Should physicists abandon Popperian falsification criterion? Many of the most brilliant ideas of modern physics are very much unpopperian. In view of this, it has become more and more difficult to hold an orthodox Popperian attitude in physics. It simply looks like more of a philosophical dogma nowadays. My question is, should physicists abandon this criterion at least partially for good? If so, what criterion should replace it?
 A: Popper's approach to the philosophy of science is of some historical importance, and quite possibly still has some value today, but it's certainly not holy writ. I think that many scientists and philosophers of science have moved beyond Popperianism, and that's fine.
As for what criterion should replace it, my vote is for Bayesian inference. The central idea of science is that evidence matters, and specifically that one must modify one's assessment of the probability of a statement's truth in the light of each additional piece of evidence. A "scientific" statement is one whose probability can be driven arbitrarily close to 1 or to 0 by the accumulation of appropriate evidence. Bayesian inference is the systematic way to think about evidence.
Thus the statement "there is life on other planets" is scientific, because we can imagine ways of gathering evidence that could support or oppose that statement in such a way as to drive its probability up to nearly 1 or down to nearly 0. Note that this statement is not "falsifiable," though, since we could never exhaustively check all planets.
I wrote a longer version of this rant here quite a while ago. Just to be clear, I'm not trained in philosophy, and my ideas are no doubt quite naive philosophically. In particular, I've never read Popper, so when I criticize Popperianism, I'm really criticizing the cartoon view of it that one seems to encounter among scientists. 
A: In my opinion no, they shouldn't. Just because things are more difficult and complicated it does not mean that scientists should "cheat". That of course does not mean that they should abandon any idea which is not immediately falsifiable. Good ideas should be given time. If you abandon falsifiability and impose rigor then it becomes mathematics. If you don't impose rigor, well then it is "theology".     
A: Physics needs to act the correct way. Physics its important to humanity and can not be fragilized.
First, I do not agree with the word 'brilliant', and this is only a matter of sensibility: 

"Many of the most brilliant ideas of
  modern physics are very much
  unpopperian."

In time theories may rise up or fall, give the authors time to elaborate, decades if we are willing to pay. Consensus must be avoided. I learn with discussions and past history of science. You can find your evidence, and myself mine, and both of us can be erroneous. I do not want to impose my viewpoint, even if I could, and I expect the same from the comunity.
Being 'unpopperian' is a problem? In the start of new ideas it is not a problem but, with the progressing of time, one must be prepared to make conclusions. 
An example: SUSY is beautiful, and makes predictions. If experience do not verify the predictions, I can expect one of the two: assume and restart, inspite of the beauty (this is not a physical criterion), or much less correct (cheat is my thought): rephrase the theory and by any kind of ... push previsions to unreacheable ranges of energy, even in the long term.
We must have clear what is a 'physical law' (relations obtained empirically and not subject to interpretation), written in stone, and a 'theory'  (a model to interpret the 'why'). Theories come and go, from time to time substituted by revolutions of thought.
Please compreend that imposing such a thing as 'electrical monopoles' by convenience of some beauty elsewhere can be monstruous. Beauty is reduce the magnetic force to a derived force that vanishes in the appropriate reference frame. Simplify is better (or KISS rule, no offense, Keep It Simple Stupid).  
Imposing a criterion based on the statistics is ridiculous. This way computers can do the work and the results are written in stone. We'll know tomorrow, the same as today, with greater accuracy.  
Data should be interpreted because data by itself can be misleading: pls read
Henri Poincaré "The measure of Time" or his sphere-world and here
