# Re: Planck Length

> On 24 Jan 2019, at 12:54, Lawrence Crowell <goldenfieldquaterni...@gmail.com>
> 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 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
>>
>
>
>
>
> 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!

Take care!

An interesting video which shed a bit of light (for me at least) is the
following talk by Susskind, although I have some problem with the notion of
“surface of a photon”, to be sure:

BTW, a rather nice (but long) introduction to GR is given here:

Bruno

>
> LC
>
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