Arbitrary meter (metre)

[FrankM]

Tweaking the velocity of light to be 300,000,000 m/s would have made that numeric value mathematically useful. The scientists at that time did not know the numeric value for the speed of light (SOL) was important to physical law, nor did they know that electromagnetic waves existed.

 

They did know when they accepted the meter as a scientific unit of measure in 1889. They also knew that the 299792458 m/s value was a problem in equations dealing with physical law, as Stoney units were created in 1881.

 

They could have made a change back then when they first knew the numeric value for the SOL created problems in equations. We know now that energy and frequency are related, the SOL currently equates to 299,792,458 Hz, thus it would be nice to have a SOL value that is not only mathematically useful but meaningful to physical law.

[snoopy]

Tweaking the velocity of light to be 300,000,000 m/s would have made that numeric value mathematically useful. The scientists at that time did not know the numeric value for the speed of light (SOL) was important to physical law, nor did they know that electromagnetic waves existed.

 

They did know when they accepted the meter as a scientific unit of measure in 1889. They also knew that the 299792458 m/s value was a problem in equations dealing with physical law, as Stoney units were created in 1881.

 

They could have made a change back then when they first knew the numeric value for the SOL created problems in equations. We know now that energy and frequency are related, the SOL currently equates to 299,792,458 Hz, thus it would be nice to have a SOL value that is not only mathematically useful but meaningful to physical law.

 

Yeah I see where you are coming from but if aliens on a far off distant world developed physics its hardly likely to be the same exact physics that we use it is however probably going to somewhat resemble ours which I think is close enough. Our physics is necessarily built on the results of a large deal of physicists and I dont think we should just start over to get something which is mathematically cleaner, better to learn what we have and why we have the physics we have.

 

c= 299,792,458 metres per second

The value of c and its units is relatively unimportant in most equations as it is just reduced to its term c.

 

But then I think values are things just to be plugged into equations anyway and dont inrest me that much I remember equations but look values up in a book.

 

But it would be nicer to have a more rounded figure.

 

Cheers :hyper:

[Qfwfq]

Yeah it would be nice, but wouldn't make a difference to physics. Although some choices are handier, they don't change the actual physics. The numeric value of c isn't important to physical law.

[FrankM]

The physics doesn't change but it makes it difficult to identify relationships when you have a set of basic units that start with arbitrary values. A couple years ago I found a web site that explained the purpose of "natural units".

 

Natural units

 

What they are really doing is choosing a relationship between a unit of time, the second, and a unit of space, the meter, so that these two units are not independent but related.

 

From my point of view, making c=1 effectively made their unit of length the distance light travels in one second, a humongous distance. They now have c=1 and T=1 by definition. I agree it makes the numeric values related, by definition. They did not alter the duration of the second, it is still the same duration extracted from the average Ephemeris second. I suspect they would like to have identified a numeric value that results in a mutual definition but they don't know how to do it

[CraigD]

The methods used to determine the "size" of the original meter resulted in a length that can be considered somewhat arbitrary, as it wasn't exactly 1/10,000,000 the distance between the equation and the pole, this running on a line through Paris.

While the high-precision value selected for a standard meter is somewhat arbitrary and ad-hoc, I wouldn’t characterize the selection of its rough size as arbitrary: Like the Imperial/American yard, it’s about the distance covered by a human being in a single stride. I suspect that every human measurement system dating back into prehistory has a “one stride” unit of some sort, making the meter, IMHO, a very “natural” unit for everyday use.

 

Similarly, the second is roughly the duration of a single resting human heartbeat, arguably the oldest “clock tick” known to humankind.

What impact would it have had on science if the meter had been slightly shorter, and its length had accidently resulted in matching a measured speed of light value of 314159265 meters/second?

I imagine the reaction of scientists if, as better experimental measurements of the speed of light were applied to the standard meter , c in m/s was found to be begin with the digits 3, 1, 4, 1, 5, 9, and 2, would have been astonishment and wonder at a one-in-ten-million coincidence. Some might have seen it as evidence of supernatural or divine influences on human affairs, a sort of godly technical joke. I doubt any rational person would have suspected it of being planned – when the meter was being stardardized, between roughly 1790 and 1875, accepted measurements of the speed of light varied between 210,000,000 (Newton’s 1704 estimate) and 313,000,000 m/s (Fizeau’s method’s 1849 result), with the best guess consensus being about 298000000 m/s.

