Brent>> all physical measurements will be rational numbers
SB> Well, it is quite a statement ;o) so you may write down an exact SB> Planck constant (h), please illustrate that... SB> If you experience difficulty to do that for ( h ) please try write SB> down an exact gravitational constant ( G )... Brent>No, problem. Like most physicists I write h=1, G=1, c=1. Apparently no problem ;o) --sb On Jul 24, 9:29 pm, Brent Meeker <[email protected]> wrote: > [email protected] wrote: > > > Brent> all physical measurements will be rational numbers > > > Well, it is quite a statement ;o) so you may write down an exact > > Planck constant (h), please illustrate that... > > If you experience difficulty to do that for ( h ) please try write > > down an exact gravitational constant ( G )... > > No, problem. Like most physicists I write h=1, G=1, c=1. > > > > > Ref: Planck constant: h = 4.135 667 33(10) × 10−15 eV s > > (10) The two digits between the parentheses denote the standard > > uncertainty in the last two digits of the value. > > The uncertainty is in the conversion to eVs. It arises because different > people > got different numbers when measuring, but each measurement was a rational > number. > > Brent > > > > > SB> there is no way to write down an exact arbitrary irrational number > > Brent> There is no problem writing down irrational numbers: > > Brent> sqrt(2), pi,... See nothing to it. ;-) > > > You miss the key word "arbitrary", it is simple to show that the > > number of irrational numbers which can be expressed/encoded with ZERO > > entropy equals to number of rational numbers (sqrt(2) is one of such > > examples). > > > --sb > > > On Jul 23, 4:30 pm, Brent Meeker <[email protected]> wrote: > >> [email protected] wrote: > >>> SBJ: Information entropy of physical fundamental constants > >>> The fundamental constant can be measured increasingly accurate, it > >>> does not seem (for me) that the repetitive pattern of rational > >>> numbers after some number of digits may take place; > >> Physical measurements are always relative, i.e. one quantify is measured in > >> units of another quantity. It is generally thought that there is a > >> smallest > >> possible unit, the Planck scale, so all physical measurements will be > >> rational > >> numbers (integers in Planck units). > > >>> if it is the case > >>> then there is not enough "room" in the universe / multiverse to > >>> accommodate such information as exact representation of fundamental > >>> constant - just in principle, there is no way to have it exact as > >>> there is no way to write down an exact arbitrary irrational number and > >>> it is not a technical limitation it is a fundamental limitation unless > >>> it may be represented as a rational number ;o). > >> There is no problem writing down irrational numbers: sqrt(2), pi,... See > >> nothing > >> to it. ;-) > > >> Of course from an information standpoint you want to know their bits. But > >> it > >> also easy to write down a quite short program that will compute whatever > >> bit you > >> want to know for those irrational numbers. But you are right that for > >> almost > >> all real numbers is impossible to give them a finite representation. But > >> why > >> believe in those numbers anyway, they are convenient fictions. > > >>> Information Entropy > >>> can be measured as an average number of bits per symbol/digit encoded > >>> by rank-0 context model + entropy encoder (let say arithmetic > >>> encoder). Therefore, there are two distinct possibilities: entropy > >>> equals zero or Log2(10) (for decimal representation) or simply: ZERO > >>> or NON-ZERO. I have my ideas how NON-ZERO case may workout but I'm > >>> interested to listen others opinions. > >> Most cosmogonies assume the (microscopic) entropy of the universe is zero. > >> It > >> started at the Planck scale, where there is room for at most one bit and > >> since > >> QM insists on unitary evolution the entropy cannot change (as measured at > >> the > >> Planck scale). The increase in entropy we see is due to our coarse > >> graining, or > >> as Bruno would say, "above our substitution level". It is impossible to > >> however > >> to use the negative information to get back to local zero because the > >> expansion > >> of the universe has carried the correlations beyond the relativistic > >> horizon. > >> At least that's the common theory. > > >> Brent --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
