Is it true that it is easier to obtain a PhD in Europe than the US on average? I am a physics undergrad, and plan to pursue a PhD in mathematical physics (string theory?). I have heard from a lot of people, who have personally seen the research scenario at universities both in the US and Europe, that it is much easier to get a PhD from a European university, that it takes about 3-4 years in a good university in Europe, while more than 5 years in American universities. Another thing I have been told is that in Europe you get your PhD after 4 years atmost by default, even if you have not done any original research. Is it true?
Short answer: No.
Long answer: Determining the minimum bar for which a PhD can be awarded is a bad exercise. If you are merely working towards the minimum you will not successfully complete a PhD.

One thing to note is that PhDs in the US tend to be open ended (to the extent you can continue to get funding) while in Europe they tend to have fixed durations. This means in Europe the bar comes whether you are ready or not while in the US you get to chose when you  defend. Neither is easier, just different.