speed of light
From Wikipedia, the free encyclopedia.
In physics, the speed of light is the speed of propagation of an electromagnetic wave, traditionally indicated with the letter c, from the Latin celeritas ("speed"), since in 1894 was thus represented by Paul Drude. In the vacuum has a value equal to c0 = 299 792.458 km / s (299 792 458 m / s using the units of the International System, [1] or about 3 × 108 m / s).
The speed of light in vacuum is a physical constant independent of the speed of the object which emits the radiation, and then by the reference system used. From October 21, 1983 it considers the value C_0 as exact or without error, and from it you define the length of the meter in the International System.
According to the relativity, c0 is also the maximum speed at which information can travel throughout the universe (energy and / or matter), and is the speed in the void of all particles without mass and related fields, including the electromagnetic radiation itself. It is also predicted by the theory of the current speed of gravity, ie, gravitational waves. In the theory of relativity, c0 interrelates the physical classical space and time finally introducing the concept of spacetime, and appears in the famous equation of mass-energy equivalence. Sometimes it happens that the speed of an object in a medium is higher than the speed of light in the medium and what is responsible for the effect Cherenkov.
Contents [hide]
1 History
1.1 The experience of Michelson and Morley
2 Description
2.1 Constant in all reference systems
2.2 Lowering of c
2.3 Calculation by Maxwell Equations
2.4 Calculation with the theory of special relativity and general relativity
3 Speed surmountable?
3.1 speed limit permitted in the physical world
3.2 Effects "superluminal"
3.3 The OPERA experiment and the observations of the MINOS
4 Notes
5 Bibliography
6 See also
7 Further reading
History [edit | edit wikitext]
Line which shows the speed of light in a scale model. From the Earth to the moon, 384,400 km, about 1.28 seconds considering the average distance the center ground / center moon
As you may know, Galileo Galilei was the first to suspect that the light does not propagate instantly and try to measure the speed, but it is possible that others before him have suggested a finite value of the speed of light. He wrote about his unsuccessful attempt using lanterns flashes of light between two opposite hills outside Florence.
Giovanni Alfonso Borelli (1608-1679), a follower of Galileo, made ingenious attempt to measure the speed of light by means of reflecting mirrors, the distance Florence-Pistoia. The first measurement of the speed of light was made by Rømer, using an anomaly in the life of the eclipses of planets moons, the moons of Jupiter discovered by Galileo. He obtained a value of about 210 800 000 m / s, due to the poor precision with which had measured the time required for light to travel the diameter of Earth's orbit. A plaque at the Paris Observatory, where the Danish astronomer working, commemorates what was, in effect, the first measurement of a universal quantity, made on this planet. Rømer published his results, which had an error of 10-25%, in the Journal des savans.
Other measures have been taken by James Bradley, Hippolyte Fizeau and others, until you reach the value accepted today.
It is a curious coincidence that the speed of the earth in its orbit is very close to a ten-thousandth of (the margin is less than one percent). This suggests how Rømer measured the speed of light. He recorded the eclipses of Io, a satellite of Jupiter: every day or two, I came in the shadow of Jupiter and then re-emerge. Rømer could see I "shut down" and "turn back" if Jupiter was visible. Io's orbit seemed to be a kind of distant clock, but which Rømer discovered ran faster when the Earth was approaching Jupiter and slow while it was receding. Rømer measured the variations in relation to the distance between Earth and Jupiter and explained by establishing a finite speed for light.
The experience of Michelson and Morley [edit | edit wikitext]
Main article: The same topic in detail: Michelson-Morley experiment.
When it rejected the model of light as a stream of particles, proposed by Descartes and supported by Newton, the wave model, his successor, had the problem of half that supported the swings. Such hypothetical means, said ether, had to have very specific characteristics: elastic, massless and resistance to motion of the bodies, moreover, had to drag the light as a current drags a boat or the wind sound waves. An ether wind would drag the light. To verify the presence of the ether by the dragging effect, Michelson and Morley repeated several times an experience with an interferometer.
If, because of the ether wind, the speed of propagation of light in the two arms AB and BC is different, the two light beams takes a different time to return to meet in A, and then the oscillations in the two bundles have a difference δ phase, as in the sinusoidal functions
A (t) = A_0 \, \ mathrm {sen} (\ omega t)
A (t) = A_0 \, \ mathrm {sen} (\ omega t + \ delta)
This causes the formation of bright and dark fringes as observed within a slit of about half a millimeter between two cards placed in front of a light source (is fine white screen of a monitor) to about 20 cm from the eye. The fringes should move by changing the orientation of the instrument with respect to the ether wind. The expected difference in the time taken by the light to travel the arms of the interferometer parallel and perpendicular to the ether wind is calculated easily.
