A Thought Experiment

Not only can you feel accelerated motion, you can easily see relative motion. I had no problem seeing the bus next to us move relative to us. My only difficulty was in telling whether they were moving or we were moving.
An example of where it is more obvious who is moving is the example of the jet flying over the Midwestern plains. In the daytime the passengers can see the farms go by; it is easy to detect the relative motion of the plane and the farms. And it is quite obvious that it is the plane moving and the farms are at rest. Or is it?
To deal with this question we will go through what is called a thought experiment where we solve a problem by imagining a sometimes contrived situation, and then figure out what the consequences would be if we were actually in that situation. Galileo is well known for his use of thought experiments to explain the concepts of the new mechanics he was discovering.

For our thought experiment, imagine that we are going to take the Concorde supersonic jet from Boston, Massachusetts to San Francisco, California. The jet has been given special permission to fly across the country at supersonic speeds so that the trip, which is scheduled to leave at noon, takes only three hours.
When we arrive in San Francisco we reset our watches to Pacific Standard Time to make up for the 3 hour difference between Boston and San Francisco. We reset our watches to noon. When we left, it was noon and the sun was overhead. When we arrive it is still noon and the sun is still overhead. One might say that the jet flew fast enough to follow the sun, the 3 hour trip just balancing the 3 hours time difference.
But there is another view of the trip shown in Figure (1). When we took off at noon, the earth, the airplane and sun were lined up as shown in Figure (1a). Three hours later the earth, airplane and sun are still lined up as shown in Figure (1b). The only difference between (1a) and (1b) is that the earth has been rotating for three hours so that San Francisco, rather than Boston is now under the plane. The view in Figure (1) is what an astronaut approaching the earth in a spacecraft might see.

Figure 1: One view of a three hour trip from Boston to San Francisco. It is possible, even logical, to think of the jet as hovering at rest while the earth turns underneath.

For someone inside the jet, looking down at the Midwestern farms going by, who is really moving? Are the farms really at rest and the plane moving? Or is the plane at rest and the farms going by? Figure (1) suggests that the latter point of view may be more accurate, at least from the perspective of one who sees the bigger picture including the earth, airplane, and sun.
But, you might ask, what about the jet engines and all the fuel that is being expended to move the jet at 1000 miles/ hour? Doesn’t that prove that it is the jet that is moving? Not necessarily. When the earth rotates, it drags the atmosphere around with it creating a 10 00 mi hr wind that the plane has to fly through in order to stand still. Without the jet engines and fuel, the plane would be dragged back with the land and never reach San Francisco.
This thought experiment has one purpose. To loosen what may have been a firmly held conviction that when you are in a plane or car, you are moving and the land that you see go by must necessarily be at rest. Perhaps, under some circumstances it is more logical to think of yourself at rest and the ground as moving. Or, perhaps it does not make any difference. The principle of relativity allows us to take this last point of view.