On Monday, January 7, 2019 at 9:25:16 PM UTC, John Clark wrote:
> On Mon, Jan 7, 2019 at 8:03 AM <agrays...@gmail.com <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 *

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