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] <javascript:>> 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 * -- 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.
