The Unbearable Lightness of Gravity

Bang on a drum and you create a disturbance. The drum’s vibrations set off a chain reaction: molecules move, air expands and is compressed, and a sound wave is born. It is straightforward to separate the cause—drum vibrations—and the effect—the sound. The harder you bang on the drum, the more energetic the sound wave.

Image by Flickr user \<, adapted under a Creative Commons license.

Now, replace the beaten drum with a gravitational disturbance, such as the sudden collapse of a stellar core into an ultra-compact neutron star or black hole. Einstein predicted that such a collapse would create gravitational waves. But do these waves carry energy and, if so, how is that energy distributed—that is, what is its density (energy per unit volume) from point to point?

Gravitational energy is notoriously hard to define. In Einstein’s equations of general relativity, celebrating their 100th anniversary this year, gravitation and energy are on opposite sides. One side of the equations—call it the geometric side—represents gravitation as distortions in the fabric of spacetime. The other—call it the material side—describes the matter and energy in each region, including all forms of non-gravitational radiation, such as light. General relativity informs us that matter and energy compel spacetime to warp, creating what we feel as gravity. For example, the Sun’s mass distorts spacetime and generates a gravitational well in its vicinity. In short, matter and energy are the cause of gravitation’s effect.

Where then does gravitational energy fit in? Is it a cause, an effect, or both? Einstein’s equations of general relativity do not offer a clear answer. Gravitational energy doesn’t neatly fit on either the geometric or material side of the equations.

Einstein recognized the situation early on, and developed a separate formula for measuring the energy and momentum of gravitational fields. Known as the Einstein energy-momentum complex, it determines the gravitational energy and momentum within any region of spacetime, given its geometric structure.

Due to mathematical limitations of Einstein’s definition, other physicists began to develop independent energy-momentum formulas. These include formulations by French-Greek physicist Achilles Papapetrou, Russian physicists Lev Landau and Evgeny Lifshitz, American physicist Steven Weinberg, and others. Each of these complexes obeys conservation laws, meaning that energy and momentum can be transformed but not lost. For basic cases, such as determining the energy of a non-rotating black hole of mass M, they beautifully match each other in predicting an energy of E= Mc2. Thus, they conform to what might be expected for a relativistic definition of energy.

Yet one prediction made by these formulas is most unsettling. In 1955, Nathan Rosen, a former assistant of Einstein, applied several different energy-momentum complexes to a particular model of gravitational waves and calculated its energy in each case to be zero. He consequently proposed that gravitational waves don’t carry energy and thereby cannot really exist in nature. His words carried special weight, since he and Einstein had worked on that very subject. Rosen offered his hypothesis at a Bern conference celebrating the jubilee of special relativity.

Few physicists believed Rosen’s conjecture. All forms of radiation carry energy; why should gravity be different? As Richard Feynman argued two years later in his “sticky bead argument,” presented at a general relativity conference in Chapel Hill, a gravitational wave could jostle a bead on a stick, moving it up and down and, through friction, generate heat—a form of energy—in the process. If the gravitational wave didn’t carry the energy, he argued, where else could it have arisen? Something must have made the bead hot. Feynman did not try to explain why the energy-momentum complexes yielded a value of zero for the energy of gravity waves; presumably, he simply thought they were incomplete or wrong.

Canadian physicist Fred Cooperstock, who had worked for a year with Rosen, takes the value of zero seriously. But while Rosen argued that gravitational waves don’t exist at all, Cooperstock argues that they are real, but carry no energy. Cooperstock’s unorthodox hypothesis is that gravitational energy exists only where the material side of Einstein’s equations is non-zero; that is, in places with matter or (non-gravitational) energy in the first place. Consequently, all empty regions of spacetime have zero gravitational energy. That precludes gravitational waves carrying energy through the void. (If there is no true void, such a point may be moot.) In his view, gravitational waves convey geometric information (ripples in curvature), but not energy, from one point to another. Fluctuations ripple through spacetime, causing notable effects, while somehow carrying no energy.

“I’ve never seen anyone prove that information must carry energy,” Cooperstock says. It is like an elderly woman texting her daughter to bring home a sizable bag of groceries. Even though the text message carries information, but not energy, it triggers some heavy lifting.

A breakthrough came in the 1970s, when Russell Hulse and Joseph Taylor detected and measured the properties of the first-known binary pulsar system, PSR 1913+16. They demonstrated that the system’s orbital period is declining with time, matching a prediction made by Einstein about the transmission of gravitational waves between two masses. It was the first indirect indication of gravitational waves, and it won them the Nobel Prize. But skeptics like Cooperstock argue that fluctuations in the curvature of spacetime caused the results without actually conveying energy through space.

