# Re: Planck Length

```On Monday, January 21, 2019 at 5:09:50 AM UTC-6, Bruno Marchal wrote:
>
>
> On 21 Jan 2019, at 00:17, Lawrence Crowell <goldenfield...@gmail.com
> <javascript:>> wrote:
>
> On Sunday, January 20, 2019 at 9:16:01 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 19 Jan 2019, at 01:42, Lawrence Crowell <goldenfield...@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 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.
>>
>>
>>
> I think we talked a bit on this list about hyper-Turing machines. These
> are conditions set up by various spacetimes where a Cauchy horizon makes an
> infinite computation accessible to a local observer. A nonhalting
> computation can have its output read by such an observer. These spacetimes
> are Hobert-Malament spaces.The Planck scale may then be a way quantum
> gravity imposes a fundamental limit on what an observer can measure.
>
> If one is to think of computation according to halting one needs to think
> according to nilpotent operators. For a group G with elements g these act
> on vectors v so that gv = v'. These vectors can be states in a Hilbert
> space or fermionic spinors. The group elements are generated by algebraic
> operators A so that g = e^{iA}. Now if we have the nilpotent situation
> where Av = 0 without A or v being zero then gv ≈ (1 + iA)v = v.
>
> A time ordered product of fields, often used in path integral, is a
> sequence of operators similar to g and we may then have that g_1g_2g_3 …
> g_n as a way that a system interacts. We might then have some condition
> that at g_m for m < n the set of group operations all return the same
> value, so the group has a nilpotent condition on its operators. This would
> then bear some analogue to the idea of a halted computation.
>
> The question of whether there are nonhalting conditions
>
>
> In a physical reality.? But once we assume mechanism, we cannot do that
> assumptions. Halting and non halting computations is a very solid notion
> which does not depend on the physical reality, nor of any choice of the
> universal complete theory that we presuppose. We still have to assume one
> Turing universal system, but both theology and physics are independent of
> which universal system we start with. I use usually either arithmetic, or
> the combinators or a universal diophantine polynomial.
> With mechanism, the physical laws are not fundamental, but are explained
> “Turing-thropically”, using the logics of self-reference of Gödel, Löb,
> Solovay.
> To test empirically the digital mechanist hypothesis (in the cognitive
> science) we have to compare the physics deducible by introspection by
> Turing machine, with the physics observed. Thanks to QM, it fits up to now.
> But we are light years aways from justifying string theory, or even
> classical physics. The goal is not to change physics, but to get the
> metaphysics right (with respect to that mechanist assumption and the
> mind-body problem). The notion of computation is the most solid
> epistemological notion, as with Church’s thesis, it admit a purely
> mathematical, even purely arithmetic, definition. Analysis and physics are
> ways the numbers see themselves when taking their first person
> indetermination in arithmetic into account.
>
>
>
> is then most likely relevant to spacetime physics of quantum fields. If we
> have a black hole of mass M it then has temperature T = 1/8πGM. Suppose
> this sits in a spacetime with a background of the same temperature. We
> might be tempted to say there is equilibrium, which is a sort of halted
> development. However, it the black hole emits a photon by Hawking radiation
> of mass-energy δm so M → M - δm it is evident its temperature increases.
> Conversely if it absorbs a photon from the thermal background then  M → M +
> δm and its temperature decreases.
>
>
> I am not sure I understand this.
>```
```
A black hole that loses mass by Hawking radiation become a little hotter.
The black hole that absorbs a quanta becomes a bit colder. There is as a
result no equilibrium condition.

LC

>
>
>
> This will then put the black hole in a state where it is now more likely
> to quantum evaporate or to grow unbounded by absorbing background photons.
>
> This might then be a situation of nonhalting,
>
>
>
> The problem of the existence of infinite computation in the physical
> universe is an open problem in arithmetic. Arithmetic contains all non
> halting computations, but it is unclear if the physical universe has to be
> finite or not. The first person indeterminacy suggests a priori many
> infinities, including continua, but the highly counter-intuitive nature of
> self-reference suggests to be cautious in drawing to rapidly some
> conclusion. With mechanism, a part of our past is determined by our (many)
> futures.
>
>
>
>
> and with gravitation or quantum gravity the moduli space is nonHausdorff
>
>
> That could be interesting. The topological semantics of the theology (G
> and G*) are nonHausdorff too.
> Could be a coincidence, of course, as physics should be in the intensional
> variants of G*.
>
>
>
>
> with orbits of gauge equivalent potentials or moduli that are not bounded.
> We might then consider quantum gravitation as an arena where the quantum
> computation of its states are nonhalting, or might they be entirely
> uncomputable. The inability to isolate a qubit in a region smaller may
> simply mean that no local observer can read the output of an ideal
> hyper-Turing machine from an HM spacetime.
>
>
> OK, I think. That would make Mechanism wrong. That is testable, but the
> evidences favours mechanism.
>
>
>
>
>
>
>
>> 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.
>>
>>
>>
> String theory does some other things that may not be right as well. The
> compactification of spaces with dimensions in addition to 3-space plus time
> has certain implications, which do not seem to be born out.
>
>
> I cannot really judge this. I can agree that this is a bit the ugly part
> of that theory (I mean the compactififed dimension), but that is not an
> argument, and taste can differ ...
>
>
>
>
>
>
>
>
>>
>>
>> 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
>>
>>
> This last part involves some deep physics on how the holographic screen is
> in entangled states with Hawking radiation.
>
>
> That is interesting. Note that with mechanism, we know "for sure” that the
> ultimate reality (independent of us the Löbian universal machine) has to be
> non dimensional (as arithmetic and elementary computer science is).
>
> Bruno
>
>
>
>
>
> LC
>
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