How would scientists have reacted if they had to use a value of c=Pi(10^8) in equations dealing with physical law?

About like they would if told they must use a value of 3 for [math]\pi[/math] – that is, they’d refuse to do so.

 

[math]314159265. 35 \not= \pi \cdot 10^8[/math]. As previous posters have noted, (though perhaps not phrased thus) a measured value can’t exactly equal a transcendental number, since one is of innately of limited precision, the other, of unlimited.

 

Even with present day technology, the speed of light - or, since the 1983 standardization of the meter in terms of the speed of light, the length of the meter – is only know to about 10 digits precision, so even if this strange coincidence had occurred, few sensible people would be confident that increasingly precise measurements would continue to generate digits of [math]\pi[/math].

 

Had such an agreement between a unit corresponding roughly to the length of a human stride, standardized by an elaborate turn-of-the-19th century French committee process, actually resulted in the unlikely matching of more than a few digits of the measure of a fundamental physical constant such as the speed of light an a unit-free mathematical one like [math]\pi[/math], I suspect that rather than seeking to adjust the standard to produce better agreement, people would have sought to adjust it worsen the agreement. In my experience, scientists and technologists are esthetically offended by coincidences with no underlying significance, and prefer to avoid them.

 

PS: Here’s a brief, un-authoritative history of the meter and the speed of light I wrote while researching this post:

-350 Aristotle publishes c=infinite

1676 Romer publishes c=226000000 m/s

1704 Newton publishes c=210000000 m/s

1728 Bradly publishes c= 298000000 m/s

1791 ADS standardizes meter

1849 Fizeau publishes c=313000000 m/s

1862 Foucault publishes c=298000000 m/s

1875 BPM produces prototype meter metal bar

1926 Michelson publishes c=299796000 m/s

1950 Essen publishes c=299792500 m/s

1983 CGPM standardizes meter s.t. c=299792458 m/s

[Qfwfq]

The physics doesn't change but it makes it difficult to identify relationships when you have a set of basic units that start with arbitrary values.

Sorry but I utterly fail to get your point here... what difficulty and for what cause? Just in case you only mean the obvious practical matter, yes it would be impractical for housewives to by tomatoes by the eV but it would be just as impractical for particle physicists to discuss the mass of a hadron in kg or even in grammes. Suppose you are dealing the purchase of a large roll of copper wire for telephony purposes, do you discuss the length and the diameter in the same units? Well, technically you might talk about the cross-section as a gauge but you know what I mean. Of course for spacelike lengths in SI the "different" units are really just neat powers of ten, but using different names is handier.

 

From my point of view, making c=1 effectively made their unit of length the distance light travels in one second, a humongous distance.

Not humongous for astronomers, to them it's actually very short. OTOH a second is a humongous time duration in describing particle collisions, even more humongous than a millimetre of length. In applications at our physiological scales, when c is important it is a large quantity, this is simply because we're not optoelectronic devices and this is the only practical reason for our choice of "ordinary" units for length and time. Unlike in the above example about copper wire, we don't even perceive these as both being lengths, just in different directions.

 

I suspect they would like to have identified a numeric value that results in a mutual definition but they don't know how to do it

I struggle here too, I don't see a nexus between choice of a numeric value and there being a mutual definition. It's obvious to me that either one (length or time) can define the other, but it's aut-aut, they can't both define each other.

 

About like they would if told they must use a value of 3 for [math]pi[/math] – that is, they’d refuse to do so.

I see your point in a sense but agree only partly and, reasoning in the hypothetical case, I disagree totally. Considering the case in which the metre had been defined, without concern of backward compatibility, to the purpose it would not be like equating [imath]\pi[/imath] with 3 at all. The value of c would be that set by the definition and no other, whether rational (as by the current definition), irrational or transcendental. For particle physicists who use Natural units, Planck's constant is equal to exactly [imath]2\pi[/imath] and no other value. It would therefore be similar if, (very) hypothetically, c were determinable only as [imath]\pi\chi[/imath] with [imath]\chi[/imath] being some easily observable velocity (and c remaining the fundamental one).

 

Where I agree only partly is:

[math]314159265. 35 not= pi cdot 10^8[/math]. As previous posters have noted, (though perhaps not phrased thus) a measured value can’t exactly equal a transcendental number, since one is of innately of limited precision, the other, of unlimited.

