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 Tags gravitational constant , irrational numbers , plank's constant

 7th May 2012, 09:31 PM #1 Magic Pancake New Blood   Join Date: Mar 2009 Posts: 5 Are physical constants irrational? Well, as the title asks, are the physical constants of the universe (such as plank's constant or the gravitational constant) rational or irrational numbers? I sure can't see a ready fraction in any of them, but then again these numbers are determined experimentally, so how can you tell for sure. How about the universe itself? Is there a countable number of states for it?As a layman I understand that units of dimensions in the universe are quantified in various Plank units, so that would seem to say that these must be countable, but is this the case? (Sorry if I mutilated some concepts.)
 7th May 2012, 09:45 PM #2 Dr. Trintignant Muse     Join Date: Mar 2007 Posts: 745 Eddington thought the fine structure constant was 1/136. Later, he changed his mind to 1/137. Both are wrong. The short answer is that we don't know, and probably never will. Any number with a non-zero error bound can be approximated with a rational number, and most likely we'll never figure out what the physical constants are from first principles--only by imprecise measurements. They certainly "look" irrational, but that's infinitely far away from knowing that they're irrational.
 7th May 2012, 10:13 PM #3 WhatRoughBeast Muse   Join Date: Apr 2011 Posts: 894 Originally Posted by Magic Pancake Well, as the title asks, are the physical constants of the universe (such as plank's constant or the gravitational constant) rational or irrational numbers? I sure can't see a ready fraction in any of them, but then again these numbers are determined experimentally, so how can you tell for sure. Almost certainly. The thing is, their specific values are expressed in terms of units which are historical accidents, and (at least in terms of details) essentially random. Consider Planck's constant. Here is a quantity which, however fundamental, is expressed in units of J-s, or alternatively, kg-m^2/sec. Look up the historical foundations of each of the 3 units. Meter: based on the then-current understanding of the size of the earth. Kilogram: originally based on the meter (1 gram = 1 cc of water at triple point). Second: 1 sidereal day divided by (24 x 3600). With units this arbitrary (from a universal perspective), why would you expect the numeric values of any fundamental constant to be other than essentially arbitrary? And since there are infinitely more irrational numbers than there are rational ones, well, you do the math. The fine constant, of course, is the unitless joker, and it's anybody's guess how that one will turn out.
 7th May 2012, 10:21 PM #4 Magic Pancake New Blood   Join Date: Mar 2009 Posts: 5 Originally Posted by WhatRoughBeast Almost certainly. The thing is, their specific values are expressed in terms of units which are historical accidents, and (at least in terms of details) essentially random. Consider Planck's constant. Here is a quantity which, however fundamental, is expressed in units of J-s, or alternatively, kg-m^2/sec. Look up the historical foundations of each of the 3 units. Meter: based on the then-current understanding of the size of the earth. Kilogram: originally based on the meter (1 gram = 1 cc of water at triple point). Second: 1 sidereal day divided by (24 x 3600). With units this arbitrary (from a universal perspective), why would you expect the numeric values of any fundamental constant to be other than essentially arbitrary? And since there are infinitely more irrational numbers than there are rational ones, well, you do the math. The fine constant, of course, is the unitless joker, and it's anybody's guess how that one will turn out. If the physical constants are rational, wouldn't it imply that the SI units, no matter how arbitrarily chosen, are multiples of them?
 7th May 2012, 10:42 PM #5 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,910 Why would one expect the fundamental constants to be rational any more than one would expect the ratio of the circumference to the diameter of a circle be rational? __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ
 8th May 2012, 12:06 AM #6 Modified Illuminator     Join Date: Sep 2006 Location: SW Florida Posts: 4,099 Plank units turn a bunch of physical constants into rational numbers (1s).
 8th May 2012, 12:49 AM #7 shadron Philosopher     Join Date: Sep 2005 Location: Colorado Posts: 5,791 Originally Posted by Perpetual Student Why would one expect the fundamental constants to be rational any more than one would expect the ratio of the circumference to the diameter of a circle be rational? On the other hand, why not? Is there some imbalance in the number of rational vs irrational numbers in the universe? What difference does it make to, say, the Plank constant that we happen to know pi is irrational?
 8th May 2012, 01:35 AM #8 supaluminal Scholar     Join Date: Oct 2011 Location: At the molecular level Posts: 84 Originally Posted by shadron On the other hand, why not? Is there some imbalance in the number of rational vs irrational numbers in the universe? What difference does it make to, say, the Plank constant that we happen to know pi is irrational? well, rational numebrs are countably infinite, irrational numbers are uncountably infinite, so from that alone, we shouldn't expect that there should be a bias towards rational numbers.
