Weighing in on Einstein’s Gravity

A massive neutron star and its lightweight companion provide a unique space laboratory to test general relativity.

pulsar-white dwarf binary
The pulsar PSR J0348+0432 is a tiny but massive neutron star with a larger, lightweight white dwarf companion. The relative sizes of the two objects in this illustration are not drawn to scale: the dwarf is actually more than 4,500 times larger than the pulsar.
ESO / L. Cal?ßada
You have to be really dense to prove Einstein right. And the pulsar J0348+0432 is really dense. Twice as massive as the Sun and roughly 20 kilometers wide, at its center this celestial lighthouse fits more than one billion tons into a sugar-cube-size volume. That gives it a surface gravity more than 300 billion times stronger than Earth’s.

So basically, forget breathing deeply.

J0348 also has a wimpy sidekick, a white dwarf less than one-tenth its mass. The white dwarf and neutron star whirl around each other in a fairly circular orbit every 2.46 hours, reaching velocities close to the speed of light.

These aspects of J0348 excite scientists who want to test Einstein’s theory of gravity in extreme environments. The binary isn’t the best all-around test of the famed physicist’s general theory of relativity, but it does probe a strong-gravity environment that hasn’t been accessible to observers before.

J0348 is one of only two neutron stars discovered with a mass of two solar masses. Before the discovery of the other object (J1614–2230) in 2010, astronomers had thought neutron stars didn’t grow above 1.5 solar masses, explains Thibault Damour (Institut des Hautes Etudes Scientifiques, France). “Now they find another one [at two solar masses], which is a big discovery in itself.”

General relativity’s no slouch when it comes to acing tests, but it’s possible that gravity might not follow those rules around massive, dense objects. Astronomers study such exotic objects to find out. They know that general relativity (the physics of big things) and quantum mechanics (the physics of the über-small) don’t meld well, so they suspect there’s a crack somewhere.

J0348 gives researchers a unique opportunity to test for those cracks. Other binary systems have similarly short periods or equally egregious disparities between the two members’ masses, but the combination of both allows observers to look for unique effects that shouldn’t be there if general relativity reigns.

The key is that the two dead stars don’t just orbit ad infinitum. They’re slowly spiraling in toward each other, radiating away energy in the form of spacetime ripples called gravitational waves. General relativity precisely predicts how much the orbit should decay with time. If extra effects are at work, other, unpredicted ripples could also appear.

With such a difference in the pulsar and white dwarf masses, this violation of Einstein’s gravity should be pretty obvious in J0348's orbit. But after careful study using radio observations to time the pulsar’s signal, John Antoniadis (Max Planck Institute for Radioastronomy, Germany) and his colleagues found no sign of extra physics. The orbital period shrinks by 8.6 microseconds each year (give or take 1.4), which is consistent with the predicted value.

J0348 complements another gravity-testing system, the double-pulsar pair J0737–3039, says study coauthor Michael Kramer (Max Planck Institute for Radioastronomy and University of Manchester, UK). J0737 has an orbital period only a couple of minutes different than J0348 — 2 hours 25 minutes versus 2 hours 28 minutes — but with two pulsars blinking steadily and a more elliptical orbit, J0737 reveals relativistic effects that the pulsar-dwarf pair doesn’t.

One really cool example is the Shapiro effect. This effect is a delayed arrival time for a signal coming from a massive object and is created because the beacon’s photons have to climb out of the ditch the object creates in the fabric of spacetime. (Even photons can’t leap over hills in a single bound.) Because J0737’s two pulsars follow elliptical orbits, they’re not always the same distance apart. That variation in turn changes the shape and depth of the gravitational well, which means that the delay also changes throughout the orbit.

J0737 will always be better in terms of the number and measurement precision of relativistic effects, Kramer says. But because its two pulsars have similar masses, effects that would only show up when the masses are different are difficult to test. That’s where J0348 comes in.

