Natural constants: are they irrational numbers?

[Trinitiet]

Do we have at present any knowledge whether our natural constants (gravity constant, Planck's constant, ...) are rational or irrational numbers?

Thanks,

Trinitiet

 

[K^2]

They are mostly irrational. The reason for that is simple. There are infinitely many more irrational number than rational. Probability of a completely random number being rational is zero. If you choose arbitrary measurement unit and measure a physical quantity, it will be irrational.

Exceptions are things like speed of light. Since we defined our distance unit so that speed of light is exactly 299,792,458m/s, it is actually an integer. But it's because we defined the unit after the physical quantity.

 

[rbj]

regarding the dimensionful physical constants, it's a meaningless question. as you can see with the speed of light, you can make it whatever you want it to be by the definition of units you choose to express length and time with.

with the dimensionless physical constants (like the fine-structure constant), those values are meaningful, but if they are truly fundamental, the only way we know their values is by measurement, which includes measurement error. within that range of values between the upper and lower standard deviations, there is a countably infinite number of rational values and an uncountably infinite number of irrational values. but that doesn't really matter. we don't know exactly what alpha is anyway.