 8th May 2012, 03:23 AM #9 xtifr Muse     Join Date: Apr 2012 Location: Sol III Posts: 766 Originally Posted by supaluminal well, rational numebrs are countably infinite, irrational numbers are uncountably infinite, so from that alone, we shouldn't expect that there should be a bias towards rational numbers. If you're going to test that theory, don't forget to account for the aleph-null hypothesis! __________________ "Those who learn from history are doomed to watch others repeat it." -- Anonymous Slashdot poster "The problem with defending the purity of the English language is that English is about as pure as a cribhouse whore." -- James Nicoll
 8th May 2012, 06:00 AM #10 Beerina Sarcastic Conqueror of Notions     Join Date: Mar 2004 Location: A floating island above the clouds Posts: 23,838 Even the irrationals can be separated into those which have a formula and those which don't. All the integers and rational numbers, and all the irrationals with a formula (which are enumerable) are an infinitely tiny set compared to all the irrationals without any possible formula. __________________ "Great innovations should not be forced [by way of] slender majorities." - Thomas Jefferson The government should nationalize it! Socialized, single-payer video game development and sales now! More, cheaper, better games, right? Right?
 8th May 2012, 06:13 AM #11 bjornart Master Poster     Join Date: Nov 2002 Posts: 2,453 No, they're not. The speed of light, for instance, is one. __________________ Well, I DON'T CARE WHAT YOU LIKE TO BELIEVE, GODDAMMIT! I DEAL IN THE FACTS! -Cecil Adams
 8th May 2012, 07:11 AM #12 Farsight Master Poster   Join Date: Mar 2008 Location: Poole, UK Posts: 2,189 Originally Posted by Magic Pancake Well, as the title asks, are the physical constants of the universe (such as plank's constant or the gravitational constant) rational or irrational numbers? Neither. See for example the NIST page on the fine structure constant. See the bit that says this: Thus α depends upon the energy at which it is measured, increasing with increasing energy, and is considered an effective or running coupling constant. Indeed, due to e+e- and other vacuum polarization processes, at an energy corresponding to the mass of the W boson (approximately 81 GeV, equivalent to a distance of approximately 2 x 10^-18 m), α(mW) is approximately 1/128 compared with its zero-energy value of approximately 1/137. Thus the famous number 1/137 is not unique or especially fundamental. It's a "running" constant, which means it varies. So it's neither rational nor irrational. It's often given as α = e²/2ε0hc, where e is the charge of the electron, ε0 is the permittivity of space, h is Planck's constant, and c is the speed of light. The e is described on the NIST website and elsewhere as "effective charge", but IMHO one should bear in mind conservation of charge. The effect of the electron's unit charge e might vary, but charge is conserved. So if α varies and e doesn't, that means ε0 and/or h and/or c vary too. You tend not to hear much about this sort of thing, but see this IOP physicsworld article Can GPS find variations in Planck's constant? Sadly what you do get to hear about is the "fine tuned" constants and the Goldilocks anthropic multiverse, which is woo.
 8th May 2012, 08:18 AM #13 Tubbythin Illuminator   Join Date: Mar 2008 Posts: 3,206 Originally Posted by Farsight Neither. See for example the NIST page on the fine structure constant. See the bit that says this: Thus α depends upon the energy at which it is measured, increasing with increasing energy, and is considered an effective or running coupling constant. Indeed, due to e+e- and other vacuum polarization processes, at an energy corresponding to the mass of the W boson (approximately 81 GeV, equivalent to a distance of approximately 2 x 10^-18 m), α(mW) is approximately 1/128 compared with its zero-energy value of approximately 1/137. Thus the famous number 1/137 is not unique or especially fundamental. It's a "running" constant, which means it varies. So it's neither rational nor irrational. It's often given as α = e²/2ε0hc, where e is the charge of the electron, ε0 is the permittivity of space, h is Planck's constant, and c is the speed of light. The e is described on the NIST website and elsewhere as "effective charge", but IMHO one should bear in mind conservation of charge. The effect of the electron's unit charge e might vary, but charge is conserved. So if α varies and e doesn't, that means ε0 and/or h and/or c vary too. You tend not to hear much about this sort of thing, but see this IOP physicsworld article Can GPS find variations in Planck's constant? Doesn't mean it can't be rational or irrational, just because it isn't actually a constant. Quote: Sadly what you do get to hear about is the "fine tuned" constants and the Goldilocks anthropic multiverse, which is woo. No it isn't. Its speculative.
