General Relativity as a Tool

By Mark Trodden | January 25, 2006 6:58 pm

Less than a century after Einstein’s development of General Relativity (GR), physicists still marvel at its geometrical beauty and the myriad observational tests it has passed. One of the best tested theories in the history of science (that’s right IDiots – it’s “just” a theory), General Relativity is mature enough that these days it is increasingly being used as a tool through which to make other scientific discoveries. One of the most successful examples of this is the use of gravitational microlensing to tell us about the presence of small mass distributions – particularly planets.

The bending of light around massive bodies, as predicted by Einstein and later confirmed by Eddington’s observations during the 1919 solar eclipse, is a basic result of GR. Taken to extremes, light from a distant object, passing precisely around a closer, massive object leads to the Einstein Ring phenomenon. More typically, what is observed is a brightening of the light from a distant object as a massive object passes across the line of sight. In the eclipse observations, the presence of a known object was used to measure the way in which light bent, and thus to test GR. But these days, GR is so well understood on these scales, that one may turn this technique on its head and use GR as a tool, interpreting the brightening of such a distant object as evidence for an intervening mass distribution.

For planet detection, the increase in light from a far away star as a closer one passes can happen in a subtle way, revealing the presence of another massive object orbiting the nearer star. This is what is being reported for the smallest object so far – a roughly Earth-sized one. As the BBC article puts it

If the foreground star has a planet orbiting it, it will distort the light even more, and will make the star behind it look even brighter. But this effect lasts for a much shorter period, giving astronomers just hours or days to detect it.

Dr Martin Dominik from the University of St Andrews is a co-leader of the PLANET collaboration, one of the microlensing networks used to detect the new planet.

“We first saw the usual brightening reaching a peak magnification on 31 July 2005. On 10 August, however, there was a small ‘flash’ lasting about half a day,” he said.

“By succeeding in catching this anomaly with two of the telescopes of our network and with careful monitoring, we were able to conclude that the lens star is accompanied by a low-mass planet.”

The planet they discovered is unusual compared to other recently discovered extrasolar planets

The planet, which goes by the name OGLE-2005-BLG-390Lb, takes about 10 years to orbit its parent star, a red dwarf which is similar to the Sun but cooler and smaller.

It is in the same galaxy as Earth, the Milky Way, but is found closer to the galactic centre.


Like Earth, it has a rocky core and probably a thin atmosphere, but its large orbit and cool parent star mean it is a very cold world.

Predicted surface temperatures are minus 220 degrees Celcius (-364F), meaning that its surface is likely to be layer of frozen liquid. It may therefore resemble a more massive version of Pluto.

Since I spend a great deal of my time thinking about and investigating the role that GR plays in the early universe, it is nice to be reminded by stories such as this of the important role that GR plays in relatively late-universe science; in this case as a tool.

You can always rely on Albert.

  • Dumb Biologist

    Impressive!…but where’d they get the stuff about the atomosphere and a surface of frozen liquid? That’s educated guesswork not informed by gravitational lensing, right?

  • Sean

    Like Mark, I heard about the new Earth-like planet and immediately wondered at the power of general relativity. I suspect this puts us in the minority.

  • Plato

    I was more entranced with the idea of Gravitational lensing and it’s application with regards to “dimensional thinking.” Has ingenuity of theoretcial thinking outpaced itself?

    I hate to think that one would not have thought experiemental processes would have been given to this, while we have been dazzled with Pound-Rebka experiment

    Any progressions, to see “ideas of this lensing” is a very strange for me, yet like you Mark, others have wonder about the implications, not just on a cosmological scale.

  • bittergradstudent

    I was simply completely taken aback at the observational power required to see this effect, considering the tiny effect that gravitational lensing has when planetary masses are the source.

    And sorry, I couldn’t resist:

    “You can always count on Albert”

    As true in physics as it is in baseball.

  • Theo

    One of the best tested theories in the history of science

    At length scales of a cm and higher. Direct probes of gravity allow large extra dimensions up to tenths of millimeters, ne?

  • Poppycock

    There is one thing I don’t understand about this microlensing. Presumably the distance from the planet to the red dwarf it orbits is very much less than the distance from the red dwarf to the star whose light is lensed?

    If so, why does the effect of the mass of the planet vary as it moves through its orbit? Considering the large distances involved (again, this is a presumption) how can the planet and the red dwarf be “resolved” into separate bodies?

