Teaching Relativity

The lead article in the May 2021 Princeton Alumni Weekly entitled “Einstein at Princeton” got me to thinking about relativity theory. While I majored in history, I did take three semesters of physics including one billed as advanced physics for non-science majors. As I recall, this course spent two weeks on special relativity and the rest of the semester retracing the historical development of quantum mechanics. I have had an interest in these subjects ever since. 

Here is an idea that came, or came back, to me as a result of the article. I doubt very much that it is original and suspect that it was part of Einstein’s thinking when he developed his general theory of relativity. 

Visualize a tall, thin rocket. (Not necessarily a rocket ship since it need not carry anything except the propellant or fuel that powers it.) Now let’s say that as the rocket approaches the speed of light — the universal speed limit — it has a lot of fuel left, say more than half. As it burns this additional fuel very little of the propulsive energy can go into increased velocity. 

The only thing that makes sense is that in order to maintain the universal speed limit the mass of the object being propelled or pushed must increase. As a result of this increase, each additional unit of fuel burned and energy expended goes less into increasing velocity and more into increasing mass. 

As indicated, I suspect this was one of Einstein’s insights as he developed his theory, a cornerstone of which is the equivalence of mass and energy. It seems to me that the illustration is simple enough that it could be taught to students at pre-college levels.