Contrary to the premise of the question, the Appalachian Mountains do stretch from Georgia to Maine—and beyond. The Appalachian chain extends approximately 1,500 miles (2,400 km) from Springer Mountain in Georgia to Mount Katahdin in Maine, continuing into Canada's Gaspé Peninsula.
Springer Mountain (4,629 ft / 1,411 m) in Chattahoochee-Oconee National Forest, Georgia, marks the southern endpoint of the Appalachian Trail and the generally accepted southern limit of the Appalachian Mountains proper. The Blue Ridge Mountains, a major physiographic province of the Appalachians, run from Georgia through North Carolina, Tennessee, Virginia, West Virginia, Maryland, and into Pennsylvania.
The White Mountains of New Hampshire and Maine are a spectacular subrange of the Appalachians, featuring Mount Washington (6,288 ft / 1,917 m), the highest peak in the Northeast. The range continues through the Mahoosuc Range, into Maine's 100-Mile Wilderness, culminating at Baxter State Park's Mount Katahdin (5,269 ft / 1,606 m)—the northern terminus of the Appalachian Trail.
The Appalachians formed over 480 million years ago through successive orogenies (mountain-building events) as ancient continents collided. Once as high as the Himalayas, they have eroded into the rounded, forested ridges characteristic today. The range spans 14 U.S. states and 3 Canadian provinces, defining ecosystems, cultures, and histories across eastern North America.