Today, several laboratories around the world are racing to detect gravitational waves directly. Leading the pack is the LIGO (Laser Interferometer Gravitational-wave Observatories) project, recently upgraded to Advanced LIGO , based in Hanford, Washington and Livingston, Louisiana. MiniGRAIL, a spherical gravitational wave detector based in Leiden, Holland, is trying to detect gravitational waves using an ultra-cold, 1,300 kilogram copper alloy sphere. A space-based mission called LISA (Laser Interferometer Space Antenna) is currently being planned.

Despite numerous efforts, as we celebrate the 100th anniversary of general relativity, gravitational energy remains an elusive construct. It has become an even weightier matter than Einstein first thought. However, if astronomers discover gravitational waves and can map out their energy, the burden of proof will finally be lifted. Understanding gravitational energy would help place it on the same footing as other natural interactions, such as electromagnetism, and will bring science closer to a modern-day “holy grail”: uniting gravity with the other forces of nature.

Go Deeper

Editor’s picks for further reading

Nature of Reality: There’s More Than One Way to Hunt for Gravitational Waves
Jennifer Ouellette explores the diverse methods with which researchers are searching for direct evidence of gravitational waves.

TED: The Sound the Universe Makes
In this video, astrophysicist Janna Levin explains how gravitational waves are made and LIGO’s role in searching for them.

Wikipedia: The Sticky Bead Argument
The history of the sticky bead argument and its influence on physicists’ thinking about gravitational waves and energy.

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Paul Halpern

    Paul Halpern is Professor of Physics at the University of the Sciences in Philadelphia. A prolific author, he has written thirteen science books, including "Einstein's Dice and Schrödinger’s Cat: How Two Great Minds Battled Quantum Randomness to Create a Unified Theory of Physics" (Basic Books). His interests range from space, time and higher dimensions to cultural aspects of science. The recipient of a Guggenheim Fellowship, Fulbright Scholarship, and an Athenaeum Literary Award, he has appeared on the History Channel, the Discovery Channel, the PBS series "Future Quest," and "The Simpsons 20th Anniversary Special." Halpern's books include "Time Journeys," "Cosmic Wormholes," "The Cyclical Serpent," "Faraway Worlds," "The Great Beyond," "Brave New Universe," "What's Science Ever Done for Us?," "Collider," and most recently "Edge of the Universe: A Voyage to the Cosmic Horizon and Beyond" (Wiley 2012). More information about his writings can be found at

    • Roto3

      Very interesting. I believe we will know soon. I’m betting with Einstein’s original prediction. I have a physics degree and have been studying the subject for 40 years. If energy bearing gravitational waves exist, it will be a monumental discovery. Equal or exceeding confirmation of the bending of photons by a gravitational mass. If not, that will be very interesting too. Fascinating.

      • Paul Halpern

        Thanks for your comments!

    • Somersetsmile

      Even if energy can not be carried across a void, the energy is not dissipated, it would be transferred to whatever matter is boarding the void. Following a path around until it either finds a matter pathway or until it energizes the matter present until the potential becomes high enough to jump across the void, that pathway would become the path of least resistance for all the built up energy which should heat that pathway as if it was a short across spacetime of the void. Any such short should be detectable, in fact that might explain some of the strange properties of the big bang.

    • ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

      Everyone has the wrong idea of what energy, forces and fields are.
      Energy is a particle vibration or movement.
      You cannot have energy without a mass, energy is mass vibrating.
      Energy cannot be out on its own. (a supposed mass-less particle is a particle nonetheless, but there are no mass-less particles, so that’s irrelevant)

      Same thing goes for forces.
      A force is a group of particles arranged in a field pulling each other… and all of the particles absolutely have to be physically connected.

      A force (a group of connected particles) can only push very short distances and in rare circumstances like same pole magnets.

      But the point is… a force has to have particles involved.
      A force cannot be out on its own.

      Most of mainstream physics is a misconception.

      There is no such thing as pure energy.
      Again… Energy is a vibration on a particle (or particle movement).

      Can energy be converted into mass?
      Ummm… no, energy already has mass involved, it is a particle vibration or movement. There is no pure energy and you are not going to convert energy into mass.

      Think of a guitar string. If you pluck it… that is the energy. If you remove the guitar string from the scenario… can you still have the energy? No, of course not.

      Can you convert the guitar string vibration into mass? No… that is ridiculous.

      Look at what everything really is…

      Dimensions and units…
      mass = [M] = kilograms
      length = [L] = meters
      time = [T] = seconds
      frequency = [T^-1] = seconds ^-1
      speed = [L] / [T] …… = m/s
      acceleration = [L] / [T^2] …. = m / s^2
      momentum = [M] [L] / [T] … = kg_m / s
      force = [M] [L] / [T^2] . = kg_m / s^2
      energy = [M] [L^2] / [T^2] = kg_m^2 / s^2

      Notice mass [M] is not equal to energy [M] [L^2] / [T^2] …the vibration is missing

      Here is what Einsteins famous equation really looks like…

      [M] [L^2] / [T^2] = [M] [L^2] / [T^2]

      Energy already is a mass times speed^2.

