Spreading of Ultrarelativistic Wave Packet and Redshift
In standard cosmology, the red shift of light coming to the Earth from distant objects is usually explained as a consequence of the fact that the Universe is expanding. This explanation has been questioned by many authors and many other explanations have been proposed. One of the examples – a recent paper by Leonardo Rubio “Layer Hubble and the Alleged Expansion of the Universe” in viXra:1206.0068.
A standard explanation implies that photons emitted by distant objects travel in the interstellar medium practically without interaction with interstellar matter and hence they can survive their long (even billions of years) journey to the Earth. I believe that this explanation has the following obvious flaw: it does not take into account a well-known quantum effect of wave-packet spreading and the photons are treated as classical particles (for which wave-packet spreading is negligible). The effect of wave-packet spreading has been known practically since the discovery of quantum mechanics. For classical nonrelativistic particles this effect is negligible since the characteristic time of wave-packet spreading is of the order of ma2/ℏ where m is the mass of the body and a – its typical size. In optics the wave-packet spreading is usually discussed in view of the law of dispersion ω(k) when a wave travels in the medium. But even if a photon travels in empty space, its wave function is a subject of wave-packet spreading.
A simple calculations the details of which can be found in my paper viXra:1206:0074, gives for the characteristic time t* of spreading of the photon wave function a quantity given by the same formula but with m replaced by E/c2 where E is the photon energy. This result can be rewritten as t* = 2πT(a/λ)2 where T is the period of the wave, λ is the wave length and a is a dimension of the photon wave function in the direction perpendicular to the photon momentum. Hence even for optimistic values of a this quantity is typically much less than a second.
If spreading is so fast then a question arises why we can see stars and even planets rather than an almost isotropic background. The only explanation is that the interaction of photons with the interstellar medium cannot be neglected. On quantum level a description of the interaction is rather complicated since several processes should be taken into account. For example, a photon can be absorbed by an atom and reemitted in approximately the same direction. This process is an illustration of the fact that in the medium the speed of propagation is less than c: because after absorbing a photon the atom lives some time in an excited state. This process plays an important role from the point of view of wave-packet spreading. Indeed, the atom emits a photon with a wave packet of a small size. If the photon encounters many atoms on its way, this does not allow the photon wave function to spread significantly.
In view of this qualitative picture it is clear that at least a part of the red shift can be a consequence of the energy loss and the greater the distance to an object is, the greater is the loss. This phenomenon also poses a problem that the density of the interstellar medium might be much greater than usually believed. Among different scenarios discussed in the literature are dark energy, dark matter and others. As shown in my papers (see e.g. viXra:1104.0065 and references therein), the cosmological acceleration can be easily and naturally explained from first principles of quantum theory without involving dark energy, empty space-time background and other artificial notions. However, the other possibilities seem to be more realistic and now they are intensively studied.