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

[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.

 

[Al68]

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.

OK, but the use or the term "dimensionless measurement" implies that there is such a thing as a "dimensionful measurement". Otherwise you would just use the word "measurement".

After all, if someone used the term "antlerless monkey", it would imply that some monkeys have antlers, wouldn't it?

So, what's an example of a "dimensionful measurement"?

Al

 

[Hernik]

Pardon my physics, I'm NOT a professional. But I think an answer to the opening post could maybe be:

According to special relativity any object traveling with the speed of light is in a universe with no distance in the traveling direction. So with the velocity c you reach any destination instantly. A speed that makes you get to your destination even faster than instantly is impossible. For something traveling at the speed of light there is no distance and no time, so a velocity larger than c would require negative distance and negative time.

 

[Dale]

OK, but the use or the term "dimensionless measurement" implies that there is such a thing as a "dimensionful measurement". Otherwise you would just use the word "measurement".

I am being redundant, for emphasis. I think it is a reasonable emphasis since it is not necessarily obvious, at least it was not obvious to me a month ago.

 

[WhoWee]

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

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

Looks like you nailed it.

http://en.wikipedia.org/wiki/Metre

 

[neopolitan]

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.

Quite, but is there not an inherent length involved?

Each state of the electron correlates with a shell, each shell has a mean distance from the nucleus, so each transition correlates to a distance change, which is a length ...

Length is not part of the definition per se, but then it was not part of the original definition of the year even though we later on worked out that a year was the time it took the Earth to travel an orbit around the sun.

I think Dale's point stands, and that further the argument that time and space definitions are intrinsically interrelated stands also (so by extension, to the extent that lengths are dimensionless, so too are times).

cheers,

neopolitan

 

[Chrisc]

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.

DH, the definition of a second is not what is in question.
The question is, can Time be defined exclusive of Length.
The answer is no, it is a comparative measure.
In context of the atomic resonance of cesium that is chosen as the base unit time, frequency is a photon "count".
To count such an event frequency, one must sum the photon detections per unit time, which is a circular definition of time measurement.
The atomic clock affords us a consistent, finite and accurate quantification of a process. The quantity it measures is a comparative measure of the dimension Length. The constancy of Length/Time comparison is the constancy of the speed of light.
We stop counting the photon emissions when light has traversed 1/299,792,458 meters.

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.

Dadface, it does make one think. The chicken-and-egg dilemma, is the wave-and-particle dilemma.
We count waves as a measure of frequency which is determined by their Length...which is a measure of time defined by Length.
We count particles (events) as mentioned above which amounts to the same dilemma, or should I say internally consistent principles of dimension.
I am not suggesting this is a dilemma, it only appears as such when we forget nature is not absolute. It is what the nature of physical dimension must be to uphold the principle of general relativity and the laws of conservation.

 

[matheinste]

Helo Chrisc

-- 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’--

I don't know if this or a similar definition still stands. By this definition the second is the time taken for a number of periods. No lengths or comparisons are involved, just counting..

Matheinste

 

[Chrisc]

...By this definition the second is the time taken for a number of periods. No lengths or comparisons are involved, just counting..

Matheinste

No, you're argument is analogous to saying - President elect Obama did not win the election because more votes were cast for him than for anyone else, but because of the number of votes cast for him. The number is only "meaningful" when "compared" to the number cast for each candidate.

Similarly, counting the photons does "define" the second but only because the comparison to Length has already been made, which is why we count photon emission instead of 9,192,631,770 geese flying past the Elm tree in the front lawn of the U.S. Naval Observatory. We count photons instead of geese because the speed of light is a constant and the speed of geese is not.

Why is the constancy of "speed" important to our measurement of time?
Because it is a measure of Length per count that is constant.

If each photon we count in marking a second traveled at different, arbitrary speeds, they would reach our detection (counting) device sooner or later than each other, making our count (a second) a different duration each time we counted.
No matter how well you embed the notion of Length or disguise its use, there is no escaping the fact that dimensional measures are meaningless (geese counts) without a comparative measure to other dimensions of equally meaningful comparisons. Time is a comparative measure of Length, Length is a comparative measure of Time, Mass is a comparative measure of Space and Time and Space and Time are comparative measure of Mass.
Don't forget the speed of light is a constant, not an absolute. It does change, as does Time, Length and Mass, but as a constant, it will never be measured to do so. As Time, Length and Mass do change, the laws of physics would be meaningless if it weren't for the fact that they each remain a comparative measure of each other.

