Why does light travel at light speed?

[zefram_c]

Goodness!
It says here that the value of mu_0 is exactly
4\pi \times 10^{-7}

how can something like 4pi be measurable?
surely this can't be an actual physical property of empty space
what kind of intrument can you picture using to measure it?

I think I know why it would be said that \mu_o and \epsilon_0 are not physically measurable. They depend on the way we define quantities like one metre, one second, one unit of current, etc. For example, in SI one Ampere is that current that enters the Biot-Savart law so that \mu_o is *exactly* as shown. These dimensionful quantities can always be redefined. I have not done the math, but I think we could say that light travels exactly one meter per second, then adjust all other fundamental quantities to recover the same physics. There is a principle that says physics must be independent of the choice of units. On the other hand, no amount of tinkering can let us redefine the value of the fine structure constant, as that is a dimensionless parameter and must be preserved if we redefine our choice of units. That is truly a fundamental parameter of the observed universe.

Not sure who I would address this to (Einstein's editor?), but names like "train paradox" and "twins paradox" are somewhat misleading. They are only paradoxes when using incorrect physics, ie applying Galilean relativity to situations where it doesn't apply. People read "twins paradox" regarding Relativity and assume its a paradox in Einstein's theory. It isn't. How about "apparent train paradox"? I guess when Einstein was doing his work though, they were still unresolved paradoxes.

An excellent point; I prefer to refer to such things as the "twin scenario" or the "twin experiment" to emphasize that there is no unsolved paradox threatening relativity there.

 

[marcus]

...
So I have come to regard this equation:
c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}
as a kind of tautology or a stacked deck
...

the way I originally wrote this, it could be misunderstood to mean
that I'm considering the speed of light to be a tautology, so I edited it
to make clear that it is this equation that represents the stacked deck.

By its defintion the value mu_0 (in SI terms) is exactly
4\pi\times 10^-7

and epsilon_0 is actually defined in terms of mu_0 and the speed of light.

so if you somehow know what mu_0 is, then you cannot possibly measure epsilon_0, what it has to be is established by convention

\epsilon_0 = 1/\mu_0c^2

So the value of epsilon_0 (in SI terms) is also conventional and is exactly

\frac{1}{299792458^2\times 4\pi\times 10^-7}

 

[hemmul]

Yes, hemmul, the particles you describe are called tachyons. Their mechanics are already well-understood, but there has been any evidence that they actually exist.

- Warren

Thanks for You reply, Warren,
well, to say the truth I'm not an expert in tachyons ;) what i posted is just some general "scatch"... actually my "question", stated like this:

One of the "difficult" questions about that is "why do we live in [0,c] range?"

is incorrect - because its basis violates the relativity principle :shy:
it's obvious, that in our RF available-velocity-range will be [0,c], but for tachionic observer this range (still talking about our range) will represent [c,2c]...?
or is it [nobody knows,nobody knows] ? - as, according to Your reply, we have no evidence of tachyons' existence (if i got it right) - so they have no evidence of our existence...

[edit]
putting all this together in a smarter, equivalent, form:
according to our knowledge about tachyons, what is their upper-bound velocity? (relatively to us)
[/edit]

 

[marcus]

I think I know why it would be said that \mu_o and \epsilon_0 are not physically measurable. They depend on the way we define quantities like one metre, one second, one unit of current, etc. For example, in SI one Ampere is that current that enters the Biot-Savart law so that \mu_o is *exactly* as shown. These dimensionful quantities can always be redefined. I have not done the math, but I think we could say that light travels exactly one meter per second, then adjust all other fundamental quantities to recover the same physics. There is a principle that says physics must be independent of the choice of units. On the other hand, no amount of tinkering can let us redefine the value of the fine structure constant, as that is a dimensionless parameter and must be preserved if we redefine our choice of units. That is truly a fundamental parameter of the observed universe.
...

