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

[matheinste]

Hello all.

Pre SR light could have any value (assuming non quantization) depending on the velocity of the observer.

Let us for now agree that in SR light speed has one value for all in all directions. It is what it is. The numerical value is dependent on the units and definitions, which are man made. It is what it is because it cannot be anything else, nature made it that way. It is exactly 299,792,458 M/S, with no decimal parts because that is how it is currently (i believe) defined.

Matheinste.

 

[Naty1]

matheinste posted:

More recently, however, it has become clear that the precision available from the kryrton-86 line is surpassed by the precision with which, on the one hand, the second, and, on the other hand, the speed of light are determinable. ... Note that, consequently, the speed of light is and remains precisely 299792458 meters per second ; improvements in experimental accuracy will modify the meter relative to atomic wavelengths, but not the value of the speed of light!-----

This is, i hope, relevant to Naty 1's last line of the last post #51

I don't think so ,but you may be right...it appears to me the "fixed" value of light is merely the standard so other stuff would be expected to vary due to those being less precise...but it seems that could conceptually change if some newer, more accurate measure for light, say to five more decimal places, were discovered.

 

[matheinste]

Helo Naty1

The quoted passage (not my words but those of Rindler, a respected author) says that the speed of light is fixed by defintion.

Matheinste

 

[Naty1]

Math...
I understand(??) and agree with your quote but I don't necessarily reach quite the same interpretation...here is another slightly different view...

There is, as yet, no intuitive explanation to why the universe should act like this. Since Maxwell's work, numerous experiments have been performed to test the prediction that electromagnetic radiation travels at the same speed for all observers - and none have failed. Instead of being a prediction from theory, it now became to be used as an assumption to build theories upon. Einstein was so convinced of its truth that he modified Newton's theory of gravity to encompass the constancy of light. Likewise, in the 1940s, Feynman, Tomomaga, Bethe and others incorporated the idea into Quantum Mechanics. The resulting theories, General Relativity and QED, are probably the most accurately tested to date - and they require that the speed of light is constant.

(I misplaced the source, sorry)

So I still have the intuitive feeling science has missed something...and that further fundamental study might yet uncover remarkable aspects of this universe and light speed in particular. As I understand Maxwell's work, his findings were originally understood within the context of "aether"...nobody realized that the speed of light was fixed as we understand that today...so despite his brilliance in formulation, he did not understand the implication, the physical interpretation, of what he had done...That took Einstein...and this is not so uncommon in mathematical physics...maybe analogous to Feynman's "sum over paths" which, if I recall correctly, he saw as a sort of "hokus pokus" which remarkably enough worked quite well! (When Wheeler explained the approach to Einstein in Princeton, Einstein thought it "crazy")

I can't help wondering why lightspeed and electric charge are fixed (constant) yet mass, time and distance vary by reference frame...truly astonishing...who would have believed this say 100 years ago??

 

[matheinste]

Hello Naty1.

Your quote refers to the constancy of the speed of light for all observers and does not refer to it's defined numerical value in the quote from Rindler in #52. What this quote says quite specifically (as far as i interpret it) is that the meter is defined as the distance traveled by light in vacuum in a time interval of 1/299792458 of a second and so a change in the accuracy of the measurement of light speed would not change its numerical value.

I am of course willing to admit the possibility that my interpretation of Rindler's words may be wrong, i am just explaining again, for clarity, what my interpretation is.

Of course if the definition quoted by Rindler no longer stands then all i have said is irrelevant. Perhaps there is a newer definition of light speed? Perhaps someone could clarify this.

Matheinste.

 

[matheinste]

Hello again

I have just looked up the current definition of light speed. According to Wiki the meter is defined such that the speed of light in vacuum is exactly 299,792,458 meters per second. Their quoted source is the International Bureau of Weights and Measures 2006.

Matheinste.

 

[neopolitan]

further fundamental study might yet uncover remarkable aspects of this universe and light speed in particular

I think you would do well to look at https://www.physicsforums.com/showpost.php?p=2011753&postcount=55". Dale may not have arrived at it first, but he does show that constancy of c is the result of the ratios between dimensionless quantities. You may not like that, I suppose, if you take it that dimensionless quantities are the result of theories which have "c is a constant" as an axiom.

However, if you look further back, someone stated that it is possible to take other axioms and arrive at the conclusion that c is a constant (even I had a hack at explaining it).

