On July 4, 1776, a document was signed declaring the American colonies independent from the British Empire that founded them. These colonists then managed to somehow win a war against one of the single most prolific imperial powers the world has ever known and subsequently the United States of America was born. And every year, in celebration of the signing of the Declaration of Independence, we in the US like to shoot fireworks into the sky and eat hot dogs. But what would the last two and a half centuries of history look like if none of this had happened? What if the American Revolution never happened?
First, some parameters: there are many points in the period of the Revolutionary War in which the rebelling colonists could have failed and the British forces would have crushed them like ants. But as this article asks what would have happened if the American Revolution simply didn't happen rather than what would have happened if it were lost, it is worth looking a bit further back to find where histories could diverge. For this reason, let us simply assume that the heightened taxation brought on by the British Empire needed to fund their wars in India simply didn't agitate the colonists into open rebellion.
The immediate implication would be that the very American notion of manifest destiny would have meant very little. Yes, Britain expanded in areas that they took over, but they were often far more interested in incurring profit from the land they took over to send back home with them. Periment settlements for the purpose of expanding and living in simply wasn't a point of interest. This ultimately means that the map of what is in our timeline the United States would look far different. The British colonies would have likely expanded inland to about the great lakes area due to its possessing largely favorable farmland and easily crossed terrain. But without a burning need to spread further, the Louisiana Purchase never would have happened. All of this land would have stayed in the possession of France and today would likely be part of a much larger Canada. Much of the southern and westernmost part of the country, likewise, would remain part of Mexico.
Speaking of France, without the American Revolutionary War to fail in entering, the poverty that caused the French Revolution to become as desperate as it was likely wouldn't have happened at nearly the same scale as it did. It still would have happened, a social unrest amongst its citizens directed at the monarchy at the time was the primary catalyst. But without the failed French intervention in the war, the people may not have been as poor and the power vacuum left to be filled by revolutionaries may not have been as intense.
Lastly, the America of this alternate timeline would simply have less of an identity.
Unlike a country like Australia, itself a British prison colony at the beginning, the American colonies would likely be too close to their land of origin and too tied to its politics and economy to be able to create one. One of the main reasons so many of Britain's former holdings are now sovereign governments in the modern day in our timeline is because they had to release them as war concessions in the wake of World War I, and the main force that pushed for them to do so was the United States. Without the U.S. this simply wouldn't have happened.
These are all very broad predictions for what a world effectively without the United States would look like. It is arguably impossible to tell what specifically would have happened due to the sheer number of variables at play. What can be understood, it that the world would be substantially different.