      How would you go about converting a mass times speed^2 into a mass times speed^2.

    • ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    • Edward N Haas

      In Esoptrics, the algebraic logic of the mirror (a/k/a Dynamic Mirror Theory), gravitational energy is “hard to define” only in the sense that Esoptrics involves such a large number of concepts and terms which — for all but perhaps 1 in a thousand — are far too different from anything they’ve ever heard before. What’s perhaps particularly difficult to grasp is that, in Esoptrics, the description of the Universe’s ultimate constituents is purely in the terms of Algebra’s abstractions. Geometry’s pictures have nothing to do with it save as a teaching aid. Starting at a level Geometry would picture as 7.34683969 x 10^-47 cm. (i.e. 2^129 x the hydrogen atom’s dia. with an electron in its outermost orbit generally given as 5×10^-8 cm.), Esoptrics says there are, before anything else, 6 sources of influence (i.e. 3 sets @ of 2 mutually opposed kinds) it labels A vs. B, A’ vs. C, and B’ vs. C’. These sources cause every one of the Universe’s ultimate constituents to be a COMPONENT state of excitation logically divisible into 6 kinds of COMPOSITE states of excitation.

      The ultimates then divide into 2 classes distinguished from one another by the way the 6 composite states of excitation relate to one another in the course of a given component state of excitation. Esoptrics calls one class “piggyback forms”, “MACRO-states of excitation”, “balanced states of excitation”, “force carriers”, and “space envelope PROVIDERS”. They can also be described as what Science might call “an ultimate kind of boson”. Esoptrics calls the other class “carrying generators”, “MICRO-states of excitation”, “unbalanced states of excitation”, “mass carriers”, and “space envelope USERS”. They can also be described as what Science might call “an ultimate kind of fermion”.

      Whereas every micro-state’s sextuplex description is unique & thus of too many kinds (c. 10^232) to list, every form’s every state of excitation, because balanced, is describable the same one way, namely: (xA + xB) + (xA’ + xC) + (xB’ + xC’) where x = a whole number from 1 to 2^256 (10th power of 2 in the sequence 2^0, 2^1, 2^2, 2^4, 2^8, 2^16, 2^32, 2^64, 2^128, 2^256). The 2^256 (10^77) values of x constitute a dimension Esoptrics calls ontological distance and OD for short. The OD of a form determines how extensive it is as a space envelope (i.e.: how many possible micro-states of excitation — “u-spaces” for short — it makes available to
      one or more generators). The number of u-spaces a form provides = (2x)^3, where
      x = the form’s current OD. That’s each space envelope’s VOLUME. The logical
      DIAMETER of every form is 2x u-spaces. Every form is forever logically concentric with a generator serving as the means by which the concentric form moves thru another form whose diameter (& thus current OD & value of x) is greater than its own. Every ultimate OCCUPANT of the Universe is thus what Esoptrics labels a “duo-combo”. Where does gravity fit into such a scenario?

      If 2 generators try to occupy the same u-space simultaneously (i.e.: try to perform the same one micro-state of excitation provided by the same form), the result is a logical collision causing one or both of their concentric forms either to rise or fall in current OD. If the collision causes one of the forms to rise in OD, it often ingests and makes concentric to itself one form for each of the OD’s thru which it passes. The result is a MULTI-combo in which each component DUO-combo’s form is at a discrete OD. That means this: Because it’s a force carrier, the accelerated form — by increasing its OD and thus its dia. in u-spaces — increases the dia. of its force’s reach. Were a form usually at OD2^128 to accelerate to one level below OD2^256, it would become a multi-combo: (1) composed of 2 less than 2^256 concentric duo-combos each at a discrete OD, (2) having a mass — relative to that of a single duo-combo — equal to the square of 2 less than 2^256 (c. 10^154), and (3) in the terms of Geometry, would — in c. 10^-19 seconds (i.e. c 10^77 steps @1 per c. 10^-96 sec.) — expand its gravitational force’s reach from 5 x10^-8 cm. (i.e. 2^129 u-spaces) in dia. to 18 trillion light years (i.e. 2 less than 2^257 u-spaces). That force’s intensity would then diminish as the inverse of the square of the distance in u-spaces from the center of the form. In short, Esoptrics’ view of gravity is a turn away from Einstein and back to Newton.

