How can electromagnetic radiation be both quantized and a wave?
Ok...this is probably one of the several
I do not know WHY it is and honestly I probably couldn't even understand why it is....but I always think of an example:
Consider that you are hungry. You think "I am hungry" and try to communicate it to others...
First you have a blind person so you TALK to him and say aloud "I am hungry". The blind person believes that thinking can only be communicated by talking (case 1, a wave, in the case of light).
Then you have a deaf person and you write on a piece of paper the same thing. The deaf person believe that thinking can only be communicated by writing (case 2, a quantized entity, in the case of light).
Now, who is right? Both of them...it depends on the specific circumstance where you need to communicate your idea. Sometimes you talk, sometimes you write.
In terms of ou example I think we are like persons that sometimes ear a message and sometimes read a message without realizing that the same message can be communicated in both ways!
In the same way when we observe light sometimes we measure a wave (interference) and sometimes we measure particles as a quantized entity (photoelectric effect).
I hope it makes sense...:-)
...but probably there are far better minds than mine and better answers to deal with this issue!