The accepted value for the speed of light in a vacuum is precisely 299,792,458 meters/second.

This value is derived from two other defined values -- the exact value of a second is "9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" and from the meter being defined as the distance light travels in a vacuum in 1/299792458 of a second.*

In a Bose-Einstein condensate, the speed of light has been made to go as slow as 17 meters/second.


* - in other words, a meter is defined by the speed of light in a vacuum and not the other way around.

Light comes to a halt. Snails throw a party.

Scientists now have managed to stop a beam of light. Completely stopped on its way. Just hanging there, weightless, motionless. Impatient, I'm sure. 

What does a light beam look like when it is not moving ? Maybe...


  
*

This opens new possibilities for storing quantum states in future quantum computers. The key to transferring information using quantum states of light, is to be able to decode the information. To do this, one has to slow down the light so one can absorb the state, without altering it. This new breakthrough makes this theoretically possible

Danish Lene Vestergaard of Harvard University and her group, and another group from Harvard-Smithsonian Center for Astrophysics both separately accomplished this feat recently, and the result can be found in Nature and Physical Review, respectively. The teams used different techniques; one being a gas at a temperature a few millionths of a degree over absolute zero (Bose-Einstein condensate) in a magnetic trap, and the other being a polarized Rubidium gas cloud.

Source: Physical Review, Scientific American, Nature, DN
Way back when in th 19th centuryeveryone's good fiend James Clerk Maxwell summarized Electromagnetic phenomena in 4 different equations, known ironically enough as Maxwell's equations. These describe the electric field as defined by carge, (like coulomb's law but better), then an equation defining magnetic field, the equation relating an electric field to a changing magnetic one, and lastly an equation relating a magnetic field to a changing electric one. An important realization of Maxwell's was that if electric field and magnetic field are related thus, then they can be oscillated. He thought of an experiment involving a DC current, with two conducting rods connected to opposite terminals of a an electrochemical cell/battery.

          Positively charged rod
          |+_ _ _ _ _ _ _
          |+_ _ _ _ _ _  \
        ^ |+_ _ _ _ _  \  \
        | |+_ _ _ _  \  \  \
     _____/        \  \  \  \
    /               \  \  \  \  
    |                \  \  \  \
   _|_                \  \  \  \
    - DC current       |  |  |  |  Electric Field lines
    |                 /  /  /  /
    |                /  /  /  /
    \_____          /  /  /  /
          |-_ _ _ _/  /  /  /
          |-_ _ _ _ _/  /  /
        ^ |-_ _ _ _ _ _/  /
        | |-_ _ _ _ _ _ _/ 
           Negatively charged rod    

Now use your imagination, and also thing that the Magnetic field lines are perpendicular the Electric field lines, and are coming out of your screen. So now if we change the power supply to AC, we can see that the electric field will all of sudden change direction. We are rapidly decelerating the electrons, or charge, and thus changing the directiong of the two fields. Inbetween we will get areas of zero field or charge, we can observe that the field itself will oscillate. Now what will be the speed of this oscillation, this wave. We can represent the strength of the magnetic field and the electric field as two sinusoidal graphs of a function of displacement r. We can conclude at any point the magnetic field is equal to the electric field.

Now onto the speed: Imagine a conductive rectangular loop (rectangular is easier). The rectangle is at points a, b, c, d. The wave travels through it with velocity v. While the position of the loop is unchanging relative to us, relative to the wave it goes to position a', b', c', d'. We let y0= ab. Going to Maxwell's third equation, the EMF(work done per unit charge) is equal to the derivative of the rate of change of Magnetic Flux, PHIB. that is:

  • EMF=d(PHIB)/dt
  • EMF=Bd(A)/dt
  • EMF=B y0vdt/dt (recall that A=length times width, and the width will be equal to velocity times change in time)
  • (recall that A=length times width, and the width will be equal to velocity times change in time)
  • EMF=B y0v

    Going back to the fact that EMF is the work per unit charge, or electric field times distance parallel.EMF=EMFab+ EMFbc+EMFcd+EMFad. Because they are perpendicular to the elctric field EMFad=EMFbc=0 Also luckily for us the Electric field hasn't travelled through segment ab, EMFab=0. Thus EMF= EMFcd=Ey0