    Sorry if this is not terribly clear, I’m not sure how to express it any better. (And I haven’t read Quantoken’s comment, but I can’t imagine the answer is contained therein – forgive me if it is.)

  • Mark

    That’s absolutely right Theo. What I mean is that not only are there huge numbers of tests that it has passed, but also that there are examples of tests where theory and experiment agree to an absurd number of significant figures.

    I’m definitely one of those interested in the possibility that GR might break down at either the small or large scale.

  • Mark

    Hi Poppycock. It is remarkable, I agree.

    Not sure what’s the right level for you, but here’s a technical article explaining the technique

    I think the point is that as the two bodies pass across the line of sight, the relative positions of the star and the planet (if you like, the geometry of the two body system) change. This leads to small variations in the light curve expected from just a star alone. I expect they then fit this data to a model of a planet orbiting a star and play with the planetary mass and orbital parameters to get the best fit. (If any true experts on the details are reading, please chirp in here).

    It is a difficult measurement, and has only become useful (for planet finding) in the last couple of years or so. See the link below for an earlier New Scientist article.

    (By the way, I deleted the earlier comment you referred to, not because it is dissenting, but because that commenter has been asked not to comment at all here after repeated poor and disruptive behavior)

  • Count Iblis

    When I heard this I was a bit surprised because I’ve heard about similar discoveries of small plantets before. But I just looked at the list of extrasolar planets and it seems that there is a rather big list of Unconfirmed, controversial or retracted planets

  • Poppycock

    Hi Mark,

    Thanks for the article. If I understood correctly they talk a bit about why the point-lens approximation is (incredibly) not appropriate.

    GR never fails to impress – mathematically and in application!

    Thanks :)

  • P.M.Bryant

    I think the point is that as the two bodies pass across the line of sight, the relative positions of the star and the planet (if you like, the geometry of the two body system) change. This leads to small variations in the light curve expected from just a star alone. I expect they then fit this data to a model of a planet orbiting a star and play with the planetary mass and orbital parameters to get the best fit.

    A slight correction, based on my understanding:

    Since the blip in the light curve from the planet’s lens effect lasted less than a day, I don’t think it changed its position relative to the star in an appreciable way. I believe the only parameters that can be measured in an event like this are the mass of the planet (from the amount of brightening of the background star) and its angular separation from its parent (based on the delay between the peak of the parent’s lens effect and the planet’s lens effect).

    From my reading, the distance to the lensing objects is not known directly, but is estimated via modelling of the galactic structure between us and the background star. Based on the data presented, that seems to nail down a probable distance to within 30-40% or so.

    With all the uncertainties, the mass of the new planet is only known to within a factor of 4. So perhaps it is small, but perhaps it is more like Uranus.

    What I find amazing about this measurement is not the technical skill and patience involved, though that is impressive, but the fact that a small planet more than 20,000 light-ears away can cause a star to brighten by 10-20% for almost a day. GR is powerful stuff!

  • P.M.Bryant

    Considering the large distances involved (again, this is a presumption) how can the planet and the red dwarf be “resolved” into separate bodies?

    I don’t think my previous comment addressed this as directly as I would have liked, so I’ll try again.

    The foreground system is moving relative to the background system. First, the planet’s parent star lenses the background star causing a prolonged (several weks) brightening due to its relatively large mass. As the star passes and its lens effect diminishes, the planet moves between us and the background star, causing a shorter (1 day or so), much smaller brightening.

    That time delay is how the planet is resolved from its parent star.

  • Poppycock

    Oh…. My understanding was somewhat wrong then – guess I best go alter my own explanation! Thanks all!

  • Dumb Biologist

    At length scales of a cm and higher. Direct probes of gravity allow large extra dimensions up to tenths of millimeters, ne?

    According to the two articles linked below, apparently modern techniques have confirmed Newton’s inverse-square law to distances at least as small as a few hundred microns, maybe smaller. I think, anyway…

  • Dumb Biologist
  • Dumb Biologist

    I guess Hoyle, et al. claim they’ve got the measurement down to about 160µ for at least one large extra dimension, and 195µ for “Yukawa interaction”, whatever those are…

  • Bluechip

    This is entirely unrelated to the topic of the post but when I read the comments this morning there was one from “Cosmic Variance” that challenged Mark to prove something. I was on my way out the door at the time so I’m not really sure what was said in it. However, now I see that the comment has been deleted. What was all that about?

