I'm interested if any of the following explanations have enough predictive capability to explain the observations we see today. The claim is that the Universe is not expanding, and that red-shift of light is caused by:
Though a couple of these are simply ridiculous, I'm still interested. Keep in mind that I am not a creationist, but am looking for reasons to see if any of these are valid or invalid.
Answer
Stellar motion would imply we're in the place where the Big Bang occurred while everything else is speeding away from us. I can see how this would be a worthwile explanation for a creationist, but it doesn't really make much sense building just on physics.
Doppler Effect has the same issue - it assumes that every star we can see moves in a speed proportional to distance with respect to us. That's extremely Sun-centric, and doesn't really work if you accept that e.g. stars in our galaxy orbit around its center, including us.
Gravitation of course does have effect on wavelength, but it's by far not enough for common stars, much less planets. And of course, the effect is only at work when you're in the gravitational well - this would imply that the Sun is again at the center of everything, with everything else orbitting around it.
Photon interaction - never been observed, doesn't really play well with accepted theories of electro-magnetism and photons. With the exception of - the expansion of space itself. Yes, photons are losing energy, that's why they're red-shifted. Even though there is a certain preference for photons to fill in similar states, this mostly manifests as a tendency for self-collimation. Interacting photons would not explain why the red-shift is correlated with distance either.
The others work in a similar fashion. Slowing of light would have huge effects on every interaction in the universe - which would mean that even things like water wouldn't be stable over time, they would change their behaviour rather a lot. Combined with the proposed age of ~6000 years for the universe, with humans from the very beginning, this is just absurd. The assumptions made by theory of relativity make this even more crazy - in relativity, speed of light is basically the maximum speed of propagation of information. So this hinges on older models of the speed of light, independent of the space-time itself.
Galaxies spiraling towards the Earth was already handled in the Gravitational red-shift explanation and the Doppler effect.
All in all, you can see why a creationist-proponent would like those theories. They mostly work on the basis that we are at the center of everything, and everything else revolves around us. It's the good old Earth-centric solar system model again, just dressed in the universe this time.
The problem is, addressing every single hypothesis put forward by people lacking in basic science practice and knowledge is fighting windmills. You can always imagine sillier and sillier explanations, and when people finally get tired of responding, you'll just say "See? The scientists have no explanation for that!" It's an uphill battle, and somewhat pointless, really.
Don't forget that when you propose an alternative theory/hypothesis, you need to explain everything the old theory did. If we find out that photons travel at lower or higher speeds than the speed of light, it might put relativity out of the question, but we'll still have to find out why it works almost all the time we've checked. It's possible to "overthrow" a well estabilished theory, but most often, you're only adding to what's already there. For example, Newton's law of gravity is wrong, but it's not thrown out outright - it's simply explained differently, and broadened to explain new observations. Most of the time, it works well enough. If it starts contradicting your observations (like the famous precession of Mercury issue), you start refining - in this case, Einstein pretty much redefined the whole universe. But it didn't make the old theory wrong outright - just incomplete. Creationist hypothesis tend to ignore this completely - they focus on one pet theory, and ignore the other explanations that need to be done to maintain a consistent model.
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