by Shane L. Larson
Science is, to some extent, a skill set that can be learned. Like playing piano or solving Rubik’s cubes or cooking Belgian cuisine. Using scientific thinking and applying it to the world is in large part a matter of practice and relentless dedication to getting better. But like all artforms, there is a small element of je ne sais quoi to it as well — a hidden reservoir of intuition and stupendous insight that is unleashed only sometimes.
Apple once had an ad campaign built around the mantra, “Think Different” (grammarians, hold your tongues, and your “ly”s and follow the mantra!). There were images of famous thinkers through the ages who approached the world differently than the rest of us. One of those was Albert Einstein.
Among a community of bright and creative people, it gives me pause to consider those people that we all think of as being remarkable. Albert Einstein is arguably the most famous scientist in history of the world, commanding the respect not just of the general populous, who have grown up immersed in his legend, but also the respect of the scientific community. Why is that? My colleague Rai Weiss, now an emeritus professor at MIT, recently noted that it wasn’t just that Einstein was smart, it was that he exhibited tremendous intuition. His great ability was to look at the same world the rest of us look at every day, and think different.
When Einstein began his quest to refine our understanding of gravity, he knew he was going to have to “think different” — this was, after all, what had led to special relativity in the first place! One of the earliest musings on the road to general relativity was a simple question: how do you know if gravity is pulling on you?
It’s a seemingly simple question, but it led to an interesting thought experiment. Imagine you and I are each in a small, windowless room with nothing but an apple and our smartphones (so we can text each other the results of the experiment I am about to describe).
Each of us drops our apple, and we see that it accelerates downward — it falls! The apple starts from rest (at our hands) and speeds up as it falls toward the floor of our small room. We excitedly text the result to each other and tweet pictures of apples on floors. Should we conclude from these experiments that we are both conducting experiments under the influence of a gravitational field?
![[Top] You and I conduct identical experiments (dropping apples) in enclosed spaces and get identical results. [BOTTOM] The reality of what is outside our little rooms may be completely different! A falling apple is equally well explained by the gravity of a planet, or by an accelerating rocket!](https://writescience.files.wordpress.com/2015/01/equivalence_fallingapples.jpg?w=500&h=603)
[Top] You and I conduct identical experiments (dropping apples) in enclosed spaces and get identical results. [BOTTOM] The reality of what is outside our little rooms may be completely different! A falling apple is equally well explained by the gravity of a planet, or by an accelerating rocket!
![[TOP] You and I both find ourselves weightless, floating without feeling forces acting on us. [BOTTOM] The reality external to our rooms could be that we are floating in space, or that we are in a freely falling elevator plummeting to our doom.](https://writescience.files.wordpress.com/2015/01/equivalence_freefall.jpg?w=500&h=607)
[TOP] You and I both find ourselves weightless, floating without feeling forces acting on us. [BOTTOM] The reality external to our rooms could be that we are floating in space, or that we are in a freely falling elevator plummeting to our doom.
It is this freefall experiment that really illustrates how we have to learn to “think different” when expanding our understanding of Nature. In Newtonian gravity, we always look at problems with an exterior, omniscient eye toward the problem. A Newtonian approach to the free fall problem says “Of course you are falling under the influence of gravity! I can see the Earth pulling you down from the top of the skyscraper toward your doom at the bottom of the elevator shaft!” But Einstein asked a different question: What does the person in the elevator know? What experiments can they do to detect they are in a gravitational field? The answer is “none.” There is no observational difference between these two situations, and the laws of physics should capture that.
The critical point here is that if you are in free fall, you feel no force! Einstein’s great insight was that the central difficulty with gravitational theory up to that point was that it was anchored in thinking about forces. This thought experiment convinced him that the right thing to think about was not force, but the motion of things.
This thought experiment came to Einstein in 1907 on a languid afternoon in the Bern patent office. Later in his life, Einstein would recall that moment and this idea with great fondness, referring to it as the happiest thought of his life. This experiment is known as the “universality of free fall,” which physicists like to give the moniker “the Equivalence Principle.”
![This is how I often imagine Einstein’s life during the years he worked in the Bern patent office! [From "The Far Side" by Gary Larson]](https://writescience.files.wordpress.com/2015/01/farside_physicshiggins_sm.jpg?w=500&h=461)
This is how I often imagine Einstein’s life during the years he worked in the Bern patent office! [From “The Far Side” by Gary Larson]

The “Leaning Tower of Niles,” a half-scale replica of the tower in PIsa. Located in Niles, IL (a suburb of Chicago).
But now, many years later and with a LOT of physics under my belt, I know that that the outcome of these thought experiments derive from a very old result that we are all familiar with — that all objects fall identically, irrespective of their mass. Galileo taught that, at least in folklore, by dropping various masses off of the Leaning Tower of Pisa. The obvious question to ask is “how is Galileo’s experiment connected to Einstein’s thought experiments?”
For the moment, imagine the various parts of your body as having different masses. Your head masses about 5 kg (a little bit more than the 8 pounds you learned from watching Jerry Maguire), where as a good pair of running shoes may mass about 1.5 kg. If you are standing happily in the elevator when the cable snaps, the traditional explanation is that everything begins to fall.
If objects of different mass fell at different rates, then your head would be pulled down faster than your shoes — you would feel a force between your head and your shoes. That force could be used to deduce the existence of a pulling force. But Galileo taught us that is not the way gravity works — your head and your shoes will get pulled down at strictly the same rate in a uniform gravitational field. Every little piece of you, from your head to your toes, your kneecaps to your freckles, falls at the same rate — there are no different forces between the different parts of your body and so you feel (you observe) yourself to be weightless. This is sometimes called the Galilean Principle of Equivalence, or the Weak Equivalence Principle.
Okay — so what? Apples and freefall, elevators and rockets. What does any of this have to do with developing a deeper understanding of gravity?
What this thought experiment reveals, what the Equivalence Principle tells us, is that thinking about forces is not the best way to think about the world because we can’t always be sure of what is going on! Instead, we should think about what we can observe — how particles move — and ways to describe that. That simple intuitive leap would, in the end, change the face of gravity. Particles move through space and time, which had brilliantly been unified by Einstein’s teacher and colleague, Hermann Minkowski, into a single unified medium called “spacetime.”
What is spacetime? It is the fabric of the Cosmos — it can be stretched and deformed. The fundamental idea of general relativity is that gravity can be described not by a force, but by the curvature of spacetime, the medium on which particles move. That will be the subject of our next little chat.
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This post is part of an ongoing series written for the General Relativity Centennial, celebrating 100 years of gravity (1915-2015). You can find the first post in the series, with links to the successive posts in this series here: http://wp.me/p19G0g-ru