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

[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.

 

[Chrisc]

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

The same applies to time and mass.
I think it's important to mention our notions of length, time and mass are all dimensional measures that require, as DaleSpam pointed out, dimensionless comparisons or ratios before they have any "physical" meaning.

The second is 9,192,631,770 cycles of excitation of the outer shell electron (jump and back) of a cesium atom.
Theory tells us the electron will only jump with a finite, minimum energy increase.
Of course how quickly it acquires this minimum energy must then be known to ensure it does not jump at a higher frequency. So microwaves of specific waveLength are used to excite it. That's right, the Length of a wave determines the frequency of jumps that determines the total jumps in a second.
What is the Length of the microwave used?
Before you consider that, consider the standard for Length since whatever the Length of the microwave is it will be a "comparison" of that value.
The standard for Length is the meter defined as the distance light travels in a vacuum in 1/299,792,458 of a second.
What should be apparent from this standard is it is fixed by a constant, the constancy of the speed of light (299,792,458 m/s)
How long is this Length? How far does light travel in a second? Well...
how long is a second?
In short, dimensional measures are and must in principle, be relative measures of each other.
The key to setting a truly universal standard is to find a unit mass, length and time that are derived
from physical constants.
For example, Length or Time (but not both) can be set by the constancy of the speed(Length/Time) of light.
Mass by the constancy of gravitational force when c is its measure of Length or Time.
Now all we need is a constant of Time or Length, whichever we don't use in c.
Unless of course Time and Length are two qualifications of the the same dimension.
Perhaps Time, Length and Mass are three qualifications of the same dimension?
It doesn't hurt to ask the question.

 

[D H]

The second is 9,192,631,770 cycles of excitation of the outer shell electron (jump and back) of a cesium atom. Theory tells us the electron will only jump with a finite, minimum energy increase.

No. The second is "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." The cesium atom is not made to oscillate between states 9,192,631,770 times.

You are setting up a straw man argument.

Of course how quickly it acquires this minimum energy must then be known to ensure it does not jump at a higher frequency. So microwaves of specific waveLength are used to excite it. That's right, the Length of a wave determines the frequency of jumps that determines the total jumps in a second.

And now you are striking down your straw man. Your straw man is of course false. A cesium clock is not based on electrons cycling back and forth 9,192,631,770 per second. What really happens is quite different. Atomic transitions are a two-way street. When an electron jumps from a higher energy level to a lower one it emits a photon with a very specific frequency. If a photon of that same frequency hits an atom with an electron in that lower energy level, the electron will absorb that photon and jump to the higher energy level. Only photons with something close to the requisite frequency will be absorbed. How close depends on the temperature of the substance and the nature of the transition. The cesium hyperfine structure allows very little variation. Technically, that transition has a very high "Q" factor. This extremely high Q factor is one of the leading reasons for the choice of the cesium hyperfine transition as the basis for the definition of the second.

The number of cesium atoms in the desired state can be detected independently of the microwave frequency used to excite the cesium atoms passing through the microwave cavity. The microwave cavity is adjusted to the frequency that maximizes the number of cesium atoms in the desired state. The detector plus the microwave act as a resonance system. Because of the high Q factor, once the microwave frequency is extremely close to 9,192,631,770 Hz when the system is tuned to maximize the number of cesium atoms in the desired state.

 

[Chrisc]

Thanks D.H.
You are right. I was making a poor analogy and should not have implied a rate or time of absorption, but I don't understand the distinction you're making.

As far as I can see the principle of the analogy still holds with respect to the comparitive measures of constants.
How do you define the requisite frequency if not Length/Time?

I am not disputing the accuracy or consistency of the "Q" factor, I am making the point that no matter
what accuracy and consistency we might find in the future, it is a measured comparison of the dimension Length.

 

[Dadface]

This has got me thinking which can be quite a rare event .In the definition of the second we are using a unit of time which is related to the caesium atom to define a unit of time,the second.Is there a chicken and egg paradox here ?I think I need to go away and think a bit more.

 

[D H]

The definition of the second does not depend on length. It depends on a process that has a well defined frequency. Length is not a part of the definition. Chrisc, you are forgetting a basic premise of science: What we measure and how we measure it are often different things.

Dadface, there is no chicken-and-egg thing here. The period of the cesium 133 ground state hyperfine transition radiation is something independent of our definition of the second. We could have chosen any multiple of period to define the second. While a multiple of 10 million would have been a bit more in line with the spirit of the metric system, we chose a multiplier of 9,192,631,770 because that conformed with the Earth rotation-based (earth rotation circa 1820) definition of the second.