Suppose someone emits some light from a far away galaxy, call it #1. On its way to earth, the light passes another galaxy, galaxy #2. Then it hits the earth. Assuming that the scale-factor is not constant (i.e. the Universe is expanding and their is cosmological redshift) is the total redshift the light experiences equal to {the redshift from the galaxy 1 to galaxy 2} + {the redshift from galaxy 2 to the Earth}?In other words is z(2,E) z(2,1) + z(1,E)Mathematically, I think the answer is no, but why is this true physically? It seems very nonintuitive.
The answer IS No. The red shift of a particular object is the red shift of THAT PARTICULAR object. Adding the different z numbers of two objects makes no logical scientific sense. Mathematically, it's like trying to add two different variables to come up with a different variable. That violates the laws mathematics. Physics is just applied mathematics. It is additive in the sense that the father away a galaxy is from Earth, the faster it is moving away from Earth.
If a redshift is interpreted as indicating velocity, then no. If is is viewed as related to age or experience with light speed and quality being variable, then maybe yes. And remember that the big bang theory idea is a theory and one interpretation of data, and it includes expanding space as well which is also a strange idea. See light speed work done by Lene Vestergaard Hau related to the properties and nature of light. Her team slowed down a beam and eventually stopped light. What this says about the nature of light over millions and billions of years old I don't know, but it's good to keep looking around and questioning the status quo. The things all light that reaches Earth has in common?.age, distance, and varied 'experience' in travel over millions of years. The velocity idea is a theory, and if you really think about the idea that everything is moving ever faster the farther away from Earth it is.well, think about that. It is a rather silly notion indeed.
If the redshift of the near galaxy as seen from Earth is X, and the redshift of the far galaxy as seen from Earth is Y, it would make sense that the redshift of the far galaxy from the near galaxy would be Y - X, except that redshift is not proportional to distance, but there's the problem. There are several kinds of redshifts -- doppler due to speed of separation, cosmological due to expansion of the universe, gravitational due to relativistic effects. Further, the doppler redshift is not linear. I may be misinterpreting something here, but the total redshift (cosmological redshift) between two objects can be considered to be the addition (the pedia article on redshift says concatenation) of the local redshifts between the bodies on the path. This make me answer your question yes
