In the tired light hypothesis if the careful consideration is taken into account, the slow spreading of the initial beam of photons is present [1]. That will make the visible size of the distant objects seems larger compare to real angle size and the corresponding surface luminosity smaller. The observation of the supernova stars relies upon the suggestion that the real size of the explosion is independent of the distance (which is of course, true) and in the absolute absence of any spreading of the light in vacuum the visible size of the supernova explosion will be proportional to 1/R^2 (thus the idea of the standard candle comes to play [2]).
In the case of uniformly expanding universe the magnitude of the peak intensity of type 1 supernovae would be linearly proportional in the corresponding coordinates to the red shift observed (see, for example Fig.9 from [3]). Magnitude expressed as apparent magnitude [4] widely accepted in astronomy - the larger the number the more dim is the light, the brightest stars in the sky have small negative numbers like -1 for Sirius)
In this figure the experimental values of magnitude μ (proportional to 1/R^2 if no dust or light scattering is present) are plotted in the corresponding coordinates versus redshift z. The linear correlation obtained in Hubble times starts to deviate at higher z, what means (assuming there is absolutely no change in light properties or supernova properties) that the rate of change of z at the close Universe (later times assuming "Big Bang") is higher compare to older times (closer to "Big Bang").
That discrepancy was explained by the presence of "dark energy" which is generated in the most recent Universe (and absent at the times closer to "Big Bang") and accelerates the expansion of the Universe (the value z from Lemaitre times is attributed to the Doppler-like effect, meaning that the universe is expanding). Faster increase of z for the closer Universe means the Universe in the recent time (because the age is measured using relation r=c*t, where c - speed of light is presumed constant not changing with time) is expanding faster (more change on z value for the same time).
How the proposed by Hubble and others theory of tired light may explain the same phenomenon? According to [1] the light emitted by any object (including supernova) is slowly scattered with time (enormously slow, not in one step like Compton scattering, but in billions and trillions of very small steps, see [1]). In this situation the change in energy (energy loss), expressed as z will be observable well before any change of direction is obvious (change of energy is directly proportional to N - number of scatterings, while the change of direction is proportional to sqrt(N) and for huge N it may be very small - well below observation abilities). But eventually the scattering is visible and the visible diameter of the bright spot associated with supernova is enlarged perceptibly (the real diameter is of course, the same, the supernova in Milky Way and supernova in the galaxy one billion light years away are exactly the same). Once such a diameter is enlarged, the brightness is smaller and the supernova looks more dim than it is. If this phenomenon is not taken into account the apparent magnitude is larger (value of μ
in the figure is larger).
Thus the simple idea of tired light being scattered not once (Compton scattering, original tired light hypothesis) but in very large number may not only easily explain all the problems with far galaxies [1], but also the "dark energy" which in fact is merely the wrong explanation of the observed supernova brightness as a function of distance. This observation in reality is the additional hint toward the nature of light - it is not as simple as piece of electromagnetic wave, it is something else (to be discovered). While in my first publication I advocated the presence of small rest mass of photon [5], in second book the idea of quantized gravitational dipole appeared [6] both those features of photon, despite being possible are still way too small to describe the phenomenon like discovered by James Webb Space Telescope [1]. Most probably photon is even more complex that many scientists believe (non-zero gravitational properties are present like in normal particle). Something even stronger is lingering in photon and much easier to observe (seems like new type of light scattering discovery is right around the corner).
References.
2.Cosmic distance ladder - Wikipedia
4.Apparent magnitude - Wikipedia
5.(PDF) The quest for new physics. An experimentalist approach (researchgate.net)