In the many experiences of Michelson, Morley and others has never observed the formation of these fringes, regardless of how it was oriented interferometer and the position of the Earth in its orbit. The explanation of this result according to Einstein is that there is no ether, and that the independence of the speed of light from its direction of propagation is an obvious consequence dell'isotropia space. The ether simply becomes unnecessary.
Hippolyte Fizeau measured the speed of light through its interferometer which consisted of a toothed wheel rotated at great speed. Through the teeth of the wheel it was made to pass a ray of light that reached intermittent a mirror placed at a great distance that reflected the light back towards the wheel, but the return beam, since meanwhile the wheel was turned, passed through the next slit, and then , note the distance that light walked, and known the time interval in which the wheel He performed the rotation needed, Fizeau, calculated the speed of light with a small error with respect to the value stated today. This video summarizes this experience.
Description [edit | edit wikitext]
The speed of light is related to the electromagnetic properties of the medium in which it propagates: precisely to the electrical permittivity \ varepsilon and magnetic permeability \ mu:
c = \ frac {1} {\ sqrt {\ mu \, \ varepsilon}}
usually refers to the vacuum: c = C_0 c_r \, \ varepsilon = \ varepsilon_0 \ varepsilon_r \ and \ mu = \ mu_0 \ mu_r \, when the relationship becomes particularly:
C_0 = \ frac {1} {\ sqrt {\ mu_0 \, \}} varepsilon_0
C_0 where is the speed of light in vacuum, \ varepsilon_0 is the electric permittivity of vacuum and \ mu_0 the vacuum magnetic permeability.
Constant in all frames of reference [edit | edit wikitext]
Main article: The same topic in detail: of velocities.
Direct experience, we are accustomed to the additive rule of velocities: if two cars approach each other at 50 km / h, it is expected that each car will perceive the other as approaching at 100 km / h (ie the sum of the respective speeds).
Located close to the speed of light, however, it becomes clear from experimental results that the additive rule is no longer valid. Two spaceships, each traveling at 90% the speed of light relative to some third observer between them, do not perceive each other as approaching to 180% of the speed of light. The apparent speed indeed results to be of approximately 99.4475% the speed of light, however, lower than 100%.
This result is given by the Einstein formula for the super-sum of the speed:
u = {v + w \ over 1 + \ frac {v \ cdot w} {c ^ 2}}
where v and w are the speed of the spacecraft relative to the observer, and u is the speed perceived by each spaceship.
Contrary to normal intuition, regardless of the speed at which one observer is moving relative to another, both will measure the speed of a beam of light with the same constant value, the speed of light.
Albert Einstein developed the theory of relativity by applying the bizarre (as opposed to daily) above consequences to classical mechanics. The experiments inspired by the theory of relativity directly and indirectly confirm that the speed of light has a constant value, independent of the motion of the observer and the source.
Since the speed of light in vacuum is constant, it is convenient to measure distances in terms of C_0. As already mentioned, in 1983 the meter was redefined in relation to c. In particular, a meter 299 792 is the 458th part of the distance covered by the light in a second. Distances in physical experiment in astronomy are commonly measured in light seconds, light minutes, or light years.
Lowering of c [edit | edit wikitext]
Passing through the materials the light undergoes the events of optical dispersion and, in many cases of interest, it propagates with a speed lower than C_0, by a factor called the index of refraction of the material. The speed of light in air is only slightly lower C_0. Denser materials, such as water and glass can slow light to fractions of 3/4 and 2/3 of C_0. There are also particular materials, said metamaterials, which have negative refractive index. The light seems to slow down due to inelastic collision: is absorbed by an atom of the crossed material that excites and returns the light delayed and diverted in direction.
In 1999, a group of scientists led by Lene Hau were able to slow the speed of a light beam up to about 61 km / h. In 2001, they were able to momentarily stop a beam. See: Bose-Einstein for more information.