 8th May 2012, 09:33 AM #14 edd Graduate Poster     Join Date: Nov 2007 Posts: 1,767 Originally Posted by Tubbythin Doesn't mean it can't be rational or irrational, just because it isn't actually a constant. Not sure I follow you there Tubbythin, but it certainly doesn't change that the zero energy value is well defined as a single number and it seems to me that it's a valid question to ask about that number. __________________ When I look up at the night sky and think about the billions of stars out there, I think to myself: I'm amazing. - Peter Serafinowicz
 8th May 2012, 09:52 AM #15 Tubbythin Illuminator   Join Date: Mar 2008 Posts: 3,206 Originally Posted by edd Not sure I follow you there Tubbythin, but it certainly doesn't change that the zero energy value is well defined as a single number and it seems to me that it's a valid question to ask about that number. I'm not sure I follow you, in turn. I was saying that just because the fine structure constant may not be a constant, doesn't meant that we it is necessarily impossible to say whether or not it is (ir)rational (in principle).
 8th May 2012, 09:53 AM #16 TubbaBlubba Knave of the Dudes     Join Date: Jul 2010 Location: Communist Kingdom of Sweden Posts: 7,994 All fundamental physical constants are equal to one. __________________ There are two kinds of fact - the trivially true, and the technically correct.
 8th May 2012, 10:20 AM #17 phunk Master Poster     Join Date: Aug 2007 Posts: 2,219 Originally Posted by bjornart No, they're not. The speed of light, for instance, is one. I think it only really matters for unitless constants. Anything with a unit can be defined as 1.
 8th May 2012, 10:28 AM #18 TubbaBlubba Knave of the Dudes     Join Date: Jul 2010 Location: Communist Kingdom of Sweden Posts: 7,994 Originally Posted by phunk I think it only really matters for unitless constants. Anything with a unit can be defined as 1. Yeah, there are those unitless buggers. __________________ There are two kinds of fact - the trivially true, and the technically correct.
 8th May 2012, 10:28 AM #19 ehcks Master Poster   Join Date: Feb 2011 Posts: 2,025 Does it really matter if they're rational numbers in base 10 SI units? __________________ Never attribute to malice that which is adequately explained by stupidity. http://en.wikipedia.org/wiki/Hanlon%27s_razor
 8th May 2012, 10:30 AM #20 TubbaBlubba Knave of the Dudes     Join Date: Jul 2010 Location: Communist Kingdom of Sweden Posts: 7,994 Originally Posted by ehcks Does it really matter if they're rational numbers in base 10 SI units? The unitless bastards are the same in any system of units, and irrational numbers are irrational in all bases, AFAIK. __________________ There are two kinds of fact - the trivially true, and the technically correct.
 8th May 2012, 10:33 AM #21 davefoc Philosopher     Join Date: Jun 2002 Location: orange country, california Posts: 7,732 Originally Posted by WhatRoughBeast Almost certainly. The thing is, their specific values are expressed in terms of units which are historical accidents, and (at least in terms of details) essentially random. Consider Planck's constant. Here is a quantity which, however fundamental, is expressed in units of J-s, or alternatively, kg-m^2/sec. Look up the historical foundations of each of the 3 units. Meter: based on the then-current understanding of the size of the earth. Kilogram: originally based on the meter (1 gram = 1 cc of water at triple point). Second: 1 sidereal day divided by (24 x 3600). With units this arbitrary (from a universal perspective), why would you expect the numeric values of any fundamental constant to be other than essentially arbitrary? And since there are infinitely more irrational numbers than there are rational ones, well, you do the math. The fine constant, of course, is the unitless joker, and it's anybody's guess how that one will turn out. I think there is a fundamental logic error here. If a physical constant is rational it will be rational regardless of what units it is expressed in as long as the units are rational. If the mass of an electron is a rational number if is measured in grams it will be a rational number if it is measured in troy ounces. Are at least some ratio type constants guaranteed to be a rational number, for instance the ratio between the mass of an electron and the mass of a proton? __________________ The way of truth is along the path of intellectual sincerity. -- Henry S. Pritchett Perfection is the enemy of good enough -- Russian proverb
 8th May 2012, 10:38 AM #22 ben m Philosopher   Join Date: Jul 2006 Posts: 5,065 I don't think it's reasonable to label a physical constant rational or irrational. The rational/irrational distinction is, in some sense, a statement about the infinite decimal expansion---if it eventually repeats forever, it's a rational number. If it doesn't, it's irrational. 1 + pi*10^(-10^(10^(10^1000000000000000))) is irrational, even though the non-repeating-zeroes behavior only shows up in the gazillionth digit. What's the difference between a world in which "e" is really precisely 1.6*10^-19 (rational), and a world in which it's 1.6*10^-19*(1 + pi*10^(-10^(10^(10^1000000000000000))) ) (irrational)? Postulate some counting experiment. In the former case, this experiment expects N counts, and in the latter case it expects N+1 counts. You can only distinguish these values of "e" if the rational/irrational distinction begins being visible at the log10(N)-th digit. But there's an upper bound on N---the visible Universe has a finite Bekenstein-Hawking entropy. You can't even imagine an experiment with a one count sensitivity to the "infinite" decimal expansion, because it would take all of the energy in the Universe to care about the Nth digit (for some large but finite N). So, no, I don't think there is any physical meaning to the 10^100th (much less the infinite-th) digit of e, or h-bar, or alpha, so I don't think there is any sense in labeling these numbers as rational or irrational.
