Why Didn't Luke Feel The Destruction Of Alderaan?

He wasn't even technically a Jedi at that point in time, so he could not feel something like that through the force.

 

When he said he felt something, he was referring to the remote he was blocking shots from.
Obviously such a novice force user wasn't in tune to what happend to Alderaan.

 

I would argue that he was Anakin's off-spring. Look how fast he started learning how to feel the Force on the Falcon.

 

You are right but remember, Anakin like Luke had the most potential in the force but as a child he only used the force while podracing. It wasn't by choice, he did it naturally, it's only when he meets Qui-gon that he gets to know what he was using. In similear fashion Luke probaly used the force while he did his canyon-racing or shooting whompa-rats. It's like never realizing that there is this whole new world open for you, without limits,boundries, but first you have to realize that it is there, which he didn't untill he went with Obi.
And as a young man he learned a lot at an amazing speed.

 

Because he was not a Jedi yet.

 

He just started of as a Jedi, and I'm not sure how could his powers evolve in only one day to be able to sense that. Maybe, if they were closer to the planet...

 

Yes, He was just starting to learn the force, so he was not that good with it.

 

Because Luke is very unexperienced at the time it is unknown if he actually felt something or not. He could've felt it without knowing it, it could've been something as small as a shiver on his back or goosebumps. Whereas Ben, whose far more experienced, felt the destruction of Alderaan in complete detail.

 

There's a difference between midichlorians and actualized potential.