Not an easy question to answer, because there really isn’t any way to be completely sure, unless we develop the ability to travel to very distant regions of the universe. And even then, testing whether the laws of physics have remained the same may not be a trivial task.
However, we can ask ourselves whether the empirical data we currently have available is compatible with the notion that the laws of physics ( or the fundamental structure of the universe ) are different in very distant regions. We can do this in a variety of ways, the easiest being to examine the spectral composition of light we receive from far-away objects. If we examine the light of objects millions or even billions of light years away ( and hence distant both in space as well as in time ), we find that the spectral lines are precisely where we would expect them to be – hydrogen has the same spectrum as it does at present here on earth, and so does every other element. This means that the laws of quantum physics ( which give rise to these spectra ) appear to be the same far away, and in the past. Furthermore, the dynamics of these objects seem to follow precisely the known laws of physics – case in hand is the recent dectection of the gravitational waves emanating from the merger of two black holes, the wave form of which was exactly as General Relativity predicted.
Even on Earth itself, we can find phenomena which allow us to test if there have been changes in the laws of physics or the fundamental constants of nature, over time – an example is the Oklo natural fission reactor.
So, everything considered, the empirical data is consistent with the assumption that the laws of physics do not change, at least not within the region of the universe which we are able to observe. This hence appears to be a reasonable premise, without which “doing science” would become very difficult indeed.
Title Graphic : http://www.chrismadden.co.uk/cartoons/science-cartoons/breaking-laws-of-physics-cartoons/breaking-scientific-laws-ridicule-cartoon.gif