# Re: Planck Length

```> On 17 Jan 2019, at 09:22, agrayson2...@gmail.com wrote:
>
>
>
> 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 ```
```
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

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