Could the interpretation of Planck mass be totally wrong?
Recent day theoretical physics is suffering from a heavy load of irrational beliefs, which are remainders from the era of classical physics but ceased to have real justification anymore. Unfortunately, those who should have told do colleagues about this have forgotten to do so. Seems that it is me who must do it;-). Here comes the list.
- Naive length scale reductionism. Super string models and M-theory were believed for some time to be the last jewel in the crown of length scale reductionism. Fractality is the obvious candidate for a vision replacing it but for some reason - probably sheer vanity - colleagues refuse to give up reductionism.
- Quantum effects are important only in microscales has prevented progress in biology. Only now this taboo has began to lose its grasp as experimental facts do not leave any other options.
- Dark matter is trivial thing - just one or two exotic particles with very weak interactions. All experiments carried out hitherto suggest that this belief is wrong.
- Heath death occurs unavoidably and all life disappears from the Universe - terribly sorry. This belief is dictated by the second law in its recent form. Although the consequences are in blatant conflict with the fact that universe has been evolving to become and more complex, this taboo is absolute. Some theoreticians even manage to take seriously the notion of Boltzman brain and are able to believe that life emerged as a random fluctuation. As more and more evidence for the presence of organic molecules in Universe emerges, it is becoming clear that this fluctuation should have had size of entire Universe.
- Planck length mystics is a further strange belief. Although it has led to dead end in the attempts to construct quantum theory of gravitation, it is still taken seriously.
A more feasible interpretation for the inverse of Planck length squared is as value of curvature scale above which gravitational fields are strong. In strong fields the perturbative expansion of standard quantum field theory ceases to make sense. In TGD framework Planck length is replaced with CP2 scale, which is both a genuine length and measure for the curvature of CP2. In TGD Planck mass is only a parameter associated with macroscopic gravity as will be explained. In super string theories gravitational constant defines only an algebraic quantity rather than defining a concretely unit of length.
To understand what is involved, one can start Newtonian gravitation.
- Gravitational potential V= GMm/r is the key notion. One might expect that when the parameter GMm/hbar is larger than unity, something terrible happens and perturbative expansion fails. The criterion would be Mm>hbar/G. This criterion involves only the product of masses, usually macroscopic masses. It does not contain any length! Could respected colleagues have been on wrong track?!
- What is interesting that for M=m the condition GM2> 1 holds true in condensed matter when M equals to the mass of large neuron with size of L≈.1 millimeters! L is definitely not the Planck length! Could it be that the size scale of big cell defines the scale in which on-perturbative quantum gravitational effects become important?! Could it be that Planck mass rather than Planck length is important relates to biology rather than with ultra short mass scales?
This seems to be the case in TGD framework as the following arguments are meant to demonstrate! Unfortunately, the entire elaborate construction of quantum gravitation based on superstrings would be deadly wrong if this were the case. Therefore I do not expect that superstringy colleagues will continue readin if they ever started it.
As an eternal optimist I do however continue.
- Nottale was the first one to introduce the notion of gravitational Planck constant hgr= GMm/v0, where v0 is a characteristic velocity assignable to the system. Nottale proposed that the motion of even planets in solar system is quantized so that one has Bohr orbits. The value of hgr however differs for inner and outer planets being 5 times larger for outer planets so that it must characterize pair of systems rather than being a fundamental constant. Note that the dark Compton length for m would be GM/v0 and same for all inner/outer planets.
- In TGD framework quantum criticality predicts a hierarchy of effective (or real - depending on interpretation) Planck constants heff=n×h. Integer n has geometric/topological interpretation as the number of sheets for space-time surface having structure of singular covering with sheets co-inciding at 3-surfaces at the boundaries of causal diamonds - and defining the ends of space-time (also restaurants and all other things reside there;-)). This is space-time correlate for the non-determinism accompanying quantum criticality. The original identification was motivated by that proposed by Nottale and was generalized to other interactions such as electromagnetic interaction: in the case of electromagnetism one would have hem= Z1Z2e2/v0.
- One can assign heff =hgr to magnetic flux tubes connecting masses M and m and mediating gravitational interaction between them. Note that string theorists have started to talk about wormholes as mediators of entanglement. In TGD framework magnetic flux tubes carrying monopoles fluxes serve as correlates of negentropic entanglement and mediate gravitational interaction. Ordinary visible matter is condensed around dark matter structures and their genuine quantum character implies the approximate Bohr orbit property of planets among other things. Also in living matter genuine quantal behavior of dark matter implies approximate quantal looking behavior of ordinary matter, which is - sad to say;-) - living in slavery under the control of dark matter.
The two identifications of Planck constant should be equivalent. This gives heff= hgr in the case of gravitational flux tubes. This leads to very nice predictions in quantum biology concerning biophotons and their role.
- In TGD framework flux tubes are also acccompaned by fermionic strings so that string theory becomes part of TGD but in a manner totally different from that in super string models , where the string tension is fixed and given by 1/G essentially. In TGD this identification would not allow macroscopic gravitation at all since strings at flux tubes serve as correlates for the formation of gravitational bound states and the strings would be hopelessly short: the distance between two gravitationally bound masses could not be much longer than Planck length. [Quite inofficially and in brackets: the situation is the same in super string models in their original form but polite manners do not allow to say this aloud for next few decades;-)]. In TGD the string tension is dynamically generated and essentially the density of magnetic energy per unit length and decreases as the string length increases.
- When does the transition to the dark phase occur? The key idea is following. Mother Nature loves the theoreticians working so hardly to understand her and since non-perturbative quantum theory is so difficult a challenge, Mother Nature has decided to be merciful. When needed, she makes a phase transition to a phase in which the Planck constant is so large that quantum perturbation series converges. In the case of gravitation a phase transition to a dark matter phase characterized by hgr= GMm/v0 should take place, when GMm is so large that perturbation theory does not converge. The naive estimate is GMm/h>1 for gravitational interactions and Z1Z2e2/h>1) for electromagnetic interactions. The perturbative parameter becomes simply v0/c<1 and everything works again. As noticed, for M=m and in condensed matter this phase transition should occur for gravitational interaction in the scale of a large cell - something like .1 millimeters. For em interactions it should occur in shorter scales and the values of Planck constants would be much smaller.
Quantum criticality is however the basic criterion. Even at LHC quantum criticality can be encountered. The phase transition to QCD plasma can be such a phase transition. What would happen that large heff phases are generated and since the collision energies are so large, resonances with masses which correspond to particles of M89 hadron physics with mass scale 512 times that of ordinary hadron physics can appear at criticality where they have large Planck constant and Compton length of order nucleon size -say. Thus quantum criticality allows to zoom up physics at much higher energies to longer length scales. This would be really marvellous! In biology dark EEG would correspond to photons with visible and UV energies and would be a zoom up of physics below micron scale!
Could this zooming up be a microscope provided by Mother Nature and be someday used as an experimental method to study physical systems, which for ordinary value of Planck constant are too small? Could the physics of dark gravitational systems scaling Compton length hbar/m to GM/v0 provide this possibility in the case of elementary particles?