I must say, in my turn, that this is an excellent point!
And then the question becomes, how are current and voltage ACTUALLY standardized and how are they actually measured at the national labs and BIPM in paris etc.

And in fact current is not, in practice, standardized by measuring the force between parallel wires but by declaring an exact conventional value for the Von Klitzing constant and using quantum hall effect.
So the current scale is referred to the voltage scale (not to force)

And in fact voltage is measured by Josephson junction and standardized by declaring an exact conventional value for the Josephson constant so the voltage scale, operationally or in practice, is based on frequency----the frequency standard of the atomic clock.

The conventional exact values of Klitzing and Josephson constants
used to establish the CIPM 1990 standard ampere and standard volt are listed at the NIST site and called R _{K_90} and K _{J_90} .


but if volt and amp are measured this way then there is no grounds to have those values we mentioned for the epsilon and mu naught.
It really is a muddle and as twisty as some theological issue like the infallibility of the pope.

I will go get the conventional exact values of R _{K_90} and K _{J_90} .
they should really make them the official definitions of volt and amp and let the chips fall where they may---get it straight and damn the consequences

They are in the "adopted values" menu at NIST
the josephson
K _{J_90} = exactly 483597.9 x 10⁹ Hz V^-1

the von Klitzing resistance is
R _{K_90} = exactly 25812.807 ohms

 

[zefram_c]

Usually the definitions of the fundamental units are set so that they can be easily used as a reference and can be reproduced worldwide. So when the speed of light could be measured more accurately than a "metre" (which I think used to be the wavelength of some atomic frequency times an integer constant), the metre was eventually redefined according to the speed of light measurement.
There is really no a priori reason to set \mu_o to what it is; and we could trade in its definition to fix, say, the von Klitzing resistance. Personally I'm all for that, since it's much better than to measure the very small attractive force between two infinitely long wires anyway. As for the Josephson constant, we can trade in the antiquated definition for the kg, which is a prototype somewhere in Paris. But there seems to be no pressing need for such changes. In any event, the system of choice for most theorists is one in which h = c = \epsilon_0 = \mu_0 = 1, or maybe multiples of pi depending on what equation you want to simplify. Under this choice, the electron charge can't be set to one.

 

[marcus]

"As for the Josephson constant, we can trade in the antiquated definition for the kg." Yes!

that would be great
get rid of the metal prototype kilo in Paris!
no pressing need?

grunge grows on Le Grand Kilo and you have to clean it
and if people are actually using the adopted values of
R_K and K_J to measure volt and amp then they are, in effect,
dispensing with the kilo in a certain domain of measurement
so there is internal fractures within the system

the key to the transition is, I believe, the Watt Balance
which allows basing standard of force (and thus mass)
on voltage and current standard

I think there is a pressing need, but that the Watt Balance is
perhaps not quite good enough yet to let people
switch over to an electric Newton and to an electric kilo

 

[marcus]

Under this choice, the electron charge can't be set to one.

Alas no! If you do that then the value for the electron charge will be a function of the fine structure constant!
The ways of the theorist are oft-times inscrutable. In their place I would imagine setting e = 1 (as you mention) and then the epsilon and mu naughts would involve alpha.

 

[pervect]

the way I originally wrote this, it could be misunderstood to mean
that I'm considering the speed of light to be a tautology, so I edited it
to make clear that it is this equation that represents the stacked deck.

The speed of light is a tautology nowadays. The meter was originaly concieved of as 10^-7 of the distance from the north pole to the equator. It was later redefined in the 1800's to be the distance between two marks on a platinum bar that was kept in paris. In the 1960's, it was defined as a certain number of wavelengths of a certain transition of krypton. Finally, in the 1980's, it was defined to be the distance that light traveled in a certain amount of time. This is the definition that's still in use today. This defintion of the meter makes the speed of light a defined constant (like 2.54 cm/in), rather than a number to be measured experimentally.

By the 1980's realtivity had been well tested, and nobody in the scientific community was (or is) in any doubt as to its accuracy. The new definition of the meter simply providied a more accurate and precise standard to measure distances.