The new pulsar-white dwarf pair does rule out some non-Einstein effects (the extra spacetime ripples). But whether gravitational hiccups arise when two strongly interacting bodies are much closer together isn’t clear. Experiments dedicated to hunting for gravitational waves, such as Advanced LIGO, which is scheduled to begin observations by 2014, might reveal more. The growing Event Horizon Telescope network will also peer into our galaxy’s innermost sanctum to determine whether gravity behaves around the supermassive black hole as general relativity predicts.

Below, you can watch a video of a pulsar-white dwarf pair. The relative sizes of the two stars aren't to scale (the neutron star is a whole lot smaller in reality), but the animation does give you a sense of gravitational waves.

Loading player...

Reference: J. Antoniadis et al. “A Massive Pulsar in a Compact Relativistic Binary.” Science, 26 April 2013.

33 thoughts on “Weighing in on Einstein’s Gravity

  1. Robert-CaseyRobert Casey

    I’m certainly no astrophysicist but I seem to remember reading somewhere that a neutron star much more massive than 1.4 Suns would collapse into a black hole. Maybe if it rotates fast enough, that doesn’t happen here?

  2. Greg Taylor

    The limit for neutron stars is around 3 solar masses. The 1.4 solar mass limit is for white dwarfs. Any larger than that, and they detonate as a type Ia supernova.

  3. Robert L. Oldershaw

    Discrete Scale Relativity predicts that the total masses of bound stellar systems will have discrete values that are multiples of 0.145 solar mass.

    The Pulsar-White Dwarf system discussed in this article has a total mass of 2.182 +/- 0.04 solar mass.

    This value agrees with one of DSR’s definitively predicted values (2.175 solar mass) at the 99.997% level.

    Robert L. Oldershaw
    Discrete Scale Relativity/Fractal Cosmology

  4. Peter WilsonPeter

    "They know that general relativity and quantum mechanics don’t meld well." So? Classic physics or quantum mechanics, there is no exact solution to any problem beyond the two-body: one proton and one electron. No exact solution exists to any physics problem involving three or more objects. Why should we expect to find an exact solution to a model that combines three forces? What if GR and QM are both correct, but like the 3-body problem, no exact solution exists?

  5. Morris

    A quick Newtonian calculation (which is good enough for separations much larger than the event horizon) will quickly show that the orbital speeds are far less than the speed of light.

  6. Robert L. Oldershaw

    When mathematics is applied to actual physical systems it invariably involves approximate models.

    If Nature is one unified system, then it will have one unified physics, but I would bet the farm that the ultimate laws governing all scales of Nature’s hierarchy require nonlinear dynamical systems modeling. Thus the unified laws will be involve deterministic chaos and fractal non-differentiability. Exactitude is a delusion.

    When we are ready to accept a more mature and clear-headed understandiing of Nature, we will realize that we have been led astray by over-idealizations like exact solutions, strict reductionism, reversible evolution laws, perfect homogeneity and other assorted untestable pipe dreams.

  7. Bruce

    Oldershaw’s statement “Discrete Scale Relativity predicts that the total masses of bound stellar systems will have discrete values that are multiples of 0.145 solar mass” would be stunning if it turned out to be true. 0.145 solar mass is approx. 2.884E29 kg, which is also about 152 Jupiters! Robert, just what is meant by “bound stellar systems”? Would that be any star system, no matter how many stars? If so the statement would imply that stars themselves would only come in discrete multiples of your 0.145 solar mass figure, unless a pair is undergoing mass transfer. Logically, shouldn’t a star be able to have any mass from just over a brown dwarf on up to the point of collapse?

  8. Robert L. Oldershaw

    Hi Bruce,

    According to Discrete Scale Relativity, which is a completely new and different paradigm for understanding nature, our thinking about the formation and physical properties of atoms, stars and galaxies would be radically changed.

    My website goes through everything in considerable detail.

    Bound means gravitationally bound.
    In this context I am referring to individual stars, binaries, planetray systems, and the rare triple and quadrupole star systems.

    Unbound isolated stars, and dark matter primordial black holes, would have masses at the (n)(0.145 solar mass) values.

