On Thursday, January 17, 2019 at 2:22:29 AM UTC-6, [email protected] wrote: > > > > On Monday, January 7, 2019 at 9:25:16 PM UTC, John Clark wrote: >> >> On Mon, Jan 7, 2019 at 8:03 AM <[email protected]> wrote: >> >> *> How does one calculate Planck length using the fundamental constants >>> G, h, and c, and having calculated it, how does one show that measuring a >>> length that small with photons of the same approximate wave length, would >>> result in a black hole? TIA, AG* >> >> >> In any wave the speed of the wave is wavelength times frequency and >> according to >> Planck E= h*frequency so E= C*h/wavelength. Thus the smaller the >> wavelength the greater the energy. According to Einstein energy is just >> another form of mass (E = MC^2) so at some point the wavelength is so >> small and the light photon is so energetic (aka massive) that the escape >> velocity is greater than the speed of light and the object becomes a Black >> Hole. >> >> Or you can look at it another way, we know from Heisenberg that to >> determine the position of a particle more precisely with light you have to >> use a smaller wavelength, and there is something called the "Compton >> wavelength" (Lc) ; to pin down the position of a particle of mass m to >> within one Compton wavelength would require light of enough energy to >> create another particle of that mass. The formula for the Compton >> Wavelength is Lc= h/(2PI*M*c). >> >> Schwarzschild told us that the radius of a Black Hole (Rs), that is to >> say where the escape velocity is the speed of light is: Rs= GM/c^2. At >> some mass Lc will equal Rs and that mass is the Planck mass, and that Black >> Hole will have the radius of the Planck Length, 1.6*10^-35 meters. >> >> Then if you do a little algebra: >> GM/c^2 = h/(2PI*M*c) >> GM= hc/2PI*M >> GM^2 = hc/2*PI >> M^2 = hc/2*PI*G >> M = (hc/2*PI*G)^1/2 and that is the formula for the Planck Mass , >> it's .02 milligrams. >> >> And the Planck Length turns out to be (G*h/2*PI*c^3)^1/2 and the Planck time >> is the time it takes light to travel the Planck length. >> >> The Planck Temperature Tp is sort of the counterpoint to Absolute Zero, >> Tp is as hot as things can get because the black-body radiation given off >> by things when they are at temperature Tp have a wavelength equal to the >> Planck Length, the distance light can move in the Planck Time of 10^-44 >> seconds. The formula for the Planck temperature is Tp = Mp*c^2/k where Mp >> is the Planck Mass and K is Boltzmann's constant and it works out to be >> 1.4*10^32 degrees Kelvin. Beyond that point both Quantum Mechanics and >> General Relativity break down and nobody understands what if anything is >> going on. >> >> The surface temperature of the sun is at 5.7 *10^3 degrees Kelvin so if >> it were 2.46*10^28 times hotter it would be at the Planck Temperature, and >> because radiant energy is proportional to T^4 the sun would be 3.67*10^113 >> times brighter. At that temperature to equal the sun's brightness the >> surface area would have to be reduced by a factor of 3.67*10^113, the >> surface area of a sphere is proportional to the radius squared, so you'd >> have to reduce the sun's radius by (3.67*10^113)^1/2, and that is >> 6.05*10^56. >> The sun's radius is 6.95*10^8 meters and 6.95*10^8/ 6.05*10^56 is >> 1.15^10^-48 meters. >> >> That means a sphere at the Planck Temperature with a radius 10 thousand >> billion times SMALLER than the Planck Length would be as bright as the sun, >> but as far as we know nothing can be that small. If the radius was 10^13 >> times longer it would be as small as things can get and the object would be >> (10^13)^2 = 10^26 times as bright as the sun. I'm just speculating but >> perhaps that's the luminosity of the Big Bang; I say that because that's >> how bright things would be if the smallest thing we think can exist was as >> hot as we think things can get. >> >> John K Clark >> > > > *Later I'll post some questions I have about your derivation of the Planck > length, but for now here's a philosophical question; Is there any > difference between the claim that space is discrete, from the claim or > conjecture that we cannot in principle measure a length shorter than the > Planck length? * > *TIA, AG * >
There are *claims* (theories, e.g. a LQG theory of space, essentially that "space is discrete") and *measurements* (data, collected from instruments). There is no fundamental regime for matching claims and measurements. Just whatever the scientific community ends up liking, in the end. What you stated are two claims: *space is discrete *and *cannot measure a length shorter than the Planck length*. Both claims are subject to whatever measurements are recorded. These two claims appear to be close, but I think there is wiggle room for them to be different. - pt -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
