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

[Naty1]

Fluidistic: Thanks for the thread referenced in post #50 here...I found something, which if accurate, was a big help.

there, HallsofIvy posted:

(And lightarrow seems to have said the same thing here in post # 25)

To clarify- it is NOT the "speed of light" that has been "defined"- as you say that is a constant of nature and we cannot just "define" it to be a specific value.

(my boldface)

This is all I was trying to say here in earlier posts. It seems self explanatory enough for me as long as the current posters in this thread agree its correct. Whether it's quoted in km/sec or mph or any other units makes little difference to me as long as both the magnitude and units are given.

Light is not instantaneous for a reason; it is constant for a reason, and it propogates at a given value for a reason (pick any unit in which you want to measure)...

For my own interest I'm going to read further about dimensionless and dimensionful constants but right now the distinction sounds like one some math wizards concocked during a binge! but maybe there are subtlies I'm missing...wouldn't be the first time!

As a matter of interest, if a theoretical foundation were found for all the "fundamental constants" in the standard model (currently independent inputs) and also for gravity (if there are any) and some/any were found to be different, (say, for example, in the twentieth decimal place beyond current measured accuracy) I'd be interested if any would then cause the speed of light to be ever so slightly refined.

 

[matheinste]

Hello all

This extract is taken from Rindler – Relativity, Special,General and Cosmological. Second Edition. Page 41. I do not know if this is still the current situation but it is interesting nontheless.

-----First of all, we need universal units of time and of length. In this age of atoms it makes good sense to fall back on atomic frequencies and wavelengths to provide these units. Thus in 1967 the (international) General Conference of Weights and Measures (CGPM-1967) defined the second as follows: ‘The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom’. The international standard of length had been defined back in 1960 in terms of the wavelength of a certain line in the spectrum of krypton-86. 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. Thus, demonstrating its complete confidence in special relativity, CGPM-1983 re-defined the meter as the distance traveled by light in vacuum in a time interval of 1/299792458 of a second. 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

Matheinste

 

[Naty1]

Cepheid posted

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.

My analogy is 'flawless'...you need to reread it...we, in fact, agree completely (i concur with your statement and was using analogous faulty logic to illustrate the faulty logic of the original post.)

 

[Naty1]

In post # 19 Strangerone repeated his original question:

What is the exact physical reality behind these observed constants. There 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 agree,,,no theory I have seen either...it's not really "accepted", just the best we can do so far.

Having reread all the posts here I am led to the conclusion we did not provide a direct answer to Strangerone's question very well, or maybe it would be better to say we sure took a round about way. What someone asks "Why does a baseball fly off a typical major league hitter's bat at about 98 mph?" getting into a discussion of dimensions is not the way to go to aid the questioner.

At least I found the Wikipedia result I quoted was misleading at best.

HallsofIvy, Dalespam, and Lightarrow I think helped clarify what was for me the subsequent confusing dialogue among posters about units/dimensionlesss/dimensionful but the language can sure be confusing.

I think Lightarrow posted:

To clarify- it is NOT the "speed of light" that has been "defined"- as you say that is a constant of nature and we cannot just "define" it to be a specific value.

and that's enough clarification for me.

Seems maybe had the original question been something like "Is there a theoretical reason the experimentally measured value for the speed of light is 300K m/sec instead of, say, 400K m/sec"...we might have been more succinct in replies.

 

[Dale]

Hi Naty1,

Sorry about the delay. I wanted to explain in more detail why the dimensionless quantities are considered more fundamental than the dimensionful quantities. I thought it might help to see an example of what it would mean to change a dimensionful quantity without changing any of the dimensionless quantities, and it took a while to work it out. Specifically, I wanted to work out what would be the experimental result if the speed of light doubled but the fine structure constant was unchanged.

