Gravity 2: The Road to General Relativity

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?

Everything I need to start developing some new ideas about gravity!

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!

Einstein realized the answer to that question should be “No!” There are multiple ways to explain what we saw.  One way is to assume our little rooms are sitting on the surface of planet Earth, where the planet’s gravity pulled the apple down. But another, equally valid way to explain this experiment is to assume the little rooms are really the space capsules of rocket ships, accelerating through empty space (the apple is pressed down to the floor — “falls” — the same way you are pressed back in your seat when a jetliner takes off).  What Einstein realized is that there is no way, based on our experimental results, to tell the difference between these two cases. As far as experiment is concerned, there is no fundamental difference — that is to say, no observational difference — between them. Einstein knew that the laws of physics had to capture this somehow.

[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.

What if we consider a slightly different case? Imagine you and I both suddenly found ourselves and our apples drifting weightlessly in the middle of our small rooms. We excitedly text each other that we finally made it to space and tweet messages that we are officially astronauts. Should we conclude that we are both deep in interplanetary space, far from the gravitational influence of a planet? Once again, Einstein realized the answer to that question should be “No!” There is no way to know if we are drifting inside a space capsule in deep space, or if we are merely inhabiting an elevator whose cable has snapped and we are plummeting downward toward 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]

I have a very strong memory of my father first telling me about the universality of free-fall in about fifth or sixth grade. When you’re not used to it, the notion that falling in an elevator is the same as floating in outer space engenders a spontaneous and vehement response: “That can’t be true!” We had many long debates about this (it was following hot on the heels of my meltdown over the existence of negative numbers — maybe my dad was trying to forestall another meltdown…), and I don’t think it ever quite sank in. I, of course, feigned understanding and dutifully repeated the tale of the falling elevator to my classmates, reveling in their confusion and indignant denial of the logic of it.  I was a tween — what did you expect?

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

Gravity 0: Discovering Gravity

by Shane L. Larson

You and I live in the future. We are connected to each other in ways that would have stunned people who lived only a century ago. I had the good fortune growing up to know my great-grandmother, who lived to be 98 years old. My Grandma Dora was born in 1895, at a time before electricity and telephones and automobiles were commonplace. The mode of transportation when she was born was the horse and buggy, though steam had been harnessed and train lines were beginning to gird the world. The Wright Flyer would not make its first epic flight at Kitty Hawk until 1903, when Grandma Dora was 8 years old. But she lived to see humans sail the void of space, space shuttles ply the skies, and humans walk on the Moon. In just about 100 years, the span of a single human life, she saw the world change.

(L) My great-grandmother Dora [center] with her sisters Mary [left] and Arta [right] in the early 1900s. (R) Around this same time, the Wright Brothers made their historic flight at Kitty Hawk, in 1903.

When she was just a girl, there was a young man living halfway around the world, in Bern, Switzerland. The Industrial Revolution was in full swing, and creative minds the world over were trying to imagine how to use technology and machines to change our lives, and how to patent those ideas and make money. Some of those attempts to capitalize on the rapidly evolving world wound their way through the Bern Patent Office (the Swiss Federal Institute of Intellectual Property) to the desk of Albert Einstein. For the young Einstein, a trained technical professional, the job at the patent office was just that — a job. He very much wanted to be a professor and work on science, so in the evenings he committed himself to physics the way some of us work day jobs but in the evenings work on writing novels (or blog posts about science). In 1905, those evening endeavours paid off when Einstein published four seminal papers that transformed his life, physics, and the world forever.

(L) Einstein when he was working at the Patent Office in Bern. (R) Einstein’s living room, still preserved, in the first floor apartment where he worked on special relativity during his years at the Patent Office.

Among those papers was the original paper to describe special relativity — the laws that govern physics at high speeds, approaching the speed of light. Nestled in that paper is one of the most important discoveries in physics and the one most germane to our story here:

Nothing can travel faster than the speed of light.

This was a stunning realization, because up to that point no one had ever really imagined that we couldn’t go faster than light. The speed of light had been measured famously by Danish astronomer Ole Romer in 1676 and by French physicist Hippolyte Louis Fizeau in 1849. But there had never been a reason to believe that the speed of light was the ultimate speed limit in the Cosmos.

Folklore is that Newton witnessed the falling of an apple when visiting his mother’s farm, inspiring him to think about gravity. It almost certain is apocryphal that it hit him on the head, but this was the beginning of the Universal Law of Gravitation, one of the most successful descriptions of Nature ever invented.

