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 -- 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.
