Note on the natural system of units

Pramana

E C G Sudarshan¹  Cristian Rivera1²  Luis J Boya1² 

[1] Physics Department, University of Texas, Austin 78712, USA$$;Departamento de Física Teórica, Universidad de Zaragoza, E-50009 Zaragoza, Spain$$

关键词: Fundamental constants;    gravitation.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We propose to substitute Newton’s constant 𝐺N for another constant 𝐺2, as if the gravitational force would fall off with the 1/𝑟 law, instead of the 1/𝑟2; so we describe a system of natural units with 𝐺2 , 𝑐 and ħ. We adjust the value of 𝐺2 so that the fundamental length 𝐿 = 𝐿Pl is still the Planck’s length and so 𝐺N = 𝐿 × 𝐺2. We argue for this system as (1) it would express longitude, time and mass without square roots; (2) 𝐺2 is in principle disentangled from gravitation, as in (2 + 1) dimensions there is no field outside the sources. So 𝐺2 would be truly universal; (3) modern physics is not necessarily tied up to (3 + 1)-dim. scenarios and (4) extended objects with 𝑝 = 2 (membranes) play an important role both in M-theory and in F-theory, which distinguishes three (2, 1) dimensions.As an alternative we consider also the clash between gravitation and quantum theory; the suggestion is that non-commutative geometry [𝑥𝑖, 𝑥𝑗] = 𝛬2 𝜃𝑖𝑗 would cure some infinities and improve black hole evaporation. Then the new length 𝛬 shall determine, among other things, the gravitational constant 𝐺N.

【 授权许可】

Unknown