In Arabic, to make pronunciation easier, when the definite article ال is introduced into a word that begins with certain letters, we don't pronounce the لـ and stress on the first letter of the word. These letters are called "sun letters" or "solar letters". There are 28 letters in the Arabic language, 14 of them are solar letters and the other 14 are moon letters. If you know the Arabic alphabet by the normal order; أ، ب، ت، ث، ... ي , then all the letters between د and ظ are solar (10 letters including د and ظ) and ت ث ل ن. The others are the lunar letters. If you don not know them by order, then you'll have to memorize them and practice to get used to them. Here is a picture to illustrate them (the red ones are the solar letters): https://upload.wikimedia.org/wikipedia/commons/6/6b/Mond-_und_Sonnenbuchstaben.svg

I was going to answer this but Masha'Allah ,the guys nailed it!. :) . A very neat explanations! , you're so lucky man to get your question answered ,in this amazing thorough way!. :D . حظاً موفقاً وشكراً جميعاً على مجهودكم الرائع .

لأن اللام فى كلمة السلام تعتبر لام شمسية و اللام الشمسية: لامٌ تُكتب ولا تُلفظ خلال القِراءة، والحروف التي تليها تأتي مُشددةً أو ما هو متعارف عليه التضعيف، وهي:{ ت، ث، د، ذ، ر، ز، س، ش، ص، ض، ط، ظ، ن، ل }، ومن الأمثلة الشهيرة: الشَّمس، We don't prounonce the letter ل in ال when it comes before these letters ت، ث، د، ذ، ر، ز، س، ش، ص، ض، ط، ظ، ن، ل شى and we stress those letters by adding شدة ّ

I would like to add to whay Ayman mentioned, the word الشمس is pronounced in the same way while القمر here ال is pronounced because of that it was named شمسي وقمري.

Good question. Actually "ال" is always "al". However, for some pronunciation convenience, it's not pronounced "al" as it's gonna sound very "heavy" on the tongue. Exercice : how do you pronounce these ? البحث، السهم، البيت، الصورة، الطفل، الناس، الشيخ، الليل،... You probably noticed that some of them are AL and some AT or AS, ASH, etc. It would be very weird to pronounce الصورة AL SOORA instead of ASSOORA. It takes less effort and "time" to pronounce it. So those are my thoughts about it. Hope there would be a "professional" teacher who maybe can explain it to you better :) Good luck