    For bound systems, you need to measure the total mass because there is some (=/< than 10%) transfer of mass/energy between the system members.

    In the Pulsar-White Dwarf system in question the more massive pulsar transfers about 0.02 solar mass to the white dwarf.

    A huge amount of information, supportive evidence and many examples are available at http://www3.amherst.edu/~rloldershaw

    Rob O

  9. Bruce

    Thanks Robert. Gravitationally bound is what I thought you meant. DSR certainly would be a radically different way of looking at things. So, according to DSR, stellar systems would share the property of atoms as to the masses only coming in discrete units. On the atomic scale the mass would be that of the neutron. To me the large mass you give of 0.145 solar masses (152 Jupiters) is what makes this suggestion so hard to accept. But your “Prediction” comment at least has the advantage of being very testable. Since “bound systems” include solitary stars, what about the best known system, ours? 1 solar mass / 0.145 solar mass = 6.897, so lets say for the sake of argument that with the rest of the solar system added in it is close enough to 7 DSR system mass units. DSR would then predict that there are only 6 steps of allowed system masses below that of ours. So, do solitary stars smaller than the sun come in only 6 sizes, or do they span the whole range of masses between a BD and the Sun?

  10. Peter WilsonPeter

    Thanks, Robert. Even if a theory-of-everything is possible, even if one equation could be written down that would describe-it-all, I still have to wonder why they are searching for some deviation from GR in a “strong-gravity environment that hasn’t been accessible to observers before.” All the king’s horses and all the king‘s men cannot put QM and GR together again, as it is. If they find deviations, the math is only going to get more complicated. How is finding deviations from GR going to make the task of unification any easier? Do they realize what they are asking for? Einstein once said, “God is subtle, but He is not malicious.” Well, if they DO find deviations from GR in high-field situations, I am going to go out on a limb and say Al was wrong: God is malicious!

  11. Robert L. Oldershaw

    The Solar System makes an excellent case in point for what Discrete Scale Relativity proposes.

    The Sun’s mass is a bit below n = 7 times 0.145. But the planetary system is more massive than a naive prediction would suggest (by the same amount!).

    When you add up the total mass of the system you get the n = 7 value to the 99.987% level of relative accuracy.

    The calculations are presented at http://www3.amherst.edu/~rloldershaw
    See: Technical Notes, #1 "Resoution of An Apparent Solar System Mass Anomaly".

    I cannot emphasize enough that virtually all questions you might have about Discrete Scale Relativity, which attempts to complete Einstein’s relativity program, can be found somewhere at my website.

    Best, Rob O

  12. Robert L. Oldershaw

    I think they have been using the wrong math and specifically the wrong symmetry group. What will be required to unify QM and GR is discrete conformal symmetry and discrete conformal geometry.

    The discrete fractal approach to modeling nature rejects the Platonic idealizations I mentioned above. It is deterministic, completely causal and applies at all levels of nature.

    Since this model implies that all systems in nature are nonlinear dynamical systems, there are inherent limits to "perfection" and exactitude.

    Einstein emphatically said GR was not the final theory in his program, but rather that it needed to be "deepened" by additional, and possibly complicated, symmetries so that it could bring quantum systems within a more comprehensive paradigm.

    Best, Rob O

  13. Robert L. Oldershaw

    The Solar System provides an excellent case in point for what Discrete Scale Relativity proposes.
    The Sun’s mass is a bit below the n = 7 value. However its planetary system has an excess mass compared to what might be expected in a naïve understanding of DSR. The deficit and excess are very nearly the same and the total mass of the Solar System agrees with the n = 7 prediction at the 99.987% level.
    The relevant calculations are given in Technical Note #1 at my website.
    The answers to almost any question you might have about DSR can be found at my website: http://www3.amherst.edu/~rloldershaw .

    Best, Rob O

  14. Robert L. Oldershaw

    Hi Bruce,

    I figured out why my comments "stopped appearing".

    Discrete Scale Relativity proposes that for every object on the Atomic Scale of nature’s unbounded and highly stratified hierarchy there is a Stellar Scale analogue that is exactly self-similar.