The fine structure constant \alpha =\frac{e^2}{2 h c \epsilon _0} has several terms, but if we suppose additionally that mass and charge do not change then we see that if c is doubled then the vacuum permittivity must be halved. And since c^2=\frac{1}{\epsilon _0 \mu _0} the vacuum permeability must also be halved. So, basically we have just c doubling and the permittivity and permeability halving and no other changes.

Now, let's determine what we measure. The http://en.wikipedia.org/wiki/Hyperfine" energy is proportional to c² which is quadrupled. So, if E for the Caesium hyperfine transition goes up by a factor of 4 then by E=hf the frequency also goes up by a factor of 4 meaning that our new seconds are a quarter of our old seconds.

Now, our new meters are equal to the distance that light travels in 1/4 of an old second and since c is doubled that distance is 1/2 of an old meter. Note that this definition of the meter leaves the numerical value of c in new meters per new seconds unchanged. This is not terribly surprising because it is a direct result of the definition of the meter, but let's use our new meters to measure the length of a bar that was 1 old meter long prior to the change in c.

Due to the doubling of c, the Bohr radius a_0=\frac{h}{2 \pi m_e c \alpha } is halved. This means that our 1 old meter bar has shrunk to 1/2 of an old meter. As we discovered above this is also the length of our new meter. In other words, a bar that was previously measured to be 1 old meter is now measured to be 1 new meter, despite the fact that c doubled and our new meter is defined based on this doubled c.

So, although our new seconds reduced by a factor of 4 and our new meters reduced by a factor of 2 when c doubled, we cannot tell any difference. Things that used to be 1 old meter long are still measured to be 1 new meter long even though all of our measurements are now distorted as are the objects themselves. This is why dimensionful parameters are not considered fundamental. A change in c (without a change in the fine structure constant) wouldn't change any physical measurement we could make. Only changes in the dimensionless parameters have physical significance.

 

[neopolitan]

First I would like to say well done to Dale, that was a brilliant, cogent approach to a deceptively simple topic.

Then my two cents.

I think the simplest way to explain that light has a specific speed, and not another (I gather that this was the OP's thrust, rather than why the defined speed is a round number), is to point out that the speed of light is a really the ratio between one fundamental division of space and one fundamental division of time. We could say it is 1:1 or one Planck length per Planck time, or one light year per year, or 299792458 m/s depending on the units we find most convenient to work with.

So, the figure we come up with is really more reflective of the number of fundamental units of space that fit in the unit of space we find convenient and the number of fundamental units of time that fit in the unit of time we find convenient.

(Strictly speaking, it is the ratio of those numbers, since while Planck units are certainly convenient, I cannot say categorically that they are truly fundamental.)

cheers,

neopolitan

 

[neopolitan]

Going back to Dale's post: since if we were to somehow change the relative speed of light, by for example, traveling towards a photon, then in the axis of that motion the decreased speed of light would result in the changes you listed such that we would measure the speed of the photon as being c, yes? At the very least, there would be no way to tell if the relative speed of light has been reduced by our motion towards the photon, which admittedly makes it impossible to say that we are moving towards the photon without bringing in another observer who is notionally at rest. But let's say we do that.

What I find interesting is that, because there could be a photon coming at us from behind (according to the introduced observer), the changes you listed would be directional, ie velocity based rather than speed based. Again it would have to be from the perspective of the notionally at rest observer.

I note that this is not what is referred to as "frame drag" but it is a description which came to mind when I thought of it. Basically the observer watching us heading towards one photon and away from another could calculate that vacuum permittivity and permeability are decreased in the direction of our motion (analogous to a fluid's resistance against motion through it?) and increased behind us (analogous to reduced pressure in a fluid behind a vehicle?).

Further, if we were to face "forwards", our time divisions are shorter T_fw=(t.c²/(c+v)²) and our spatial divisions are shorter X_fw=(x.c/(c+v)) - assume we chose dimensions so that x/t=c. This means that in our inertial dimensions the closing velocity according to the observer (c+v) will be X/T according to us. In other words, we won't be able to measure any speed for the photon other than c. If we face "backwards", our time divisions are longer T_bw=(t.c²/(c-v)²) and our spatial divisions are longer X_bw=(x.c/(c-v)) but the closing velocity according to the observer (c-v) will still be X/T according to us.