If you accept that neither space or time is infinitely divisible, then you arrive at the conclusion that there must be a maximum speed limit (see https://www.physicsforums.com/showpost.php?p=2005236&postcount=35"for the logic). Such a maximum speed limit would turn up all over the place in physics, even in contexts where you aren't really talking about anything moving (E=mc², as a simplified example). Think about the characteristics of that which could travel at the maximum speed. It could not be a mass, which consists of many particles interacting. It would be moving from fundamental division of space to another in one fundamental division of time, therefore it would have to "fit" into one fundamental division of space, so (at least roughly speaking) you are talking about a fundamental particle. Then, ask yourself, how fast do these things move?

cheers,

neopolitan

 

[Dale]

Just to follow-up on this. Originally I took the fine constant and used it, together with the standard definition of the second and the meter, and the Bohr radius to determine that the "optical" meter and the "bar" meter were still the same after doubling c and halving the vacuum permittivity.

I expanded on this idea and included also the gravitational coupling constant and a "pendulum" second so that I could have something to compare to the "atomic" second. I then allowed c, h, G, and the vacuum permittivity to be multiplied by the factors {1/2, 1, 2} (81 possible permutations) and calculated the resulting impact on the fine constant, the gravitational constant, and observables like the ratio of a "pendulum" second to an "atomic" second and the ratio of an "optical" meter to a "bar" meter.

I found that, for all combinations, the observables (pendulum/atomic and optical/bar) were a function only of the dimensionless parameters. It is not a general proof, but after this exercise I feel pretty confident that the dimensionless parameters are the only ones with any physical meaning beyond our choice of units.

 

[epenguin]

Have we reached a consensus on this thread?
If it is helpful I summarize my view saying it is rather a false question within present physical understanding but becomes a scientific one when turned upside down.

E.g. the question why is the speed of light that? becomes, when the Kr-86 line was the length standard, why is this Kr-86 line that long, a scientific question that can be answered by a theory that has c as one of its inputs.

Likewise the question on another thread 'why is light so fast?' can be transformed into questions like why are we so slow, or better why can we usually achieve relative velocities so small compared with c, why are we and atoms the size they are? which are scientific questions that can find an answer.

Analogously why is the Boltzmann constant Boltzmann constant exactly 1.3806503 × 10^-23 m² kg s^-2 K^-1 . or why is the degree centigrade exactly what it is in terms of the Boltzmann constant is a sort of non-question unless inverted in which case it is a question answerable in terms of molecular forces and statistical mechanics of water.

Or why does the sun come overhead at Greenwich exactly at midday is a non-question about the sun, but in different form answerable as a scientific question if we call history a science.

 

[D H]

Analogously why is the Boltzmann constant exactly 1.3806503 × 10^-23 m² kg s^-2 K^-1.

The Boltzmann constant does not have a defined value. It has a relative uncertainty of about 1.7×10^-6, see http://physics.nist.gov/cgi-bin/cuu/Value?k. The Boltzmann constant is defined as k=R/N_A, where R is the gas constant and N_A. The uncertainty in k results primarily from the uncertainty in R.

or why is the degree centigrade exactly what it is in terms of the Boltzmann constant

The degree Kelvin is exactly 1/273.16 of the triple point of water, see http://www.bipm.org/en/CGPM/db/13/4/. In particular, it is not defined in terms of the Boltzmann constant.

Or why does the sun come overhead at Greenwich exactly at midday is a non-question about the sun

This is a very real question about the Earth's rotation rate and the nature of time.

The Sun does not "come overhead at Greenwich exactly at midday." The second is no longer defined by the rotation of the Earth. There are three reasons why the Sun does not "come overhead at Greenwich exactly at midday." First, there is a difference between apparent http://en.wikipedia.org/wiki/Solar_time" .

I gave wikipedia references because wikipedia a pretty good job of describing these concepts in lay terminology. For the official descriptions, see http://www.iers.org or http://tycho.usno.navy.mil .

 

[neopolitan]

DH, you awoke the pedant in me.

You said that there are three reasons why the sun is not directly above Greenwich at exactly noon. A fourth is that the sun is 8 light minutes away, so the position of the sun is only apparent. Since the sun subtends about 0.5 of a degree and the sun moves around the world in 24*60 minutes, that means the apparent position is about 6.4 sun-widths from the "real" position. At high inclinations this won't seem like much.

