Why is the speed of light exactly exactly 299 792 458 meters per second ?

[Strangerone]

Is there any published theory that explain and proves why the speed of light is exactly 299 792 458 merters per second ? I do not know of any ! Do you ?

Best regards
Me :-)

 

[Phrak]

The length of a meter is defined in terms the distance light travels in one second.

 

[jtbell]

We define the speed of light to have that value, thereby defining the meter as the distance light travels in 1/299792458 second.

Before we did that (in 1983), we had great confidence that the speed of light was always that value, based on the theory of relativity and experimental measurements (taking experimental uncertainties into account of course).

See section 3 of What is the experimental basis of Special Relativity?

 

[templedog]

No there isn't, so far. I just read a book called Beyond Belief by A. K Dewdney. The speed of light is one of the 8 unreasonable things speaks of.

 

[Naty1]

Maxwell's equations compute the speed of light as 1/(sq rt [(permittivity)(permeability)]

Wikipedia, http://en.wikipedia.org/wiki/Maxwell's_equations

under "In Vacuum"...and played a big part in causing Einstein to develop special relativity

 

[Dale]

Is there any published theory that explain and proves why the speed of light is exactly 299 792 458 merters per second ? I do not know of any ! Do you ?

As Phrak mentioned this is a result of the http://www.bipm.org/en/si/si_brochure/chapter2/2-1/metre.html" . This definition was chosen because measurements of the speed of light immediately prior to this time had become so precise that the primary source of error was the uncertainty in previous standards for the meter.

 

[epenguin]

I think it's the third time we got this question in a week: others were "reason for value of c"
and "Why does light travel so fast?"

Does this happen every week? (Or is it like London buses, which come rarely but then three at a time?)

 

[Dale]

Does this happen every week? (Or is it like London buses, which come rarely but then three at a time?)

The most popular FAQs seem to be the value of c, the reference frame of a photon, and the twins' paradox. I think that all of them are about once per week on average, but very "streaky" with the first in a streak quickly prompting two or three others and then it dies down for a month or so.

I guess we are ending a "value of c" streak, we just finished a "reference frame of a photon" streak, and I think we just had the first installment of the next "twins' paradox" streak earlier today.

 

[Fredrik]

That must be a great comment, because I was thinking almost exactly the same thing. But you forgot to mention the mass of the photon.

 

[Dale]

That must be a great comment, because I was thinking almost exactly the same thing. But you forgot to mention the mass of the photon.

D'oh! You are absolutely right. And that one is actually even more frequent than it appears since it gets split between here and the QM forum.

 

[epenguin]

D'oh! You are absolutely right. And that one is actually even more frequent than it appears since it gets split between here and the QM forum.

You should recombine them and get a diffraction pattern.

 

[Strangerone]

Maxwell's equations compute the speed of light as 1/(sq rt [(permittivity)(permeability)]

Wikipedia, http://en.wikipedia.org/wiki/Maxwell's_equations

under "In Vacuum"...and played a big part in causing Einstein to develop special relativity

Thanks to you all for good arguments and links ! :-)

Regarding the equations that include the permittivity and permeability:

Ok, this constants, the permittivity and permeability, works fine in the equations. But if I understands this correctly such an equation does not reveal anything about why the speed of light is exactly what we observe it to be. The equation only moves the problem from one area to another area, from the area of quantummechanics to the area of the permittivity and permeability of the medium of space ! And therefore this theory does no answar the question, if I understand it correctly.

Best regards
Me :-)

 

[Strangerone]

The permittivity and permeability of the medium of space is just another constant.

 

[Dale]

The value of the permeability of free space is a result of the http://www.bipm.org/en/si/si_brochure/chapter2/2-1/ampere.html" . And then (together with the definition of the meter which defines the speed of light) the permittivity of free space is also defined exactly.

You seem to think that there is some reason for the value of these constants other than the choice of units. There is not. The values of all of the dimensionful fundamental constants are simply an artifact of our choice of units and are therefore completely arbitrary. For example, http://en.wikipedia.org/wiki/Planck_units" makes the convenient choice that all of these dimensionful fundamental constants are equal to 1.