In January 2003, Mikhail Lukin, with scientists at Harvard University and the Lebedev Institute in Moscow, succeeded in completely halting light inside a gas of rubidium atoms to a temperature of about 80 ° C: the atoms, in the words of Lukin, "they behaved as small mirrors" (Dumé, 2003), because of the interference patterns of two rays of "control". (Dumé, 2003)
In July 2003, the University of Rochester Matthew Bigelow, Nick Lepeshkin and Robert Boyd have both slowed down which accelerated the light at room temperature, in a crystal of alexandrite, exploiting the changes in the refractive index due to the interference quantum. Two laser beams are sent on the crystal, in certain circumstances one of the two suffers a reduced absorption in a certain range of wavelengths, while the refractive index increases in the same range, or "spectral hole": the group velocity is therefore very low. Instead using different wavelengths, it was possible to produce a "spectral antibuco", in which the absorption is greater, and therefore the superluminal propagation. You were observed speed of 91 m / s for a laser with a wavelength of 488 nanometers, and -800 m / s [Citation] to wavelengths of 476 nanometers. The negative rate indicates a superluminal propagation, because the impulses seem to come from the crystal before being entered.
In September 2003, Shanhui Fan and Mehmet Fatih Yanik Stanford University have proposed a method to block the light within a solid state device, where photons bounce between pillars of semiconductor creating a kind of standing wave. The results were published in Physical Review Letters in February 2004.
Calculation by the Maxwell equations [edit | edit wikitext]
It is possible to derive the speed of light in vacuum (since it is an electromagnetic wave), starting from the Maxwell equations. From the third Maxwell equation, by applying the operator rotor, you get:
\ Vec {\ nabla} \ times (\ vec {\ nabla} \ times \ vec {E}) = - \ vec {\ nabla} \ times \ frac {\ partial \ vec {B}} {\ partial t}
we recall that:
\vec{\nabla}\times(\vec{\nabla}\times\vec{E})=-\nabla^{2}\vec{E}+\vec{\nabla}(\vec{\nabla}\cdot\vec{E})
But, since it is considered an ideal situation or the presence of the vacuum, it is had that \ vec {\ nabla} \ cdot \ vec {E} = 0 since there are charged and \ vec {J} = 0 in as there is no current.
From the two equations, taking into account the latter's consideration, and considering that the gradient operator is made with respect to the spatial coordinates, you get:
\ Nabla ^ {2} \ vec {E} = \ vec {\ nabla} \ times \ frac {\ partial \ vec {B}} {\ partial t} = \ frac {\ partial} {\ partial t} (\ vec {\ nabla} \ times \ vec {B})
At this point, using the fourth Maxwell equation, we get the first of the two equations of the electromagnetic waves:
\ Nabla ^ {2} \ vec {E} = \ epsilon_ {0} \ mu_ {0} \ frac {\ partial ^ {2} \ vec {E}} {\ partial t} ^ {2}
The solution of this equation, also known as d'Alembert equation, is represented by waves that propagate with velocity v = \ frac {1} {\ sqrt {\ epsilon_ {0} \ mu_ {0}}}.
Calculating with the theory of special relativity and general relativity [edit | edit wikitext]
The formula that describes the space-time in the theory of relativity by Einstein was used to calculate the speed of light:
\ Delta s ^ 2 = \ Delta x ^ 2 + \ Delta y ^ 2 + \ Delta z ^ 2
In general relativity, the expression of the element ds is given by the fundamental tensor covariant:
ds ^ 2 = g _ {\ mu \ nu} dx ^ {\ mu} dx ^ {\ nu}
Einstein remarked then that if you know the direction, that are known to be associated dx_1: dx_2: dx_3, the equation ds returns sizes
dx_1 / dx_4, dx_2 / dx_4, dx_3 / dx_4,
and, in consequence, the speed (defined in the sense of Euclidean geometry):
\ Gamma = \ sqrt {(dx_1 / dx_4) ^ 2 + (dx_2 / dx_4) ^ 2 + (dx_3 / dx_4) ^ 2}.
The last formula is that of the calculation of the magnitude of a vector, applied to the velocity vector of the light.
Spacetime has four dimensions, while the Euclidean has three: to use Euclidean geometry has made a restriction from four to three dimensions, eliminating the time.
Expressing the three spatial terms in units of time (it is divided by dx_4) you obtain the components of the velocity vector.
The term dx_4 is set for difference from relativity, known the other three terms.
Speed overcome? [Edit | edit wikitext]
Speed limit permitted in the physical world [edit | edit wikitext]
C_0, fixed size, independent of the reference system, as in introduction to relativity, is the maximum speed that can travel a physical body as energy, matter and information in Minkowski spacetime, modeled precisely on the basis that for every Event is possible to draw a cone of light and divide the space into disjoint regions: the future, the past and the present event.
