Can Tired Light Theory Explain Redshift Without Expansion of the Universe?

[malebrok]

Homework Statement

The assignment is to find the energy loss constant for the theory of tired light. If redshift isn't caused by the expansion of the universe but from a loss of energy, how much of a photons energy is lost per unit distance(MegaParseC) for some set Hubble constant.

Homework Equations

The equation:
dE/dr = -K*E
r is the distance and K is the energy loss constant.

The Attempt at a Solution

Because photon energy is determined by E=h*f, the energy loss must correspond to the decrease in frequency. The relative frequency (per MPC in this instance) loss comes from the Doppler equation(c being the speed of light): f=(c/(c+H0))*f0
So with a Hubble constant (H0) of 70km/s per MPC gives loss in frequency of ~ 0.00033 % per MPC.

From here I'm kind of lost. How do i convert this to a relative energy loss (as the is no set frequency). With these formulas I'm still working with the electronvolt of the Planck constant, but i know the K constant does not have an energy dimension (it is only has MPC^-1).

I would be very thankful for any kind of pointers.

 

[jambaugh]

It might help to work with logarithms of ratios. dE/dr = -KE so dE/E = -kdr or d( ln E ) = -k dr. That means d (ln E - ln E_0) = -kdr or d ln (E/E_0) = -k dr. Integrating gives Ln(E/E_0) = -K r +C. with E=E_0 at r=0 C = 0.

(Remember when a rate of change is proportional to the value you have an exponential function).

This though doesn't directly address your problem. But indirectly it should. Rewrite your Doppler shift in terms of a ratio of frequencies f/f_0 and work from there.