# Re: Planck Length

```On Thursday, January 17, 2019 at 6:31:06 AM UTC-6, Bruno Marchal wrote:
>
>
> On 17 Jan 2019, at 09:22, agrays...@gmail.com <javascript:> 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 *
>
>
> 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
>```
```
The Planck length is just the smallest length beyond which you can isolate
a quantum bit. Remember, it is the length at which the Compton wavelength
of a black hole equals its Schwarzschild radius. It is a bit similar to the
Nyquist frequency in engineering. In order to measure the frequency of a
rotating system you must take pictures that are at least double that
frequency. Similarly to measure the frequency of an EM wave you need to
have a wave with Fourier modes that are 2 or more times the frequency you
want to measure. The black hole is in a sense a fundamental cut-off in the
time scale, or in a reciprocal manner the energy, one can sample space to
find qubits.

The levels of confusion over this are enormous. It does not tell us that
spacetime is somehow sliced and diced into briquets or pieces. It does not
tell us that quantum energy of some fields can't be far larger than the
Planck energy, or equivalently the wavelength much smaller. This would be
analogous to a resonance state, and there is no reason there can't be such
a thing in quantum gravity. The Planck scale would suggest this sort of
state may decay into a sub-Planckian energy.  Further, it is plausible that
quantum gravity beyond what appears as a linearized weak field
approximation similar to the QED of photon bunched pairs may only exist at
most an order of magnitude larger than the Planck scale anyway. A
holographic screen is then a sort of beam splitter at the quantum-classical
divide.

LC

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