This limit to our physical space leans against the causal structure and C_0 is a constant which supports and articulates the whole theory on the dimensionality of the physical observable, and in which we move. C_0 is maximum speed of all massless particles and associated fields. Even particles, of kind imaginary, as tachyons, while traveling at speeds higher than those of light, are not accelerated to such a speed, and even can be slowed down in speed subluminali, you can only accelerate at higher speeds.
Also in this case, at present a purely theoretical construct, C_0 remains an impassable wall.
Although the physical theories, in the twentieth century, this speed is not so considered surmountable, and this in keeping with the experimental observations, there are situations, in quantum mechanics, where effects are observed instant, then of infinite speed, as the 'quantum entanglement, where, although you do not send information with infinite speed, in infinite speed quantum teleporting a quantum state. The effects have been observed experimentally.
Effects "superluminal" [edit | edit wikitext]
Main article: The same topic in detail: superluminal speed and tachyon.
In the current state of scientific knowledge, C_0, as said above, is the maximum speed in the universe. A particular physical phenomenon, the Cherenkov effect, is due to particles which are to travel to below c0 but above the c of the medium in which they move, and "holding back" by emitting radiation. The limit imposed by relativity for speed so there is a limit on the speed of propagation of objects and signals but is a limit on the speed at which it can propagate the information. Although these two things coincide almost always this fine distinction allows, in some cases, to obtain so-called superluminal effects. In these cases, one can see short light pulses that exceed the obstacles with a speed apparently greater than C_0. Exceeding the group velocity of the light in this manner is comparable to exceeding the speed of sound by arranging a row of appropriately spaced, and making him scream "I'm here!", One after the other at short intervals timed by a clock, so You should hear the voice of the person earlier before you can scream. In this type of phenomena, however, the phase velocity of a package (multiple frequencies) is less than that of light.
According to the theories of special and general relativity is not possible that the information is transmitted faster than C_0 in a space-uniform. It would be possible for example using a wormhole, but the existence of the latter is not supported by experimental tests.
Astrophysical objects (stars and galaxies) are commonly observed superluminal. For this type of makeup objects resides in the motion of approaching of these objects in the direction of the earth. The speed of an object can be measured, trivially, as the distance between two points traversed by the object divided by the time needed for this route. For astrophysical objects in space and time information about where the start and end route is transmitted to the viewer through the light. If the end point of route is closer to the observer for the starting point, the light of the starting point journey is delayed and the end point early in his arrival on Earth. The ride is, well, started later and finished first, that is minor. The result can, therefore, also an apparent speed greater than that of light.
The OPERA experiment and the observations of the MINOS [edit | edit wikitext]
At present they were not designed large particle physics experiments, designed specifically to test the superabilità of C_0.
In September 2011 a group of scientists from the National Laboratories of Gran Sasso (as part of the OPERA) published the results of their observations, collateral, as part of research to define and test the neutrino oscillation, a phenomenon that would change the particles from one group to another between the muon, tau and the electronic, suggesting that these particles possess mass, as already theorized by Bruno Pontecorvo in 1969.
In these observations, it appeared that beams of muon neutrinos, launched by CERN to the Gran Sasso, were traveling at speeds just above that of light, even taking into account the uncertainty of measurement equal to one part in 40 000. This anomaly corresponds to a relative difference between the speed of the muon neutrino and the speed of light:
\ Frac {vc} {c} = \ left (2.48 \ pm 0.28 \; (statistical) \; \ pm 0.30 \; (systematic) \; \ right) \ times 10 ^ {- 5} .
Confirmation is not falsified the theory of relativity, but rather would have suggested incomplete, making it necessary to develop a theory more extensive as was the case with the relativity in turn compared to the Newtonian mechanics, probably with the support of the theory of strings. [2] On February 22, 2012 however, the same researchers responsible for the project associated with a measurement error of the instruments the anomaly of the speed of neutrinos. [3]
From time it is assumed some generalizations of relativity in 2007 took a similar experience at the Main Injector Neutrino Oscillation Search in Minnesota, a neutrino experiment inaugurated in 2005 that works with particles from Fermilab. By studying the neutrino oscillation through three different families [4] were measured speed anomalous neutrinos, but the increased uncertainty about the exact locations of the detector and emission, made less significant the possibility of overcoming C_0.