  • Ey0= B y0v
  • E= B v
  • E/B=v
  • 
                                          d'   d          a'
        __          __          __         _ _  __________ ____  a
       /  \        /  \        /  \       !    |          !     |
      /    \      /    \      /    \      !    |          !     |
     /      \    /      \    /      \     !    |          !     |
    /        \__/        \__/        \    !_ _ |__________!_____| b
                                          c'   c          b'
    
    

    Now we'll use the sqame diagram as above, except now the wave refers to the Magnetic field (remember in both incidence the other field is going through the computer screen). Using Ampere's Law that has been processed using Gauss' Law we come up with the equation:

  • sum(B||dl)=mu0e0d(PHIE)/dt
  • We let dc=z0, thus:
  • sum(B||dl)=mu0e0Ez0v
  • Now the part of B parallel(||) to dl is going to be zero for all but dc as discussed above for electric field. so:
  • Bdc=mu0e0Ez0v
  • B=mu0e0vBv
  • 1/(mu0e0)=v2

    Then we just sqrt(not a typo, but abrv) it, and we get the speed of the wave. But we need to know mu and e, (0's ommitted to save time and HTML formatting). These two constants are permeability of free space and permittivity of free space respectively. These two are used to describe the force of a magnetic and electric field repectively. However the sqrt of the reciprocal is equal to about 300000 km/s. and indeed experiments later should that the wave produced by this were similar to light waves only of a lowever frequency. Indeed it was shown light was an electromagnetic wave, through experimentation, and also with more accurate values for the constants the value for c is exactly what 3.9x10^-43 mentioned above. I think that's nifty


    Addition

    The speed of light can be very easily determined by easy manipulation of Maxwell's equations. One need only to take the curl of Faraday's law, and then insert Ampere's law in the place of the time derivative of the curl of magnetic field. Biot-Savart's law states that the divergence of magnetic field is zero, and Gauss' law states that the divergence of electric field is charge density over epsilon zero. Then for a system without charge or current density the equations simplify to the wave equation for electric field, which propagates at a speed of 1/(mu0epsilon0).

  • The speed of light in a vacuum is accepted as a universal constant, the same value for all observers and all types of electromagnetic radiation. First determined in 1676 by Danish scientist Olaf Rømer using astronomical observations, it is now expressed in electromagnetic quantities through Maxwell's equations. The speed of light in a vacuum is defined to be exactly 299,792,458 meters per second (about 186,000 miles per second), thus fixing the length of the meter in terms of the second. The speed of light can be altered in certain conditions, such as by gravitational, magnetic, or material interference.

    Symbol: c
    See also: special relativity

    Generally (under "normal conditions") considered to be:

    • 186,000 miles per second
    • 11,160,000 miles per minute
    • 669,600,000 miles per hour
    • 16,070,400,000 miles per day
    • 482,112,000,000 miles per month
    • 5,865,696,000,000 miles per year (a light year!)
    • 586,569,600,000,000 miles per century
    • 297,600 kilometers per second
    • 17,856,000 kilometers per minute
    • 1,071,360,000 kilometers per hour
    • 25,712,640,000 kilometers per day
    • 179,988,480,000 kilometers per week
    • 9,359,400,960,000 kilometers per year
    • 9,359,400,960,000,000 kilometers per millennium
    • 327,360,000, yards per second
    • 19,641,600,000 yards per minute
    • 1,178,496,000,000 yards per hour
    • 28,283,904,000,000 yards per day
    • 10,323,624,960,000,000 yards per year
    • 10,351,908,864,000,000 yards per leap year
    • 103,236,249,600,000,000 yards per decade
    • 982,080,000 feet per second
    • 58,924,800,000 feet per minute
    • 3,535,488,000,000 feet per hour
    • 84,851,712,000,000 feet per day
    • 30,970,874,880,000,000 feet per year
    • 11,784,960,000 inches per second
    • 707,097,600,000 inches per minute
    • 42,425,856,000,000 inches per hour
    • 1,018,220,544,000,000 inches per day
    • 7,127,543,808,000,000 inches per week
    • 31,564,836,864,000,000 inches per month
    • 371650498560000,000 inches per year
    • 372,668,719,104,000,000 inches per leap year
    • 3,716,504,985,600,000,000 inches per decade
    • 37,165,049,856,000,000,000 inches per century
    • 371,650,498,560,000,000,000 inches per millennium
    and one foot per nanosecond! (thanks Ed Halley)
    The speed of light is dependent on the medium it is travelling through. To find the velocity of light in any given substance, one must use

