Friday 1 November 2019

cosmology - As the universe expands, the wavelengths of photons are stretched, and energy is lost. What about electrons?


Will electrons, and other particles, also loose energy as they travel through the cosmos? They have wavelengths. Do they get "stretched"? My guess is that the EM force, somehow, counteracts this effect. What about neutrinos?


Reference found: http://books.google.com/books?id=AmlEt6TJ6jAC&pg=PA96&lpg=PA96&dq=redshift+of+de+broglie+wavelength&source=bl&ots=oAW0q9bmaj&sig=nAwE-ohARZ3YTCZrHDBBjZ_IYfQ&hl=en&sa=X&ei=0lQDVJjtLMKEjAL80IHQCw&ved=0CB4Q6AEwAA#v=onepage&q=redshift%20of%20de%20broglie%20wavelength&f=false



Answer



The answer is yes. The de Broglie wavelengths of freely propagating particles (i.e. forget the influence of interactions and gravity perturbations, just consider the Universe as a whole) are redshifted by the expansion of the universe. Another way of saying this is that their peculiar momenta with respect to a co-moving local volume decrease as the inverse of the scale factor.


Neutrinos are an example of a particle with a non-zero mass (maybe of order 0.1 eV - see http://adsabs.harvard.edu/abs/2014PhRvL.112e1303B ). They decouple from the rest of the Universe at about 1 second and freely propagate. The expansion then reduces their momenta to the extent that they should have a temperatures $<2$K in the present-day Universe, typical kinetic energies of 0.2 meV (e.g. see http://adsabs.harvard.edu/abs/2010PhRvD..82f2001K ) and may have speeds of only (depending on their actual masses) perhaps $\sim 10^3-10^4$ km/s and so are non-relativistic.


Electrons would behave in the same way, if they could be considered not to be strongly (or rather electromagnetically!) interacting with other particles and photons. I don't think this can be satisfied except in the very early universe and a typical free, intergalactic electron in the present day universe has an energy of $\sim 0.1$ keV due to heating by radiation from stars and galaxies.


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