From Wikipedia, the free encyclopedia.
In physics, the speed of light is the speed of propagation of an electromagnetic wave, traditionally indicated with the letter c, from the Latin celeritas ("speed"), since in 1894 was thus represented by Paul Drude. In the vacuum has a value equal to c0 = 299 792.458 km / s (299 792 458 m / s using the units of the International System, [1] or about 3 × 108 m / s).
The speed of light in vacuum is a physical constant independent of the speed of the object which emits the radiation, and then by the reference system used. From October 21, 1983 it considers the value C_0 as exact or without error, and from it you define the length of the meter in the International System.
According to the relativity, c0 is also the maximum speed at which information can travel throughout the universe (energy and / or matter), and is the speed in the void of all particles without mass and related fields, including the electromagnetic radiation itself. It is also predicted by the theory of the current speed of gravity, ie, gravitational waves. In the theory of relativity, c0 interrelates the physical classical space and time finally introducing the concept of spacetime, and appears in the famous equation of mass-energy equivalence. Sometimes it happens that the speed of an object in a medium is higher than the speed of light in the medium and what is responsible for the effect Cherenkov.
Contents [hide]
1 History
1.1 The experience of Michelson and Morley
2 Description
2.1 Constant in all reference systems
2.2 Lowering of c
2.3 Calculation by Maxwell Equations
2.4 Calculation with the theory of special relativity and general relativity
3 Speed surmountable?
3.1 speed limit permitted in the physical world
3.2 Effects "superluminal"
3.3 The OPERA experiment and the observations of the MINOS
4 Notes
5 Bibliography
6 See also
7 Further reading
History [edit | edit wikitext]
Line which shows the speed of light in a scale model. From the Earth to the moon, 384,400 km, about 1.28 seconds considering the average distance the center ground / center moon
As you may know, Galileo Galilei was the first to suspect that the light does not propagate instantly and try to measure the speed, but it is possible that others before him have suggested a finite value of the speed of light. He wrote about his unsuccessful attempt using lanterns flashes of light between two opposite hills outside Florence.
Giovanni Alfonso Borelli (1608-1679), a follower of Galileo, made ingenious attempt to measure the speed of light by means of reflecting mirrors, the distance Florence-Pistoia. The first measurement of the speed of light was made by Rømer, using an anomaly in the life of the eclipses of planets moons, the moons of Jupiter discovered by Galileo. He obtained a value of about 210 800 000 m / s, due to the poor precision with which had measured the time required for light to travel the diameter of Earth's orbit. A plaque at the Paris Observatory, where the Danish astronomer working, commemorates what was, in effect, the first measurement of a universal quantity, made on this planet. Rømer published his results, which had an error of 10-25%, in the Journal des savans.
Other measures have been taken by James Bradley, Hippolyte Fizeau and others, until you reach the value accepted today.
It is a curious coincidence that the speed of the earth in its orbit is very close to a ten-thousandth of (the margin is less than one percent). This suggests how Rømer measured the speed of light. He recorded the eclipses of Io, a satellite of Jupiter: every day or two, I came in the shadow of Jupiter and then re-emerge. Rømer could see I "shut down" and "turn back" if Jupiter was visible. Io's orbit seemed to be a kind of distant clock, but which Rømer discovered ran faster when the Earth was approaching Jupiter and slow while it was receding. Rømer measured the variations in relation to the distance between Earth and Jupiter and explained by establishing a finite speed for light.
The experience of Michelson and Morley [edit | edit wikitext]
Main article: The same topic in detail: Michelson-Morley experiment.
When it rejected the model of light as a stream of particles, proposed by Descartes and supported by Newton, the wave model, his successor, had the problem of half that supported the swings. Such hypothetical means, said ether, had to have very specific characteristics: elastic, massless and resistance to motion of the bodies, moreover, had to drag the light as a current drags a boat or the wind sound waves. An ether wind would drag the light. To verify the presence of the ether by the dragging effect, Michelson and Morley repeated several times an experience with an interferometer.
If, because of the ether wind, the speed of propagation of light in the two arms AB and BC is different, the two light beams takes a different time to return to meet in A, and then the oscillations in the two bundles have a difference δ phase, as in the sinusoidal functions
A (t) = A_0 \, \ mathrm {sen} (\ omega t)
A (t) = A_0 \, \ mathrm {sen} (\ omega t + \ delta)
This causes the formation of bright and dark fringes as observed within a slit of about half a millimeter between two cards placed in front of a light source (is fine white screen of a monitor) to about 20 cm from the eye. The fringes should move by changing the orientation of the instrument with respect to the ether wind. The expected difference in the time taken by the light to travel the arms of the interferometer parallel and perpendicular to the ether wind is calculated easily.