    A brown dwarf with a typical mass of about 0.02 solar mass would correspond to muon, and a brown dwarf with a mass of about 0.08 solar mass would correspond to a kaon.

    Preliminary empirical results for the peaks in the substellar mass function are consistent with where the DSR peaks should be for the electron, muon and kaon. However, the empirical substellar mass function is still fairly crude and uncertain. Eventually this subject will be a great test of DSR’s ideas and predictions.

  15. Mike W. Herberich

    It is extremely interesting to follow this post, mainly but not only due to Robert O.’s DSR proposal. I wish you guys would go on for ages discussing these paradigms. One possibly subversive (or just outright stupid?) question to you, Robert: do you see any analogy or correspondence between your fractal approach and the Loop-Quantum nodes and edges at approximately Planckh lengths? A second question: have endeavors been undertaken to verify the .145 solar mass "atom" against many known star (systems), near or far? Or is it impossible because we do not know their exact total masses (planets and other dark constituents)?

  16. Bruce

    Camille, don’t want to leave you out. Great article, and I loved the humor of you opening line, “You have to be really dense to prove Einstein right.” Mike, yes this is a most fascinating thread. We would have to live a very long time to “go on for ages discussing these paradigms.” Not impossible! (See John 17:3) Peter, how very flippant of you to suggest that the finding of any “deviations from GR in high-field situations” would imply that “Al was wrong: God is malicious!” Even dear old Albert himself was humble enough to know that GR was just a beginning and that many improvements would be needed. I think that in the end the universe will be found to be no more complicated than it needs to be for it and organisms like us to exist. (See Occam’s Razor.) Robert, thanks for your answers, and I have been delving into your website. You flailed however to address my main question, which is related to Mike H.’s second question, namely: Is there any evidence that single star systems mass function obeys the (n)(0.145 solar mass) rule? You addressed this question for substellar systems but I was really asking about STARS in the sub solar mass realm. If this question is addressed in your literature can you direct us as to its location?

  17. Robert L. Oldershaw

    I do not see any connection to Loop Quantum Gravity models.

    The revised Planck scale proposed by Discrete Scale Relativity, and used to solve the Vacuum Energy Density Crisis and retrodict particle masses at the 99.9% level, is discussed at http://www3.amherst.edu/~rloldershaw in Technical Notes #9. Particle masses are retrodicted in the New Developments section.

    The (n)(0.145 solar mass) stellar mass spectrum is discussed and tested at many places at http://www3.amherst.edu/~rloldershaw and specifically on the page entitled "Stellar Scale Discreteness".

    Seek and ye shall find,
    Rob O

  18. Robert L. Oldershaw

    Someone might wonder whether Discrete Scale Relativity is serious science that can potentially provide a unifying paradigm for physics in the same way that Darwinian Evolution provided a unifying paradigm for biology, or whether DSR is just one more of the 1000s of crackpot theories that seem to pop up like mushrooms from amateur and professional physicist "gardens" in comparable numbers.

    Here is a good way to decide. See the 15 definitive predictions of DSR, including the ones that have already been verified and the ones that are on the verge of vindication.


    Or search on "Predictions of Discrete Scale Relativity"

    Definitive predictions are prior, feasible, quantitative, NON-ADJUSTABLE and unique to the theory being tested.

    Definitive predictions define, test, and identify the best science.

    Best, Rob O

  19. Mike W. Herberich

    Thank you, Robert, for the 2 links. They’d have answered my 2 questions, had I not been to lazy to read up on it there, beforehand. A third question, namely the self-similarity ad infinitum to both sides, up and down, I also found (is that correct?). (By the way, there is a little typo in the text of the Planck section: Greek Alpha is used in the formula for the fine structure constant, but Latin "a" in the text beneath). A fourth (and possibly likewise lazy/ stupid) question is: do alpha and/ or epsilon(-sub zero) NOT have to be scrutinized/ adjusted/ revised within your DSR theory?

