Is The Speed of Light Everywhere the Same?
math.ucr.edu
math.ucr.edu
Einstein does not mean "speed" when he uses the word "velocity" here or anywhere. He means "a vector quantity consisting of a speed and direction".
While it has long been observed that hypothetical changes in the speed of light would be difficult to measure if certain other quantities changed with it in lockstep (and by "long" I mean 100+ years, going all the way back to the original debates around relativity), it is still meaningful to ask if the speed of light has changed relative to the quantities that it seems to related to.
If that turns out to be the case, it will mean that our definition is wrong, not that the speed of light isn't changing. Our definition is a constant because we believe it to be a constant. If we're wrong, it will need to change.
I could define Pi as 3 and it would be CONSTANT. We'd then argue over what shape a circle looked like, but my maths would certainly be easier than yours due to lack of irrationality.
But it does, it falls out of the geometric relationship between the three space dimensions and the time dimension. In a way, the speed of light can be thought of as the speed of time.
Think of the relationship between space and time as orthogonal, as a right angle -- which makes sense, since the time dimension is at right angles to the three space dimensions. If you move quickly through space, you can't also move quickly through time, and the relationship between your time and space velocities is just what you would expect for an orthogonal relationship:
t' = t √(1-v^2/c^2)
t = time at rest
t' = time at velocity v
c = speed of light
Einstein wrote the above in 1905, then his math teacher (Minkowski) read Einstein's paper, saw the above equation, and realized it meant time was a fourth dimension. Minkowski then famously said, "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."
In response, Einstein said, "Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore."
But from that point to 1915, Einstein acquired much more math knowledge and used it to write the General theory.
Actually that argument was had and ended a long time ago; you can set pi to 3 and you get a thing called a spherical geometry. See, for instance, http://mathforum.org/library/drmath/view/55021.html . Between the word "spherical geometry" and what you find in that link you'll have the keywords to continue digging if you want to.
Perhaps the relevant point is that the speed of light is not a number, but a dimensioned (if that's a word) quantity; and now the question becomes: is the dimensioned quantity (either its numerical value, or the meaning of the units) changing? I agree that it's hard to know how to make sense of the notion of units changing, though.
t' = t √(1-v^2/c^2)
That's pretty clear and easy to interpret. So measurements of c may be messy and subject to controversy, but the geometry expressed in the above equation, and what it tells us about spacetime, is much more clear.
This is the average speed of photons in vacuum, right? Because according to the quantum field theory, photons should have a probability of hitting virtual particles that popped into existence, which would slow it down a little.
If you take a large-scale view, you get really good results by using a mathematical model that says that the light is behaves like a wave with a certain speed, and that the speed is slower in water.
If you take a small-scale view, you get decent results by using a model that says that individual photons have a small chance of being absorbed by the water molecules and then new photons are radiated again.
Supposedly there is a quantum mechanical view which applies on all scales and gives even more accurate values, but I have never seen it worked out for something as complicated as the interaction between light and a surface of water molecules. Both of the others I have worked out myself back when I was a physics student.
Light has no rest mass. But, light can never be at rest.
Light does however, have momentum. And when it is reflected/refracted, it will transfer some of that momentum to whatever it hit.
Also remember that forces act on pairs of things. Light can be deflected by gravity (which will change it's momentum); therefore it must produce a gravitational field (which will in return change the momentum of whatever deflected it). And of course gravity is proportional to mass.
Light which is moving towards and object will gain momentum, like a falling rock would. Only instead of moving faster (since it's at a fixed speed), it shifts towards higher frequencies. If you look at the equations slightly differently, you get gravitational time dilation.
In a convex lens, photons take longer to pass through the thickest part, which creates a concave wavefront that naturally converges on a focal point:
http://arachnoid.com/example/index.html#Lens_Example
Photons don't need to have mass for this to happen, because they aren't being deflected like billiard balls, they're being slowed by their interaction with atoms.
[1] http://en.wikipedia.org/wiki/Vernor_Vinge#Zones_of_Thought_s...
> Yes. Light is slowed down in transparent media such as air, water and glass.
[...]
> Special Relativity
> [...]
