Return to Answer

First of all, it doesn't make sense to assign an absolute number to a physical quantity like length and volume. The number can be different with respect to different "units" of measurement.

But one can still question the ratio of two lengths, in this case:

According to Bekenstein entropy limit(information) I guess there should be some maximum level of precision.

If a rod has an irrational length, then it demands an infinite amount of information(write the length in a binary format like this sequence 11010100001000....).

Since irrational numbers don't have any pattern( repetition of a finite sequence) I guess it should be impossible to retain all that information on a Quantum Mechanical piece of rod.

Moreover one can be even more critical and accept the existence of lengths only with a finite code(rather than a finite repetitive pattern)! so that one can deny even a rod with a non-integer rational number length.

This sounds like the emergence of integers(quantas) in Quantum Mechanics!

First of all, it doesn't make sense to assign an absolute number to a physical quantity like length and volume. The number can be different with respect to different "units" of measurement.

But one can still question the ratio of two lengths, in this case:

According to the Bekenstein entropy limit(information), I guess there should be some maximum level of precision.

If a rod has an irrational length ratio, then it demands an infinite amount of information(write the length in a binary format like this sequence 11010100001000....).

Since irrational numbers don't have any pattern( repetition of a finite sequence) I guess it should be impossible to retain all that information in a Quantum Mechanical world.

Moreover one can be even more critical and accept the existence of length ratios only with a finite code(rather than a finite repetitive pattern)! so that one can deny even a rod with a non-integer rational number length ratio.

This sounds like the emergence of integers(quantas) in Quantum Mechanics!

According to Bekenstein entropy limit(information) I guess there should be some maximum level of precision.

If a rod has an irrational length, then it demands an infinite amount of information(write the length in a binary format like this sequence 11010100001000....).

Since irrational numbers don't have any pattern( repetition of a finite sequence) I guess it should be impossible to retain all that information on a Quantum Mechanical piece of rod.

Moreover one can be even more critical and accept the existence of lengths only with a finite code(rather than a finite repetitive pattern)! so that one can deny even a rod with a non-integer rational number length.

This sounds like the emergence of integers(quantas) in Quantum Mechanics!

First of all, it doesn't make sense to assign an absolute number to a physical quantity like length and volume. The number can be different with respect to different "units" of measurement.

But one can still question the ratio of two lengths, in this case:

According to Bekenstein entropy limit(information) I guess there should be some maximum level of precision.

If a rod has an irrational length, then it demands an infinite amount of information(write the length in a binary format like this sequence 11010100001000....).

Since irrational numbers don't have any pattern( repetition of a finite sequence) I guess it should be impossible to retain all that information on a Quantum Mechanical piece of rod.

Moreover one can be even more critical and accept the existence of lengths only with a finite code(rather than a finite repetitive pattern)! so that one can deny even a rod with a non-integer rational number length.

This sounds like the emergence of integers(quantas) in Quantum Mechanics!

According to Bekenstein entropy limit(information) I guess there should be some maximum level of precision.

If a rod has an irrational length, then it demands an infinite amount of information(write the length in a binary format like this sequence 11010100001000....).

Since irrational numbers don't have any pattern( repetition of a finite sequence) I guess it should be impossible to retain all that information on a Quantum Mechanical piece of rod.

Moreover one can be even more critical and accept the existence of lengths only with a finite code(rather than a finite repetitive pattern)! so that one can deny even a rod with a rational number length.

This sounds like the emergence of integers(quantas) in Quantum Mechanics!

According to Bekenstein entropy limit(information) I guess there should be some maximum level of precision.

If a rod has an irrational length, then it demands an infinite amount of information(write the length in a binary format like this sequence 11010100001000....).

Since irrational numbers don't have any pattern( repetition of a finite sequence) I guess it should be impossible to retain all that information on a Quantum Mechanical piece of rod.

Moreover one can be even more critical and accept the existence of lengths only with a finite code(rather than a finite repetitive pattern)! so that one can deny even a rod with a non-integer rational number length.

This sounds like the emergence of integers(quantas) in Quantum Mechanics!