With Einstein’s realization, we began to examine the laws of physics that had been discovered up to that point, and we found a curious fact. Some of those laws, unbeknownst to us, had the secret about light hiding in them, like a pearl in an oyster.  Most notable among these were Maxwell’s Equations for Electrodynamics. Curiously, Newtonian Gravity did not have the ultimate speed limit. The classical Universal Law of Gravitation, which Newton had penned more than 200 years earlier, was built on the idea of instantaneous communication over any distance, an impossibility if there was a maximum speed of travel. Einstein recognized this and set about to resolve the issue. He would dedicate the next 10 years of his life to the endeavour. During those years, he would finally leave his job at the patent office for the life of an academic, holding professor positions at several universities around Europe. All the while, he worked steadfastly on merging gravity and special relativity.

This was not a simple matter of “imagining something new.” Newtonian gravity worked perfectly well in the solar system, where things moved slowly and gravity was weak. Einstein knew that whatever Nature was doing with gravity, it had to look like Newtonian Universal Gravity at slow speeds and in weak gravity, but not be confined by instantaneous propagation of signals. He went through a meticulous procession of thought experiments, explored new applications of mathematics (the language of science) and developed new intuitive ways of thinking about gravity. His long hours and years of brain-bending culminated in 1915 with his presentation of the Field Equations of General Relativity, now known as the Einstein Field Equations.

In 1902, Georges Méliès (L) created the film “Le Voyage Dans La Lune” where an enormous cannon (C) was used to launch a space capsule carrying explorers to the Moon (R).

I think about this age of the world often, my thoughts fueled by memories of talking with my great-grandmother. What was the world like when the young Einstein was thinking about lightspeed and gravity?  It was an age of horse and buggy travel. What was the fastest people could imagine travelling in that era? In 1903 the great French director Georges Méliès told at tale of travelling to the Moon — “Le Voyage dans la Lune” — using a new technology called “moving pictures.” In that remarkable tale, he imagined a band of intrepid explorers attaining great speeds by being launched from an enormous cannon, still far slower than the speed of light.

The horse and buggy set the speed of life in those days. This is an ambulance for the Bellevue Hospital in New York in 1895, the year my grandmother was born.

The speed of life was slow in those days, far slower than the speed that Einstein was contemplating.  But still Einstein was able to apply his intellect to a question that perhaps seemed outrageous or unwarranted. At the time, the derivation of general relativity was mostly a curiosity, but today, a century later, it plays a central role in astrophysics, cosmology, and as it turns out, in your everyday lives!

Applications of general relativity, and the frontiers of general relativity in modern physics and astronomy. (TL) GPS system. (TR) Planetary orbits (LL) Black holes (LC) Wormholes (LR) Singularities.

In 2015 we are celebrating the Centennial of General Relativity. That means all your gravitational physicist friends will be all a-pitter-patter with excitement for the next 12 months, and impossible to quiet down about gravity at dinner parties.

On the off chance that you don’t have any gravitational physics friends (gasp!), for the next 13 weeks I’ll be exploring the landscape of general relativity right here at this blog. We’ll talk about how we think about gravity, the history of testing and understanding general relativity, modern observatories that are looking at the Universe with gravity instead of light, and some of the extreme predictions of general relativity — wormholes, black holes, and singularities.

My great-grandmother, Dora Larson.

My great grandmother passed away shortly after I went to graduate school, where I made gravity and general relativity my profession. In a time shorter than the span of her life, this little corner of physics had grown from the mind of a patent clerk into one of the most important aspects of modern astrophysics, at the frontiers of scientific research. Grandma Dora and I never got the chance to sit around and talk about black holes or the equivalence principle, but I often wonder what she would have thought of all the hoopla that gravity commands in modern life and modern science? What would she have seen, through eyes that saw the world grow up from horse drawn carts to space shuttles and GPS satellites?

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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).  This is the introductory post of the series. For the first time, I’m trying short 3.5 min videos with each post to capture the essential bits of each one. Here is the YouTube Playlist with all the videos (let me know how you like them — it’s an experiment!).

Links to the successive blog posts in this series are below for reference:

Gravity 0: Discovering Gravity (28 Dec 2014)

Gravity 1: Seeing the Invisible (7 Jan 2014)

Gravity 2: The Road to General Relativity (15 Jan 2015)

Gravity 3: Curvature & the Landscape of the Cosmos (24 Jan 2015)

Gravity 4: Testing the New Gravity (7 Feb 2015)

Gravity 5: Putting Einstein in the Navigator’s Seat (12 Feb 2015)

Gravity 6: Black Holes (28 Feb 2015)

Gravity 7: Recipe for Destruction (Making Black Holes) (7 Mar 2015)

Gravity 8: Black Holes in the Cosmos (15 Mar 2015)

Gravity 9: The Evolving Universe (27 March 2015)

Gravity 10: Signatures of the Big Bang (8 April 2015)

Gravity 11: Ripples in Spacetime (24 April 2015)

Gravity 12: Listening for the Whispers of Gravity (14 May 2015)

Gravity 13: Frontiers (27 May 2015)