As I indicated, pure pedantry :)

cheers,

neopolitan

PS I just got in my mind the image of someone using the wrong method to work out the location of a distant celestial body to try to reach it. It would be similar in some ways to Zeno's paradox. The idiotic astronavigator would look at the distant body, work out how far away it apparently is, and in which direction, put those details in the ship's control press "engage" and arrive in empty space, with the target in another spot. If the process was repeated, the astronavigator and crew would never get there (although of course they would if the spaceship's speed was sufficiently high since the errors would just get smaller and smaller till they were insignificant in the real world).

 

[Dadface]

An interesting question and one that can be extended to all of the constants.If we look at the unitless constants then the answer ,if there is one,becomes independant of the units of measurements used.The simplest example I can think of is pi,although this is an irrational number its value is the same whether we measure length in metres ,inches or any other units we choose.If someone was to make a list of the great unanswered questions in physics the question as to why do the constants have the values that they have would rank very high on the list.

 

[D H]

Pi is not a physical constant. It has nothing to do with length, or physics per se (it is a mathematical concept, after all). There is no mystery to pi. That it pops up a lot in physics is a horse of a different color.

 

[Naty1]

Have we reached a consensus on this thread?

A difficult question on many of these threads...Most often here, in my limited experience, various posters post until exhausted, or post one comment not to return, and go away with their own impressions. I do. That enables all of us to post ad nauseum and to repeat our positions during susbequent threads...all in all, a good bit of fun! Not always so helpful to the person asking the question.

Your consensus question would be like asking whether all quantum physicsts agree on what the calculations in quantum theory mean...after almost 100 years there are still substantial disagreements according to guys like Lee Smolin and formerely Richard Feynman ("Shut up and calculate") !

Dale posted:

It is not a general proof, but after this exercise I feel pretty confident that the dimensionless parameters are the only ones with any physical meaning beyond our choice of units.

I just don't fully understand that...it's not that I disagree, and it's a concept I will keep in mind for further reading, but it seems the charge of the electron, for example, or the speed of light, has a particular value that IS related to some physical aspect of our universe, maybe, for example, an initial condition at the origin of the universe. I tried reading Wikipedia but it has so many categories of "quantities" "constants" "dimensionless" and "dimensionlful" quantities and sub categories it did not seem worth the effort to make such distinctions. (Seems to me Wikipedia revels in details and omits relationships rather frequently.)

I'd also readily agree that several dimensionless quantities might well have such a "fundamental" origin and maybe the electron charge and speed of light derives from one or more of those... I do understand that if the charge of the electron turned out slightly different, our universe would probably not be here...many, many such "basic" parameters have very narrow allowable values that would permit our universe to evolve and stablize. It's either remarkable coincidence, the result of a "plan", or a random result from many possibilities.

 

[Dadface]

For D.H What do you understand by the two words physical and constant and what do you understand when they are lumped together namely" physical constant"?Pi in common with all other unitless and dimensionless constants has units that cancel by division.As an example when we calculate the area of a circle we have ,in terms of units only,metres squared equals metres squared times the units of pi.By your criteria e is just a mathematical concept as well and has nothing to do with the real physical processes of radioactive decay and the numerous other areas of science,not just physics where it turns up.Do you think that the topic of units ,constants and the like would make an interesting thread?Best wishes

 

[matheinste]

Hello Dadface

Quote:-

---As an example when we calculate the area of a circle we have ,in terms of units only,metres squared equals metres squared times the units of pi---

What are these units (dimensions) of pi ?

Matheinste.

 

[Dadface]

There are no units for pi ,it is a unitless and dimensionless number .Take any equation with pi in it,arrange it so that pi is the subject of the equation throw in the units and they will cancel out by division.There are many such examples in physics.

 

[D H]

Dadface, there is a world of difference between mathematical constants and unitless physical constants. Mathematical constants, such as 0, 1, pi, and e, have defined values. We can calculate them to any degree of precision desired.

The fundamental physical constants such as the fine structure constant are something quite different. There is no mathematical reason (not that we know of, anyhow) for why they have the specific values that they have. We have to measure these values based on experimental observations rather than calculate them based on mathematical definitions.

 

[neopolitan]

there is a world of difference between mathematical constants and unitless physical constants. Mathematical constants, such as 0, 1, pi, and e, have defined values.

Actually, there could be a physical meaning to pi. The value of pi in our universe may be a reflection of the extent to which space is, or perhaps is not, curved.

Think of the surface of a hemisphere, on which you use rulers which have the same curvature as the sphere's surface. The circumference of a full circle drawn on that hemisphere could be calculated in terms of the length of the ruler (which is really an arc) and a constant.

