Why does the Universe look the same in all directions we look, considering an expanding Universe created by the Big Bang?

I've struggled to comprehend this. Looking away from the Earth, we are looking back into the history of the Universe's expansion since the Big Bang. Astronomers report that in any direction we look, at the farthest "distance and time" we can currently see, it appears there is a consistancy in what we see. Galaxies appear to be in the same "time state" of development, etc. If I carry this reasoning out to it's conclusion to where I can eventually see the edge of the Universe in all directions I look (assuming a finite Universe with a boundary), wouldn't that imply the Earth was actually at the center of the Universe? If the light coming back to me showing me the past is representing that in every direction I look I will see the same (time-wise) early state of the objects in the Universe, wouldn't I have to be in the center of it? If I wasn't centered, I should be seeing different "time states" of objects in the Universe depending on the direction I looked after the Big Bang expansion started.

I'm NOT asking this in a religious context. I'm NOT implying the Earth is actually in the center of our Universe to try to support any belief or faith. I'm looking for a theoretical physics explanation that will allow me to comprehend the observation without the Earth being centered in the Universe.

I just can't grasp the concept that if the Earth was a result of the Big Bang expansion, why does it LOOK like I'm in the center instead of off to the side closer to one edge of the Universe than the other? The probability of the Earth actually ending up in the center would be astronomical.

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