### Cosmic redshift as a purely kinematic effect

In cosmic redshift the frequency of the photon or graviton decreases and wave length increases with distance from the source. E= h×f implies that also the energy decreases. This is what Hubble's law says.

The redshift looks somewhat problematic prediction since it seems to be in conflict with the conservation of energy and momentum unless there exists a mechanism which explains how massless particle loses its four momentum gradually. In general relativity one might accept this since the very notions of energy and momentum become ill-defined. In TGD the situation is different. Four-momentum is conserved and one must understand how cosmic redshift manages to be consistent with this.

One must be very careful here since the values of wavelength and frequency, and four-momentum depend on the state of motion for the measuring system relative to the emitting system.

- Consider first empty Minkowski space. If the measuring system is in motion with respect to source with constant velocity, one obtains a redshift or blueshift depending on the velocity and direction of the motion. The Lorentz boost inducing the shift relates different orientations of time axis for the source and receiver. The 3-D tangent space of time= constant section of receiver is obtained by Lorentz boost from that for source and the velocity associated with this boost determines the redshift.

- Consider now what happens if time=constant slice is replaced with the cosmic time=constant slice of future directed light-cone. This surface is hyperboloid and mathematically equivalent with cosmic time=constant section of empty Robertson-Walker cosmology predicting cosmic redshift. The cosmic redshift can be understood using very simple argument. The redshift is determined by the relative orientations of the 3-D tangent spaces of hyperboloid at the positions of the source and receiver at the hyperboloid. The Lorentz boost relating the orientations of 3-D tangent spaces depends on the mutual distance and gives the cosmic redshift in empty Robertson-Walker cosmology defined by future light-cone. Cosmic redshift is mostly purely kinematical effect present already in empty space.

- Consider next 4-D space-time surface so that also the small effects of matter are included. The time coordinate of the space-time surface could be anything but in zero energy ontology, where space-time surfaces are inside causal diamonds (intersections of future and past directed lightcones) the light-cone proper time associated with either light-like boundary of CD is the natural time coordinate defining cosmic time. Now one considers the M
^{4}projections of the 3-D tangent space of the 3-D time= constant section of the space-time surface and the Lorentz boost relating the 3-D projections for source and receiver determines the redshift. The non-flatness of space-time surface gives some small corrections to the formula obtained for the case of future light-cone.

- What about the energy of photon or graviton? Does it decrease with the distance from the sender as E=h× f requires? And is this consistent with the conservation of energy and momentum? In General Relativity one would of course have a serious problem and GRT indeed forces to give up conservation laws of four-momentum and angular momentum in long scales since these notions are not even well-defined. This was the basic motivation for TGD.

In TGD there is no need to give up the conservation laws since the reduction of four-momentum predicted by redshift formula is a purely kinematic effect since the tangent spaces of sender and receiver corresponds to different states of motion.

The motivation for writing this comment came from proposals that cosmic redshift could be understood in terms of Planck constant, which would decrease with time in such a manner that that E=h×f would remain constant and energy would therefore be conserved despite the fact that frequency decreases (see this). At first the idea looks attractive in TGD framework, where energy is conserved. The purely kinematical explanation is however exponentially more feasible.

I have however proposed the possibility that at least part of gravitons are dark as one implication of h_{gr} = GMm/v_{0} hypothesis. The gravitons with given frequency would have much larger energies than expected and this might dramatically affect the detection of gravitational radiation since the dark gravitons could be sees as bunches of ordinary gravitons carrying much larger energy than ordinary gravitons and could be discarded as noise. If most of gravitons are dark, the experiments trying to detect gravitons might give null results.

## 6 Comments:

Still IMHO there is a second possibility, of a sort of tired light system created by the proliferation of micro dark matter black holes in and outside galaxies and nebula. As a result the universe is able to contract at the same time.: see:

https://www.academia.edu/5925140/Hubble_Redshift_Despite_Universal_Contraction_is_possible

One of the big differencies between light as photon and a graviton is that the graviton get stronger with distance, in the same way as gluon does. The Photon and em-force gets weaker.

http://article.sapub.org/10.5923.j.astronomy.20130201.02.html maybe this?

Reshift is a real challenge for TGD approach where four-momentum is conserved. Tired light is what comes first in mind and I have years ago considered also the possibility that during travel photon emits gravitons and loses gradually energy.

This is however rather complex model as compared with the model involving just the kinematics of special relativistic Doppler effect generalised to the level of tangent space of 3-surface with M^4 projection which varies.

Also in string model compactifications four-momentum is conserved for M^4xS time compactification and geometric view about gravitation in 4-D is assumed to somehow emerge. It would be interesting to know whether string model builders have considered this problem at fundamental level without assuming directly the QFT limit.

To Ulla:

Thanks for the mystery link relating to the increasing Planck constant: it strangely disappeared from Thinking Allowed after I had commented it as also the other link raising between the lines the possibility that Planck constant might not be so constant after all.

I would not say that graviton is like gluon. Both em and gravitational forces are 1/r^2 long range forces which gets weaker with distance. Color force gets stronger and is color potential is proportional to distance in simple parametrisation.

Ulla: thenks for the url. IMHO,a variable ( lengthening) Planck constant is present around black holes and the main origin of the redshift.

If we image the vacuum as a tetrahedral structure with variable edge length around BHs. see:

https://www.flickr.com/photos/93308747@N05/15434862534/in/photostream

It is usually said that gravity becomes stronger with distance, and that's why it keeps universe together. Today the opposing force in DE is stronger, however. As it clearly acts on matter, interactive, it would mean a net inflyux of energy?

Plancks constant would maybe be better described as a quantization constant, which more clearly says it is a product of its surroundings in form of uncertainty, hence it vanishes with the uncertainty too. I have asked many why it is reintroduced with black holes, as they also describes a quantum system with uncertainty.

Here Miles Mathis thoughts around it. http://milesmathis.com/planck.html

http://physics.info/photoelectric/ they describe also a threshold effect.

Ulla, Miles Mathis introduces the dual Higgs as vacuum particle, which I support with the idea that even mass in unaccelerated motion uses the differences in Higgs pressure on their spinning and Lorentz polarized fermions. see:

https://www.flickr.com/photos/93308747@N05/8718462642/in/photostream

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