  • Dumb Biologist

    Ah, I guess the Yukawa interaction in this case has to do with the coupling of matter fields with the Higgs field…

  • Mark

    Hi Bluechip. The comment was by a person who used to comment on this blog by another name and was incredibly insulting and disruptive. After repeated warnings and private correspondence the person nevertheless continued to behave in this way and we were forced to ban them. When I saw the comment was from them, I deleted it consistent with this policy.

    The person has had their misconceptions explained to them many times, and their comment was a repeat of one we’d seen many times on earlier posts both on this blog and on mine and Sean’s separately.


  • Bluechip

    Thanks Mark. As I said, I didn’t really have time to read it properly but you’re right, it did seem to be needlessly confrontational.

  • Torbjorn Larsson

    For me, the marvelous thing is that these new observations may result in statistics on rocky Earthlike planets and so more knowledge on solar system formation.

    One of the early articles (which I can’t find again) said that since Jupiter analogs are so much easier to see, these observations can perhaps already show that Earth analogs are much more common and that strengthened the case of the standard formation model. P.M.s post above seems to indicate that the case is not so clearcut.

  • BK

    Has anyone noticed that general relativity does not jive with vortex dynamics, even though the sun and planets follow the laws of vortex dynamics? We all know that the planets are orbiting the sun in a counterclockwise fashion with the sun as a foci. Consider any two of the planets as Mass A and Mass B (just two to simplify this but any number of masses will do.) Vortex dynamics says that the two masses orbit around a foci because they are caught in each other’s flow fields, and the foci is the RESULT of them being in each other’s flow fields. If you were to take away the two rotating masses then the foci between them would also disappear and in fact, the foci would not exist in the first place without the two orbiting masses that create it.
    General relativity says the sun bends spacetime and gravity is the result, but according to the actual engineering law covering the motion of the sun and the planets, the PLANETS (masses A and B) create gravity because they are caught in each other’s flow fields and the foci between them, the sun, is the RESULT of this mutual attraction between the planets. And since vortex dynamics are LAW and general relativity is THEORY this should be taken as a serious flaw in how we view the solar system.
    James Vanyo’s book ROTATING FLUIDS IN ENGINEERING AND SCIENCE has a great chapter on vortex dynamics.
    BK (reached at a cool little lady’s email

  • Science

    BK, general relativity is not a speculative theory, but solar vortex theory is the obsolete speculation of Descartes.

    The best way to understand that the basic field equation of GR is empirical fact is extending Penrose’s arguments:

    (1) Represent Newton’s empirical gravity potential in the tensor calculus of Gregorio Ricci-Curbastro and Tullio Levi-Civita: R_uv = 4.Pi(G/c^2)T_uv, which applies to low speeds/weak fields.

    (2) Consider objects moving past the sun, gaining gravitational potential energy, and being deflected by gravity. The mean angle of the object to the radial line from the gravity force from the sun is 90 degrees, so for slow-moving objects, 50% of the energy is used in increasing the speed of the object, and 50% in deflecting the path. But because light cannot speed up, 100% of the gravitational potential energy gained by light on its approach to the sun is used to deflection, so this is the mechanism why light suffers twice the deflection suggested by Newton’s law. Hence for light deflection: R_uv = 8.Pi(G/c^2)T_uv.

    (3) To unify the different equations in (1) and (2) above, you have to modify (2) as follows: R_uv – 0.5Rg_uv = 8.Pi(G/c^2)T_uv, where g_uv is the metric. This is the Einstein-Hilbert field equation.

    At low speeds and in weak gravity fields, R_uv = – 0.5Rg_uv, so the equation becomes the Newtonian approximation R_uv = 4.Pi(G/c^2)T_uv.

    GR is based entirely on empirical facts. Speculation only comes into it after 1915, via the “cosmological constant” and other “fixes”. Think about the mechanism for the gravitation and the contraction which constitute pure GR: it is quantum field theory, radiation exchange.

    If you want a “vortex dynamics” explanation of gravity, check out LQG and the “spin foam vacuum” QFT -> GR solution of Smolin et al.