 

[Phrak]

The standard meter was originally supposed to be a convenient length of 1/10,000,000th the distance from the Equator to the pole. (The calculated distance from equator to pole was not as precise as hoped, but the calculated meter survives today, in refined form.) It became defined as the distance between two scratched on one particular beam of material stored in some environmentally controlled vault somewhere. France, I would guess. There were copies of this beam distributed around the world in various national institutes of standards. As the desire for precision increased the distance between the centers of two scratches became limiting. Added to this was the ever present fear that the original could be destroyed, throwing everyone's data and standards into bias.

I hope I haven't been too inventive in the above. I'm recalling this from memory.

 

[Strangerone]

There seem to be a manmade constant at the bottom of this bottle wherever I look ! First, the constant of C, then the constant "permittivity and permeability" related to the medium of space, and now the value of "ampere" which is a consequense of the "magnetic constant", also known as the permeability of free space, measured at exactly 4 x 10–7 henries per metre, 0 = 4 x 10–7 H/m.

 

[Naty1]

You seem to think that there is some reason for the value of these constants other than the choice of units. There is not.

If I understand this comment correctly, I could not disagree more. The purpose of physics is to both explain how things work (say via math) and also why they work. We are not so good at the latter as the former, I think.

There has to be an underlying reason why light speed is what it is, regardless of units chosen...Lights moves at "it's own pace" regardless of the units we choose to use to describe it's speed. It's a contsant for a reason and has a value for a reason. Electromagnetic waves propagate at "c" for a fundamental reason(s) that is as yet unknown. (I can guess why c is constant because if it varied a lot, nothing would be here...electromagnetic waves would take on a life of their own and atoms would likely never form or if they did would likely break apart immediately...)

And there is a mass energy equivalent involving lightspeed for reasons I have not seen...why should mass and energy be related by lightspeed? Exactly what causes mass? all of these are unanswered "why" questions.

 

[Alfi]

lol @ Strangerone
I'm one of the 'zero' haters.
It does go a bit round and round to prove itself.

I believe the Kilogram is the last artifact yet to be mathematically derived.hehehe
Mass must weigh heavily upon physicists.

 

[Strangerone]

What is the exact physical reality behind these observed constants. Theres is, as far as I know, no published theory that can tell this. There is only math related to these observed constants. But why does scientists accept this?

 

[Naty1]

while reading Wikipedia just now on Lorentz Transformations,
under DERIVATIONS
http://en.wikipedia.org/wiki/Lorentz_transformation

I (accidentally) came across the following...

The usual treatment (e.g., Einstein's original work) is based on the invariance of the speed of light. However, this is not necessarily the starting point: indeed (as is exposed, for example, in the second volume of the Course in Theoretical Physics by Landau and Lifgarbagez), what is really at stake is the locality of interactions: one supposes that the influence that one particle, say, exerts on another can not be transmitted instantaneously. Hence, there exists a theoretical maximal speed of information transmission which must be invariant, and it turns out that this speed coincides with the speed of light in vacuum.

(my boldface.)

I don't doubt what is said, but neither do I understand it...this is kind of the point I was trying to make in my last post above...I've never seen a statement quite like this...Anybody know what the above text says about WHY the speed of information transmission must be invariant?

 

[Naty1]

There is only math related to these observed constants. But why does scientists accept this?

I don't think we should assume this a "acceptable", just that it reflects our current lack of understanding. Maybe when we eventually unify quantum theory and relativity we may gain insights as to how all the constants emerged from "nothing" at the start of the universe...maybe there are an infinite number of such combinations and only a few lead to viable universes, maybe there are only a fixed number of possibilities (analogous to the only three possible shapes of our universe, flat, spherical, saddle shaped) or maybe quantum foam has a group of rigidly fixed "constants" hiding...just waiting to pop out...

It's like asking "Why do scientists accept that we can't cure the common cold". It's because so far "virus's" are smarter than we are!

 

[Strangerone]

while reading Wikipedia just now on Lorentz Transformations,
under DERIVATIONS
http://en.wikipedia.org/wiki/Lorentz_transformation

I (accidentally) came across the following...



(my boldface.)

I don't doubt what is said, but neither do I understand it...this is kind of the point I was trying to make in my last post above...I've never seen a statement quite like this...Anybody know what the above text says about WHY the speed of information transmission must be invariant?

