### Strange: quasars do not show time dilation in their dynamics

Lubos Motl told about Discovery that quasars don't show time dilation mystifies astronomers by Hawkins. I also received a link from Kram about this: thank you. The finding is rather strange.

Consider first what one expects. Lorentz invariance implies red shift for frequencies and in time domain this means the stretching of time intervals so that the evolution of distant objects should look the slower the longer their distance from the observer is. In the case of supernovae this seems to be the case. What was studied now were quasars at distances of 6 and 10 billion years. The time span of the study was 28 years. Their light was red shifted by different amounts as one might expect but their evolution went on exactly the same rhythm! This looks really strange.

One must notice that the frequency assigned to electromagnetic signature is not ordinary light frequency. For instance, is it analogous to a frequency assignable to massive particle or massless particle? Consider ordinary Doppler effect as an analog. If the redsift is effectively that of a massive particle then the redshift is given by f→ (1-v^{2})^{1/2}f =(1+z)f and for small relative velocities the redshift is about z=Δf/f =v^{2} smaller than for massless case f→ ((1-v)/(1+v))^{1/2}× f=zf giving z=Δ f/f =v in the same approximation. In the recent case however redshifts are large. From z+1= Hr, with redshift z=7 associated with r=.75 billion years one deduces z=56 for 6 billion ly and z=93.3 for 10 billion ly. Therefore the redshifts for massive and massless case are related by a factor of 2 as one easily finds.

Consider now the situation in TGD framework.

- Causal diamond defined as the intersection of future and past directed light-cones is the fundamental geometric object in zero energy ontology. In cosmological scales a possible interpretation of CD is as sub-cosmology. In particular, our comology would correspond to this kind of CD having sub-CDs having .... CDs possess moduli space. CD has M
^{4}position identified as say that of the lower tip. One can perform Lorentz boosts for CD leaving the lower tip invariant. The proper time distance between tips of CD is Lorentz invariant and defines an internal time standard of CD. For instance, for electron, d, and u quarks this time is .1 seconds, 1/1.28 milliseconds, and 6.5 milliseconds defining fundamental biorhytms. - p-Adic length scale hypothesis follows if the light-cone propert time distance between the tips of the CD is quantized in powers of two. This means that future light-cone is replaced with a union of light-cone proper time constant hyperboloids with size scales coming as powers of two. Cosmic time identified as the distance between the tips would be quantized and cosmic time would increase in jumps. As a matter fact, the relative coordinate between the tips should be quantized quite generally so that the light-cone proper time constant hyperbloids would be replaced with discrete lattice like structures. This would predict quantization of cosmic redshifts and explain the claimed strange phenomena like God's fingers containing galaxies along the line of sight with a quantized redshift.
- Could the quantization of cosmic time relate to the strange observation? What does the dynamics of objects with a frozen value of cosmic time look like when viewed from Earth? What is clear that the distant object does not recede away during the studied evolution period. The overall redshift for the studied events during its evolution is same. No dilation of the time interval between periodic events would takes place. But isn't this the case
in good approximation also in the measurements? And obviously this argument does not say anything about the time dilations associated with the samples at different distances.
This means that the time-like direction defined by the vector connecting tips of CD in M

^{4}is same as the direction of the time-like vector pointing from the tip of the very big CD defining what we call our Big Bang cosmology a to the M^{4}point at which the CD containing astrophysical object is located. This position characterizes all points of given CD so that the time dilation is constant the for internal dynamics of systems inside the CD. - Why the Lorentz boosts of quasar CDs in the two samples should be identical? Could the explanation relate to the fact that quasars are extremely distant objects meaning that the corresponding CDs are very large? Could the quasars in the two samples belong to the same CD?! If so then the internal dynamics would obey same rhytm but there would be a purely cosmological redshift! This effect would be basic prediction of zero energy ontology in cosmological scales and would become visible in very long length scales.

For background see TGD and Cosmology.

## 2 Comments:

http://www.newscientist.com/article/mg20627550.200-enter-the-matrix-the-deep-law-that-shapes-our-reality.html?full=true

During years I have been speculating about possible role of Riemann Zeta in fundamental physics.

Now it is clear that more general Zeta function defined by the generalized eigenvalues of the modified Dirac operator is a basic aspect of quantum TGD. See

this. From this it is a long way to concrete applications. Zeta functions appear also in string theories.

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