The overall effect, according to our observer would then seem to be a form of root mean square:

x' = ct' = sqrt (X_fw . X_bw) = sqrt ((x.c/(c+v).(x.c/(c-v))
= sqrt (x².c²/(c²-v²)
= x.sqrt (1/(1-v²/c²)

The figures seem to work out ok.

Is there any validity to them? Perhaps it is all too ethereal?

cheers and Merry Christmas,

neopolitan

 

[Dale]

First I would like to say well done to Dale, that was a brilliant, cogent approach to a deceptively simple topic.

Thanks neopolitan!

What I find interesting is that, because there could be a photon coming at us from behind (according to the introduced observer), the changes you listed would be directional, ie velocity based rather than speed based. Again it would have to be from the perspective of the notionally at rest observer. ...

Is there any validity to them? Perhaps it is all too ethereal?

cheers and Merry Christmas

That is interesting, I hadn't considered that since it took me a couple of days just to work out the part that I did, but you could be right. The thing that would worry me is that the factors are different than the regular relativistic gamma factor, and they are different for time and space. But you are right, it is very much like the Lorentz aether theory in the sense that clocks and rulers change to make a change in c undetectable.

Merry Christmas to you too!

 

[neopolitan]

Just a quick response, note that I used x where x=ct and x'=ct' and the unprimed frame is the notionally at rest frame. I didn't make that clear enough.

If I was deriving the length contraction equation, I would have had to use different notation, probably L and L', and would be using a different frame as my starting point.

The equation I provided could be used for deriving time dilation.

cheers,

neopolitan

 

[Al68]

I think the simplest way to explain that light has a specific speed, and not another (I gather that this was the OP's thrust, rather than why the defined speed is a round number), is to point out that the speed of light is a really the ratio between one fundamental division of space and one fundamental division of time. We could say it is 1:1 or one Planck length per Planck time, or one light year per year, or 299792458 m/s depending on the units we find most convenient to work with.

How about terafurlongs per fortnight? That makes c=1.8, nice easy number to work with.

 

[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.

 

[matheinste]

Hello DaleSpam

Quote:-

---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. ----

I agree with what you say but i find the fact that c is constant and finite is not as astoundingly thought provoking as its frame invariance.

Matheinste.

 

[Dadface]

I would like to reply to several of the messages above but first an apology,I am a total dope when using computers and I still haven't worked out how to do paragraphs and the like so my presentation will be poor . Firstly for Chrisc.It will take me time to digest your message but can I make some first impression and possibly misguided remarks.I refer to your last sentence.Are mass length and time the only factors and would not other quantities such as charge come into the analysis?Secondly and this is completely beside the point but I would value your opinion anyway-where would all this be if CERN found evidence that suggested that the Higgs bosun did not exist.For PF MENTOR.I do not understand your point about not being able to get pi because the same applies to experimental measurements of quantities such as c.In fact we don't even know if c is a constant and the best we can say is that it has a value which lies somewhere between the ranges of experimental uncertainty for those environments and times within which the measurements have been made.I would like to add that statements about mathematics also apply to physics We cannot draw any boundaries between the two disciplines any attempt to do so being counter productive.Revisiting the theoretical framework on which our theories are based often leads to greater insights and for physicists in particular,that framework includes the framework of mathematics.Finally pi ,e and other numbers are out there in our physics theories,pi features in Schrodingers equations for example.matheinst thank you for recommending the book.It sounds a bit too heavy going for me and I probably would not get beyond the first page.

 

[Dale]

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, ...

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 have avoided changing charges and masses in my above analyses, but I feel more confident about it now so I think I can make the attempt. I will report the results when I have done so. FYI, another way of interpreting the fine constant is as the ratio of the electron charge to the Planck charge (or rather the square of that ratio).