 

Even with present day technology, the speed of light - or, since the 1983 standardization of the meter in terms of the speed of light, the length of the meter – is only know to about 10 digits precision, so even if this strange coincidence had occurred, few sensible people would be confident that increasingly precise measurements would continue to generate digits of [math]pi[/math].

and I think this shows where you misunderstand me, almost certainly because I failed to stress the essential. :doh: Anyway in making the remark about 'since 1983' you miss that it isn't the determination of a number (except in expressing its ratio to other lengths of independent definition) but this isn't the real essence.

 

The direct result of a measurement can't be an irrational number, let alone transcendental. True, and let's neglect the matter of when the value of interest is being measured indirectly i. e. calculated from a direct result. What I failed to stress is that this goes for the single measurement, and for each next and more precise one and I agree up to here, but the limit of a Cauchy sequence of rational values can be irrational and even transcendental. In fact more of them have irrational limits than rational, the ratio being the cardinality of [imath]\mathbb{R}[/imath]; it quite simply follows from how [imath]\mathbb{R}[/imath] can be constructed from [imath]\mathbb{Q}[/imath] (topological completion).

 

Now I'd say that NO sensible people would be confident that increasingly precise measurements would continue to generate digits of [math]\pi[/math] in the pure coincidence case and as long as independent definitions were kept (while no sensible people would have any doubt when it is by definition). In the independent case, what prevents the expectation of a transcendental or any rational value in the ultimate limit is the implausibility of both units being defined with no uncertainty themselves. As I pointed out above (and previously), the uncertainty inherent in each unit's definition is not a numerical one (the quantity itself, not the measure of it), however it leads to one in the ratio between the quantities defined.

 

Therefore, if we keep the krypton definition of the metre and the caesium one for the second, the numerical value of c would in fact be defined no more precisely than these (Even in ideal conditions, the spectral lines are a distribution.) and so the numerical "value" in question would still be a distribution; it would comprise infinitely many rational numbers and even more infinitely many irrational ones and transcendental ones too. In short, NO sensible people would be confident that the ultimate number would be irrational, but also NO sensible people would be confident that it would be rational either.

 

This discussion has reminded me of a guy at physics back when we were both students. He was laughing at his juvenile misguidedness and telling us of when he couldn't get over the paradox of Avogadro's number not being integer, despite it being a number of indivisible objects by definition. It was a while later he realized that, when you multiply the mantissa by the power of ten, all those digits in the textbook are no longer after the decimal point. :lol: Very naïve indeed! However I soon realized that, with the kilogram defined independently of a carbon 12 atom's mass, it is still wrong (perhaps only a bit less naïve) to expect it must be an integer and even that it must be rational.

 

The conflict with the fact that the definition's wording suggests an integer number could be lousily patched by changing "as many elementary entities as there are atoms in 0.012 kilogram (or 12 grams) of carbon-12" into "as many elementary entities as the greatest number of carbon-12 atoms which do not exceed 0.012 kilogram (or 12 grams)"; I however would modestly propose a different solution with much greater advantage. Since mass units are still defined by the old piece of platinum-iridium locked up at Sèvres, I would re-define the gramme in terms of the mass of carbon 12 according to the best current determination of Avogadro's number or, better, the handiest choice that wouldn't break backward compatibility.

 

Actually, after looking up the definition, I'm somewhat surprised no one has already thought of this and before hitting the submit button I took the time out to look up contacts of the CIPM and I submitted my suggestion just in time for the next meeting (from 7th to 9th of November 2007). You never know, they might consider it. :D

[FrankM]

The CODATA Task Group on Fundamental Constants has its own views on how the base units of measures should be defined.

• the importance of the fundamental constants to the scientific community because of their role in relating different branches of pure and applied science,

 

• the importance of defining the base units of the SI in terms of invariant physical quantities, and

 

• the significant reduction in uncertainty associated with the values of many fundamental constants that would occur if the Planck constant, the elementary charge, and the Boltzmann constant were to have exact values,

 

CODATA, The Committee on Data for Science and Technology

 

Based upon the above considerations, I have difficulty justifying a scientific unit of measure as being something that must be convenient to "everyday human use". It seems everybody has been culturally conditioned to accept that a single set of units should serve scientific and everyday commercial and people usage. We already know that specific scientific disciplines have their own units as do various trades. Why not have a separate set of units for scientific usage? The metric system was originally structured to facilitate trade and still be people friendly, they can keep SI units.

