Does Redshift Indicate Mutual Movement Between Distant Galaxies?

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SUMMARY

The discussion centers on the interpretation of redshift in the context of distant galaxies and their movement relative to each other. It establishes that a substantial redshift observed from our galaxy indicates that the distant galaxy is moving away, and conversely, observers in that distant galaxy would also perceive a redshift in the spectrum of the Milky Way. This mutual observation is rooted in the principles of special relativity and the Doppler effect, emphasizing the importance of frames of reference in understanding cosmic movement.

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aerogurl2
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I don't understand whether this is true or false. It goes like this:
if a distant galaxy has a substantial redshift ( as viewed from our galaxy) then anyone living in that galaxy would see a substantial redshift in a spectrum of the Milky Way galaxy.

I know redshift is when the object is moving away from our galaxy, then wouldn't we see that galaxy moving away as well? am i offtrack??
 
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Yes, we would see the galaxy moving away from us too, but what does that have to do with the question? The question is hinting at frames of reference.

Do you know about special relativity and the doppler effect?
 

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