> On 24 Jan 2019, at 12:54, Lawrence Crowell <[email protected]> > 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!
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 > > -- > 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <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.