> The speed of light does not vary with time or place.
These two different ways of talking about speed of light caused megabytes of meta bickering on the Wikipedia page for speed of light, and a case for Arbitration, with topic bans and warnings. (Also the suggestion that you can measure the speed of light in SI units, because after 1983 the SI units use light to define them.)
http://en.wikipedia.org/wiki/Wikipedia:Arbitration/Requests/...
The SoL page shows some of the problems of WP. Articles should have a simplistic lead (with caveats), a general introduction, and then higher level discussion of the oddities as currently understood. The WP page ignores all that, and leaps in at the deep end which means the article isn't much good for anyone.
That's just an assumption.
> That's just an assumption.
Supported by evidence. (And no counter-evidence is known.)
That was true for Newtonian mechanics for a long time too.
https://en.wikipedia.org/wiki/Jo%C3%A3o_Magueijo
For a good review of the VSL Theories (Varying Speed of Light Theories) and the evidence behind them see http://arxiv.org/abs/astro-ph/0305457
According to your second link: "The evidence is currently slim".
The universe can expand faster than c because there is not actually any information moving between the center and the perimeter.
(It may help to observe that an object with nonzero mass moving at the speed of light would have infinite momentum, and then it maybe makes sense that "zero times infinity" becomes a finite number)
When you shine light through glass the maximum propagation speed, the speed at which you start getting photons out the other side, is about 2/3 the speed of light. This implies that the overwhelming majority of photons are adsorbed and re-emitted. So this explanation cannot be correct, as I can look through a pane of glass, but you're saying any photon adsorbed is re-emitted in any direction, and the overwhelming majority of photons must be adsorbed and re-emitted.
In my comment, I talked about actual absorption, which means that there is a finite time interval when the photon does not exist and the atom/molecule who absorbed it can be observed in a different state than usual (electron in a higher orbital for an atom, different vibrational modes for a molecule). Later, the atom/molecule will go back to its normal state emitting a photon with the same energy as the first one, or several lower energy photons. This actual re-emission will not have a favourite direction. Depending on the typical time scale of the re-emission, you may call this process fluorescence or phosphorescence (http://en.wikipedia.org/wiki/Phosphorescence).
But then why is the speed of light in glass smaller than in vacuum?
A time varying electromagnetic field is produced by moving charges (except for a minor distinction about steady currents). The direction of motion of the charges determines the polarization of the emitted field. Later on, when the field encounters matter it produces an identical motion of charges i.e; if originally an East-West charge motion produced a North-South field then a N-S field will induce an E-W motion among new charges which in turn re-emit N-S light. The original light and the re-emitted light interfere, the delay is what slows the light down, as noted by others. But you can see why the direction is the same.
Note: I suppose this picture is somehow tied to reciprocity of the Maxwell equations between sources and fields, I need to go look it up again.
The short answer is, they don't. They emit the photon in a random direction.
Fine, you say, but what about refraction and reflection, there the photons are emitted in another direction. What makes the atom "decide" what direction to emit a photon after it's absorbed?
They don't decide anything, they still just emit in a random direction. The mind fuck is that on the whole, statistically, almost all photons except for those travelling in the direction of refraction/reflection destructively interfere!
[1] http://vega.org.uk/video/subseries/8 [2] http://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/069...
http://en.wikipedia.org/wiki/Path_integral_formulation
So the reason you have a coherent wavefront moving through a lens, as one example, is not because the photons are emitted in a particular direction, but at a particular time.
When you go through quantum field theory, photons are defined in terms of freely propagating particles, not interacting with other fields. When the disturbance in the EM field propagates into, e.g. a dielectric material, and strongly couples to various nuclear and electronic excitations, it is better described in terms of a massive quasiparticle, the polariton, which is a hybrid of the photon, phonon and electron fields and, being massive, propagates at less than c. You can, of course, describe it in terms of perturbations to the free photon corresponding to various types of virtual absorption and re-emission, but it's a bit misleading to think of it being physically absorbed and re-emitted with little stopovers. If anything, the classical model of a continuously interacting medium interacting with the EM wave creating a coherent response wave which interferes with and appears to slow down the EM wave is more instructive.