> 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] <javascript:> 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. > > 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. > 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 > > 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.