  20. Peter WilsonPeter

    Just trying to have fun. Nobody took the bait, so I’ll answer my own question: observed deviations in Mercury’s orbit in the 19th century showed something was missing, initially thought to be an interior planet. "J0348 gives researchers a unique opportunity to test for (such) cracks," in the 21st century. The difference is, Newtonian gravity was already troubled by its infinite speed of gravity, and mathematically variant with respect to moving and accelerating frames of reference. Einstein fixed all three problems. The result is a model that is conceptually coherent, having a finite speed of propagation of the gravitational field, and mathematically invariant with respect to both moving and accelerating frames of reference. The cost being a huge leap in mathematical difficulty. Suppose some "cracks" in the predictions of GR are found. Then what? Physicists already have a problem they cannot solve: combining GR & QM. Deviations from the predictions of GR will only make matters worse. Why do they hope for that? Why are physicists hoping an intractable problem will turn out to be even more trying than it is?

  21. Peter WilsonPeter

    Just trying to have fun. Nobody took the bait, so I’ll answer my own question: observed deviations in Mercury’s orbit in the 19th century showed something was missing, initially thought to be an interior planet. "J0348 gives researchers a unique opportunity to test for (such) cracks," in the 21st century. The difference is, Newtonian gravity was already troubled by its infinite speed of gravity, and mathematically variant with respect to moving and accelerating frames of reference. Einstein fixed all three problems. The result is a model that is conceptually coherent, having a finite speed of propagation of the gravitational field, and mathematically invariant with respect to both moving and accelerating frames of reference. The cost being a huge leap in mathematical difficulty. Suppose some "cracks" in the predictions of GR are found. Then what? Physicists already have a problem they cannot solve: combining GR & QM. Deviations from the predictions of GR will only make matters worse. Why do they hope for that? Why are physicists hoping an intractable problem will turn out to be even more trying than it is?

  22. Robert L. Oldershaw

    Alpha is dimensionless so it is the same on all cosmological Scales.

    All constants scale according to their dimensionality according to Discrete Scale Relativity.

    There is much more on theses issues at the website.

  23. Robert L. Oldershaw

    As I said in an earlier posting, Einstein knew GR would have its limits of applicability.

    The question is how to further generalize the theory so that it is even more comprehensive, includes quantum phenomena, and extends to more (all?) of natural phenomena.

    It is important to see where GR begins to have trouble so that we get hints about how to modify it with new symmetry properties or other extensions.

    Einstein called this "deepening the theory".

    Discrete Scale Relativity is an attempt to do just that.

  24. Mike W. Herberich

    Thanks, Robert. I understand the [alpha] is [less] statement. So, epsilon-zero (and mu-zero, for example) do actually scale, do they? I know, I know, I should read through your entire website: can you suggest an order or starting point to do just that best, please? I noticed not all is downloadable as pdf.

  25. Robert L. Oldershaw

    Epsilon-zero and mu-zero have relatively complicated dimensionality, but when you put it all into M, T and L dimensions and cancel appropriately, then the scale factor = 1, which means the values are the same for different cosmological Scales.

    It is very interesting that several major constants in EM, like c, ep-0 and mu-0 are completely scale invariant.

    But charge and the Coulomb constant (I think I am remembering this correctly) do change with cosmological Scale. Certainly charge does.

    One can skip around the website for a while and get a feel for its scope. Then I would go through Selected Papers 0, 1 and 2 quite slowly and carefully. This is hard work but it pays off by giving the reader a solid foundation.

    Anything that is not in PDF format can be highlighted (selected) and printed out. Sorry but I have not been paid for 35 years and I have to pay someone else out-of-pocket to manage my website. There are many things I would like to do if I won the lottery.

