Is The Speed of Light Everywhere the Same?(math.ucr.edu)
math.ucr.edu
Is The Speed of Light Everywhere the Same?
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
54 comments
Modern definition of distance is derived from speed of light. So by definition speed of light is CONSTANT.
https://en.wikipedia.org/wiki/Metre#Timeline_of_definition
https://en.wikipedia.org/wiki/Metre#Timeline_of_definition
That's begging the question, in the original sense of the term.
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.
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.
Indeed, and we too will also need to change ourselves accordingly.
It's been defined as a constant to make calculations/measurements via physics/maths easier/possible, but that doesn't mean defining it as a constant is correct, or necessarily a good idea.
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.
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.
"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."
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.
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.
Thanks for the link. Perhaps the higher order sequel to flatland is looking for an author?
I think it works from the other direction. You don't get to say Pi=3.14 and then suddenly circles; the value of Pi is defined by whatever works for circles. Likewise, the speed of light is derived from whatever makes space and time one thing, thus you can't just assign a value to it. The value comes from the underlying structure of theory of relativity.
That light speed is a constant is a premise, an assumption. It doesn't fall out of any math or other physics relationship, right? We keep measuring C to more decimal places, on the assumption that what we measure here will be the same somewhere else. Which is, necessarily, an untested hypothesis.
> That light speed is a constant is a premise, an assumption. It doesn't fall out of any math or other physics relationship, right?
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.
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.
Suddenly there are 1.90986 people in an average marriage.
To be fair, I've always felt sorry for the .4 kid in the average family.
I take your meaning, and it seems literally correct word-for-word, but it's hard to know what to make of it: a quantity is constant or it is not, and definitions do not change it.
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.
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.
It's best to separate two elements here -- the measured speed of light, and the relationship between space and time. The relationship between space and time is easily expressed in closed form:
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.
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.
> the speed of light is only guaranteed to have a value of 299,792,458 m/s when measured by an inertial observer in a vacuum.
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.
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.
Ward-Takahashi identities prevent, in some sense, the virtual particles from screwing up the speed of light.
Does anyone know why refraction occurs when light doesn't have mass/weight?
It actually does. Kind of. (But it doesn't have anything to do with why it can be refracted.)
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.
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.
The light interacts with the water molecules.
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.
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.
It still moves as a wave and has a wavelength. That wave is electromagnetic and interacts with the electrons and protons in the atoms of whatever it's traveling through. The medium it's refracting through acts like a viscus fluid compared to the vacuum.
Yes. Refraction takes place because photons are slowed down through interactions with matter. If a photon is absorbed briefly and re-emitted, this can be taken to represent a reduction in velocity, even though the photon travels at c when between atoms.
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.
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.
I'm trying to understand the motivation of your question. Why the mass/massless of photons is related to the refraction?
It is possible that the speed of light is anisotropic, thus leads to a theory formulated by frank tangherlini
And also creationist nonsense.
I heard this said on NPR this afternoon. I thought I misheard the guest. I guess I didnt! Interesting
Surely the only answer possible to this is we don't know because we've not been everywhere?
Surprised no one has mentioned Vernor Vinge's wonderful, awesome, mind exploding Zones of Thought novels[1].
[1] http://en.wikipedia.org/wiki/Vernor_Vinge#Zones_of_Thought_s...
[1] http://en.wikipedia.org/wiki/Vernor_Vinge#Zones_of_Thought_s...
tl;dr: No.
> Does the speed of light change in air or water?
> 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.
> 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.
I hope this clarifies the appartent contradiction. Light can't help but move at any other speed than c = 2.997 x 10^8 m/s. It can't go faster, nor slower. So how does the speed of light appear to slow down in certain circumstances? In a vacuum, the speed of light is always c. There is nothing to interfere with the propogation of the individual photons (little atoms of light) as they move through the vacuum. However, in a material such as glass the individual photons of light are absorbed and reemitted many trillions of times by the molecules making up the glass. The photons do a "stop over" and don't move at all, the velocity of these photons is zero (actually the photons temporarily don't exist except as energy absorbed by the atoms in the glass). Between lattice points or individual atoms the photons travel at velocity c. The combination of stop overs (absorbtion and reemission events) and free propogation gives the appearance light is travelling at a slower overall velocity than c.
This argument and explanation is constantly coming up on the subreddit askscience. I don't violently oppose it as much as some do, since I think it's somewhat helpful, but I would like to say that my preferred interpretation is that a `photon' isn't really a well defined object when inside strongly-coupled materials. For example, can you really sensibly talk about a freely propagating radio wave when its still within a quarter wavelength of an antenna? When atoms are spaced tenths of a nanometre apart and visible light has a wavelength of hundreds of nanometres it seems a bit silly to talk about it propagating freely in a material.
