Wednesday, April 18, 2007

New strange finding about dark matter

Below a popular summary about the article Dark Energy-Dark Matter Interaction and the Violation of the Equivalence Principle from the Abell Cluster A586 by O. Bertolami, F. Gil Pedro and M. Le Delliou. The article reports an experimental finding interpreted as a possible violation of Equivalence Principle. This finding certainly provides important information about the real nature of dark matter but I would not interpret it in terms of the failure of Equivalence Principle.

"If Galileo could have dropped a lump of dark matter and a lump of normal matter from the top of the Leaning Tower of Pisa, he might have expected them to fall at the same rate," says Orfeu Bertolami at the Instituto Superior Técnico in Lisbon, Portugal. "But he would have been wrong." Bertolami and his colleagues studied a galaxy cluster known as Abell cluster A586 to see if dark matter and normal matter fall in the same way under gravity. He says this cluster is ideal because it is spherical, suggesting that it has settled down: "The only motion we are seeing now is due to gravity toward the cluster's centre."

The team studied 25 galaxies in the cluster using gravitational lensing - the shift in the apparent position of a light source caused by gravity bending the light. When they analysed the positions of galaxies using conventional models, things just didn't add up. "It only makes sense if the normal matter is falling faster than the dark matter," Bertolami says.

This is the first astronomical observation to suggest that Einstein's principle of equivalence is violated, says Bertolami ( ). "If dark energy interacts with dark matter in some way, it could be affecting its motion."

In the article an estimate for the ratio ρKW of the kinetic energy and potential energy densities of visible matter around Abell cluster is deduced. It is found to be about -.76 +/-.05 instead of -.5 predicted by virial theorem. If dark matter accelerates slower radially, its contribution to the potential energy per volume is smaller at a given distance and potential energy density remains smaller than otherwise so that ρKW is larger than predicted by the virial theorem.

Let us assume that this finding is not a fake. How could one one understand it in TGD framework? The characteristic difference between ordinary and dark matter in TGD framework is that dark matter in astronomical length scales corresponds to very large values of Planck constant forming macroscopic quantum phases in astrophysical length scales. The rate of dissipation is expected to be proportional to 1/hbar and should therefore be much slower for the dark matter than its visible counterpart. This conforms with the much longer time scale of quantum coherence.

Consider in this framework the free fall experiment for objects consisting of visible and dark matter.

  • One cannot just pick up two objects which are both at rest. One must assume that in the initial situation both matter and dark matter have non-radial velocity component with respect to the galaxy cluster which is gradually reduced by dissipation so that finally a radial fall towards center results. For dark matter this reduction occurs at much slower rate so that the assumption that dark matter would have ended in a free radial fall need not hold true or it has ended in free radial fall much later. Therefore the radial component of the velocity for dark matter should be smaller as the naive interpretation of observations suggests.

  • If dark matter is in quantum state at Bohr orbit situation is like in hydrogen atom: dark matter makes transitions to lower orbitals through discrete quantum jumps with the duration of quantum jump scaling like hbar. It would never end up to the situation in which radial free radial fall takes place! One would have a situation similar to that what one encountered more than century ago with hydrogen atom: no infrared catastrophe was observd although classical theory predicted it. If so, the solution of the recent depressing situation in quantum gravitation (to put it mildly) would be the same as in the similar situation for a century ago (also at that time physics was thought to be done apart from some minor details!)

The idea about Bohr orbits of astrophysical size sounds of course weird but the basic finding which led to the evolution of ideas about dark matter and spectrum of Planck constants was the Bohr quantization of orbital radii for inner planets and outer planets with a huge value of Planck constant hbar= GMm/v0, v0≈ 10-4. Evidence for a similar quantization has been observed for exoplanets. The explanation would be that dark matter moves along Bohr orbits and planetary visible matter attached to it gravitationally follows.

For references about planetary Bohr orbitology and details about TGD based model for it, see the chapter TGD and Astrophysics of "Classical Physics in Many-Sheeted Space-Time".


At 4:35 PM, Anonymous Carl Brannen said...

Gosh, 0.75 instead of 0.5? It sounds like the kinetic energy has 3x as many degrees of freedom as it should. This seems to be consistent with the quasinormal modes of oscillation of black holes. See section 4 of Lubos Motl's paper gr-qc/0212096.

Let's see if I can link it here: gr-qc/0212096

At 10:26 PM, Blogger Matti Pitkanen said...

Dear Carl,

it would be interesting to have an opinion of professional about the plausibility and real significance of the claimed result.

I got interested because dark matter with large Planck constant would predict all kinds of exotic effects.

*Large scale variants of molecular symmetries (Saturn hexagon in Kea's blog and Red Square).

*Preferred quantization directions manifest in astrophysical scales(might relate to the anomaly of microwave background).

*Planetary Bohr orbitology.

*Anomalously low rates of dissipation of dark matter.