 

[matheinste]

Hello Chrisc.

The number of photons emitted in a second has nothing to do with light speed or length. It is a number. The same as counting geese. If there are twenty geese taking off (goose emission)and flying past you then there are twenty geese taking off and it does not matter how fast they fly as long as you can count them.

Matheinste

 

[Chrisc]

The number of photons emitted in a second has nothing to do with light speed or length.

Hi matheinste
I did not say the number of photons emitted had anything to do with the speed of light. I said the speed of light had to do with the rate of detection.

... it does not matter how fast they fly as long as you can count them.

Matheinste

According to your statement, the speed of each photon emitted by the resonating cesium can be as random as the speed of flying geese and you would still consider each count of 9,192,631,770 photons "measures" a second, even if it takes one such group a year to reach your detector and the next group ten minutes.
Perhaps you are thinking the constancy of the resonance is all that is needed to quantify the number of photons that comprise the "definition" of a second? If that's the case, you are right.

But again that has nothing to do with whether or not Time can be measured as a meaningful quantity exclusive of the dimension Length. The constancy of the speed of light was the OP question, which required a qualification of dimensional and dimensionless constants that DaleSpam provided with significant clarity.
If you can offer an example of a method of "measuring" Time that does not include Length, please do.

 

[matheinste]

Hello Chrisc.

First of all let me say that I am now discussing from a genuine acceptance that I may well be wrong and I am just seeking clarification for my own satisfaction.

I think to get anywhere we must assume the constancy of the rate of photon emission and allow a correlation between the number of single photon emissions and the number of wavelengths of the emitted radiation.

I still feel that the rate of photon emission is a fact not dependent on length, but the time it takes us to observe/count these emissions is dependent on non temporal factors. BUT, of course, this observed count is all we have to go on and is at the heart of the definition. So yes in that case I must concede that the result is dependent on non temporal factors.

So I suppose what i am saying is that if N emissions take place, the “time” it takes us to observe/count these N emissions (dependent on length) is not necessarily the same as the “time” taken (not dependent of length)for the actual emissions. But i suppose this could be interpreted as saying that the actuality is in some way unknowable. But this could be applied to everything and so i am not at all happy with this point of view. I feel it is wrong but cannot clearly see why. Anyway that verges on philosophy and is not at home in this thread.

Matheinste

 

[Dale]

Just for clarity: I was not intending to attempt to unify length with time; it might be possible to do so, but I am still just learning about dimensionless measurements and have not gotten that far yet in my thinking.

What I was describing is simply that it is not possible to physically measure a time without comparing it to some other time. In other words, if we had a pendulum clock, a quartz clock, and an atomic clock we could tell if the ratio of any pair changed, but we would not be able to measure if they all changed by the same fraction.

 

[DrGreg]

A little confusion has arisen in this thread.

In the official definition of the second¹ you are counting waves, not photons. In principle, you could take a single photon, measure its frequency using an uncalibrated clock, then calibrate your clock to give a frequency of exactly 9 192 631 770 Hz.

But the point still stands that all you need to do is count. You count the number of peaks of a wave that pass a point, and you need no knowledge of any units of distance to perform that count. It doesn't matter whether you measure length in metres, inches, light-years or furlongs, it still takes 9 192 631 770 wave-cycles from a caesium 133 atom to define a second.

____________
¹The 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 (at rest at absolute zero).

Ref: http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html[/color]

 

[neopolitan]

A little confusion has arisen in this thread.

In the official definition of the second¹ you are counting waves, not photons. In principle, you could take a single photon, measure its frequency using an uncalibrated clock, then calibrate your clock to give a frequency of exactly 9 192 631 770 Hz.

But the point still stands that all you need to do is count. You count the number of peaks of a wave that pass a point, and you need no knowledge of any units of distance to perform that count. It doesn't matter whether you measure length in metres, inches, light-years or furlongs, it still takes 9 192 631 770 wave-cycles from a caesium 133 atom to define a second.