I gather that the original old prototype of the meter (scratches on a bar) is still kept somewhere in Paris. However, because relativity is valid, one should expect that one could replace the current definition of the meter with (a copy of) the less accurate "scratched bar" meter and come up with basically the same answer. Of course the bar is subject to problems like changes in length with temperature and deformation due to forces that has to be taken into account in such a comparison, problems that the new definition doesn't have. So claiming that you can heat the bar and expand it shouldn't be seen as a disproof of relativity, it should be seen as an indication that the bar is an imperfect standard (it was the best standard for a long time, nowadays we do much better).

si-meter
si-meter-2

 

[Chronos]

Interestingly enough, sound waves also travel at constant speed. All frequencies arrive at our ears at the same time from a train whistle... despite being emitted at different frequencies. If the transmission media has a retarding effect, shouldn't low frequency signals travel faster than higher frequencies, given they travel less total distance? [this is a classical question and merely a test].

 

[Pythagorean]

Interestingly enough, sound waves also travel at constant speed. All frequencies arrive at our ears at the same time from a train whistle... despite being emitted at different frequencies. If the transmission media has a retarding effect, shouldn't low frequency signals travel faster than higher frequencies, given they travel less total distance? [this is a classical question and merely a test].

Is this true? Do sound (if so, I'm assuming all) waves travel at a constant velocity regardless of observers velocity?

 

[Pythagorean]

In general reading of this thread, I realized that space/time hasn't really been defined. I will be going into my first physics class in less than a month, and I've only gotten as far as caclulus 1 in math, but here is my understanding of relativity from a philosophical (laymen) perspective that may help to understand one more thing.

Please correct me if I'm wrong. This is what I learned from Brian Greene's "The Fabric of The Cosmos"

Firstly, when Einstein created his theory, he did not want to call it the Theory of Relativity, because it was inevitebly about an absolute, called space/time. Space and time are relative like voltage and amps, but space/time is an absolute, the absolute being this in laymen terms:

the faster you travel through space, the slower you travel through time
the slower you travel through space, the faster you travel through time

this is where the twins paradox comes from.

now, philosophically, this implies to me that light does not age, or is not otherwise affected by the phenomenon we call time. That is why it appears to be have a constant velocity to us regardles of our speed, because of the difficulty in separating our observations from the concept of time.

 

[selfAdjoint]

No, that is not what Einstein did. He didn't even have a spacetime concept in his early papers, that was introduced by the mathematician Minkowski, and Einstein had to chew it over a little before he accepted it.

Relativity is relative! Speed has no meaning except as it relates to two specific objects which have a relative speed between them. If the relative speed is higher they will see each other's lengths shorter and each other's time running slower. Einstein emphasized from the beginning that that is all there is, no standard observer exists to tell us "what really happened."

Einstein, not in his first paper but eventually, settled on two postulates from which all of relativity can be derived logically:

1. Every unaccelerated observer can do physics and get the same answers as every other unacclerated observer.

2. All unaccelerated observers will measure the same speed for light.

Books which then prove the Lorentz transformations and all the rest of special relativity from these postulates by theorem-proof math are not the easy way to learn SR, but they exist, and physicists know and can follow them.

 

[Pythagorean]

I do not refute your points, as I am inexperienced.

I will, however quote the book to clear up my original statements which were not precise:

"Absolute spacetime is as absolute for special relativity as absolute space and absolute time were for Newton, and party for this reason Einstein did not suggest or particularly like the name, "realativity theory." Instead, he and other physicists suggested invariance theory, stressing that the theory, at its core, involves something that everyone agrees on, something that is not relative."