Extreemly well observed Naty1 :-)

Have a nice evening .

 

[MeJennifer]

What is the exact physical reality behind these observed constants. Theres is, as far as I know, no published theory that can tell this. There is only math related to these observed constants. But why does scientists accept this?

I do not think you understand it.

The question is only whether the speed of light is limited or unlimited. Clearly it is limited but the numerical value is completely arbitrary since it depends solely on the chosen units of measurement.

 

[lightarrow]

while reading Wikipedia just now on Lorentz Transformations,
under DERIVATIONS
http://en.wikipedia.org/wiki/Lorentz_transformation

I (accidentally) came across the following...

...

I don't doubt what is said, but neither do I understand it...this is kind of the point I was trying to make in my last post above...I've never seen a statement quite like this...Anybody know what the above text says about WHY the speed of information transmission must be invariant?

*IF* you can prove what Landau says, that is that:
"there exists a theoretical maximal speed of information transmission"
then it's quite easy to prove it's invariant: if it wouldn't be, you could always find a frame of reference in which it has a greater value, so it wouldn't have been the maximal...
The problem is to prove that statement...

 

[lightarrow]

If I understand this comment correctly, I could not disagree more. The purpose of physics is to both explain how things work (say via math) and also why they work. We are not so good at the latter as the former, I think.

There has to be an underlying reason why light speed is what it is, regardless of units chosen...

Lights moves at "it's own pace" regardless of the units we choose to use to describe it's speed. It's a contsant for a reason and has a value for a reason. Electromagnetic waves propagate at "c" for a fundamental reason(s) that is as yet unknown. (I can guess why c is constant because if it varied a lot, nothing would be here...electromagnetic waves would take on a life of their own and atoms would likely never form or if they did would likely break apart immediately...)

And there is a mass energy equivalent involving lightspeed for reasons I have not seen...why should mass and energy be related by lightspeed? Exactly what causes mass? all of these are unanswered "why" questions.

If with "why light speed is what it is" you mean the *numerical value*, then, as others have explained, there is no deep reason, just choice of units. If you mean "It's a constant for a reason" and you are talking about the experimental fact (and not the theory, because in the theory it's constant as postulate), then we can discuss about it...
About mass and energy, if you chose the units of time and space to have a completely different value of c, then the energy value changes too and you still have the same value for your mass. The fact that mass and energy are related by that equation it's another story, it doesn't have to do with the numerical value of c.

 

[D H]

You seem to think that there is some reason for the value of these constants other than the choice of units. There is not.

If I understand this comment correctly, I could not disagree more.

Dale is (almost) correct. I say almost because a poor choice of standards will result in poorer comparison of experimental results. Dale is completely correct in that our choices are quite arbitrary. The meter is not an inherently better unit of length than a foot or a furlong or a light year.

There are a very small number of fundamental quantities, the familiar ones being time, length, mass, charge, and temperature. To use those quantities numerically, we have to define scale factors (i.e. the units) for the quantities. In other words, a set of standards. One way (the old way) of defining the standards is to construct a prototype. The meter was, for a long time, the distance between two scratch marks on a metal bar kept under strict environmental conditions in some building in Paris. Copies of this metal bar were made (a source of error) and distributed to a few select locations around the world. Copies of these copies were made (more error) and distributed further. A much better approach is to define standards based on some known physical constant. The speed of light is one such physical constant.

The purpose of physics is to both explain how things work (say via math) and also why they work. We are not so good at the latter as the former, I think.

This is a lay mischaracterization of science. Physics explains how, not why. While physicists are obtaining an ever deeper understanding of how the universe operates, at some point the answer to a "why" question is exactly the same answer you got when you kept pestering your parents: "because that's the way it is".

 

[mgb_phys]

The meter is not an inherently better unit of length than a foot or a furlong or a light year...
The meter was, for a long time, the distance between two scratch marks on a metal bar kept under strict environmental conditions in some building in Paris. Copies of this metal bar were made (a source of error) ...
A much better approach is to define standards based on some known physical constant. The speed of light is one such physical constant.

