Yes, but one issue is that the amount of redshift depends on the motion of the emitter, so we would have to artificially assign some four-velocity to your surroundings in order to give them some redshift. There doesn't seem to be a "natural" choice for how to do this.
TLDR: redshift depends not only on the position of the source, but also its velocity.
Since you don't notice any red-shift with your eyes in daily life, why is zero velocity relative to the camera not a natural choice? Or maybe I'm not following you?
If you put the source infinitely far away (as we are doing here) and at zero velocity relative to the camera, then there is no redshift effect at all, so you could say that this is the choice of redshift that we made :)
If you want the details, they're too long to put in this comment but essentially what I mean is that the r->infty limit of the redshift factor in Eq. (B22) of this paper is unity: https://arxiv.org/abs/2211.07469
Yes, but one issue is that the amount of redshift depends on the motion of the emitter, so we would have to artificially assign some four-velocity to your surroundings in order to give them some redshift. There doesn't seem to be a "natural" choice for how to do this.
TLDR: redshift depends not only on the position of the source, but also its velocity.
Since you don't notice any red-shift with your eyes in daily life, why is zero velocity relative to the camera not a natural choice? Or maybe I'm not following you?
If you put the source infinitely far away (as we are doing here) and at zero velocity relative to the camera, then there is no redshift effect at all, so you could say that this is the choice of redshift that we made :)
If you want the details, they're too long to put in this comment but essentially what I mean is that the r->infty limit of the redshift factor in Eq. (B22) of this paper is unity: https://arxiv.org/abs/2211.07469
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