- For the gravitational magnetic body of Earth the gravitational Compton length is Lgr= GME/2/β0 ≈.5 cm (β0=1). For Sun one has Lgr,S≈ RE/2 (β0= 2-11 for the inner planets), where RE the radius of Earth. The corresponding time scales are rather short: .16 ns for the Earth and 10 μs for the Sun.
- For the electric fields of Earth and Sun the values of "IQ" defined by the electric Planck constant heff= ℏem are considerably higher than for the corresponding gravitational fields.
- The electric Compton length Lp,em for protons in the case of Earth corresponds to the thickness of the thermosphere where the plasmoids would live, which puts bells ringing.
- For the Sun the electric Compton length Lp,em is about 1 AU, the distance of Earth from the Sun, bells are ringing again. The time scales Tp,em = Lp,em/c would be rather short. For the Earth one would give Tp,em ≈ 4.8 ms, the time scale of the nerve pulse. For the Sun one would have Tp,em ≈8 minutes. This time scale might be perhaps assigned with short term memories or an attention span of some kind. For the electron the time scale is 26.7 hours which is slightly longer then one day (24 hours).
- For a pair formed by say charge Z and mass M and Sun, the electric Compton length and time are scaled up by a factor Zmp/M from those of protons. This factor is in general smaller than one so that historical times scales cannot be obtained by increasing the charge.
- Consider first gravitational magnetic bodies.
- For the Milky Way the mass is about 1.55× 1012MS, the gravitational Compton length Lgr would be for β0=1 equal to about Lgr≈ 1.55×1012 × β0(Sun) km ≈.8×109 km, which would give Tgr ≈ .8× 107 seconds, which rather near to year which is 3.2× 107 seconds! For β0=1/4 one would obtain a year. Also now the bells are ringing.
- To get historical time scales in the gravitational case, one should have a larger astrophysical object, perhaps a local galaxy cluster. Galaxy clusters have masses 102-103 times the mass of the Milky Way. This would give a time scale of 100-1000 years which is historical.
- What about electric Compton time for the Milky Way in the case of dark protons? Galaxy is estimated to have a Coulomb charge of about 1031 Coulombs. For β0=1, this would give for proton Compton time of about Tem,p=1015 years, considerably longer than the age about 1010 years of the cosmos!
- The gravitational Compton length does not depend on the mass of the particle (Equivalence Principle).
- Quite generally, the increase of the charge of the paired particle is accompanied by corresponding increase of the mass which tends to reduce the value of electric Compton length from that for protons (or electrons).
- The example of DNA illustrates the situation in the electric case.
- DNA is exceptional since there is constant change density of 2 elementary charges per nucleotide making the charge of DNA very large. Therefore DNA maximizes the electric Compton length and time. The length of DNA does not however increase these parameters.
- Human DNA has about 3.2× 108 base pairs. Base has an average mass of 320 proton masses. Base pair has a charge of 2e. The mass and charge are scaled by a factor of order 1011 from those of protons. Hence the charge per mass ratio using proton mass as a unit is about 1/320. The electric Compton lengths and times are scaled down by factor about 1/320.
- For DNA, Tem,p=1015 years for proton-Milky-Way pair would scale down to Tem,DNA= 3× 1012 years, still 300 times longer than the estimated age of the Universe. For an ion with charge Z and mass of Mega Dalton (million proton masses) electrically paired with the Milky Way, one would have Tem= Z × 109 years and thus same order of magnitude as the age of the Universe.
- The charge/mass ratio is for biomolecules in general smaller than for DNA so that as macroscopic quantum systems they would correspond to shorter Compton lengths and times. For instance, for ions with mass number A, one would have Tem,A=Tem,p/A.
For a summary of earlier postings see Latest progress in TGD.
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.