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.
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.
Indeed. In the CFL-phase of color superconductors the photon mixes with the diagonal gluon. One specific combination remains massless while the orthogonal combination gets a mass. My colleagues and I jokingly called them the phuon and the gluton when talking privately.
Why do the molecules reemitt the light in the same direction as they absorbed it?
This is actually a very deep question. If you want a better answer than I'm about to give, read Feynman's QED lecture videos [1] or read the book [2].
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...
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...
Very good question. Here's the gist of it, a rough way of thinking about it.
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.
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.
They don't. A photon absorbed by an atom/molecule can be re-emitted in any direction. Imagine a thick piece of glass being traversed by a light beam: most of the photons will traverse it undisturbed (and thus maintain their original direction), but a few will be scattered all around (and that's the light you can see if you watch "inside" the glass from one of its sides).
On the other hand, depending on the light frequency and the crystalline structure of the material, photons can be scattered by the whole lattice itself, rather than by the single atoms/molecules. In this case, the direction follows the "rule of the mirror", which is dictated by quantum mechanics.
Problem with that:
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.
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.
Sorry, my fault! We were talking about "absortion"/"stop over" as a way to describe in layman's term the interaction of photons with the glass atomic structure. In this sense, as others pointed out, we are talking about scattering and the final direction is indeed related to the original one. Anyway, light scattering is a quantum process and there is no way of observing the "moment" between "absorption" and "re-emission".
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).
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).
> most of the photons will traverse it undisturbed
But then why is the speed of light in glass smaller than in vacuum?
But then why is the speed of light in glass smaller than in vacuum?
On average it's a requirement of the conservation of momentum. But note that sometimes photons come out in a different direction (scattered), including to opposite direction (reflection). In these cases the momentum is absorbed by the medium.
You're either very confused, or you have a much deeper understanding of physics than me. I love that it could be either.
Does the conservation of momentum apply to things with no intrinsic mass?
Yes. You can define a special-relativistic momentum and it's a conserved quantity, and it does have a nonzero value even for things with zero rest mass (which necessarily move at the speed of light).
(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)
(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)
Indeed. That's the idea behind things like solar sails, for instance. Check out the article here- http://en.wikipedia.org/wiki/Radiation_pressure
and scroll down to "Radiation pressure by particle model: photons" if the top is confusing.
They don't. But the re-emitted photons become part of a coherent wavefront through what Richard P. Feynman called a Path Integral:
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.
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.
They don't -- they are re-emitted in random directions that are statistically related to the original direction: http://en.wikipedia.org/wiki/Scattering .
> The speed of light does not vary with time or place.
That's just an assumption.
That's just an assumption.
If we take relativity at face value, the speed of light is c = 2.997 x 10^8 <<<locally>>>. <<<Globally>>> the speed of light can be anything. Cosmologists talk about the universe expanding faster than light during the inflationary phase, which sounds confusing because we're told nothing can move faster than light. While it is true that the speed of light must propogate at only one velocity for all freely moving frames of reference, the speed at which space itself expands can be anything! Relativity does not restrict the speed at which space itself expands or contracts. TL;DR The maximum local speed of anything moving through space in a freely moving frame of reference is c. The speed at which space itself expands or contracts is not limited in any way by Einstein's theory and is consistent with observations of the the inflationary universe in which the universe expanded at faster than the speed of light.
I like to think of it as the speed of information. The quickest any information can move from point A to point B is c. (Even if those points are themselves moving.)
The universe can expand faster than c because there is not actually any information moving between the center and the perimeter.
The universe can expand faster than c because there is not actually any information moving between the center and the perimeter.
Also, the speed of light in a different part of the universe could be different.
> > The speed of light does not vary with time or place.
> That's just an assumption.
Supported by evidence. (And no counter-evidence is known.)
> That's just an assumption.
Supported by evidence. (And no counter-evidence is known.)
There is plenty of evidence, but it would require to change some of our cosmological models (so it's not without controversy). A physicist that has explored the issue in detail is Joao Magueijo:
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
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
> There is plenty of evidence
According to your second link: "The evidence is currently slim".
According to your second link: "The evidence is currently slim".
> Supported by evidence. (And no counter-evidence is known.)
That was true for Newtonian mechanics for a long time too.
That was true for Newtonian mechanics for a long time too.
Not for very long. There were things unexplained by Newton starting the first day, right?
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".