I am not able to see any obvius connection with black hole chemical potential but this might be just my lack of familiarity with this topics. I looked the Motl's paper. Kea said something about this in in her blog. I would interpret the partition function as Fermi Dirac with chemical potential mu= -log(3) so that there would be no mystery. Lubos talked about "tripled Pauli" which does not make sense to me.


At 3:43 PM, Blogger CarlBrannen said...

"Chemical potentials" make a good rug to hide the details of more fundamental physics; they amount to defining a special energy that depends on details that are being modeled as an energy. They are a convenient way to do the mathematics, but they hide the fundamental details. In chemistry, one can eliminate chemical potentials by going to a deeper analysis using protons, neutrons, electrons, and their interactions.

For the paper you quoted, equation 28 defines the ratio of the kinetic and potential energy densities as
\rho_K / \rho_W = -0.75
while the classical expectation would be -0.5.

If classical theory miscounted the number of kinetic energy states by a factor of 3, the ratio will change from 1/(1+1) = 0.5 to 3/(1+3) = 0.75, which accounts for the change in the ratios.

But to do this, you have to triple the number of states. Hence tripled statistics. The "Pauli" is another story, but a similar one.

If the spin statistics theorem is true (and it is a very complicated and long theorem, so it is easy for it to be wrong), then the statistics of a spin-0 object is Bose, and it is impossible to combine Bose objects into a Pauli spin thing.

If the spin statistics theorem is wrong, and tripled Pauli statistics is right, then it is possible to combine spin-0 objects to make a spin-1/2 object. This is what I've been working on.

To do this, you treat the left and right handed chiral fermions as spin-0 objects with existence separate from each other.

At 8:23 PM, Blogger Matti Pitkanen said...

I understand how you get the number
but it remains unclear to whether one can estimate this kind of ratio as a ratio of kind you are suggesting.

As a matter fact, the use of virial theorem is questionable in any case. What we have is the ratio of kinetic to potential energy and virial theorem says that this should be -1/2. Virial theorem is obtained from mv^2/r= +dV/dr = -V/r giving mv^2/2= -V/2 and reflects 1/r character of Newtonian gravitational potential in the idealization that space is empty around the cluster.

One could question the assumption that space is empty: dark matter is there! In galactic halos M(r) behaves like r and kinetic energy would be constant whereas gravitational force would behave as 1/r and Newtownian gravitional potential as log(r) so that virial theorem would not hold true. If M propto r holds true around galactic cluster, one cannot apply the virial theorem in the proposed form.

This does not however spoil the argument. Suppose that the presence of dark matter changes the situation so that one has V(r) propto 1/r^(1-epsilon). epsilon should be positive since one has F= -G(M(r))/r^2 and M(r) grows. In this case one would have something like T= ((1-epsilon)/2)*V so that the factor would get smaller and the situation would actually improve.


At 9:34 PM, Blogger CarlBrannen said...

Matti, thanks for sharpening my argument (also known as cutting away the dull stuff).

The virial theorem is related to the assumption of equipartition of energy. When you triple the number of ways of obtaining the same kinetic energy (i.e. tripled Pauli statistics), you triple the statistical weight. The result is that there is 3x as much energy put into the kinetic portion than otherwise expected. Hence the 3/(3+1) = 3/4 ratio instead of the 1/(1+1) = 1/2 standard QM would expect.

It should be mentioned that all these calculations are done using natural units. What is going on here is that the usual h-bar of QM is apparently not the h-bar of general relativity. If you used different h-bars for astronomy and QM, (that is, different thermodynamics for the two regimes) one could not detect the problem.

In statistical mechanics, changes to the effective value of h-bar can arise from degrees of freedom being frozen out at low energies. (If a reader wants to understand this better, look up "equipartition" in wikipedia and read what they have to say about frozen degrees of freedom.)

Thus, the unavoidable interpretation of both the quasinormal degrees of freedom in Motl's paper and the violation of the virial theorem in the paper discussed here is that the full number of degrees of freedom in GR is 3x larger than the degrees of freedom that QM would count.

Since it is GR that counts the larger number of degrees of freedom, it is QM that must be adjusted. That is, QM is missing a factor of 3 in the way it counts degrees of freedom.

Everybody already knows that the standard model is not correct at high energies, that is, it is only an "effective" QFT and works at low temperatures. What these results do is give a big hint on how to fix QFT. Namely, the underlying theory (the unified field theory everyone is looking for), has triple the number of degrees of freedom as the standard model.

At 12:20 AM, Blogger Matti Pitkanen said...

Thank you for explaining your idea. The partition function brings in my mind 3-fold ground state degeneracy.

This kind of ground state degeneracy appears also in p-adic mass calculations based on p-adic thermodynamics and is due to the fact that one can created from "tachyonic" ground state with negative conformal weight massless grounds state with vanishing conformal weight in several manners using Virasoro algebra generators.


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