Ok, then my most recent post may well have been in error - in so much as I was thinking about the transition of an electron between states (in one shell, then in another) rather than the radiation resulting from that transition.

However, aren't you just pointing out the circularity?

We can just think about the frequency of the radiation of something remarkably stable, invert it to work out the period and then count up a number of them and say "This is the second". But then each period of the radiation relates to one wavelength (peak to peak, for example), mediated by the speed of the radiation, which is c.

So you end up without being able to express a time without reference to another time (for example a number of periods of radiation) or a length (for example the time taken for the radiation to travel far enough so that two consecutive peaks pass your measuring point); and without being able to express a distance without reference to another distance (for example a standard metre length) or a time (which is basically what the standard metre is, a distance traveled in a given time). All we seem to have left is the speed of light, and we can't even express that without reference to both a length and a time, in such a way that this value is, at the very least effectively, dimensionless because the speed of light is merely a ratio between what we use to express lengths and what we use to express times.

I become more and more persuaded that:

c = 1 fundamental unit of space / 1 fundamental unit of time

Any other value ascribed to it would represent no more than the magnitudes of the units of space and time we find convenient (noting that some find c=1 to be most convenient).

cheers,

neopolitan

 

[matheinste]

Hello DrGreg.

Thanks for pointing out the error. I had for some reason got it into my head that we could count one photon per wave period.

Matheinste.

 

[DrGreg]

neopolitan,

It's true that the caesium 133 radiation has a wavelength, but the point is that you don't need to have measured that wavelength in order to define a second. You could define your unit of length to be anything at all you liked but the second's definition would still be valid and unaltered.

In fact, you could define a metre to be 299792458/9192631770 wavelengths of caesium 133 radiation, and in some ways that would be a better definition because all you have to do is count wavelengths without needing to have a definition of time-units. This would make length "independent" of time in terms of its definition considered in isolation. Of course, considering this definition of distance and the definition of time simultaneously shows the two are linked, but logically you can arbitrarily choose either one to be independent and then the other becomes dependent.

To put it another way, you have one degree of freedom in choosing how to measure either time or distance, but once you've made that choice then the method of the other measurement is effectively fixed apart from a conversion factor c.

The spacetime view is that time and space are just different dimensions of a unified structure and c is just the conversion factor that links the two together.

 

[Chrisc]

Before this ends up in the bleachers and to ease my guilt for taking this beyond the lucidity of DaleSpam's and D H's answers (#14, #26, #55), let me attempt to redeem myself with what appears to me to be a consensus.

First a point of clarification: a, the, any "definition" of a second does not require any reference to the dimension Length.

A definition of any quantity of dimension can be expressed in two ways: as a portion or sum of some other predefined quantity of the same dimension - an hour is sixty minutes, a minute is sixty seconds, etc.- or, as a portion or sum of a physical "action" of known (experimentally verified) value which again need not have any reference to any other dimension.
For a unit Time, the latter is a repeatable, finite and extremely accurate definition when it is defined as the atomic "action" corresponding to the transition between the two hyperfine levels of the ground state of cesium 133 and the second is the sum of 9 192 631 770 periods of the radiation of this action.
It is important to note that the temporal constancy of this action is irrelevant to the "definition" of the unit second, but crucial to the validity of theory of the action.

With respect to my comments regarding a "measure" of time being a comparative measure of Length, I will give way to DrGreg's far more concise and enlightening post above regarding degrees of freedom.(#121)

Now, at the risk of this going out of the park, I will offer one more point that is crucial to understanding the role of dimensionless constants in the development of physics.
A point that comes back to the OP question regarding "Why" light or any physical constant is in fact - Constant. We can rationalize the numerical values associated with a constant and make every possible representation that proves, empirically, its constancy. But this does not answer Why.
To answer Why, we must look beyond kinematical descriptions of dimensions to dynamics. What is the dynamic law, theory or model from which constancy arises as a natural indeed necessary consequence? This is a/the fundamental quest of physics. Until a theory can "give rise" to the dimensionless constants, we are still dealing with shadows.

 

[neopolitan]

The spacetime view is that time and space are just different dimensions of a unified structure and c is just the conversion factor that links the two together.

That's the one I would go with then

cheers,

neopolitan