> 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: 

https://www.youtube.com/watch?v=2DIl3Hfh9tY

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

https://www.youtube.com/watch?v=foRPKAKZWx8

Bruno


> 
> LC
> 
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