[PAOLO137 (OP)]

Sometimes, I find a description of uncertainty principle which is (according to me) grossly misunderstood.
There are people, even pretending to be experts, which say the uncertainty is due to the "disturbance" caused by the observer by means of his "instrument" (may be a photon launched against an electron to verify its location).
I don't agree at all with this type of explanation : according to my concept, it must be true that the act of measurement introduces a "part" of the uncertainty (it's inevitable). But even if I will manage to make this disturbance minimal beyond any limit, the product of uncertainties will always be of the order of h, and then not
dependent by the measurement.  Am I right? Thank You, Paolo.

[Bill S]

Sounds good to me, Paolo; but then, I'm not even a scientist. 

This might help.

http://www.newscientist.com/article/mg21428702.100-sorry-einstein-the-universe-needs-quantum-uncertainty.html   

[JP]

Yes, you always have an uncertainty relationship that holds for the particle, no matter what you do to it.  The product of uncertainties in conjugate variables (position and momentum, or space and time) will always be greater than or equal top some value proportional to h.  This holds whether your measurement strongly influenced the system or whether it didn't influence it at all.  I also dislike the explanation that a measurement involves particles hitting electrons or photons which change their state, introducing uncertainty.  (This was due to Heisenberg himself, actually, and it's fallen out of favor.)

But even if I will manage to make this disturbance minimal beyond any limit, the product of uncertainties will always be of the order of h, and then not
dependent by the measurement. 

Indeed, but if your measurement introduces minimal disturbance, then you gain minimal information from that measurement, since the detector has barely interacted with the particle.

[Bill S]

I also dislike the explanation that a measurement involves particles hitting electrons or photons which change their state, introducing uncertainty.  (This was due to Heisenberg himself, actually, and it's fallen out of favor.)

What has taken its place?  (History suggests that you might be able to explain this in an understandable way) 

[JP]

There are a lot of ways to understand it, but the easiest for me is to think of other cases of waves that are more familiar (at least to me).  If you have a laser pointer and shine it at a distant wall, you see that the beam is very narrow and doesn't spread out a lot as it moves through the air.  One explanation for this (there are always many ways to explain a phenomenon) is in terms of constructive and destructive interference.  That's the fact that when two waves overlap, they can reinforce each other to make a bigger wave or they can cancel each other out, leaving very little (or no) wave.  If you look at any cross-section of the laser beam, the wave is structured so that as is propagates forward, light spreading out away from the beam is mostly cancelled by destructive interference, while light going forward is reinforced.  The net result is that you get a beam that doesn't spread much in direction. 

Now, if you take the same beam, but pass it through a pinhole in a sheet of cardboard or aluminum foil, you'll see that it spreads out in all directions after the pinhole, making a very wide spot on the wall.  One explanation for this is that you've blocked out most of the laser beam so that there isn't enough wave present in the cross-section at the pinhole to cancel out the light going out at large angles.  You can then get rigorous about it and show how this mathematical description places limits on product of the width of the beam and the angular spreading of the beam.  This an uncertainty relationship and it is directly analogous to the Heisienberg principle in quantum mechanics.  I started here since there's no wave-particle issues to confuse matters.  Uncertaintly relationships occur whenever you have waves and describe how squeezing in one variable prevents the wave from being arbitrarily narrow in some other variable: in this case position and direction. 

In quantum mechanics, particles are waves and the same train of thought holds.  As a particle evolves in time, in order for it's wave to move in mostly one dimension, it has to be wide enough in position so that any wave spreading out in direction gets cancelled.  This means as you make it arbitrarily narrow in position, it gets wide in direction.  In this case, it gets wide in momentum which is direction times speed.  (In the case of light, the speed is constant, so it's just spread in direction.)

Now, if you buy all that, the explanation of why a measurement changes things is simply that a measurement of position restricts a particle and therefore it's wave to be somewhere in space.  If a particle goes through the pinhole, you know that it passed out of the pinhole and was therefore restricted to a small region of space.  This means it's going to spread out a lot.

How would you explain that a particle passing through a pinhole spreads out in momentum by using electrons/photons hitting that particle?  You'd have to have a model for how particles in the pinhole screen were interacting with the test particle and figure out how that spread out it's momentum.  This is almost certainly possible, but it's not simple or intuitive.  The idea that a wave must spread out from a pinhole due to the restricted size of the pinhole is both simple and intuitive (at least to people who have training in classical physics and waves).