Thursday, April 26, 2007

In what sense dark matter is dark?

The notion of dark matter as something which has only gravitational interactions brings in mind the concept of ether and is very probably only an approximate characterization of the situation. As I have been gradually developing the notion of dark matter as a hierarchy of phases of matter with an increasing value of Planck constant, the naivete of this characterization has indeed become obvious. While writing yesterday's long posting Gravitational radiation and large value of gravitational Planck constant I understood what the detection of dark gravitons might mean.

During the last night I realized that dark matter is dark only in the sense that the process of receiving the dark bosons (say gravitons) mediating the interactions with other levels of dark matter hierarchy, in particular ordinary matter, differs so dramatically from that predicted by the theory with a single value of Planck constant that the detected dark quanta are unavoidably identified as noise. Dark matter is there and interacts with ordinary matter and living matter in general and our own EEG in particular (identified in standard neuroscience as a noise however correlating with contents of consciousness, God Grief!) provide the most dramatic examples about this interaction. Hence we can consider the dropping of "dark matter" from our vocabulary altogether and replace "dark" with the spectrum of Planck constants characterizing the particles (dark matter) and their field bodies (dark energy).

A. Background

A.1 Generalization of the imbedding space concept

The idea about quantized Planck constant in ordinary space-time is not promising since in a given interaction vertex the values of Planck constants should be identical and it is difficult to imagine how this could be realized mathematically. With the realization that the hierarchy of Jones inclusions might relate directly to the value hierarchy of Planck constants emerged the idea about the modification of imbedding space obtained by gluing together H→ H/Ga×Gb, Ga and Gb discrete subgroups of SU(2) associated with Jones inclusions along their common points (see this and this). Ga and Gb could be restricted to be cyclic and thus leaving the choice of quantization axis invariant. A book like structure results with different copies of H analogous to the pages of the book. Each sheet corresponds to a particular kind of dark matter or dark energy depending on whether it corresponds to a particle or its field body.

A.2 Darkness at the level of elementary particles

If elementary particles are maximally quantum critical in the sense that the corresponding partonic 2-surfaces belong to the 4-D intersection of all copies of the imbedding space (assuming Ga and Gb are cyclic and leave quantization axes invariant) so that one cannot say which value of Planck constant they correspond to. The most conservative criterion for the darkness at elementary particle level is that elementary particles are quantum critical systems so that only their field bodies are dark and that particle space-time sheet to which I assign the p-adic prime p characterizing particle corresponds to its em field body mediating its electromagnetic self interactions. Also Compton length as determined by em interaction would characterize to this field body. Compton length would be completely operational concept. This option is implied by the strong hypothesis that elementary particles are maximally quantum critical meaning that they belong to sub-space of H left invariant by all groups Ga×Gb leaving quantization axis invariant so that all dark variants of particle identified as 2-D partonic surface would be identical.

The implication would be that particle possess field body associated with each interaction and an extremely rich repertoire of phases emerges if these bodies are allowed to be dark and characterized by p-adic primes. Planck constant would be assigned with a particular interaction of particle rather than particle. This conforms with the formula of gravitational Planck constant hbargr= 211×GMm (not the most general formula but giving order of magnitude, for details see this), whose dependence on particle masses indeed forces the assignment of this constant to the gravitational field body as something characterizing interaction rather than particle.

Of course, nothing prevents from accepting the existence of elementary particles, which are not completely quantum critical and the subgroups of Ga×Gb define a hierarchy for which elementary particle proper is also dark. This extends the repertoire and leads to idea like N-atom in which electrons correspond to N-sheeted partonic 2-surfaces so that as many as N electrons can be in identical quantum state in the sense as the word is used in single sheeted space-time. I have proposed applications of N-atom and hierarchy of subgroups to the basic biology (see this, this, and this.)

B. How various levels of dark matter hierarchy interact?

At classical level the interaction between various levels of hierarchy means that electric and magnetic fluxes flow between sectors of the imbedding space with different values of Planck constant. Faraday's induction law made it from beginning clear that the levels of the hierarchy must interact.

It became also clear that dark bosons can decay to ordinary bosons by a phase transition that I called de-coherence. For instance, a dark boson defining an N-sheeted covering of M4 decays in this process to N 1-sheeted coverings. The N-fold value of Planck constant means that energy is conserved if the frequency is not changed and "Rieman sheets" ceases to form a folded connected structure in the process.

The so called massless extremals (see this, this, and this) and define n(Ga)×n(Gb) fold coverings of H/Ga×Gb, n(Ga)-fold coverings of CP2, and n(Gb)-fold coverings of M4. They are are ideal representatives for dark bosonic quanta. The proposal was that dark EEG photons with energies above thermal energy at room temperature can have non-negligible quantum effects on living matter although their frequencies would correspond to ridiculously small energies for the ordinary value of Planck constant. Those who are weak can combine their forces! Marxism (or synergy, as you will) at the elementary particle level!