In the many experiences of Michelson, Morley and others has never observed the formation of these fringes, regardless of how it was oriented interferometer and the position of the Earth in its orbit. The explanation of this result according to Einstein is that there is no ether, and that the independence of the speed of light from its direction of propagation is an obvious consequence dell'isotropia space. The ether simply becomes unnecessary.
Hippolyte Fizeau measured the speed of light through its interferometer which consisted of a toothed wheel rotated at great speed. Through the teeth of the wheel it was made to pass a ray of light that reached intermittent a mirror placed at a great distance that reflected the light back towards the wheel, but the return beam, since meanwhile the wheel was turned, passed through the next slit, and then , note the distance that light walked, and known the time interval in which the wheel He performed the rotation needed, Fizeau, calculated the speed of light with a small error with respect to the value stated today. This video summarizes this experience.
Description [edit | edit wikitext]
The speed of light is related to the electromagnetic properties of the medium in which it propagates: precisely to the electrical permittivity \ varepsilon and magnetic permeability \ mu:
c = \ frac {1} {\ sqrt {\ mu \, \ varepsilon}}
usually refers to the vacuum: c = C_0 c_r \, \ varepsilon = \ varepsilon_0 \ varepsilon_r \ and \ mu = \ mu_0 \ mu_r \, when the relationship becomes particularly:
C_0 = \ frac {1} {\ sqrt {\ mu_0 \, \}} varepsilon_0
C_0 where is the speed of light in vacuum, \ varepsilon_0 is the electric permittivity of vacuum and \ mu_0 the vacuum magnetic permeability.
Constant in all frames of reference [edit | edit wikitext]
Main article: The same topic in detail: of velocities.
Direct experience, we are accustomed to the additive rule of velocities: if two cars approach each other at 50 km / h, it is expected that each car will perceive the other as approaching at 100 km / h (ie the sum of the respective speeds).
Located close to the speed of light, however, it becomes clear from experimental results that the additive rule is no longer valid. Two spaceships, each traveling at 90% the speed of light relative to some third observer between them, do not perceive each other as approaching to 180% of the speed of light. The apparent speed indeed results to be of approximately 99.4475% the speed of light, however, lower than 100%.
This result is given by the Einstein formula for the super-sum of the speed:
u = {v + w \ over 1 + \ frac {v \ cdot w} {c ^ 2}}
where v and w are the speed of the spacecraft relative to the observer, and u is the speed perceived by each spaceship.
Contrary to normal intuition, regardless of the speed at which one observer is moving relative to another, both will measure the speed of a beam of light with the same constant value, the speed of light.
Albert Einstein developed the theory of relativity by applying the bizarre (as opposed to daily) above consequences to classical mechanics. The experiments inspired by the theory of relativity directly and indirectly confirm that the speed of light has a constant value, independent of the motion of the observer and the source.
Since the speed of light in vacuum is constant, it is convenient to measure distances in terms of C_0. As already mentioned, in 1983 the meter was redefined in relation to c. In particular, a meter 299 792 is the 458th part of the distance covered by the light in a second. Distances in physical experiment in astronomy are commonly measured in light seconds, light minutes, or light years.
Lowering of c [edit | edit wikitext]
Passing through the materials the light undergoes the events of optical dispersion and, in many cases of interest, it propagates with a speed lower than C_0, by a factor called the index of refraction of the material. The speed of light in air is only slightly lower C_0. Denser materials, such as water and glass can slow light to fractions of 3/4 and 2/3 of C_0. There are also particular materials, said metamaterials, which have negative refractive index. The light seems to slow down due to inelastic collision: is absorbed by an atom of the crossed material that excites and returns the light delayed and diverted in direction.
In 1999, a group of scientists led by Lene Hau were able to slow the speed of a light beam up to about 61 km / h. In 2001, they were able to momentarily stop a beam. See: Bose-Einstein for more information.
