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 <[email protected]> >>>> 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 <[email protected]> >>>>> wrote: >>>>> >>>>> On Thursday, January 17, 2019 at 6:31:06 AM UTC-6, Bruno Marchal wrote: >>>>>> >>>>>> >>>>>> On 17 Jan 2019, at 09:22, [email protected] wrote: >>>>>> >>>>>> >>>>>> >>>>>> On Monday, January 7, 2019 at 9:25:16 PM UTC, John Clark wrote: >>>>>>> >>>>>>> On Mon, Jan 7, 2019 at 8:03 AM <[email protected]> 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! > > 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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