 

I struggle here too, I don't see a nexus between choice of a numeric value and there being a mutual definition. It's obvious to me that either one (length or time) can define the other, but it's aut-aut, they can't both define each other.

 

I have held that opinion myself until I found I was wrong, length and time can mutually define each other. Length is now defined in relationship to the velocity of light, an electromagnetic phenomenon, using a predefined duration of time. Length and time have a natural relationship within electromagnetic phenomenon, but we do not exploit the relationship to allow it to mutually define each other.

[Qfwfq]

We already know that specific scientific disciplines have their own units as do various trades.

Certainly, and eV is an excellent basis for the HEP crowd, while working out the phenomenology, but they need to relate it to SI units as well.

 

I have held that opinion myself until I found I was wrong, length and time can mutually define each other. Length is now defined in relationship to the velocity of light, an electromagnetic phenomenon, using a predefined duration of time. Length and time have a natural relationship within electromagnetic phenomenon, but we do not exploit the relationship to allow it to mutually define each other.

It seems we're still shouting from opposite sides of a busy highway.

 

I previously mentioned the fact that SI currently defines the metre as a unit derived from the second via c which therefore assumes an exact value by definition in these units, but I don't call this mutual, it's only one that defines the other. It couldn't be both ways at once; that's what I said yesterday. An experimental determination of c may only tell us the ratio between the length and time employed, therefore it can be used to derive only one unit from the other.

 

BTW I don't consider the natural relationship as being within electromagnetic phenomena, it's more fundamentally the way space-time is; photons are just the most convenient physical instrument for the determination.

[FrankM]

One of the contentions I am presenting is that the speed of light can be any value we want it to be, this dependent upon the "size" of the units we use to define its parameters, length and time.

 

CraigD present a succinct history of the measurement of the SOL but he converted all values into meters. The meter did not exist officially until 1799 and it was not used consistently in the scientific community until the 20th century. This conversion to meters distorts the history of its "numeric value", it changes radically depending on the units used.

 

Velocity of light Roemer

 

It couldn't be both ways at once; that's what I said yesterday.

 

And I stated that I was proven wrong, length and time (the duration) can be mutually defined when those parameters are expressed relative to the known characteristics of electromagnetic phenomenon.

 

Certainly, and eV is an excellent basis for the HEP crowd, while working out the phenomenology, but they need to relate it to SI units as well.

Perhaps SI units should be forceably dragged into the 21 century.

 

Astronomers also use "Eddington units" and I do not read of any attempts they are trying to define them to the Candela.

[Qfwfq]

One of the contentions I am presenting is that the speed of light can be any value we want it to be, this dependent upon the "size" of the units we use to define its parameters, length and time.

That's what I was saying, except that the same goes for the tangent of the bisector of the cartesian axes, by choosing different scales for one and the other. In the case of space-time, the ratio between these two scales in SI is exactly 299,792,458 by definition.

 

length and time (the duration) can be mutually defined when those parameters are expressed relative to the known characteristics of electromagnetic phenomenon.

I don't see how. :phones:

[FrankM]

I don't see how.

 

We apply what we already know. The physical size, scaled or unscaled, of the intrinsic wavelength is not known until we compare it to a physical scale that is familiar. I could have used inches rather than centimeters, it just has to be a length we can relate to.

 

http://vip.ocsnet.net/~ancient/Speed_of_Light_Derivation.pdf

[FrankM]

The scientific community should not be shackled to what appeared to be appropriate unit "sizes" for universal use some 200 years ago. The people that created the meter did not know about electromagnetic waves, thus they had no knowledge of how the numeric value of its propagation speed would effect the study of physical law or the structure of a set of base units.

 

http://vip.ocsnet.net/~ancient/Speed_of_Light_Derivation.pdf

 

I did not choose where the "intrinsic wavelength" came from. Is it a quirk of the mathematical relationship or a fundamental characteristic of physical law? At the moment, for lack of a better term, I refer to it as the "neutral hydrogen paradox".

[FrankM]

Non-arbitrary means something is "not subject to individual determination". It seems a given that this definition is equally applicable to the subject of dimensions.

 

When two dimensions are determined by geometric relationships that exploit physical law are they arbitrary or non-arbitrary?