Do the same laws of physics hold in two different locations that are infinitely far away from each other? Another way of asking the question:
Suppose there are two locations A and B, and the distance between A and B is infinite. Suppose there are two observers, one at each location, and finally assume that initially the laws of physics are the same in both locations.
If the laws of physics suddenly changed at location A s.t observer A is able to get different results when conducting the same experiments as observer B, would observer B eventually detect a change in the laws of physics at his location? My initial impression would be no, because I assume that any changes to reality at location A would never "reach" location B, but I could be wrong.
 A: I am afraid your questions is more or less meaningless, for several reasons:
(a) two locations cannot be an infinite distance apart. Even in an infinite universe, the distance between any two given locations must be finite. The term "infinite universe" simply means that there is no upper bound on the set of finite distances between locations in that universe.
(b) we have never observed a change in the fundamental laws of physics (although our understanding of them has changed over time). So we have no idea how such a change might propagate through space. Maybe its propagation would be limited by the speed of light - but on the other hand that is one of the fundamental laws of physics that might change ...
(c) as pointed out in the comments, even if we did observe an apparent change in one of the laws of physics, then we would simply say that our understanding of that law had been incomplete, and we would seek to incorporate the new observational data into a wider, more general law. For example, if we found that gravity acts differently from how we expect when we look at very large or very small scales (and this is an active area of research right now) then we would have to modify general relativity to accommodate that new data. So, almost by definition, the fundamental laws of physics cannot change because if they did they would not be laws.
(d) our observational data about the universe is limited by the size of the observable universe. We have no way of ever knowing what the universe is like far outside of this region (or even whether the universe is or is not infinite in extent). The best we can do is assume that the region of the universe that we can observe is representative of the whole, and the same laws of physics apply everywhere in the universe - since even if they did not, it is not clear how that could possibly affect us.
A: Here is another way to think of this.
We look out into deep space with our telescopes, make observations, and then ask ourselves if the fundamental constants of nature that we measure here on earth are the same on opposite sides of the observable universe, as represented by what our telescopes can tell us.
Note however that there was a time in the distant past when points on opposite sides of the observable universe were practically on top of one another: during the big bang. Our question then becomes: during the big bang, did the fundamental constants of nature vary from point to point on vanishing small distance scales, so that when the universe gets expanded out to its present size over 13 billion years, different regions of the universe far apart from one another possess different values of those constants?
The best models developed so far to describe the overall characteristics of the observable universe at its current age in terms of what went on during the big bang succeed in getting the picture right with no assumptions that the constants of nature were different in different regions of the big bang while it was happening. This argues against the hypothesis that different regions of our universe today have different values of the fundamental constants, or different types of physics altogether.
A: It is impossible to give an authoritative answer to your hypothetical question, since without knowing what changes occurred to the laws of physics at A, and why those changes occurred, how could we know their consequences?