  • BK

    When vortex dynamics are applied to the solar system, as the field certainly is since it is nothing more really than looking at objects from the point of view of their spin direction and their size and how it relates them to each other. General relativity itself of course does not change, but our view of the solar system, when using general relativity does not take into account the complexities encountered when the the whole solar system is viewed as one big vortex, all spinning counterclockwise, like water in a drain with the sun in the drain hole. It is not as crude a comparison as one might think, because it shows us how connected every component of the solar system is, how dependent each component is on the others.
    When two objects the same size spin in the same direction they cannot bind together and will create a foci point between them; mars and earth are somewhat comparable in size for instance, rotating counterclockwise and have the sun foci between them. But if mars, say, were to turn clockwise with earth close by then instead of a foci between them the pair would coalesce and move forward in one direction instead of in a nearly circular orbit. The point is that spin direction is very important. Electrons are the same size but they repel each other, not doubt because they all spin counterclockwise as components of a counterclockwise moving body, earth. Only when one of the electrons spins clockwise can it create an entangled electron. Gravity studies and equations must include the spin direction of the masses to be complete.

  • Science

    BK, it is a crude comparison unless you deal with it mathematically. What you’re saying is in Descartes’ book, complete with a diagram of planets swirling around the sun. It doesn’t work because the quarks and electrons of the earth have very, very large gaps between them. Any vortices caused in the spacetime fabric are similar in size, subatomically small. I agree that fundamental particles have spin which in an abstract way is related to vortices. Maxwell in fact argued that magnetism is due to the spin alignment of tiny vacuum field particles.

    The problem is that electron is nowadays supposed to be in an almost metaphysical superposition of spin states until measured, which indirectly (via the EPR-Bell-Aspect work) leads to the entanglement concept you mention. But Dr Thomas Love of California State University last week sent me a preprint, “Towards an Einsteinian Quantum Theory”, where he shows that the superposition principle is a fallacy, due to two versions of the Schroedinger equation: a system described by the time-dependent Schroedinger equation isn’t in an eigenstate between interactions.

    “The quantum collapse occurs when we model the wave moving according to Schroedinger (time-dependent) and then, suddenly at the time of interaction we require it to be in an eigenstate and hence to also be a solution of Schroedinger (time-independent). The collapse of the
    wave function is due to a discontinuity in the equations used to model the physics, it is not inherent in the physics.”

  • BK

    Let’s deal with spacetime fabric, mathematically so as to get rid of the “crudeness.” General relativity says spacetime fabric is composed of the sun in the center, bending the fabric of spacetime, and the planets on the outer edge of the spacetime fabric. Spacetime then is composed of no less than these three things; planet/masses on the outer edge (all of which happen to be moving counterclockwise,) the sun/foci in the center of them, and the fabric itself.

    When we speak of entangled electrons which vortex dynamics says can only be entangled because one of the electrons moves counterclockwise and the other clockwise, we notice they do not have a foci between them; they would have to both be moving the same direction to have a foci. Therefore entangled electrons do not meet the criteria for existing in spacetime because they have no foci, one of general relativity’s three requirements. So what is the mathematical formula for spacetime? It is one that encompasses the sun, planets and the spacetime amongst them.
    Vortex dynamics has the equation to describe a vortical unit as “Mass 1 + Mass 2, M1>M2 and both spinning the same direction and creating a foci between them, divided by the distance squared between them,” and this distance is measured from the center of each mass. If we call mass 1 earth and mass 2 mars, and the distance squared between them (measured from their centers) and containing their foci between them, the sun, then this equation from vortex dynamics describes general relativity but in a more precise manner. More precise because masses 1 and 2 are attracting each other because they are caught in each other’s flow fields (gravitation defined,) and the foci of their attraction, the sun, is quite electromagnetic don’t you think? Electromagnetism and gravitation are together in one vortical motion law! So there is every reason to consider vortical law when considering general relativity and again, this view does not contradict science because the solar system is already a vortex and so already falls under the mathematical law of vortex dynamics, but it goes further in explaining the workings of spacetime.

  • Science

    “General relativity says spacetime fabric is composed of the sun in the center, bending the fabric of spacetime, and the planets on the outer edge of the spacetime fabric.” -BK

    It doesn’t say that because it’s a mathematical equation. Until some underlying dynamics for quantum gravity are widely accepted, you can’t rule out that the spacetime fabric causing general relativity (gravity and contraction) is outside the system, as Feynman explained in his Nov 1964 Cornell lectures which were filmed for BBC TV, “The Character of Physical Law” (broadcast on BBC2 in 1965), published in his book of similar title, pp. 171-3:

    “The inexperienced [theorists who have never made contact with reality by getting a theory which predicts something measurable], and crackpots, and people like that, make guesses that are simple, but [with extensive knowledge of the actual facts rather than speculative theories of physics] you can immediately see that they are wrong, so that does not count. … There will be a degeneration of ideas, just like the degeneration that great explorers feel is occurring when tourists begin moving in on a territory.”