 8th May 2012, 11:01 AM #23 Ryan O'Dine OD’ing on Damitol     Join Date: Nov 2004 Location: Walk in an ever expanding Archimedean spiral and you’ll find me eventually Posts: 1,185 Originally Posted by Magic Pancake ...snip... How about the universe itself? Is there a countable number of states for it?As a layman I understand that units of dimensions in the universe are quantified in various Plank units, so that would seem to say that these must be countable, but is this the case? I'm in the middle of Brian Greene's latest The Hidden Reality, which addresses your second paragraph. Here's a quote: Originally Posted by Brian Greene ...the number of distinct possible particle configurations within a cosmic horizon is about 1010122 (a one followed by 10122 zeros). This is a huge but decidedly finite number. -- p.33 -- So within the region of the universe that could possibly affect you, there are indeed a finite number of possible configurations, or "a countable number of states," in your phrasing. __________________ I collect people like you in little formaldehyde bottles in my basement. (Not a threat. A hobby.) Last edited by Ryan O'Dine; 8th May 2012 at 11:12 AM. Reason: typo
 8th May 2012, 11:37 AM #24 Tubbythin Illuminator   Join Date: Mar 2008 Posts: 3,206 Originally Posted by TubbaBlubba The unitless bastards are the same in any system of units, and irrational numbers are irrational in all bases, AFAIK. I suppose you could use base pi, then pi would be rational in that base. So I'm guessing irrational numbers are irrational in all rational bases only. But I am guessing.
 8th May 2012, 11:41 AM #25 TubbaBlubba Knave of the Dudes     Join Date: Jul 2010 Location: Communist Kingdom of Sweden Posts: 7,994 Originally Posted by Tubbythin I suppose you could use base pi I'm not sure what base pi even means. Do you count 0, 1, 2, .1415... or what? Is "base" even defined for irrational numbers? __________________ There are two kinds of fact - the trivially true, and the technically correct.
 8th May 2012, 12:10 PM #26 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,910 Some of this stuff is just plain silly. The concept of base is defined only for integers. If a number is irrational it is irrational; base has no bearing of the meaning of irrational or rational regarding numbers. But many of the comments here are certainly irrational. __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ
 8th May 2012, 12:39 PM #28 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 27,150 Originally Posted by Tubbythin I suppose you could use base pi, then pi would be rational in that base. The "base" of a number system is a method of representing numbers with symbols. But it only applies to a certain category of number representation (Roman numerals don't have a "base"), and it is currently by definition integer only. If you want to introduce the concept of non-integer base, you need to define what you even mean by that, and I know of nobody who has done so in any sort of coherent form. But even if one did, that would not make pi rational. Rationality is not determined by the compactness of a representation. One can easily form representations in which some irrational numbers have compact representations and integers have infinitely long representations (for example, just rescale: use a standard integer "base" but have the symbols represent multiples of an irrational number rather than integers), but doing so does nothing to change the actual nature of the numbers themselves. We chose our number system because it has a simple representation of integers, they aren't integers because they have a simple representation in our number system. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 8th May 2012, 01:29 PM #29 Tubbythin Illuminator   Join Date: Mar 2008 Posts: 3,206 Originally Posted by Ziggurat The "base" of a number system is a method of representing numbers with symbols. But it only applies to a certain category of number representation (Roman numerals don't have a "base"), and it is currently by definition integer only. If you want to introduce the concept of non-integer base, you need to define what you even mean by that, and I know of nobody who has done so in any sort of coherent form. Wikipedia has some stuff on the idea. Whether it has a consistent form or not is another matter. Quote: But even if one did, that would not make pi rational. Rationality is not determined by the compactness of a representation. One can easily form representations in which some irrational numbers have compact representations and integers have infinitely long representations (for example, just rescale: use a standard integer "base" but have the symbols represent multiples of an irrational number rather than integers), but doing so does nothing to change the actual nature of the numbers themselves. We chose our number system because it has a simple representation of integers, they aren't integers because they have a simple representation in our number system. Point taken.