To slightly derail the thread. The original definition of the metre was 1/10,000,000 the distance from the North Pole to the equator. The intention was that by making the metre based on known physical constant (the radius of the Earth) there would be no need to make unreliable copies - since anyone with a knowledge of surveying could make their own standard.

So in this way it was fundamentally better than earlier units.
In practice the Earth isn't regular enough and a standard physical metre had to be built to compare against, but using the speed of light is going back to the original intention.

 

[cepheid]

I don't doubt what is said, but neither do I understand it...this is kind of the point I was trying to make in my last post above...I've never seen a statement quite like this...Anybody know what the above text says about WHY the speed of information transmission must be invariant?

To prevent violations of causality?

The usual treatment (e.g., Einstein's original work) is based on the invariance of the speed of light. However, this is not necessarily the starting point: indeed (as is exposed, for example, in the second volume of the Course in Theoretical Physics by Landau and Lifgarbagez), what is really at stake is the locality of interactions: one supposes that the influence that one particle, say, exerts on another can not be transmitted instantaneously. Hence, there exists a theoretical maximal speed of information transmission which must be invariant, and it turns out that this speed coincides with the speed of light in vacuum.

This time it's my boldface.

 

[D H]

To slightly derail the thread. ... So in this way it was fundamentally better than earlier units.

I disagree. The original definition of the meter was inherently faulty in the sense that it was unrealizable and non-standard. The standard was unrealizable because the length of the surface of the Earth from the equator to the North pole is a heck of a lot longer than ten million meters -- how long is the coastline of Brittain? -- and varies with the line of latitude. It is a bad standard. Fortunately, it was never used.

The French Academy of Sciences chose the earth-based definition of a meter as the standard in 1791 and commissioned a partial survey lasted from 1792 to 1799. The commissioned survey did not measure the length specified by the standard. They instead set out to measure a surrogate distance. Well before the survey was completed, the Academy in 1793 developed a prototype metre bar as the standard. When the survey was completed six years later and the result was found to be in conflict with the standard, the measurement-based standard was thrown out.

 

[cepheid]

I don't think we should assume this a "acceptable", just that it reflects our current lack of understanding. Maybe when we eventually unify quantum theory and relativity we may gain insights as to how all the constants emerged from "nothing" at the start of the universe...maybe there are an infinite number of such combinations and only a few lead to viable universes, maybe there are only a fixed number of possibilities (analogous to the only three possible shapes of our universe, flat, spherical, saddle shaped) or maybe quantum foam has a group of rigidly fixed "constants" hiding...just waiting to pop out...

It's like asking "Why do scientists accept that we can't cure the common cold". It's because so far "virus's" are smarter than we are!

Huh? Okay, first of all your analogy is flawed, because scientists don't accept that it is not possible to cure the common cold in principle, they only accept that it is not possible to cure it in practice, given our current level of scientific understanding. Your discussion of a "theory of everything" possibly leading to a greater understanding of what these "magic numbers" are is, as far as I know, only applicable to dimensionless fundamental constants. This is not the same situation at all as it is with the speed of light. The operative words in the OP's original question were why is the speed of light exactly what it is in metres per second? That question has been answered. You and Strangerone need to please read stuff like this more carefully:

I do not think you understand it.

The question is only whether the speed of light is limited or unlimited. Clearly it is limited but the numerical value is completely arbitrary since it depends solely on the chosen units of measurement.

You seem to think that there is some reason for the value of these constants other than the choice of units. There is not. The values of all of the dimensionful fundamental constants are simply an artifact of our choice of units and are therefore completely arbitrary. For example, http://en.wikipedia.org/wiki/Planck_units" makes the convenient choice that all of these dimensionful fundamental constants are equal to 1.

 

[mgb_phys]

I disagree. The original definition of the meter was inherently faulty in the sense that it was unrealizable and non-standard.

It was good idea in theory!
Obviously nobody intended to measure the actual distance to the pole - all you need to measure is the latitude of 2 points a known distance apart. Measuring latitude accurately is relatively easy.

The intention that any country could establish it's own standard meter without needing diplomatic relations with the country holding the standard (which was a problem for the USA after 1776) and the idea that units should be determined by science rather than length of some part of a king's anatomy were valid.