Quite generally, field bodies can mediate interaction between particles at any level of the hierarchy. The visualization is in terms of the book metaphor. Virtual boson, or more generally 3-D partonic variant of the field body mediating the interaction, emitted by a particle at a given page leaks via the rim of the book to another page. The mediating 2-surface must become partially quantum critical at some stage of process. This applies to both the static topological field quanta (quanta of electric and magnetic fluxes) connecting particles in bound states and to the dynamical topological field quanta exchanged in the scattering (say MEs). Thus dark matter and ordinary matter interact, and only the value of Planck constant associated with the mediators of the interaction is different and should explain the apparent darkness.

C. What does this mean experimentally?

At this moment I would say that dark matter has standard interactions but because of large value of Planck constant these interactions occur in different manner. Even gravitons would be dark. Single graviton with a large value of hbar generates much larger effect than the ordinary graviton with the same frequency.

The good news is that the possibility to detect gravitational radiation improves dramatically. The bad news is that experimenters firmly believe in the dogma of single universal Planck constant and continue to eliminate the signals which are quite too strong as a shot noise, seismic noise, and all kind of noises produced by the environment. Ironically, not only gravitational radiation but also dark gravitons(!), might have been detected long ago, but we continue to get the frustrating null result just because we have a wrong theory.

The same would apply to dark quanta of gauge interactions and we might be receiving continually direct signals about dark matter but misinterpreting them. The mystery of dark matter would be generated by a theoretical prejudice just as the notion of ether for a century ago.

From the foregoing it should be clear "dark" is just an unfortunate letter combination, which I happened to pick up as I started this business. My sincere apologies! To sum up some basic points.

  1. In TGD Universe dark matter interacts with the ordinary matter and is detectable but the interactions are realized as bursts of collinear quanta resulting when a dark boson de-coheres to bosons at the lower level of hierarchy. This quantum jump corresponds to some characteristic time interval at the level of the space-time correlates and things look classical from the point of detector at the lowest level of the hierarchy. After the elimination of noise the time averages for the detection rates over sufficiently long time interval should be identical to those predicted by a theory based on ordinary Planck constant.

  2. In the previous posting I told about additional fascinating aspects related to the detection of dark gravitons due to the fact that gravitational Planck constant hgr= 211GMm (in the simplest case) of absorbed dark graviton characterizes the field body connecting detector and source and is proportional the masses of receiver and source. Both the total energy of dark graviton and the duration of process induced by the receival of large hbar graviton are proportional to the masses of the receiving and emitting system and thus carry information about the mass of the distance source. Some day this could make possible the gravitational counterpart of atomic spectroscopy. This additional information theoretic candy gives one further good reason to take the hierarchy of Planck constants seriously.

  3. Planck constant should carry information about the interacting systems also in the case of other dark interactions. In the case of em interactions the condition hbar= 211Z1Z2e2 or its generalization should hold true when perturbative approach fails for the em interaction between two charged systems. Z1Z2e2> 1 is the naive criterion for this to happen. Heavy ion collisions would be an obvious application (I discussed RHIC findings as one of the earliest attempts to develop ideas by applying them, see this). Gamma ray burst might also be an outcome of single very dark boson giving rise to precisely targeted pulse of radiation. The criterion should apply also to self interactions and suggests that in the case of heavy nuclei the electromagnetic field body of the nucleus becomes dark. Color confinement provides also a natural application.

  4. Dark photons with large value of hbar could transmit large energies through long distances and their phase conjugate variants could make possible a new kind of energy transfer mechanism essential in TGD based quantum model of metabolism and having also possible technological applications. Various kinds of sharp pulses suggest themselves as a manner to produce dark bosons in laboratory. Interestingly, after having given us alternating electricity, Tesla spent the rest of his professional life by experimenting with effects generated by electric pulses. Tesla claimed that he had discovered a new kind of invisible radiation, scalar wave pulses, which could make possible wireless communications and energy transfer in the scale of globe (for a possible but not the only TGD based explanation see this). This notion of course did not conform with Maxwell's theory, which had just gained general acceptance so that Tesla's fate was to spend his last years as a crackpot. Great experimentalists seem to be to see what is there rather than what theoreticians tell them they should see. They are often also visionaries too much ahead of their time.

For more details see the chapter TGD and Astrophysics of "Classical Physics in Many-Sheeted Space-time". For the applications of dark matter ideas to biosystems and living matter see the online books at my homepage and the links in the text.

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