This is an introduction to SR and Newton's Bucket on the position (or lack of position) of space. (that was a pun).

edit: italicized invariance theory

 

[Chronos]

Explaining light speed in terms of mu and epsilon an interesting concept. The fact that c is finite also has some important ramifications. If c were infinite, the universe, including time itself, would cease to exist! So the question is what exactly do mu and epsilon represent. Simple speaking, they can be explained in terms of strain wave propogation [I believe it was Kelvin who first remarked on the similarities between strain wave propogation and electromagnetic wave propogation]. Epsilon represents the elasticity constant and mu is the inertial constant. Combined, the result is the vacuum impedence, which is directly measurable and known to be 377 ohms. Direct measurement of mu and epsilon is, unfortunately, problematic. It could, however, yield vital clues about how the universe evolved.

NOTE: I do not view this the same as saying 'free space' has intrinsic properties, merely that interactions at a distance between mass possessing bodies behave as if free space was an elastic medium [trying to avoid an 'aether' controversy].

 

[Mike2]

...Epsilon represents the elasticity constant and mu is the inertial constant. Combined, the result is the vacuum impedence, which is directly measurable and known to be 377 ohms. Direct measurement of mu and epsilon is, unfortunately, problematic. It could, however, yield vital clues about how the universe evolved...

If a substance has elasticity and inertia, can it also break, rip, or tear? Can a wave be set up such that the medium cannot sustain the rate of change and tears in the process, like a wave that crests when it approaches the shore?

Thanks.

 

[loke137]

There is no pointing talking about what is spacetime...is it a bed?? a elastic medium?? jelly beams??...if you are a physicist, that shouldn`t matter...what matters is the model that your theory predicts fits reality..and don't start question what is reality! hehee, measurements...
However, if you are an epistemologist, then it is another matter.

 

[loke137]

And sorry, I forgot to point my view on the thread subject. Eletromagnetic waves move with speed c because we constructed a theory in which there was a ent which moved with c, to which we gave the name eletromagnetic wave. It is not proclamation of Fortune, but a prediction of a theory, which could be wrong. <classical eletrodynamics>
However, if you like General Relativity. A photon moves in such way in vacuum because it is a massless boson, thus definying its geodesic (see we gave its name, not the other way around), and the prediction is that such geodesic is localy straight and has a tangent vector (spacial) of magnitude c!

 

[Marijn]

Anyspeed light travels at is lightspeed?

 

[selfAdjoint]

As used in relativity, light speed (c) is the speed light or any electromagnetic radiation traavels in the vacuum. The behavior of light in media is not a topic for relativity but for quantum theory.

 

[DrDaleCoxStudent]

As you approach the speed of light time slows down. At the speed of light time stops.

 

[Nereid]

As you approach the speed of light time slows down. At the speed of light time stops.

I think you mean, 'as perceived by an observer in one frame, time in a moving frame is slower; however, within your own frame, to you time passes at the rate it always does, no matter what anyone else in other frames perceives' ... or something like that.

 

[Gerinski]

It seems to me that light (EM radiation) does not "travel" at any "speed".

The terms "travel" and "speed" imply the existence of space and time. There must be a distance in space to travel through, if 2 points are not separated by any distance you don't "travel" between them, you are simultaneously in both of them.
And the same about time, the term "speed" implies a measurement of a time interval, since speed will be the distance in space which has been covered divided by that time interval. If 2 events are not separated by any time interval, you can not have any "speed" between them, you experience both of them simultaneously.

For the EM radiation, space distance does not exist, space is shrinked to zero size so all the points which we perceive as being "swept" by a light beam are actually a single point for the radiation itself, all of those spacetime points (which we perceive as being separated by distance) are coexisting "at the same place".
Time too is frozen ( I think that means that rather than being shrinked to zero size it is extended to infinite size, which in fact amounts to much the same as being shrinked to zero size).
All of the events covered by the light beam (what we would picture as a diagonal line in a light-cone diagram) are actually "the same place at the same instant", they coexist. Light would not measure any distance nor time interval between them.