I've not done the calculations, but thinking about it logically it seems to me that the constant would not be pi (or any other value) irrespective of the curvature because if you maintain the length of the arc-ruler and vary the size of the hemisphere, you get a larger circumference as you approach an infinitely large hemisphere - at which point the curvature is zero.

Of course here we are thinking about a hemisphere in our universe, a universe in which we tend to deal with three dimensions and any curvature of space would involve a fourth. Such curvature would place an upper limit on the circumference of circles, ie what we could call "flat circles". We could envisage increased curvature, within the influence of a massive body for example. What would be difficult to imagine is something which could unbend space, if space has a default curvature, and thereby give us a region where circles have a greater circumference.

(Note about areas. The arc on a hemisphere is a function of the angle subtended and pi. The area of a curved circle is therefore a function of half the circumference squared and a ratio related to the curvature - a ratio between the arc length and the length subtended by that arc on a tangent which intersects the centre of the curved circle. I strongly suspect that the overall effect of this is that where the curvature does not equal zero, pi cancels out leaving you with a curvature constant and the length of the arc-ruler to work with.)

Well, that was a lot more complicated than I expected.

cheers and Happy New Year to all,

neopolitan

 

[matheinste]

Hello neopolitan

The value of pi is the (constant) ratio of the circumference of a circle to its diameter in Euclidean (flat) space.
This ratio is not necessarily the same in a non-Euclidean space. But in such a space it presumably would not be called pi. Perhaps a mathematician could expand on this.

Matheinste.

 

[D H]

Hello neopolitan

The value of pi is the (constant) ratio of the circumference of a circle to its diameter in Euclidean (flat) space.
This ratio is not necessarily the same in a non-Euclidean space. But in such a space it presumably would not be called pi. Perhaps a mathematician could expand on this.

Matheinste.

That is correct. Pi is the ratio of circumference of a circle on a Euclidean plane to its diameter and has a very specific value. Suppose we find definitive evidence showing space is not flat. That finding will not change the value of pi one iota. Pi is not a measured physical constant. It is a defined mathematical constant.

 

[neopolitan]

I certainly think that if pi does have a physical meaning, it would be reflective of either that space is flat or the curvature it does have is inescapable - it is not as if pi seems random after all. A lot of other numbers could be random, but a number which doesn't end as you seek higher and higher accuracy is not.

Note I don't think it is "chosen". I merely don't think that if things were very slightly different then we would be living in universe which had pi=3. The fact that pi=pi is either very deeply ingrained into the universe or it is a fundamental consequence of the physical laws. In any event, I am not sure that it is fair to write pi off as a purely mathematical construct.

cheers,

neopolitan

 

[matheinste]

Hello neopolitan.

Pi is defined as above. Because of the relationship between pi and circular (arc, radian, angle) measure it is deeply ingrained in the physical description of the universe. Work done and many other physical measurements depend on angular measure and wherever you have angles even when given in degrees, you are relating to pi as there are 2.pi Radians in 360 degrees. So pi is everywhere.

Although pi is a mathematically defined construct I don't think that D H is saying that it has no physical relevance.

Mateinste.

 

[Dadface]

Pi turns up in the uncertainty(indeterminancy)principle of Heissenberg.Numbers are the basic building blocks of mathematics and mathematics and physics are inextricably tied together.At the most basic level what do we mean exactly when we state that one plus one equals two?

 

[HallsofIvy]

Oh, this is getting silly. "1+ 1= 2" is not a physics statement, it is a statement about mathematics. Similarly the statement "the circumference of a circle is \pi times its diameter" is a mathematics statement not a physics statement.

The original question "Why is the speed of light exactly 299 792 458 meters per second" was answered long ago: because that is the way "meter" is defined.

 

[matheinste]

Hello Dadface

Quote:-

----At the most basic level what do we mean exactly when we state that one plus one equals two?----

If you really want to know, at an almost philosophical level try Frege - The Foundations of Arithmetic. Don't be fooled by the title. Its not kid's stuff.

As HallsofIvy said the original question has been answered.

Matheinste.

Frege - !The Foundations of Arithmetic 2nd ed. revised

 

[neopolitan]

It may be silly, but to me a mathematical thing is what you can on paper, and may have relevance in the real world. Fiddling around with simple matrices for instance.

However mathematical things become physics things when they certainly do have relevance in the real world and, I would go so far as to say, when they can be related to real world measurements. Pi is one of those. Draw a real world circle and measure it.

Perhaps I am wrong about the separation between mathematics and physics, perhaps there is another philosophy book on the topic.