Completely screwing up the execution while accidentally founding the science of geodesy in the process is just one of those things that happen ;-)

 

[lightarrow]

The usual treatment (e.g., Einstein's original work) is based on the invariance of the speed of light. However, this is not necessarily the starting point: indeed (as is exposed, for example, in the second volume of the Course in Theoretical Physics by Landau and Lifgarbagez), what is really at stake is the locality of interactions: one supposes that the influence that one particle, say, exerts on another can not be transmitted instantaneously. Hence, there exists a theoretical maximal speed of information transmission,which must be invariant and it turns out that this speed coincides with the speed of light in vacuum.

I have that book (Theoretical Physics 2: "Field Theory") but I sincerely have never been able to understand that phrase. While it's an experimental fact that the "influences" we know are not transmitted instantaneously, why do we need to suppose a general validity of it?

 

[jnorman]

of course, if you use the original "cubit" established around 3200BC by Zoser's Chief Vizier and Architect, Imhhotep, the speed of light is exactly 6x10^8 cubits/sec, as it should be.

i thought there was some talk a few years back about defining the speed of light to be exactly 3x10^10 cm/sec, and adjusting the length of the meter accordingly. what happened to that idea?

 

[Dale]

Wow! Go to work and miss a lot on this forum sometimes!

There seem to be a manmade constant at the bottom of this bottle wherever I look ! First, the constant of C, then the constant "permittivity and permeability" related to the medium of space, and now the value of "ampere" which is a consequense of the "magnetic constant", also known as the permeability of free space, measured at exactly 4 x 10–7 henries per metre, 0 = 4 x 10–7 H/m.

Yes, there is always at least one arbitrary man-made convention at the bottom of any dimensionful physical constant.

There has to be an underlying reason why light speed is what it is, regardless of units chosen...

How can you even express a dimensionful quantity like the speed of light without choosing units (let alone answering questions about why it is what it is)? Do you understand the difference between dimensionless and dimensionful quantities?

Your discussion of a "theory of everything" possibly leading to a greater understanding of what these "magic numbers" are is, as far as I know, only applicable to dimensionless fundamental constants. This is not the same situation at all as it is with the speed of light. The operative words in the OP's original question were why is the speed of light exactly what it is in metres per second?

This is exactly correct, and is precisely why I explicitly limited my comment to dimensionful physical constants only. As you mention, a complete Theory Of Everything would eliminate the current http://math.ucr.edu/home/baez/constants.html" . That does not apply to dimensionful physical constants like c, which would still be defined by arbitrary man-made conventions even within a complete Theory of Everything.

 

[neopolitan]

Anybody know what the above text says about WHY the speed of information transmission must be invariant?

Hi Naty1,

I'm going to conveniently ignore the context of your question (ie in terms of the text you quoted) and provide my explanation of why the speed of information transmission must be invariant.

I put it down to the structure of spacetime. If there is a quantum unit of time and a quantum distance, then there is going to be a maximum distance something can travel in a minimum amount of time. Such granularity of spacetime will result in a universal speed limit.

Proving that might not be easy. I think of it this way: any particle can conceptually have a minimum distance traveled (in a given frame), that would be not moving at all - being at rest, v=0. (Note that such a frame may not be strictly valid.)

Otherwise, a particle could move one quantum distance in one quantum unit of time. I would argue that in one quantum unit of time, a particle could not move more than that because it would imply two "location changes" in one quantum unit of time, and further imply that the quantum unit of time is divisible.

That would mean that the maximum speed for a particle is one quantum distance over one quantum unit of time, and that just happens to be the speed of light, and the speed of information transmission.

A final option is for a theoretical particle to move, but at rate less than one quantum distance per quantum unit of time. Here is where the movement would be statistical, you'd never know precisely which quantum cube a subluminal particle is in. However, when the positions are averaged out and the time elapsed measured you would end up with x quantum distances traveled in t quantum units of time (where x < t).

Since this sort of subluminal motion pertains to masses, you would really average out the positions of a large number of particles to find that the mass as a whole moves at less than one quantum distance per quantum unit of time. I suspect that at the quantum level the basic constituents of the mass would move at lightspeed, but not consistently in one direction as photons tend to.

cheers,

neopolitan