The Equivalence Principle
Einstein's "Happiest Thought" and the General Theory of Relativity
When Albert Einstein first realized that gravitational mass and inertial mass were the same thing, the resulting thoughts led him to expanding the theory of relativity.
Here is a brief thought experiment to help explain the concept that began Albert Einstein on his fateful journey toward creating a more “general” version of this original theory of relativity:
Imagine that you are entirely enclosed in an elevator on Earth, standing on the floor. All of a sudden, the cable snaps and the elevator begins plummeting to the Earth and you find yourself suddenly in “freefall” inside the space, you can no longer feel the effects of gravity as you accelerate toward the ground, but know that this will certainly change in a very dramatic way just as soon as you reach the Earth. Now, picture that this elevator suddenly passes through a portal which teleports it into outer space without your knowledge.
What, if anything, will have changed as far as your perception of your surroundings go? Einstein realized that in a situation like this, you would have no way of knowing that you were now in space and no longer plummeting toward the Earth.
Now, to take this little story even further, imagine that an alien spacecraft suddenly attaches a rope to the elevator which is floating in space, and rockets forward, towing the elevator at an acceleration of about 9.8m/s² (the same as the standard acceleration due to Earth’s gravity). You are suddenly thrust back onto the floor of the elevator due to the sudden change in speed and direction.
According, once again, to Einstein, in such a case as this the observer would surely believe themselves to still be on the Earth, and for the elevator to have merely stopped descending. To them, the sudden acceleration which increases their inertial mass and keeps them standing on the floor of the elevator as it hurtles through space would feel identical to the mass created by the force of gravity on Earth.
Why, Einstein asks, is this?
Einstein’s “Happiest Thought”
The answer is that these two phenomenon – gravitational and inertial mass – are not just too different things which have similar effects. They are the exact same thing.
When Galileo proved in the 17th century that objects of different mass fall at precisely the same speed toward the Earth, it was uncertain exactly why this was. When Newton discovered his equation which defined the effects of gravity, it was seen as a mere “coincidence” that the force of gravity and inertia just happened to be identical – there was no explanation for it.
Einstein’s response was, in many respects, rather simple. It is not mere coincidence, for there is no difference between these two forces.
Objects of different masses fall at the speed because of this:
When less massive objects fall to Earth they are pulled by gravity, and because they have little mass, gravity has an easier time pulling them. While more massive objects seem like they would fall faster because they contain a higher propensity for inertia, gravity has to work harder against that same inertia to pull them toward the Earth, so it all evens out in the end.
When Einstein realized this, he called it “The happiest thought of my life.”
Why is this Equivalence Important?
What was it about this equivalence which made Einstein so giddy?
Because it added still another facet to his Special Theory of Relativity. Where the special theory had previously only covered basic linear, constant motion, the fact that gravitational and inertial mass was the same enabled Einstein to expand relativity to cover changing motion.
For if we find ourselves in an enclosed space, standing on the Earth, there is no experiment we can perform which tells us for certain that the force holding us to the floor is due to the Earth’s gravity or due to inertial forces due to motion. We cannot tell because they are the same thing.
While this may have been an important breakthrough for Einstein, it left him facing even more difficult questions: Most importantly, why is this the case?
What is gravity really? It is answer this question which became the core element of general relativity.
References:
Einstein, A. (1961). Relativity: The Special and the General Theory - A clear Explanation that Anyone can Understand. New York, NY: Random House.
Einstein, A. (1922). The Meaning of Relativity: Including the Relativistic Theory of the Non-Symmetric Field, fifth edition. New York, NY: Barnes and Noble Books.
Feynman, Richard. “The Feynman Lectures on Physics.” 1971
Gardner, M. (1962). Relativity Simply Explained. Mineola, NY: Dover Publications, Inc.
