He looks old. (You notice it with your eyes.) Physics seems difficult for him. (No eyesight is needed for the observation.) Physics appears difficult for him. (The same as seems, just more formal.)
For me, if someone says "You appear [something]" it would sound like that person had doubts about whether I really was [something] or was just trying to make it look that way.
You can use the 'seem' when it takes a little time to make a judgement. However, we use 'look' when it is something we can quickly see or understand. For example,
You seem happy. (You were singing all day and bought me lunch. I'm guess you are happy, but you might not be smiling.)
You look happy. (I see you smiling. I know very easily and quickly that you are happy.)