[syhprum (OP)]

The solar system is located within a spiral galaxy immersed in a sea of dark matter and subject to the gravitational field of the mass of stars and the central black hole.
How justified are we in assuming that that laws that we have deduced concerning gravity and space time apply to the whole universe.

[yor_on]

We can presently detect around 100,000,000,000 galaxies from the earth. The distribution of these galaxies looks the same to us no matter where we look, and that makes the universe being isotropic a good guess. And if the universe looks isotropic everywhere then it has to be homogeneous too. And a non isotropic inflation would be very strange, wouldn't it, and the same seems to go for our 'expansion'?

[solaris]

I think this is only our best possible guess. The fact that the universe looks the same everywhere we look does not necessarily mean that the laws of physics should be the same everywhere. Just think about the vastness of space we are talking about.
 

[imatfaal]

. And if the universe looks isotropic everywhere then it has to be homogeneous too.

No - the concepts are quite closely related but not identical.  An observer in the centre of a ping-pong ball sees the same in every direction (that is isotropic) but it is clearly not homogenous.  You need two or more separated observers to change isotropy into homogeneity

[yor_on]

hmm

Depends on your definition maybe? When I say homogeneous I just mean that it looks much the same and that it then seems reasonable to assume it to be of the same constituents as we have, at a generalized plane and obeying the same laws of 'nature/physics' or whatever definition one should use there.

Do explain more Imatfaal, so I can see your idea better.

[imatfaal]

Yoron - the general definitions are that

isotropic means that an observer at a single point will make the same observations regardless of the direction.  what ever direction we look we see a roughly uniform distribution of galaxies and clusters if we look on a large enough scale. an observer situated at the centre of a ping pong ball sees his outlook as isotropic (even direction gives same answer) but could calculate that others would not see the same (ie those weirdos that live near the inside surface)

homogeneous means that the same observations are available to all observers at each point of the universe. an observer roaming on the surface of a ping pong ball that is one of an infinite line of balls in space would understand that any of the ping pong balls gives exactly the same observations but it is not an isotropic view (in two directions the line of balls stretches away - and everywhere else is open space).

It does take some effort to separate the two - hopefully some of the others can check that my examples do work (I think they do).  Each of the two is necessary for the other to be true - but not sufficient for the other to be true.  The Cosmological Principle states that on large enough scales that the universe is isotropic and homogeneous - ie at every point in the universe observations of every direction will be the same.  I am led to believe that without this the maths becomes impossible (shell theorem fails etc) and you are left with a multibody problem of almost infinite complexity.

[yor_on]

Okay, now I see how you thought
Yep, I agree. The ping-pong ball is a interesting example, but if I apply that on the universe it seems to assume a finite universe? And I think you're right, if the universe wasn't obeying the same laws, depending on position, we would have a wild west with all kinds of possibilities. Like you crossing 'the border' and suddenly travel at 33 'c'

I remember reading a really good SF, old one, describing just that but from the point of our mind 'slowed down' depending on where we was. Wish I remember the name of it, it was thought provoking starting with them developing some sort of drive taking them out of the solar-system and suddenly becoming 'super intelligent' a must read, better than the 'animal farm' in some ways and discussing a lot of the same problems. If anyone knows this one please link it up, or let me do it 

[Bill S]

hopefully some of the others can check that my examples do work

I think your example works well. Perhaps I can subject this extract from my notes to the same scrutiny by others.

 "Two important assumptions grew out of the idea that no galaxy occupied a special position, these were: homogeneity and isotropy.  Homogeneity is the property of being the same everywhere; given that a sufficiently large sample is taken.  Isotropy is the property of being, or looking, the same in all directions, whatever your choice of viewpoint.  The two concepts are closely related, easily confused, but not identical.  Consider, for example, a chess board, the surface of which is a two-dimensional example of something that is both homogeneous and isotropic.  As long as your sample size is equal to two squares, or more, then any sample, whatever its position or orientation, will contain roughly equal amounts of black and white.  Also, any straight line drawn across the board, in any direction, will pass through equal amounts of both black and white.  Now, imagine that the board, instead of having alternating coloured squares, has alternate black and white stripes of the same width as the squares.  As long as your sample area is square, and large enough to have covered four squares on the original chess board, this striped board will pass the test for homogeneity, but it is certainly not isotropic.  If you take it that the stripes run from top to bottom, then any line drawn horizontally will pass through roughly equal parts of black and white; whereas any vertical line will be entirely contained within either a white or a black stripe." 

[syhprum (OP)]

what I really meant to ask are we making enough allowance for the dark matter in which we are immersed and the local gravitational fields when we form our ideas about the greater universe

[imatfaal]

Bill - yeah I like that one - I would have to add caveat that chessboard must be sufficiently wide/long to prevent any observer from being able to observe edge, as that instantly destroys both isotropy and homogeneity.

Syhprum - are you questioning that due to at present unknown local conditions the observations we make and the laws based upon them are skewed/wrong?  If so, I think the answer is that it is possible, but it would have to be quite subtle.

If it were not isotropic we would have noticed - that galaxies to the left have different rotation:mass than those to the right etc  (this has been claimed - group in Oz I think a few months back claim to have got figures for FSC that vary in space, but not confirmed by any stretch).  Additionally all our calculations that link the gravitational lensing we see/use locally (ie solar lensing) and non-locally (ie using distant super-cluster) work well - I don't believe there is a discontinuity, ie we use same equations and they work in both circumstances.

 I think what I am saying is that if the variation caused by local dark matter or other unforeseen gravitational effects is so subtle that it is isotropic and un-noticable in the transition from a few light minutes within the solar system to billions of light years then we are safe to ignore it for the time being.