# Re: Planck Length

```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 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
>>>
>>>
>
>
> 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

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