Amateur question: isotropy and the cosmologic principle

[lead341]

As far as I am aware of the current and accepted theory regarding the size and structure of the universe, based on Hubble´s insights, says, that space is isotropic: that means at any place in the universe an imaginary observer would get the "same picture" - that implies also the same rates of expansion and red shifts.
For example: the picture we have from the universe relates to our specific view on earth. From here, for example, we can observe galaxies in more than 10 billion light years distance. So now let us place this imaginary observer exactly on a planet in one of these "border" galaxies (from our point of view the most redshifted one). What exactly would he see? Isotropy says: the same as from here. So he would see our galaxy, 10 billion light years distant, red shifted. But if he saw into the other direction, he himself would, again, see galaxies in about 10 billion light years distance (i.e. 20 billion lj from earth). And on these galaxies another observer again...so resuming this would imply that the universe, and with it matter, is infinite and never-ending. Is this understanding correct?

Now let us focus "back" to the imaginary observer in 10 billion lightyears distance from here. We would see him, and the largest number of objects between him and us red-shifted, that means expanding or getting more and more distant from us. However, when he watches "towards" us, he would see the same thing, i.e. everything between moving away from him towards us. But isn´t there a contradiction implied? How can be explained that everything between him and us is getting more and more distant simultaneously from him and us?

Thanks in advance for the replies.

 

[IsometricPion]

this would imply that the universe, and with it matter, is infinite and never-ending. Is this understanding correct?

The universe is thought to be either infinite or finite but unbounded. That is, it is either like (considering only spatial dimensions and reducing their number to 2) the cartesian plane (since the universe happens to be approximately flat), or the surface of a sphere (if the universe turns out to have a slight positive curvature). In either of these cases the principle of isotropy applies (since the surfaces have constant curvature, the distribution of stress-energy must be uniform (or vice versa)). In the case of positive curvature, if you continue to choose observers in the same direction at the edge of the previous one's observable universe, eventually you will choose an observer that can see our region of the universe (you will have chosen circles whose centers lie on a circle, which must eventually close).

But isn´t there a contradiction implied? How can be explained that everything between him and us is getting more and more distant simultaneously from him and us?

Think of three points on a line in an expanding universe, the distance between each of these points increases as time passes. So, no matter which point you choose, the other two points are moving away from it, and the farther they are from the point the faster they are moving away from it.

 

[mathman]

How can be explained that everything between him and us is getting more and more distant simultaneously from him and us?

Why do you think this a problem? Take a rubber band and stretch it. All points between the two ends get further away from both ends.

 

[lead341]

Thank you for your replies, that was quite enlightening. I hadn´t especially thought about possible curvature and the surface of the sphere - this is indeed an intriguing thought.

I would like to add another question which is - remotely - connected to the topic of this thread. As far as I understood, isotropy not only dictates a homogenous space-time-continuum, but as I understood also a relatively homogenous distribution of matter (despite this homogeneity is not absolute, so you have filaments, voids etc.).
My question refers to this picture that I added - the galaxy map of the Sloan Digital Sky Survey.
1) The description says that in the center of it is Earth and our galaxy - I suppose, however, this is only due to the perspective, i.e. the fact that Earth is our "basis of observation" - expressed differently: it is an "imaginary or subjective" center.

2) Every dot or point on the map represents a large structure like a galaxy. Why does it appear that in the center region (i.e. where our galaxy is located) the concentration is strongest - as if there were a much larger mass concentration compared to the peripheral region? Is this also an observation bias?

Greetings Andreas

 

[IsometricPion]

The SSDS (like all telescopes) can only detect galaxies brighter than a certain magnitude, the http://en.wikipedia.org/wiki/Sloan_Digital_Sky_Survey" than the co-moving distance (which gives a redshift of about 0.40). I do not know which notion of distance is used in the picture, but this corresponds to a light travel time of ~4.3 billion years (so less than a third of the largest possible). I do not know enough about the SSDS or the picture to determine if this is the source of the overdensity/underdensity, but it seems plausible.