    On page 38 of this book, Feynman has a diagram which looks basically like this: >E S

  • Science

    >E S

  • Science

    where E is earth and S is sun. The arrows show the push that causes gravity. This is the LeSage gravity scheme, which Feynman also discusses in his full Lectures on Physics, where he shows that the contraction of general relativity is like a pressure of the spacetime fabric compressing the earth’s radius by 1.5 mm, with a related gravitational time-dilation because of the spacetime inter-relationship. He finishes by saying (pp. 57-8 of “Character of Physical Law”):

    “It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.”

  • BK

    Occum’s-the simplest is correct. Crackpots quote theorists when simple LAW- vortical law, undisputable LAW which the solar system follows- is all that is needed.
    Relativity has something wrong with it, otherwise it would match up with quantum. Its well known that the problem lies somewhere in relativity, not quantum, so relativity has something illogical going on and when spin is added to its equation it makes much more sense. If the sun were a gravitating body following the same laws as the planets, then where is the foci between it and the planets that vortical LAW says MUST be present? There is no scientific dispute that the solar system follows vortical law.
    In these matters one must stick to law, not quotes that have no law backing them.

    Here’s another one. Light contains energy, even when it is cold. According to relativity this energy should have generated mass and the mass should have generated gravity, but it does not and the reason why is not understood. UNLESS, of course, its role as the foci of two bodies is examined. Vortical law states the foci owes its existence to the masses surrounding it; take away the two masses and their foci disappears, therefore the foci does not have its own gravity, it is in essence “borrowing” its existence from the masses rotating about it.
    Protons and electrons exchange photons so that the proton may hold the electron nearby (Feynman, Six Easy Pieces.) We aren’t studying protons and electrons in outer space somewhere, it’s being done right here on counterclockwise spinning earth, making protons and electrons actual constituents of earth therefore rotating with it. So the proton is rotating counterclockwise, the electron is rotating counterclockwise- lo and behold! hardly a coincidence that a photon, light, is found between these bodies.

    Indeed, the LAWS are revealed and the machinery is simple. Its predictions are quite measurable.

  • BK

    Going to work, I’ll be back at 9 pm this evening. I have enjoyed Mr. Science’s point of view.

  • BK

    Vortex dynamics is a science built on laws not theories. It is already in the public domain so any observations about it are just that, not new theories. I’m sure the alpha in all of us is looking for a new theory to name after ourselves! but the observations I bring up here are not new and anyone can look them up.

    For instance. It is fact that our solar system rotates and is considered a vortex. Are usual concept of our solar system is that we are out here in space floating all alone in an isolated manner. But a theorem attributed to Helmholtz says that a vortex filament (also called a vortex tube, the small end of the vortex) cannot end in a fluid. It must extend to infinity, form a closed loop (like a smoke ring) or end at a solid wall of some sort. What does the vortex tube for our solar system do? We don’t resemble a smoke ring so we probably aren’t forming a closed loop. If our vortex tube extends to infinity so much the better, since this would solve the mystery of why so many of our equations result in infinity. String theory has been so popular because it resolves infinity but since it is riddled with problems many think it is likely not the answer.
    There are so many stars in the night sky and if each one represents the foci of a vortex, as our solar system does, then each star has a vortex tube extending from it and coursing through space. Trillions of vortex tubes…could this be dark matter?


Discover's Newsletter

Sign up to get the latest science news delivered weekly right to your inbox!

Cosmic Variance

Random samplings from a universe of ideas.

About Mark Trodden

Mark Trodden holds the Fay R. and Eugene L. Langberg Endowed Chair in Physics and is co-director of the Center for Particle Cosmology at the University of Pennsylvania. He is a theoretical physicist working on particle physics and gravity— in particular on the roles they play in the evolution and structure of the universe. When asked for a short phrase to describe his research area, he says he is a particle cosmologist.


See More

Collapse bottom bar