era refers to one of the three phases of the known universe, the other two being the Matter-Dominated Era and the Dark Energy Dominated Era...
where spacetime is identified to space-entropy with a
metricIn mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric...
conformally flatA Riemannian manifold is conformally flat if each point has a neighborhood that can be mapped to flat space by a conformal transformation.More formally, let be a pseudo-Riemannian manifold...
. However it should be noted that while this was the first VSL model to be published, and the sole to date where an evolution law is given relating the joint variations of constants through time while leaving the physics unchanged, these papers received few citations in the later VSL literature.
The idea from Moffat and the team Albrecht-Magueijo is that light propagated as much as 60 orders of magnitude faster in the early universe, thus distant regions of the expanding universe have had time to interact since the beginning of the universe. There is no known way to solve the horizon problem with variation of the fine-structure constant, because its variation does not change the
causal structureCausality describes the relationship between causes and effects, is fundamental to all natural science, especially physics, and has a basis in logic. It is also studied from the perspectives of philosophy, computer science, and statistics. In physics it is useful to interpret certain terms of a...
of
spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions...
. To do so would require modifying gravity by varying Newton's constant or redefining
special relativitySpecial relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies"...
(See
equivalence principleIn the physics of general relativity, the equivalence principle refers to several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...
for further details). Classically, varying speed of light cosmologies propose to circumvent this by varying the dimensionful quantity
c by breaking the Lorentz invariance of
EinsteinAlbert Einstein was a theoretical physicist. His many contributions to physics include the special and general theories of relativity, the founding of relativistic cosmology, the first post-Newtonian expansion, explaining the perihelion advance of Mercury, prediction of the deflection of...
's
theories of general and special relativityThe theory of relativity, or simply relativity, generally refers specifically to two theories of Albert Einstein: special relativity and general relativity...
in a particular way.
Alternative VSL models have also been proposed .
External links