> On 17 Jan 2019, at 09:22, [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] <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
That is a very good question. I have no answer. I don’t think physicists have an answer either, and I do think that this requires the solution of the “quantum gravity” or the “quantum space-time” problem. With loop-gravity theory, I would say that the continuum is eventually replaced by something discrete, but not so with string theory; for example. With Mechanism, there are argument that something must stay “continuous”, but it might be only the distribution of probability (the real-complex amplitude). Bruno > > -- > 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