 8th May 2012, 03:30 PM #30 Modified Illuminator     Join Date: Sep 2006 Location: SW Florida Posts: 4,099 Originally Posted by Ziggurat One can pick units for which some constants are rational numbers. But even if one were to do this, some of them still must be irrational. For example, with the right set of units one could make hbar a rational number. But then h would necessarily be irrational. Conversely, if one makes h rational, then hbar must be irrational. Same thing for k and epsilon (two different forms of the constant for Coulomb's law): they're related by irrational numbers, so they cannot both be rational (but they can both be irrational). What if we allow irrational terms that can be determined to any desired precision mathematically (pi, etc.)? In other words, using the "best" base units possible (plank units?), how many physical constants can not be represented as equations involving only rational numbers and mathematical constants?
 8th May 2012, 04:19 PM #31 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 27,150 Originally Posted by Modified What if we allow irrational terms that can be determined to any desired precision mathematically (pi, etc.)? In other words, using the "best" base units possible (plank units?), how many physical constants can not be represented as equations involving only rational numbers and mathematical constants? Given that the Planck scales are basically just ratios of other constants, if we used them as our units, that would guarantee that those specific constants would end up rational. But we have no reason to think that other constants (for example, the electron mass) would turn out to be rational in such units. And given the infinity of rational numbers, it's impossible to prove that one cannot do so. But we do know that you can't express all constants as an integer multiple of such scales. The Planck mass, for example, is far larger than any particle mass, so it would have to be a fraction of the Planck mass. We don't have infinite precision on the mass of an electron, so one could always find a rational fraction (actually, an infinitude of rational fractions) within our uncertainty, but that doesn't really demonstrate anything. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 8th May 2012, 05:18 PM #32 Beerina Sarcastic Conqueror of Notions     Join Date: Mar 2004 Location: A floating island above the clouds Posts: 23,838 Originally Posted by davefoc I think there is a fundamental logic error here. If a physical constant is rational it will be rational regardless of what units it is expressed in as long as the units are rational. If the mass of an electron is a rational number if is measured in grams it will be a rational number if it is measured in troy ounces. Hmmmm. Are ounces and grams relatively rational? I suppose if they're both ultimately derived from a rational multiple of the same base unit, like mass equivalent of energy transitions of some electron, then obviously. __________________ "Great innovations should not be forced [by way of] slender majorities." - Thomas Jefferson The government should nationalize it! Socialized, single-payer video game development and sales now! More, cheaper, better games, right? Right? Last edited by Beerina; 8th May 2012 at 05:19 PM.
 8th May 2012, 06:34 PM #33 Dr. Trintignant Muse     Join Date: Mar 2007 Posts: 745 Originally Posted by ben m So, no, I don't think there is any physical meaning to the 10^100th (much less the infinite-th) digit of e, or h-bar, or alpha, so I don't think there is any sense in labeling these numbers as rational or irrational. It's at least conceivable, if not very likely, that some of the unitless constants will turn out have a computable value based on theoretical calculations, and from that we can decide if the number is rational or not. The googolth digit of pi is also totally irrelevant to our universe, but nevertheless we know it's transcendental. Last edited by Dr. Trintignant; 8th May 2012 at 06:36 PM.
 8th May 2012, 06:42 PM #34 Dr. Trintignant Muse     Join Date: Mar 2007 Posts: 745 Originally Posted by Beerina Hmmmm. Are ounces and grams relatively rational? I suppose if they're both ultimately derived from a rational multiple of the same base unit, like mass equivalent of energy transitions of some electron, then obviously. Most (all?) of the common customary units are currently defined as a rational multiple of metric units. The avoirdupois ounce is exactly 28.349523125 g.
