# Re: Planck Length

```
On Thursday, January 24, 2019 at 5:54:46 AM UTC-6, Lawrence Crowell wrote:
>
> On Monday, January 21, 2019 at 6:49:12 PM UTC-6, Philip Thrift wrote:
>>
>>
>>
>> On Monday, January 21, 2019 at 6:19:07 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> 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>
>>>> 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
>>>>>>> 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
>>>> 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
>>>>
>>>>
>>
>>
>> One of the oddest of things is when physicists use the language of
>> (various) theories of physics to express what can or cannot be the case.
>> It's just a language, which is probably wrong.
>>
>> There is a sense in which the Church/Turing thesis is true: All out
>> languages are Turing in their syntax and grammar. What they refer to is
>> another matter (pun intended).
>>
>> - pt
>>
>
>
>
> My point is that in physics what might be called a halting condition is an
> attractor point or limit cycle. Equilibrium is the terminal point in the
> evolution of some system, say thinking according to Landauer's original
> paper on thermodynamics and information. The quantum field theory of black
> holes has no equilibrium condition. Now if the black hole runs away with
> Hawking radiation it will “explode” in a burst of gamma rays and other
> quanta. A Turing machine that does not halt can also be said to burn itself
> out, and if anyone has programmed assembler there were loops you could put
> a machine into that might do damage.
>
> Sorry for being slow on this. I forgot to get flu shots this year and I
> have been hit with a real doozy of a flu. Since Sunday night until
> yesterday I was horribly ill, and only now am beginning to feel normal. Get
> the shots, you really do not want this flu!
>
> LC
>```
```
I used to think that there *could be* true hypercomputation (what is called
super-Turing machines) in nature, but now I think that there is no such
thing (but anything remains possible, of course).

*But the idea of substrate-independent Turing machines is incomplete.*

I shouldn't say (if will jinx me!) but I've never gotten a flu shot and I
haven't gotten the flu in over 40 years.

But I hope the flu program doesn't start running in / affect my substrate!

- pt

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