    n = c / v

    That is the index of refraction of the substance equals the speed of light in a vacuum divided by the speed of light in the substance. Since, by definition, n cannot be smaller than 1, the velocity of light is the fastest in a vacuum. All other mediums slow light down.

    Thus, the speed of light is determined by dividing the speed of light in a vacuum by the index of refraction of the medium.

    One qualitative point which might bear mentioning is that the popular description of the speed of light as a 'universal speed limit' is extremely prone to misinterpretation.

    Consider that you are planning a trip, and know that you must cover 100 miles of open highway to reach your destination. You know that the speed limit is 100 mph. . . To make this seem more like a 'natural law' than a human one, let us say that the fiendishly legislative powers that be have required cars to be installed with a device that triggers a massive implosion if you exceed the posted speed limit. Assuming that you cannot get around the device, then you know that it is impossible that you will arrive at your destination in less then one hour.

    Unlike this hypothetical box of lethal over-regulation, the theory of special relativity imposes no theoretical constraints on the time it takes for you to cover any distance... from your perspective.

    This is because one of the central features of the special theory is that perception of 'time' is not an absolute, but depends on a specified frame of reference. This is presumably well covered in Special Relativity.. if not, go to the source and try the eminently readable Relativity: The Special and General Theories by A. Einstein.

    As a brief example: Most people with coffee table knowledge of relativity are aware of the anecdotal example in which one of two brothers leaves the earth, travels in a rocket at relativistic velocities, then returns to find that whereas he has aged only days, his brother has aged years. I created this node because a great many people familiar with that anecdote don't seem to have made the leap to realizing that relativity does not impose limits on how long it takes for a person to travel between point A and point B... it simply defines a series of time and distance dilations between frames of reference that are at motion with respect to one another…

    So, whereas relativity imposes limits on 'social' activities, such as how fast two people can communicate with one another, and how long it takes someone else to get from one place to another from your perspective, it affects in no way your own personal mobility.

    The restrictions on your own travel are practical ones, such as fuel and the ability to withstand acceleration. If you could accelerate at the modest rate of 1g for an extended period of time, you could reach alpha centauri in weeks, and exit the galaxy within months.
    Varying Speed of Light?

    There have been theories going around in the undergrowth of theoretical physics for some years that propose that c, the speed of light in a vacuum, may have varied over the course of cosmological evolution. Jakob Bekenstein, John Moffat, Joao Magueijo, John Barrow and Andreas Albrecht have all contributed to "VSL", which is sometimes touted as an alternative to inflation to solve the horizon problem and other puzzles of cosmology. The basic idea is that light was much faster in the early Universe - many orders of magnitude faster. Then at some point it jumped down to the current value. Thus, faraway parts of the observed Universe would have time to communicate with each other, which could explain why they appear so uniform (homogeneous and isotropic).

    Recently the measurements of varying alpha (alpha being the fine structure constant) by John Webb and the team at UNSW have revived speculation about varying c, since alpha is defined as e2/(4h-bar c). A veritable storm of media coverage resulted, with headlines like "Was Einstein Wrong?", "Light is Slowing Down", "Is Light strolling along at hot-summer-day-pace?", etc.

    Problems

    However, both VSL cosmologies and the interpretation of varying alpha as "varying c" suffer from a big problem - that of units. As you will have learnt by reading the other writeups in this node, the metre is defined as the distance travelled by light in 1/299,792,458 seconds. Thus, using this definition, c always takes the same value. What does "varying c" mean now?

    Also, suppose you now take a different set of units: the standard second, and the length of a piece of metal containing a certain number of atoms laid end-to-end. The length of the piece of metal in metres will depend on the fine structure constant because of the effect of electromagnetic interactions. So, if alpha varies over time, the speed of light in bits-of-metal per second will also vary. You could also take a different standard of time: a pendulum clock, say. But for every different set of units, the apparent variation in c will be different! Clearly the variation in c is not a physically well-defined thing.