Therefore I would say that the "universe inhabited" by EM radiation is in fact a single point.
Rather than light "travelling at any speed", it's us (matter) that when "sweeping through" that point, from our perspective the point "unfolds" outwards and appears as extended events in spacetime (different places at different times).
All the "different" events along the course of that light-cone line, are just different perspectives of a single event, which shows us a different face as we look at it from different points of our extended spacetime.

The surface of the sun at the moment it emits a photon, the Earth 8 minutes
later, alpha-centauri 4 years later ..., all are different faces of a single "thing" (although for what concerns us they are surely and very really different places at different times !) it's just that "what something is to us" may not necessarily be the same as "what it really is" when released free from our material constraints.
It's just our fate that we can not perceive all the faces of the point simultaneously, we are forced to see them one after another, forced to move to a different position in space and time to see a different face, if we are in the Earth today looking at the sun, we have no way but to wait at least over 4 years if we want to see the "alpha-centauri face" of this event.

(would this suggest that in fact its the extended universe of matter the one that "travels" through a miriad of "radiation point-like "things" "?)

 

[Gerinski]

Originally Posted by DrDaleCoxStudent
As you approach the speed of light time slows down. At the speed of light time stops.

I think you mean, 'as perceived by an observer in one frame, time in a moving frame is slower; however, within your own frame, to you time passes at the rate it always does, no matter what anyone else in other frames perceives' ... or something like that.

I understand this relativity principle between material objects, but I'm not so sure it applies all the same for light itself ... If really so, then I guess all my reasoning above was incorrect and I'm sorry for confusing the subject even more.
But can you please reconfirm ? in the frame of reference of the light itself, space and time look exactly the same as for us? I mean, distances and time intervals have the same extension?
I read things like "it takes no time for light itself to travel between the event "sun at Earth's time 2004" and the event "alpha-centauri at Earth's time 2008", an hypotetical clock on the light beam would not measure any time interval"
If this is correct, then I guess my previous reasoning still holds

 

[aekanshchumber]

look the light answer is that because it is light. but detailed is,as you might know that a photon has zero mass so a a very little energy willaccelerate it and will reach the ultimate speed that's of cource is 'c'.

 

[Prometheus]

I read things like "it takes no time for light itself to travel between the event "sun at Earth's time 2004" and the event "alpha-centauri at Earth's time 2008", an hypotetical clock on the light beam would not measure any time interval"

Light, once emitted, does not age. Once emitted, light does not pass through time. Light involves no motion through time, and all of its motion is constant motion through space. The statement "it takes no time" is a roundabout, and I consider somewhat confusing and misleading, way to make this statement.

 

[Blueplanetbob]

I always thought that photons could not travel faster than light speed because the balance of the universe dictated that speed?

 

[Gerinski]

Light involves no motion through time, and all of its motion is constant motion through space

Thanks, this seems to support a bit my previous discussion, doesn' it?
Since the light wave is present in several points in spacetime (it's light-cone line), but it involves no motion through time, the term "travelling" does not seem appropiate for what light "does" through our specetime. WE perceive the "timeless" or "coexisting" presence of the light wave in those points as a movement or "travel", because those points appear to us separated in different places and different times.
But regardless of how we perceive it, as for light itself all those points in spacetime might be considered as being "together".

Again it seems to me that a "timeless -or atemporal- presence" is perceived by us as a motion, "at the speed of light".

Thanks so much for this clarifying discussion ! as you can guess I'm just an afficionado, and I always found the issue of the speed of light as one of the most intriguing!

 

[jcsd]

Be careful light does not have a rest frame, consequently statemnts like:"an hypotetical clock on the light beam would not measure any time interval" and "Light, once emitted, does not age", have no meaning in relativity.

 

[aekanshchumber]

best possible explanation is,
we know that there is light travels at ultimate speed, the maximum possible speed that could be attained in the universe. when you move past or toward the light you tries calculate the speed of light, which is constant. You are calculating something that happens instantaneously of course the value will be the same 'c'.

 

[Chronos]

Apologies for interrupting. jcsd gave the correct explanation.