 8th May 2012, 06:48 PM #35 mijopaalmc Philosopher   Join Date: Mar 2007 Posts: 5,512 If physical constants are derived by their relation to physical object and spacetime is quantized, physical constants are rational. Their mathematical abstractions, however, aren't.
 8th May 2012, 09:40 PM #36 WhatRoughBeast Muse   Join Date: Apr 2011 Posts: 894 The question is unanswerable, and the reason can be summed up in two words: experimental error. We only know the value of fundamental constants, regardless of numeric base, through experiment, and all experimental results have some range of uncertainty, Therefor, any ratio of two fundamental constants will also have a range of uncertainty. Within this range there are an infinite number of possible rational values, and an infinitely larger number of irrational possibilities.
 9th May 2012, 01:13 AM #37 nathan Zygoticly Phased     Join Date: Nov 2004 Location: Arkham City Posts: 3,255 Originally Posted by Dr. Trintignant Most (all?) of the common customary units are currently defined as a rational multiple of metric units. The avoirdupois ounce is exactly 28.349523125 g. Right, but that's been achieved by (a) measurement and (b) changing the definition of the non-metric unit. There's plenty of opportunity for an irrational number to hide in the (impossible to measure exactly in new units) original definition. For instance, an inch used to have some funky definition that was very nearly but not quite 25.4mm, but then its definition was changed to be exactly 25.4mm. Even the metric definitions are mutable. It used to be that the metre was so many wavelengths of a certain kind of light, (after it stopped being the length of a specific lump of metal) now its a specific fraction of how far light goes in 1 second. Those aren't exactly the same. The speed of light had an error range when measured using the wavelength definition. The new definition simply decreed that error range to be zero. __________________ Crank works have one advantage: they don't really lose anything in translation. Skeptic That's the beauty of Paranormal claims - there are no failures, only newly discovered restrictions on the ability. Ashles
 9th May 2012, 04:18 AM #38 WhatRoughBeast Muse   Join Date: Apr 2011 Posts: 894 Originally Posted by nathan The speed of light had an error range when measured using the wavelength definition. The new definition simply decreed that error range to be zero. Really? And how, exactly, does one measure a time duration of one second with zero uncertainty? I don't mean "to very high precision", I mean zero uncertainty.
 9th May 2012, 04:38 AM #39 TubbaBlubba Knave of the Dudes     Join Date: Jul 2010 Location: Communist Kingdom of Sweden Posts: 7,994 Originally Posted by WhatRoughBeast Really? And how, exactly, does one measure a time duration of one second with zero uncertainty? I don't mean "to very high precision", I mean zero uncertainty. It's not measured, it's defined. If a second is measured to be longer, the meter is longer. __________________ There are two kinds of fact - the trivially true, and the technically correct.
 9th May 2012, 04:48 AM #40 nathan Zygoticly Phased     Join Date: Nov 2004 Location: Arkham City Posts: 3,255 Originally Posted by WhatRoughBeast Really? And how, exactly, does one measure a time duration of one second with zero uncertainty? I don't mean "to very high precision", I mean zero uncertainty. I think you're confusing the definition of a unit with producing a physical example of that unit. The definition of a metre really is what I said it is -- an exact fraction of the speed of light. Now to go and produce an example metre, you'd need to measure the speed of light, and that means accurate timing. That timing will have an error range associated with it, so your example metre will have an error range. My Science Data Book (first published 1971) gives c as 2.997924590(8) 108 m s-1. That '(8)' is the +/- uncertainty in the final digit. The metre definition is given as 1650763.73 wavelengths in vacuo of the orange light emitted by 86Kr in the transition from 2p10 to 5d5. You'll see that wavelength count is given to 1 part in 108 and c has an error of about 1 in 108. So at that point, they were kind-of equally accurate. The definition was changed because it's easier to measure the speed of light with current technology to equal or greater accuracy than it is to count the wavelengths needed by the earlier definition (it happens to be much simpler to state too). The current value for c is defined to be 2.99792458 108 m s-1 *exactly*. Does that help? NB If you go and look at the definitions for the SI fundamental units, you'll see all but one are in terms of measurements you can make some specified physical system. The Kg is the only one that's still defined in terms of a unique physical object. There are efforts to redefine the Kg in terms of things like 'number of atoms of Si', but that involves determining how to count 10^23 atoms. I'm not sure how successful those attempts currently are. __________________ Crank works have one advantage: they don't really lose anything in translation. Skeptic That's the beauty of Paranormal claims - there are no failures, only newly discovered restrictions on the ability. Ashles Last edited by nathan; 9th May 2012 at 04:50 AM.

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