    The underlying principle is that only the variation in dimensionless numbers can be measured unambiguously. This is exactly what we do when we use units: we can say that the dimensionless ratio of the length of a table to the standard metre is 1.43. If the number turns out to be 1.45 tomorrow, something is clearly a bit odd, but you can't say definitely whether the table is bigger or the metre is smaller.

    As I indicated, variations in dimensionless numbers such as alpha are all that is needed to relate the measurements in one system to those in another. This interconvertibility extends to the so-called VSL theories. Indeed John Barrow has a paper in which he tells us that any theory of varying alpha that includes electromagnetism and general relativity can be written either as "varying c" or "varying e".

    Is Einstein dead?

    Now, when all that is said, varying alpha is still very strange. In a theory which had just EM and GR, it would not happen. So it tells us there is something beyond these two. But we knew this already - since the Standard Model cannot be the theory of everything. If we stick in some scalar fields, then it is relatively easy to get a theory that still respects the principles of general relativity but allows a solution where alpha and other stuff vary. Heck, temperature and density already vary over the evolution of the Universe - on a large scale, Lorentz invariance is already broken by these effects of the Big Bang. To say this again, the underlying theory may have Lorentz invariance, but we undoubtedly live in a solution that does not.

    When we come to the more radical VSL-type proposals, they hit another minefield: they are non-covariant. This means that Lorentz invariance is broken right there in the definition of the theory. Instead of using a dynamical, varying scalar field to induce varying alpha and (maybe) solve some cosmological problems, one introduces an arbitrary function c(t) which suddenly at some point jumps by several orders of magnitude. All sorts of principles like conservation of energy are broken at this point. There is no dynamical mechanism put forward to explain why it should happen this way: it's the cosmological equivalent of a deus ex machina. Technically, the theory is not a closed system of equations (it leaves open the choice of c(t)), so at the "jump" one has to make up a series of rules that are supposed to describe how the matter and radiation and stuff react to the sudden and enormous changes taking place. Sometimes the proponents of the theory wave their hands and talk about phase transitions, but no definite explanation has emerged from this as yet.

    Now remember that the value of c can always be set to the same number by a choice of units. When you have done this, the theory looks like a sudden, gigantic discontinuity in the contents of the Universe which happens for no apparent reason and solves the cosmological problems. The entire content of the proposal is in these rules for what happens at the jump - rules which can't be derived from a underlying action (a functional of the fields in the theory that determines its entire behaviour) but are put together according to what the authors think might be reasonable. This doesn't sound like theoretical physics to me.

    Can some things travel faster than the speed of light?

    A couple of years ago I was working on construction sites. Builders use these things called "Dumpy levels" that are like a laser light-house on a tripod. The self-leveling turret of the light-house revolves, scanning a point of laser light round and round. The line this point of light describes is in the horizontal plane (depending on the accuracy of the level) to within a tiny fraction of a degree, accurate enough for builders to use as a datum while building.

    I started to wonder whether, if the room was big enough, the spot of light revolving at (say) one revolution per second would be traveling faster than the speed of light.

    So I did some maths. Assuming pi to be 3.1415926 and the speed of light to be 300000km/second, a round 'room' with a radius exceeding 47746.48374 km, with a laser light-house in the centre revolving at one revolution per second, would produce a spot of light on the wall traveling faster than the speed of light.

    This thought experiment assumes that you could find a laser capable of throwing a coherent beam 48000 odd kilometres, and a large enough 'room'. But I think it would succeed for the following reasons.

    The spot of light is a virtual object. That is to say, it is not a physical object but a place where stuff happens. When the blades of a pair of scissors close, the place where they intersect travels away from the pivot point much faster than either blade aproaches the other. The place where the blades intersect is not itself an object, but a place defined by the relation between two objects. It is thus not a physical object, but a virtual one.

    Similarly, the zone where photons are striking the wall could travel faster than any of the individual photons.

    Therefore, virtual objects can travel faster than the speed of light.

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