In January 2003, Mikhail Lukin, with scientists at Harvard University and the Lebedev Institute in Moscow, succeeded in completely halting light inside a gas of rubidium atoms to a temperature of about 80 ° C: the atoms, in the words of Lukin, "they behaved as small mirrors" (Dumé, 2003), because of the interference patterns of two rays of "control". (Dumé, 2003)
In July 2003, the University of Rochester Matthew Bigelow, Nick Lepeshkin and Robert Boyd have both slowed down which accelerated the light at room temperature, in a crystal of alexandrite, exploiting the changes in the refractive index due to the interference quantum. Two laser beams are sent on the crystal, in certain circumstances one of the two suffers a reduced absorption in a certain range of wavelengths, while the refractive index increases in the same range, or "spectral hole": the group velocity is therefore very low. Instead using different wavelengths, it was possible to produce a "spectral antibuco", in which the absorption is greater, and therefore the superluminal propagation. You were observed speed of 91 m / s for a laser with a wavelength of 488 nanometers, and -800 m / s [Citation] to wavelengths of 476 nanometers. The negative rate indicates a superluminal propagation, because the impulses seem to come from the crystal before being entered.
In September 2003, Shanhui Fan and Mehmet Fatih Yanik Stanford University have proposed a method to block the light within a solid state device, where photons bounce between pillars of semiconductor creating a kind of standing wave. The results were published in Physical Review Letters in February 2004.
Calculation by the Maxwell equations [edit | edit wikitext]
It is possible to derive the speed of light in vacuum (since it is an electromagnetic wave), starting from the Maxwell equations. From the third Maxwell equation, by applying the operator rotor, you get:
\ Vec {\ nabla} \ times (\ vec {\ nabla} \ times \ vec {E}) = - \ vec {\ nabla} \ times \ frac {\ partial \ vec {B}} {\ partial t}
we recall that:
\vec{\nabla}\times(\vec{\nabla}\times\vec{E})=-\nabla^{2}\vec{E}+\vec{\nabla}(\vec{\nabla}\cdot\vec{E})
But, since it is considered an ideal situation or the presence of the vacuum, it is had that \ vec {\ nabla} \ cdot \ vec {E} = 0 since there are charged and \ vec {J} = 0 in as there is no current.
From the two equations, taking into account the latter's consideration, and considering that the gradient operator is made with respect to the spatial coordinates, you get:
\ Nabla ^ {2} \ vec {E} = \ vec {\ nabla} \ times \ frac {\ partial \ vec {B}} {\ partial t} = \ frac {\ partial} {\ partial t} (\ vec {\ nabla} \ times \ vec {B})
At this point, using the fourth Maxwell equation, we get the first of the two equations of the electromagnetic waves:
\ Nabla ^ {2} \ vec {E} = \ epsilon_ {0} \ mu_ {0} \ frac {\ partial ^ {2} \ vec {E}} {\ partial t} ^ {2}
The solution of this equation, also known as d'Alembert equation, is represented by waves that propagate with velocity v = \ frac {1} {\ sqrt {\ epsilon_ {0} \ mu_ {0}}}.
Calculating with the theory of special relativity and general relativity [edit | edit wikitext]
The formula that describes the space-time in the theory of relativity by Einstein was used to calculate the speed of light:
\ Delta s ^ 2 = \ Delta x ^ 2 + \ Delta y ^ 2 + \ Delta z ^ 2
In general relativity, the expression of the element ds is given by the fundamental tensor covariant:
ds ^ 2 = g _ {\ mu \ nu} dx ^ {\ mu} dx ^ {\ nu}
Einstein remarked then that if you know the direction, that are known to be associated dx_1: dx_2: dx_3, the equation ds returns sizes
dx_1 / dx_4, dx_2 / dx_4, dx_3 / dx_4,
and, in consequence, the speed (defined in the sense of Euclidean geometry):
\ Gamma = \ sqrt {(dx_1 / dx_4) ^ 2 + (dx_2 / dx_4) ^ 2 + (dx_3 / dx_4) ^ 2}.
The last formula is that of the calculation of the magnitude of a vector, applied to the velocity vector of the light.
Spacetime has four dimensions, while the Euclidean has three: to use Euclidean geometry has made a restriction from four to three dimensions, eliminating the time.
Expressing the three spatial terms in units of time (it is divided by dx_4) you obtain the components of the velocity vector.
The term dx_4 is set for difference from relativity, known the other three terms.
Speed overcome? [Edit | edit wikitext]
Speed limit permitted in the physical world [edit | edit wikitext]
C_0, fixed size, independent of the reference system, as in introduction to relativity, is the maximum speed that can travel a physical body as energy, matter and information in Minkowski spacetime, modeled precisely on the basis that for every Event is possible to draw a cone of light and divide the space into disjoint regions: the future, the past and the present event.
