Are physical constants irrational?

[Beerina]

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]

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]

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]

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]

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]

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]

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]

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]

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.