From: jyablon@nycap.rr.com   
      
   On Wednesday, May 9, 2018 at 5:07:54 PM UTC-4, Phillip Helbig (undress to   
   reply) wrote:   
   >   
   > First, G doesn't appear in the Planck formula.  If we imagine changing   
   > the value of G, we would not change the Planck formula, but would change   
   > the appearance of Wheeler's vacuum, noticeably if G were changed   
   > drastically (ignoring for the moment other effects of such a change).   
   > There would then be a difference which, as you argue, we don't observe   
   > today.  My guess is that the Planck formula would still work, but then   
   > give results different to what you expect from the Wheeler vacuum.   
   >   
   > In another sense, it is not a coincidence that Hawking radiation has a   
   > black-body spectrum, so perhaps at some level this equivalence is   
   > already there, though perhaps not in the form you describe.   
   >   
   > Analogs of cosmological redshift in particle accelerators?  I've never   
   > heard of such a thing.   
      
   First, if there is no "cosmological redshift in particle accelerators"   
   (and I am NOT arguing that there is), then this is important simply   
   because it tells us that at least in this way, there is a breakdown in   
   the often-employed analogy between looking far into the heavens and   
   looking deeply into the microscopic world.  And it is always good to   
   know how and where analogies break down.   
      
   Next, you make a very interesting point about changing G.  While I am   
   skeptical that G changes (and I sure as heck would never buy that c or   
   h-bar or the Boltzmann constant k_B would ever change), let’s look at   
   the mathematics – really the simple algebra – of the Planck scale, and   
   what would happen if G was to change, including "other effects" that you   
   ignored "for the moment."   
      
   Recall that G*Mm from the numerator of Newton’s law has the exact same   
   physical dimensions as h-bar*c, and that h-bar*c when each of h-bar and   
   c are set to 1 is the unit of "interaction strength."  Recall also that   
   Coulomb’s k_C*Qq where k_C is Coulomb’s constant also measures   
   interaction strength, and that the running EM coupling   
   \alpha=1/137.036…=k_Ce^2 where e is the quantum of charge (electron or   
   proton).  Similarly, the weak and strong \alpha couplings measure   
   interaction strength.  Grand Unified Theories (GUTs) tell us that all of   
   these couplings merge to the same strength at the gravitational coupling   
   at the Planck scale, and that the asymptotic freedom signified by   
   decreasing coupling strength with deep probe of the non-abelian strong   
   coupling begins to reverse itself with by showing an increased coupling   
   strength.   
      
   So, with that in mind, the Planck mass M_P is defined such that   
   G*M_P^2==h-bar*c, i.e., such that M_P makes these two interaction   
   strengths equal, thus M_P=sqrt(h-bar*c/G).  Then everything else is very   
   simple algebra.  The Planck energy is E_P=M_P*c^2.  The Planck length is   
   the Compton wavelength \lambda=h-bar/M_P*c of the Planck mass, and the   
   Planck time is the Planck length divided by c.  Finally, importantly for   
   this discussion, the Planck temperature is related to the Planck energy   
   by T_P=E_P/k_B, and this is the temperature that we expect in the   
   Wheeler vacuum to drive the blackbody spectrum.  It is on the order of   
   1.4x10^32 K.  Rather toasty.   
      
   So, if G was to change as you have suggested we imagine, then so too   
   would the Planck temperature change.  Specifically, if G was to become   
   larger, then the Planck temperature would become smaller as one probed   
   deeper and deeper into the micro-world with hotter temperatures, and   
   thus the Planck spectrum of the vacuum would become redshifted relative   
   to what you would otherwise expect if G was constant as we all generally   
   assume.  This would then be analogous to the cosmological experience of   
   looking far away in distance and far back in time, to find that   
   everything was hotter long ago, but also that all this long-ago heat and   
   its higher-frequency blackbody spectrum was offset by a redshift because   
   it is also far away and moving away and thus causing a Doppler effect.   
      
   So, whether subconsciously or not, you have provided one possible answer   
   to my question: if G was larger in the past and is now growing smaller,   
   cosmologically this would mean that matter attracted matter more   
   strongly in the past than it does at present.  Microscopically, this   
   would mean that as we make make the vacuum hotter and hotter, the Planck   
   temperature will diminish.  So, while we may be expecting 10^32 K, we   
   might find, say, 10^25 K and conclude that there was some unexplained   
   redshift.  In this event, the big-and-small analogy would not break   
   down, at least insofar as redshift is concerned.   
      
   The math one does to flesh this out would have to change G just enough   
   so that the "redshift" is linear with "smallness" suitably-defined, just   
   as it is in cosmology.  In this event, one would get down to the Planck   
   scale more "rapidly" than we presently expect.  Whether this would hold   
   any water, I have no idea at present.  But it seems that one would look   
   for empirical signs of this on the nuclear and sub-nuclear scale,   
   possibly in some unexpected changes to the running strong interaction   
   coupling, which would start its upward turn from asymptotic freedom   
   toward Plank-scale GUT unification at larger distances, i.e., less   
   smallness, than we presently expect.   
      
   This would also beg the question whether some of what we presently take   
   for granted in the cosmological world, including the cosmological   
   redshift and it origins in a big bang, can alternately be explained as   
   evidence of a changing G.  Again, I am very skeptical of changing G. But   
   G is the one physics constant to which fair number of knowledgeable keep   
   an open mind insofar as its true "constancy."   
      
   Thanks for the good food for provoking thought.   
      
   Jay R. Yablon   
      
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