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] > <javascript:>> 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 > > -- > 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] <javascript:>. > To post to this group, send email to [email protected] > <javascript:>. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > -- 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.