      Understand what Esoptrics’ multi-combos are all about, and you’ll also understand what so-called “black holes” and “dark matter and energy” are really all about rather than what physicists mistakenly think they are.


    • Peter

      First of all, thank you for writing this article. I have had little motivation to share what I have found for many reasons. I am a nobody and there is no reason for anyone to listen. Not to mention, my ideas compare to those that had to convince society that the world was not flat. Luckily for me there are less severe consequences today for being deemed insane. However, it is comforting to know that others have tried to discredit gravity as it is known today. I have read some of Einstein’s books but was unaware of Nathan Rosen. Thank you for bringing him to my attention.
      It would not be appropriate to share my exact ideas for the time being but a quick explanation should hopefully probe the right minds. Using two laws of physics, which are currently well accepted, I found an energy to mass ratio. I then compared the energy at the macro scale to the micro scale. With the conservation of energy in mind, I reasoned that I could split the comparison in to a “max” and “min” situation. I considered a purely kinetic situation and then potential, comparing each to internal energy. The same energy to mass ratio found earlier appeared in both situations.
      It was a very interesting find for me but with little motivation and the idea that there is little chance someone like me found what seems to have been found, I have not pursued further. I will have to look in to what Nathan Rosen found and see if that can shine more light on my current situation. Again, thanks.

    • Don Baxley

      I would think no gravitational waves would be created for 2 reasons. Light does not get added speed from being launched from a moving object so space has some unique quality that doesn’t react like normal matter does and the collapse of a star would create a vacuum that pulled space in not send out vibrations. The blast might look that way but space would not vibrate.

      • If you were going to test if there is a medium for the conveyance of light, would you…
        a) Test if the Earth is rushing through the medium.
        b) Test if there is a medium.

    • Steve Francis

      If you were to make the sun dissappear for one second, would it’s gravity have to require the earth instantly or would there be a 9 minute delay? Is the field repairable or instantaneous?

    • SpecialAgentA

      We still don’t really know what gravity is?

    • HAL 9000

      “I’ve never seen anyone prove that information must carry energy,”

      I’ve never seen anyone prove that information does not carry energy. The analog with the cellphone text is easily deconstructed; of course the information used energy – the phone’s battery, the cell network, grandma’s fingers typing the keys, etc. Too easy there.

      Indeed, a verb (‘carry’ in the case above) implies the 2nd law. The whole nerd-war over blackhole and information integrity centers on the energy properties. Any change in the universe involves energy.

      I’ll take Feynmann’s common sense here.

    • andrewp111

      If gravitational waves carry no energy, then there is no limit on their speed of propagation either. But I don’t believe any of this. Binary pulsars lose energy that matches the GR predictions of gravitational radiation, and that energy must go somewhere. If it isn’t carried away by gravity waves, then where did it go? A calculation that says gravity waves have no energy is reminiscent of calculations more than a century ago that said atoms were not stable, and theories that could not explain the T to the 4th power law of thermal radiation from black bodies. Those anomalies were solved by quantum theory, and something similar may be needed for gravity.

    • William Jacobs

      Is there a small chronological error in the article? As implied later when discussing Rosen’s 1955 jubilee paper, it is special (not general) relativity that is celebrating its 100th anniversary this year. Einstein proposed his theory of general relativity in 1915.

    • Hugo Ortega

      I am beginning to suspect that gravity is nothing like we imagine it to be. Is it possible that gravity is an emergent phenomena arising from matter clumping together? All that is absolutely known about gravity is that it is tied to mass. Perhaps what we are observing isn’t a field like electromagnetism; but space/time being pulled by the collective tug of every single particle clumped together in an object. Wouldn’t that solve a major problem with the relative weakness of gravity on atomic scales? Since any one atom only exerts a tiny amount of gravitational “pull” you don’t begin to see major distortion of space/time until you have a large amount of atoms together all contributing their tiny gravitational force in one focused area of space/time. Then you don’t need gravity waves or energy traveling and transferring information because all you are seeing is space/time compressing and affecting any other matter inside it.

    • seescaper

      According to Milo Wolff’s WSM theory, “Gravity is caused by the mass-energy density of space. This mass-energy
      density of space is determined by the square of the Wave-Amplitude and is
      always positive (squares are always positive). The Wave-Velocity
      is inversely proportional to the square root of the mass-energy
      density of space, the higher the mass-energy density of space,
      the slower the Wave-Velocity. As Matter and its resultant mass-energy density
      of space are always positive, this causes a slowing of In-Waves as they
      travel through other matter/wave-motions, and it is this property of Space
      that causes the natural ‘Gravitational’ attraction of all bodies,
      and explains why Gravity is always attractive.For more in depth discussion google “beyond the point particle.”

    • jeff123

      their is no such thing as gravity. Its space time wrap that holds things together or down.