speed of light

[AntonioLao]

for all electromagnetic waves, the speed is the product of wavelength and frequency. Frequency must, by its definition of cycle per unit period, be a rational number. For fractional periods imply the existence of a smaller fundamental period. So, there must exist also a smallest period which can be identically zero if time is a continuous function of itself. If the speed of light is known as an irrational number then the wavelength must be an irrational number so that the speed can be the product of an irrational and a rational number.

[Guille]

What are (or you think are) the two ratioanl and irrational numbers that have the product which is the speed of light? Can this be measured?

[AntonioLao]

What are (or you think are) the two ratioanl and irrational numbers that have the product which is the speed of light?

the wavelength and frequency of a photon with a given energy.

[Guille]

the wavelength and frequency of a photon with a given energy.

Which is the irrational and which is the rational? And mostimportantly, why is each this?

[AntonioLao]

the frequency must be rational otherwise the definition of a period is meaningless or its values is exactly zero and infinite. The wavelength can be irrational because any length larger than Planck length is continuous and continuity is another name for irrationality.

[Guille]

the frequency must be rational otherwise the definition of a period is meaningless or its values is exactly zero and infinite. The wavelength can be irrational because any length larger than Planck length is continuous and continuity is another name for irrationality.

So space-time is irrational if it is looked from higher than planck's legth and time, but rational when looked from there downwards?

[AntonioLao]

but rational when looked from there downwards?

there is still no answer to this question unless spacetime is quantized.

[Guille]

there is still no answer to this question unless spacetime is quantized.

Now I see. If something can be infinatelly diveded it is irratioanal. If not, rational.

[AntonioLao]

rational numbers are numbers expressable by fractions and fractions are the ratio of integers. The quantum numbers of quantum mechanics can only be integers. This can imply that all quantum theories must use rational descriptions. But the most important constant of QM is Planck's constant of action and it is an irrational number.

[Guille]

rational numbers are numbers expressable by fractions and fractions are the ratio of integers. The quantum numbers of quantum mechanics can only be integers. This can imply that all quantum theories must use rational descriptions. But the most important constant of QM is Planck's constant of action and it is an irrational number.

Maybe planck's constant as a fraction is not irrational?