In A New Hope, we see that Obi-Wan is visibly affected by the destruction of Alderaan. If this was such a huge thing to elicit a response, why didn't it affect Luke as well?
He likely wasn't yet sensitive enough to the force to understand. He didn't understand his emotions... or rather, he wasn't tuned to them yet.
The force may have been disturbed, but Luke wasn't attuned enough to recognize it... or just missed it. Obi-wan had been trained to identify and recognize when a disturbance in the force had happened.
Luke relied too much on external physical stimulus to see beyond the obvious. This was evident in his training, where he was focusing too much on the physical sphere instead of allowing the force to guide him. It was also evident when he turned off his targeting computer and fully allowed the force to take over.
It was as much about listening and comprehending as it is about receiving.
A radar dish that is super sensitive isn't much good if you don't have an operator who doesn't know how to read the display.
It's like when you feel bad occasionally after eating... but only after being educated understand that those bad feelings are due to a food allergy or intolerance. Once you recognize the symptoms, you can identify and understand the signals. You have to learn how to listen before you can understand. ( Perhaps not the best analogy, but you get the idea )
Luke hadn't been trained yet -- he just didn't know how to feel things with the Force very well. Just prior to the scene in which Obi-Wan felt the destruction of Alderaan, we saw Luke training with his lightsaber and the remote droid. Obi-Wan taught Luke to
stretch out with your feelings
Star Wars: Episode IV A New Hope (see script)
while Luke's eyes were covered by his helmet's blast shield. Luke managed to deflect the remote's shots with his lightsaber despite the blast shield, and afterward he remarked
You know, I did feel something. I could almost see the remote.
Star Wars: Episode IV A New Hope
Since Luke could barely sense the remote that was right in front him it would be extremely difficult for him to sense the destruction of a planet light years away (even if it did involve the loss of so much life). Although he had the theoretical capability to sense the destruction of Alderaan, he hadn't yet learned how to stretch out with his feelings in order to do so.
It might help to recall what the Force is and how Force-sensitive individuals communicate with and use it. Obi-Wan explained the Force as:
The Force is what gives a Jedi his power. It's an energy field created by all living things. It surrounds us and penetrates us; it binds the galaxy together.
Star Wars: Episode IV A New Hope
And Qui-Gon explained how a Jedi communicates with that energy field:
Midi-chlorians are a microscopic lifeform that reside within all living cells and communicates with the Force...Without the midi-chlorians, life could not exist, and we would have no knowledge of the Force. They continually speak to you, telling you the will of the Force.
Star Wars: Episode I The Phantom Menace
Luke had a high midi-chlorian count (he was "Force-sensitive") but had not yet learned how to "speak" to the midi-chlorians ("stretch out with his feelings") well enough to sense the destruction of Alderaan.