This limit to our physical space leans against the causal structure and C_0 is a constant which supports and articulates the whole theory on the dimensionality of the physical observable, and in which we move. C_0 is maximum speed of all massless particles and associated fields. Even particles, of kind imaginary, as tachyons, while traveling at speeds higher than those of light, are not accelerated to such a speed, and even can be slowed down in speed subluminali, you can only accelerate at higher speeds.
Also in this case, at present a purely theoretical construct, C_0 remains an impassable wall.
Although the physical theories, in the twentieth century, this speed is not so considered surmountable, and this in keeping with the experimental observations, there are situations, in quantum mechanics, where effects are observed instant, then of infinite speed, as the 'quantum entanglement, where, although you do not send information with infinite speed, in infinite speed quantum teleporting a quantum state. The effects have been observed experimentally.
Effects "superluminal" [edit | edit wikitext]
Main article: The same topic in detail: superluminal speed and tachyon.
In the current state of scientific knowledge, C_0, as said above, is the maximum speed in the universe. A particular physical phenomenon, the Cherenkov effect, is due to particles which are to travel to below c0 but above the c of the medium in which they move, and "holding back" by emitting radiation. The limit imposed by relativity for speed so there is a limit on the speed of propagation of objects and signals but is a limit on the speed at which it can propagate the information. Although these two things coincide almost always this fine distinction allows, in some cases, to obtain so-called superluminal effects. In these cases, one can see short light pulses that exceed the obstacles with a speed apparently greater than C_0. Exceeding the group velocity of the light in this manner is comparable to exceeding the speed of sound by arranging a row of appropriately spaced, and making him scream "I'm here!", One after the other at short intervals timed by a clock, so You should hear the voice of the person earlier before you can scream. In this type of phenomena, however, the phase velocity of a package (multiple frequencies) is less than that of light.
According to the theories of special and general relativity is not possible that the information is transmitted faster than C_0 in a space-uniform. It would be possible for example using a wormhole, but the existence of the latter is not supported by experimental tests.
Astrophysical objects (stars and galaxies) are commonly observed superluminal. For this type of makeup objects resides in the motion of approaching of these objects in the direction of the earth. The speed of an object can be measured, trivially, as the distance between two points traversed by the object divided by the time needed for this route. For astrophysical objects in space and time information about where the start and end route is transmitted to the viewer through the light. If the end point of route is closer to the observer for the starting point, the light of the starting point journey is delayed and the end point early in his arrival on Earth. The ride is, well, started later and finished first, that is minor. The result can, therefore, also an apparent speed greater than that of light.
The OPERA experiment and the observations of the MINOS [edit | edit wikitext]
At present they were not designed large particle physics experiments, designed specifically to test the superabilità of C_0.
In September 2011 a group of scientists from the National Laboratories of Gran Sasso (as part of the OPERA) published the results of their observations, collateral, as part of research to define and test the neutrino oscillation, a phenomenon that would change the particles from one group to another between the muon, tau and the electronic, suggesting that these particles possess mass, as already theorized by Bruno Pontecorvo in 1969.
In these observations, it appeared that beams of muon neutrinos, launched by CERN to the Gran Sasso, were traveling at speeds just above that of light, even taking into account the uncertainty of measurement equal to one part in 40 000. This anomaly corresponds to a relative difference between the speed of the muon neutrino and the speed of light:
\ Frac {vc} {c} = \ left (2.48 \ pm 0.28 \; (statistical) \; \ pm 0.30 \; (systematic) \; \ right) \ times 10 ^ {- 5} .
Confirmation is not falsified the theory of relativity, but rather would have suggested incomplete, making it necessary to develop a theory more extensive as was the case with the relativity in turn compared to the Newtonian mechanics, probably with the support of the theory of strings. [2] On February 22, 2012 however, the same researchers responsible for the project associated with a measurement error of the instruments the anomaly of the speed of neutrinos. [3]
From time it is assumed some generalizations of relativity in 2007 took a similar experience at the Main Injector Neutrino Oscillation Search in Minnesota, a neutrino experiment inaugurated in 2005 that works with particles from Fermilab. By studying the neutrino oscillation through three different families [4] were measured speed anomalous neutrinos, but the increased uncertainty about the exact locations of the detector and emission, made less significant the possibility of overcoming C_0.
