Are physical constants irrational? - Page 2

Beerina · 9th May 2012, 05:19 AM

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?

This. Unless they are derived from the same thing in a roundabout way, two random irrationals are almost certainly relatively irrational to each other.

Of course, this also assumes that a fine enough measurement of the universe will yield an irrational constant, no matter how closely you measure. Perhaps the universe isn't "fine grained" beyond what rationals could cover. Then the constants need only be rational at most, and thus are relatively rational to each other.

TubbaBlubba · 9th May 2012, 06:22 AM

Originally Posted by nathan

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.

What about one cubic decimetre of water?

edd · 9th May 2012, 06:42 AM

Originally Posted by TubbaBlubba

What about one cubic decimetre of water?

Too difficult to get it accurate enough. I expect you have to worry about an awful lot more than with a standard lump of platinum-iridium or silicon - you have to get the temperature and pressure spot on, have to have it very chemically pure, very isotopically pure and have no dissolved gases and so on, and once you've got such a sample it will deteriorate a lot faster in purity than your solid kg and can't be cleaned anything like as easily.

Ziggurat · 9th May 2012, 08:08 AM

Originally Posted by Beerina

Hmmmm. Are ounces and grams relatively rational?

They are now. NIST, for example, actually defines units like ounces and inches as rational fractions of their SI counterparts. If one were to construct an independent set of definitions (for example, using a different object to define your standard pound), that probably wouldn't be the case, but it's simpler to do it this way. So 1 avoirdupois pound = 0.45359237 kilogram, by definition (at least in the US). That's not a pretty rational number, but it is rational.

nathan · 9th May 2012, 10:10 AM

Originally Posted by TubbaBlubba

What about one cubic decimetre of water?

Is that a serious question? That definition proved to be insufficiently precise, hence the move the the platinum-iridium cylinder.

TubbaBlubba · 9th May 2012, 10:46 AM

Originally Posted by nathan

Is that a serious question? That definition proved to be insufficiently precise, hence the move the the platinum-iridium cylinder.

I suppose repeatability in measurement trumps universality.

Bill Thompson 75 · 9th May 2012, 11:56 AM

Originally Posted by WhatRoughBeast

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.

This is a good answer and it goes to the point that science does not even know if most of the physical constants are actually constant.

Dancing David · 9th May 2012, 06:37 PM

Originally Posted by Bill Thompson 75

This is a good answer and it goes to the point that science does not even know if most of the physical constants are actually constant.

If I understand correctly, some constants have been constant because it would change the spectroscopy of distant objects, something about alpha the fine structure constant.

Perpetual Student · 9th May 2012, 07:24 PM

It seems to me that if any fundamental constant were to be suspected of being a rational number, there would be a search for some cause of its rationality and a suspicion that it is not fundamental.

9th May 2012, 05:19 AM	#41
Beerina Sarcastic Conqueror of Notions Join Date: Mar 2004 Location: A floating island above the clouds Posts: 23,835	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? This. Unless they are derived from the same thing in a roundabout way, two random irrationals are almost certainly relatively irrational to each other. Of course, this also assumes that a fine enough measurement of the universe will yield an irrational constant, no matter how closely you measure. Perhaps the universe isn't "fine grained" beyond what rationals could cover. Then the constants need only be rational at most, and thus are relatively rational to each other.
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9th May 2012, 06:22 AM	#42
TubbaBlubba Knave of the Dudes Join Date: Jul 2010 Location: Communist Kingdom of Sweden Posts: 7,415	Originally Posted by nathan 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. What about one cubic decimetre of water?
	__________________ Disagreement begets progress.

9th May 2012, 06:42 AM	#43
edd Graduate Poster Join Date: Nov 2007 Posts: 1,563	Originally Posted by TubbaBlubba What about one cubic decimetre of water? Too difficult to get it accurate enough. I expect you have to worry about an awful lot more than with a standard lump of platinum-iridium or silicon - you have to get the temperature and pressure spot on, have to have it very chemically pure, very isotopically pure and have no dissolved gases and so on, and once you've got such a sample it will deteriorate a lot faster in purity than your solid kg and can't be cleaned anything like as easily.
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9th May 2012, 08:08 AM	#44
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 26,215	Originally Posted by Beerina Hmmmm. Are ounces and grams relatively rational? They are now. NIST, for example, actually defines units like ounces and inches as rational fractions of their SI counterparts. If one were to construct an independent set of definitions (for example, using a different object to define your standard pound), that probably wouldn't be the case, but it's simpler to do it this way. So 1 avoirdupois pound = 0.45359237 kilogram, by definition (at least in the US). That's not a pretty rational number, but it is rational.
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9th May 2012, 10:10 AM	#45
nathan Zygoticly Phased Join Date: Nov 2004 Location: Arkham City Posts: 3,169	Originally Posted by TubbaBlubba What about one cubic decimetre of water? Is that a serious question? That definition proved to be insufficiently precise, hence the move the the platinum-iridium cylinder.
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9th May 2012, 10:46 AM	#46
TubbaBlubba Knave of the Dudes Join Date: Jul 2010 Location: Communist Kingdom of Sweden Posts: 7,415	Originally Posted by nathan Is that a serious question? That definition proved to be insufficiently precise, hence the move the the platinum-iridium cylinder. I suppose repeatability in measurement trumps universality.
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9th May 2012, 11:56 AM	#47
Bill Thompson 75 Graduate Poster Join Date: Apr 2010 Posts: 1,420	Originally Posted by WhatRoughBeast 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. This is a good answer and it goes to the point that science does not even know if most of the physical constants are actually constant.

9th May 2012, 06:37 PM	#48
Dancing David Penultimate Amazing Join Date: Mar 2003 Location: Central Illinois Posts: 34,727	Originally Posted by Bill Thompson 75 This is a good answer and it goes to the point that science does not even know if most of the physical constants are actually constant. If I understand correctly, some constants have been constant because it would change the spectroscopy of distant objects, something about alpha the fine structure constant.
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9th May 2012, 07:24 PM	#49
Perpetual Student Illuminator Join Date: Jul 2008 Location: USA Posts: 3,707	It seems to me that if any fundamental constant were to be suspected of being a rational number, there would be a search for some cause of its rationality and a suspicion that it is not fundamental.
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