    Best, Rob O

  26. Mike W. Herberich

    Thanks, Robert, for your detailed explanation and advice. Very interesting to hear that epsilon-0 and mu-0 are invariant. That c is invariant I could have sort of anticipated. And, come to think of it, since c is related to the inverse product of both (square root, if I’m not mistaken), I could have guessed they would not scale either. I’ve already skipped about your site a little. I’ll try to do 0, 1 and 2 first, then, as far as I haven’t already. I snooped around yesterday and found hints to many of your publications: anything there that one could sort of start with best, aside from your site? I understand your austerity well (if that is the right word; sorry, I’m not a native English speaker). I just find it clumsy sometimes to read from in front of a screen, especially when it is rather sophisticated or involved or lengthy stuff: I favor bed or the bad tub ;-}. That’s where books and magazine formats still come in very handy! And: I do adore the black board. Very obsolete, I know.

  27. Robert L. Oldershaw

    Another source of relevant paper relating to Discrete Scale Relativity, including more recent ones, can be found at arxiv.org.


    There are about 12 papers there and they can be downloaded for free.

    The one entitled "Discrete Scale Relativity" might be a good one to start with.

    Best, Rob O

  28. Mike W. Herberich

    Does General Relativity also know mass gain depending on velocity, as Special Relativity does (as 1/sqrt(1-v^2/c^2)? If so, that should be pretty considerable here, since, as the article states, these two objects orbit each other at nearly the speed of light! Moreover, chances are, one might "see" masses fluctuating heavily, depending on their altering radial velocities and inclination due to their circular orbits. Also all kinds of weird phenomena should be detectable, due to enormous time and length dilations at these speeds, again, only if that is similar to Special Relativity. — (Thanks for the directions, Robert).

  29. Robert L. Oldershaw

    Hi Mike,

    GR does not contradict SR, but generalizes it to include accelerating reference frames as well as inertial frames.

    It is true that in GR c is no longer an absolute constant, and there are some other new subtleties, but time dilation and mass effects are still applicable.

    See Abraham Pais’ book ‘Subtle is the lord…’ for a readable review of GR and its development.

    I assume the authors of the pulsar-white dwarf research include all relativistic corrections.

  30. Mike W. Herberich

    I, too, do sincerely hope the researchers include these things; in dubio pro reo. Thanks again for the book tip, Robert. The review of Pais’ book sounds like the perfect thing to re-kindle my interest/ endeavors to finally attack the extended vector concept, tensors, which seems to make the discerning pre-requisite from SR to GR. The title, by the way, alludes to the Einstein quote mentioned further above in this blog: "Raffiniert ist der Herrgott, aber boshaft ist er nicht" ("Subtle is the Lord, but malicious He is not", where "subtle" is not the best translation for "raffiniert", in my opinion; "subtle" is too tame or neutral a word). The 9 pages of your latest reference I’ve read and found very understandable (whereas the simple GR formula in the beginning I just had to take for granted, having no clue about its actual derivation). I’m interested in how anti-matter does fit in DSR … and more. I hope to find this in your leads. What was the initial spark for DSR to posit the infinite fractal scheme, up and down?

  31. Robert L. Oldershaw

    This subject is discussed several times at my website.

    Selected Papers #1 and #2 introduce some basic arguments.

    Technical Note #6 on "Nature’s Geometry…" is also relevant.

    Inventing cutoffs for nature’s hierarchy seems to me to be exceedingly anthropocentric (putting us roughly in the middle of a truncated hierarchy. This seems like mediocre natural philosophy ("anti-Copernican").

  32. Mike W. Herberich

    I couldn’t agree with you more on that anthropocentric remark of yours, Robert. Also, your remark about there being nothing like exactitude in nature further above, I thought, was very useful to call out loudly (or write markedly, as it is), for once. Eventually, there is an inherent self-similarity of a different kind here: our limited mind (grown and still growing with and within evolution as an instrument) tries to match all phenomena to an internal representation, or vice versa, if you like. The only defense we have against that eternal, inherent and implicit bias/ limitation is our knowledge that it could actually be so (what a marvelous tool! Greetings from Gödel). Plus, therefore scrutinizing and questioning all results until the majority of people can’t help but agree, over time, … and then some, in theory. In practice it all works different, of course. I just finished "Thinking, Fast and Slow" by Nobel prize winning Daniel Kahnemann, which essentially says something along those lines.

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