I apologize for the disorganization and length of the remainder of this message. These are still relatively new ideas for me so I haven't had time to really internalize them the way I would like. Also, I understand that you are not disagreeing with me so don't misunderstand my intent here. I am just showing you my thought process in the hopes that some random fragment of one of my thoughts may be helpful to you as you think about the subject.

Last week, after doing the analysis that I posted above, I had a kind of conceptual crisis. I had managed to convince myself that the only physically important universal constants were the dimensionless ones, but then I was faced with the following problem:

How can any number of dimensionless parameters be combined to make a dimensionful parameter? In other words, how could I derive a dimensionful physical unit like the length of a meter using only these dimensionless parameters that I believed to be fundamental?

Well, the answer is, of course, that you cannot. There is no possible way to combine the fine constant and the gravitational coupling constant or any other dimensionless constant to get a meter. So then how are the dimensionless parameters fundamental?

I thought a little more about this and I realized two things. First, all of my "physical measurements" were, in fact, dimensionless numbers. For instance, the ratio of the length of the old platinum bar meter standard to the length of the new optical meter standard. If the optical meter and and the platinum bar meter both double then we can detect no change because the ratio has not changed. We can only detect changes in the ratio.

Second, whenever we think we are making a dimensionful measurement we are actually making a dimensionless measurement. For instance, the pen here on my desk is .15 m long. Althought that looks like a dimensionful statement, what I am actually saying is the dimensionless ratio of the length of the pen to the length of a meter is .15 (pen = .15 meter -> Lpen/Lmeter = .15). Since dimensionful equations always have the same dimensions on either side you can always rearrange to make a dimensionless expression.

We can only physically make dimensionless measurements. I cannot directly measure the length of the pen, I can only compare it to the length of a meter or some other standard. Then any measurement is always inherently a ratio to some standard.

So, although I cannot combine the fine constant and the gravitational coupling constant to obtain a meter I can combine them to obtain the length of a pen/the length of a meter. The former is not physically observable, but the latter is.

I realize that this is what I had instinctively done when I did the calculations above, but it took a bit for my rational side to catch up. Again, I apologize for the length and disorganization of this post, these ideas are still shakey in my mind, but writing this helps.

 

[Dale]

Finally pi ,e and other numbers are out there in our physics theories

Nobody is saying that these numbers are not incredibly important to physics. DH specifically mentioned it in his "horse of a different color" comment above. But the usual definition of a physical constant is one whose value can only be obtained experimentally. Numbers like pi and e, as important to physics as they are, simply do not fit that definition. It is not a question of their physical utility or physical importance, it is simply a question of how the value is obtained (through physical experiment or through purely mathematical computation).

John Baez http://math.ucr.edu/home/baez/constants.html" : "Some of them are numbers like pi, e, and the golden ratio - purely mathematical constants, which anyone with a computer can calculate to as many decimal places as they want. But others - at present - can only be determined by experiment. "

 

[Chrisc]

...Are mass length and time the only factors and would not other quantities such as charge come into the analysis?

I did not mean to imply that physical dynamics are restricted to gravitation.
Charge, strong and weak force dynamics can all be questioned in the same manner.
There is a reasonable consensus among physicists that QFT should be background free.
That is the "final" theory of all four forces should not depend on a "hand-made" or an a-priori
metric, the space-time geometry required to define the dynamics should arise from the dynamics.
As in GR - the metric is the field.
This puts the nature of space, time and mass back into the fundamental dynamics of all the forces.

Secondly and this is completely beside the point but I would value your opinion anyway-where would all this be if CERN found evidence that suggested that the Higgs bosun did not exist.

I don't think (and this is intuition not science) the detection or failure to detect, a Higgs boson
will answer as many questions as it will raise. I think the cascade of particles that will likely be detected
at the power necessary to squeeze out a Higgs particle will start a whole new and very interesting
chapter in physics.
The evidence being seen in condensed matter physics today is already so strange that I don't think
many particle physicists are expecting to close the book on the Standard Model with the detection of
the Higgs particle.

