# Re: Planck Length

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On Thursday, January 17, 2019 at 2:22:29 AM UTC-6, agrays...@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> 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

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