One problem with estimating the size of a proton from the size of the universe is that it implies that the proton or one of the constants it is derived from isn't constant.
Using a rough order of magnitude calculation, the volume of the universe divided by its entropy (given by its boundary surface area in Planck units) gives the volume of a proton. The volume of the universe is on the order of (Tc)^3 where T is the age of the universe (13.8 billion years = 4.35E17 s) and c is the speed of light (2.998E8 m/s). A Planck length is sqrt(hbar G/c^3) where hbar is the reduced Planck constant h/2pi = 1.054E-34 kg m^2/s and G is the gravitational constant 6.6743E-11 m^3/kg s^2. Thus, the area of the universe in Planck units is of the order A = T^2 c^5/hG and the volume of a proton is of the order A/(Tc)^3 = c^2/hGT. The proton radius is the cube root of that. Since T is increasing, it means either that protons are getting smaller, or c is increasing, or G or h is decreasing. But there is no evidence for any of that. The only constant that we can't measure precisely enough to detect any changes in a few years is G. But if G were changing we should be able to see the effects in distant galaxies. An exact value using the Bekenstein bound (A/(4 ln 2)) of the Hubble radius gives 2.96E122 bits and a proton radius of 1.959E-15 m (1.959 fm). The Compton wavelength (mass/h) is 1.321 fm and the measured radius using electron scattering is 0.84-0.87 fm. One problem is Tc is not the actual size of the universe. The event horizon we see at 13.8B light years is now 46B light years away, and would be infinite if the universe weren't accelerating away. And this is just part of a larger universe of unknown size that we can't see because it would take longer than the age of the universe for its light to reach us. Also the Bekenstein bound is just an upper bound on entropy that is only reached for black holes. The universe apparently only has 31% of this mass (4% stars and 27% dark matter, which I presume consists of ordinary matter in smaller objects not orbiting stars. Dark matter forms halos around galaxies, exactly where we would expect rogue planets and comets to be scattered). The other 69% is dark energy, which is what ordinary gravity would look like to an observer falling into a universe sized black hole. The event horizon would appear to wrap around due to gravitational lensing and cause other galaxies to accelerate away in all directions. If this is so, then there should be a small opening, which I believe is the CMB cold spot behind the Eridanus void, the largest known region of empty space in the universe. We really should point Hubble or JWST at it to see what's there. How is this related to AGI? It is pretty obvious that this universe is finely tuned to be compatible with intelligent life. If the relative masses of the proton and neutron were different, or if G, c, h, or alpha differed much, then stars would not undergo fusion or go supernova and scatter the right elements to form planets with complex molecules. The anthropic principle suggests that the universe is as big as it needs to be. There are 10^24 planets in the observable universe and an unknown number, immensely larger, beyond that. You only need one to evolve life. If you were hoping to throw together some chemicals and see molecules start to self replicate and evolve, you may be waiting a long long time. On Thu, Apr 4, 2024, 4:55 PM James Bowery <jabow...@gmail.com> wrote: > I suppose it is worth pointing out that there is another CH4 coincidence, > not quite as impressive as the protonAlphaG coincidence, but involving > multiplying the 1/2 electron spin by 2 for a full return to its original > phase: > > 0.8±0.15% relative error with the light age of the universe > > (* Electron Phase Factor 1 and Light Age of the Universe *) > ReducedElectronComptonWavelength=codata["ElectronComptonWavelength"]/(2*Pi) > FullSpinElectron = 2 * ReducedElectronComptonWavelength (* 720 degrees = > spin 1 *) > LightAgeUniverseCH4=UnitConvert[CH4*FullSpinElectron,"LightYear"] > LightAgeUniverse = > UnitConvert[codata["UniverseAge"]*codata["SpeedOfLight"],"LightYear"] > RelativeError[LightAgeUniverse,LightAgeUniverseCH4] > (3.86159267\[NegativeVeryThinSpace]\[NegativeVeryThinSpace]\[NegativeVeryThinSpace](96\[NegativeThinSpace]\[PlusMinus]\[NegativeThinSpace]12\[NegativeVeryThinSpace])*10^-13)m > (7.72318535\[NegativeVeryThinSpace]\[NegativeVeryThinSpace]\[NegativeVeryThinSpace](92\[NegativeThinSpace]\[PlusMinus]\[NegativeThinSpace]23\[NegativeVeryThinSpace])*10^-13)m > (1.388932811\[NegativeVeryThinSpace]\[NegativeVeryThinSpace]\[NegativeVeryThinSpace](2\[NegativeThinSpace]\[PlusMinus]\[NegativeThinSpace]4\[NegativeVeryThinSpace])*10^10)ly > = (1.3778\[PlusMinus]0.0020)*10^10ly > = 0.0081\[PlusMinus]0.0015 > > On Wed, Apr 3, 2024 at 1:38 PM James Bowery <jabow...