 

[Enoy]

I did not mean to imply that physical dynamics are restricted to gravitation.
Charge, strong and weak force dynamics can all be questioned in the same manner.
There is a reasonable consensus among physicists that QFT should be background free.
That is the "final" theory of all four forces should not depend on a "hand-made" or an a-priori
metric, the space-time geometry required to define the dynamics should arise from the dynamics.
As in GR - the metric is the field.
This puts the nature of space, time and mass back into the fundamental dynamics of all the forces.



The evidence being seen in condensed matter physics today is already so strange that I don't think
many particle physicists are expecting to close the book on the Standard Model with the detection of
the Higgs particle.

Hello
I just loved to read this tread. The questions raised by Strangerone and all the replies is both fundamental and equal important. I should like to know what Strangerone has submitted to APJ and what kind of response to it he has got.

 

[Naty1]

Dalespam posts:

How can any number of dimensionless parameters be combined to make a dimensionful parameter? In other words, how could I derive a dimensionful physical unit like the length of a meter using only these dimensionless parameters that I believed to be fundamental? Well, the answer is, of course, that you cannot.

So glad YOU said that...I thought about that briefly over the holidays, figured, I was missing something, and moved on to other confusing pieces of this puzzle...Good post! I'm relieved!

Dalespam, (Now I AM mad at you!)..just when some pieces seemed to be coming together you had to bring this up:

First, all of my "physical measurements" were, in fact, dimensionless numbers...Second, whenever we think we are making a dimensionful measurement we are actually making a dimensionless measurement.

How do you expect me to make meaningful distinctions when less/ful are blurred this way...now it again seems like we are splitting hairs...UGH!

But the usual definition of a physical constant is one whose value can only be obtained experimentally.

Now that's just a crazy notion!. (Seems like a lazy scientists approach.) But I realize its today's convention.
I have to believe when and if we have the ultimate theory of everything, that ALL constants should be theoretically accessible. Why should some constant be "hidden" from theoretical determinism if we really understand the physical universe?

We may never get there, but I want to know why something like the fine structure constant is what it is...why the ratio of square (electron charge/ Planck length)??...In fact doesn't SOMEBODY wonder why, if lengths vary relativistically, how can the fine structure be "constant"...(why doesn't Planck length vary in differents frames...every other length does!) Or maybe Planck length is like the speed of light..invariant? If so, WHY? What's it's special status, if any?

This is still frustrating! Time to sign off and watch some football...

 

[Dale]

How do you expect me to make meaningful distinctions when less/ful are blurred this way...now it again seems like we are splitting hairs...UGH!

Can you pick up a pen from your desk (or any other convenient object) and tell me how long it is without relating it to any other length? As soon as you relate it to another length you have made a dimensionless measurement, the ratio of two lengths.

 

[Al68]

Can you pick up a pen from your desk (or any other convenient object) and tell me how long it is without relating it to any other length? As soon as you relate it to another length you have made a dimensionless measurement, the ratio of two lengths.

If I compare the length of my pen to another length, isn't the "other" length the dimension?

If I say that my pen is 10 finger widths long, isn't "finger widths" the dimension?

Isn't the comparison of an unknown length to a standard length the definition of a dimensionful quantity?

Al

 

[Dale]

If I compare the length of my pen to another length, isn't the "other" length the dimension?

If I say that my pen is 10 finger widths long, isn't "finger widths" the dimension?

Isn't the comparison of an unknown length to a standard length the definition of a dimensionful quantity?

No, the other length is the unit. The dimension is still length. The meter is the SI unit which has dimensions of length.

In the case of your example you have:
1 pen length = 10 finger widths
or
(pen length)/(finger width) = 10
Which is dimensionless since pen lengths and finger widths both have dimensions of length.