Certainly, if we are questioning the summation of two ones, then we are being less useful than those discussing the gyrations of pin-head angels. The topic has strayed, I find it interesting, but it is no longer relevant to the the thread, so I will back out.

cheers,

neopolitan

 

[HallsofIvy]

It may be silly, but to me a mathematical thing is what you can on paper, and may have relevance in the real world. Fiddling around with simple matrices for instance.

However mathematical things become physics things when they certainly do have relevance in the real world and, I would go so far as to say, when they can be related to real world measurements. Pi is one of those. Draw a real world circle and measure it.

"Draw a real world circle and measure it" and you will NOT get pi as the ratio of the circumference to the diameter. You may well get something close to pi but certainly not pi iteslf!

Perhaps I am wrong about the separation between mathematics and physics, perhaps there is another philosophy book on the topic.

Certainly, if we are questioning the summation of two ones, then we are being less useful than those discussing the gyrations of pin-head angels.

I don't know why you would say that. Since I don't believe in the existence of angels, I can see nothing at all useful in discussing them. I do, however, believe in the existence of "1", "+", "=", and "2" and a discussion of "1+ 1= 2" might tell me useful things about those. It is, simply, not a physics questions.

The topic has strayed, I find it interesting, but it is no longer relevant to the the thread, so I will back out.

cheers,

neopolitan

 

[Chrisc]

I've read many posts that begin with a question regarding fundamental constants that then turn to distinguishing dimensional constants from dimensionless constants. Most end up discussion the numerical value of these constants without distinguishing the numerical value from the fact that it is constant.
This is the first, thanks to DaleSpam and D.H. that explains more than the concept of unity of units.
As DaleSpam pointed out above, changing the numerical value of a dimensional (dimensionful) constant, a constant that defines a ratio of dimension does not change the laws of physics but merely changes the quantitative values of physical dimensions, a condition that would be imperceptible to measurement.
Changing a dimensionless constant is as DaleSpam pointed out with the fine structure constant, something that would change the laws of physics. Why, because the dimensionless constants reflect the dynamics(qualitative measures) of the laws whereas the dimensional constants reflect the kinematics (quantitative measures). A cup that holds 10-oz or 1000-oz still obeys or possesses the dynamics of the law of cups, its kinematic value of 10-oz or 1000-oz changes the kinematic value of its dynamics, but not the dynamics (laws [of cup]).

I think the core issue that seems intuitively expressed by most is that constants and their numerical or quantitative values must be recognized in physics as more than ratios of numbers and dimensions. That they are constant in mathematics is an expression of the axioms of mathematics as D.H pointed out.
That they are constant in physics is an expression of dynamics.
If we ask why is the speed of light 300000-km/s, it is because of our choice or international standard of choice of meter and second. If we ask why is it always 300000-km/s it is because we always measure it to be so. If we ask why do we always measure it to be so, it is because of the geometry of space-time(note that is the dimension speed distance/time) follows the principle of relativity keeping all our measurements relative. If we then ask why is it constant, we can understand our question is really asking why are the dimensions space and time relative measures.
Now we get to what is intuitively seen but seldom understood in the questions of constants.
Why (in the case of c) are space and time relative measures? We can fall back on the empirical evidence of c
and claim "because" it works. We can explain the detailed mechanics of SR and show that it does work.
But neither of these answer the real question which I think is more easily understood as:
What is the fundamental nature of space, time and mass that our measures of each are conditioned by motion and proximity to mass? SR and GR define the framework for accurately predicting our measurements, but they do
not answer the question. Einstein left the "dynamics" of GR, the energy of mass, to future theory.
At present the best model we have is the Standard Model with the incorporation of the Higgs field that offers
a model for the manifestation of mass.
So the question becomes - what is the nature of space, time and mass that a physical dynamic can be constant?

 

[Dale]

This is the first, thanks to DaleSpam and D.H. that explains more than the concept of unity of units.

Thank you!

If we ask why is the speed of light 300000-km/s, it is because of our choice or international standard of choice of meter and second. If we ask why is it always 300000-km/s it is because we always measure it to be so. If we ask why do we always measure it to be so, it is because of the geometry of space-time(note that is the dimension speed distance/time) follows the principle of relativity keeping all our measurements relative. If we then ask why is it constant, we can understand our question is really asking why are the dimensions space and time relative measures.

I agree with the sentiment you express here. The questions about why c is constant, finite, and frame invariant are (IMO) much more interesting and important than why it has the specific value that it does.