@gmail.com> wrote: > >> BTW* These proton, gravitation Large Number Coincidences are strong >> enough that it pretty much rules out the idea that gravitational phenomena >> can be attributed to anything but hadronic matter -- and that includes the >> 80% or so of gravitational phenomena attributed sometimes to "dark" >> matter. So, does this mean some form of MOND (caused by hadronic matter) >> and/or alternatively, some weakly interacting form of hadronic matter is >> necessary? >> >> * and I realize this is getting pretty far removed from anything relevant >> to practical "AGI" except insofar as the richest man in the world (last I >> heard) was the guy who wants to use it to discover what makes "the >> simulation" tick (xAI) and he's the guy who founded OpenAI, etc. >> >> On Wed, Apr 3, 2024 at 1:23 PM James Bowery <jabow...@gmail.com> wrote: >> >>> Mark Rohrbaugh's formula, that I used to calculate the proton radius to >>> a higher degree of precision than QED or current measurements, results in a >>> slightly higher relative error with respect to the Hubble Surface >>> prediction, but that could be accounted for by the 11% tolerance in the >>> Hubble Surface calculation derived from the Hubble Radius, or the 2% >>> tolerance in the Hubble Volume calculation taken in ratio with the proton >>> volume calculated from the proton radius: >>> >>> >>> pradiusRohrbaugh=(8.41235641\[NegativeVeryThinSpace]\[NegativeVeryThinSpace]\[NegativeVeryThinSpace](35\[NegativeThinSpace]\[PlusMinus]\[NegativeThinSpace]26\[NegativeVeryThinSpace])*10^-16)m >>> pradiusRohrbaughPL=UnitConvert[pradiusRohrbaugh,"PlanckLength"] >>> pvolumeRohrbaugh=(4/3) Pi pradiusRohrbaughPL^3 >>> h2pvolumeRohrbaugh=codata["HubbleVolume"]/pvolumeRohrbaugh >>> >>> RelativeError[QuantityMagnitude[h2pvolumeRohrbaugh],QuantityMagnitude[hsurface]] >>> (8.41235641\[NegativeVeryThinSpace]\[NegativeVeryThinSpace]\[NegativeVeryThinSpace](35\[NegativeThinSpace]\[PlusMinus]\[NegativeThinSpace]26\[NegativeVeryThinSpace])*10^-16)m >>> (5.20484478\[NegativeVeryThinSpace]\[NegativeVeryThinSpace]\[NegativeVeryThinSpace](84\[NegativeThinSpace]\[PlusMinus]\[NegativeThinSpace]16\[NegativeVeryThinSpace])*10^19)Subscript[l, >>> P] >>> (5.90625180\[NegativeVeryThinSpace]\[NegativeVeryThinSpace]\[NegativeVeryThinSpace](6\[NegativeThinSpace]\[PlusMinus]\[NegativeThinSpace]5\[NegativeVeryThinSpace])*10^59)Subsuperscript[l, >>> P, 3] >>> = (1.025\[PlusMinus]0.019)*10^123 >>> = -0.123\[PlusMinus]0.022 >>> >>> >>> >>> On Tue, Apr 2, 2024 at 9:16 AM James Bowery <jabow...@gmail.com> wrote: >>> >>>> I get it now: >>>> >>>> pradius = UnitConvert[codata["ProtonRMSChargeRadius"],"PlanckLength"] >>>> = (5.206\[PlusMinus]0.012)*10^19Subscript[l, P] >>>> pvolume=(4/3) Pi pradius^3 >>>> = (5.91\[PlusMinus]0.04)*10^59Subsuperscript[l, P, 3] >>>> h2pvolume=codata["HubbleVolume"]/pvolume >>>> = (1.024\[PlusMinus]0.020)*10^123 >>>> hsurface=UnitConvert[4 Pi codata["HubbleLength"]^2,"PlanckArea"] >>>> = (8.99\[PlusMinus]0.11)*10^122Subsuperscript[l, P, 2] >>>> RelativeError[QuantityMagnitude[h2pvolume],QuantityMagnitude[hsurface]] >>>> = -0.122\[PlusMinus]0.023 >>>> >>>> As Dirac-style "Large Number Coincidences" go, a -12±2% relative error >>>> is quite remarkable since Dirac was intrigued by coincidences with orders >>>> of magnitude errors! >>>> >>>> However, get a load of this: >>>> >>>> CH4=2^(2^(2^(2^2-1)-1)-1)-1 >>>> = 170141183460469231731687303715884105727 >>>> protonAlphaG=(codata["PlanckMass"]/codata["ProtonMass"])^2 >>>> = (1.69315\[PlusMinus]0.00004)*10^38 >>>> RelativeError[protonAlphaG,CH4] >>>> = 0.004880\[PlusMinus]0.000022 >>>> >>>> 0.5±0.002% relative error! >>>> >>>> Explain that. >>>> >>>> >>>> On Sun, Mar 31, 2024 at 9:45 PM Matt Mahoney <mattmahone...@gmail.com> >>>> wrote: >>>> >>>>> On Sun, Mar 31, 2024, 9:46 PM James Bowery <jabow...@gmail.com> wrote: >>>>> >>>>>> Proton radius is about 5.2e19 Plank Lengths >>>>>> >>>>> >>>>> The Hubble radius is 13.8e9 light-years = 8.09e60 Planck lengths. So >>>>> 3.77e123 protons could be packed inside this sphere with surface area >>>>> 8.22e122 Planck areas. >>>>> >>>>> The significance of the Planck area is it bounds the entropy within to >>>>> A/4 nats, or 2.95e122 bits. This makes a bit the size of 12.7 protons, or >>>>> about a carbon nucleus. https://en.wikipedia.org/wiki/Bekenstein_bound >>>>> >>>>> 12.7 is about 4 x pi. It is a remarkable coincidence to derive >>>>> properties of particles from only G, h, c, and the age of the universe. >>>>> >>>>>> >>>>>> *Artificial General Intelligence List > <https://agi.topicbox.com/latest>* / AGI / see discussions > <https://agi.topicbox.com/groups/agi> + participants > <https://agi.topicbox.com/groups/agi/members> + delivery options > <https://agi.topicbox.com/groups/agi/subscription> Permalink > <https://agi.topicbox.com/groups/agi/Teaac2c1a9c4f4ce3-M625d0f25b9beb1e955623fb0> > ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/Teaac2c1a9c4f4ce3-Mb48080f054312fa0d2924979 Delivery options: https://agi.topicbox.com/groups/agi/subscription
