# Re: Planck Length

```> On 19 Jan 2019, at 01:42, Lawrence Crowell <goldenfieldquaterni...@gmail.com>
> wrote:
>
> 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. ```
```
That makes some sense. It corroborates what Brent said. To “see” beyond the
Planck resolution, we need so much energy that we would create a black hole,
and ost any available information. This does not mean that a shorter length is
no possible in principle, just that we cannot make any practical sense of it.

>
> The levels of confusion over this are enormous. It does not tell us that
> spacetime is somehow sliced and diced into briquets or pieces.

I agree. Besides, this might depend heavily on the solution of the quantum
gravity problem. Loop gravity, as far as I understand it, does seem to impose
some granularity on space-time. Superstring do not, apparently.

> 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.

OK.

> 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.

This is a bit less clear to me, due to my incompetence to be sure. If you have
some reference or link, but it is not urgent. I have not yet find to study the
Holographic principle of Susskind, bu I have followed informal exposition given
by him on some videos. Difficult subject, probably more so for mathematical
logician.

Bruno

>
> LC
>
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