Friday, February 12, 2016

Strong Field Predictions Of General Relativity Confirmed


Black holes and the existence of gravity waves were two of the most notable predictions of the theory of general relativity devised by Albert Einstein almost exactly a century ago (although the implications of that theory took much longer to work out with most of the main conclusions that we have reached so far in place by the 1970s).

Black holes are concentrations of matter that are so strongly bound by gravity that not even light can escape them.* They can range in mass from about 3 times the mass of the Sun to 10,000,000,000 time the mass of the Sun in supermassive black holes at the center of the largest galaxies (in principal, there is no upper limit on the mass of a black hole, but no larger black holes have ever been inferred to exist).**  In Newtonian gravity, photons aren't affected by gravity and even if they were, gravity can never get strong enough to prevent them from escaping a massive object because Newtonian gravity involve linear rather than non-linear field strengths.

Indirect experimental evidence (such as gravitational lensing) has long ago indicated that black holes exist and measured their masses.

In Newtonian gravity, gravity's effects are transmitted instantly at all distances.  In general relativity, gravity's effects are transmitted via gravitational waves in space-time that propagate at the speed of light "c".

What did LIGO See?

The LIGO gravity wave experiment formally announced yesterday that it had detected the merger of two roughly equal mass black holes with a combined mass of 65 times the mass of our Sun about 1.3 billion light years away from Earth that converted roughly 5% of their combined mass into gravity waves (of course, there was immense momentum energy in addition to rest mass present in the binary wave system).  The resulting combined black hole was a Kerr black hole which means that it has angular momentum (a Schwartzchild black hole is a special case of a Kerr black hole with zero angular momentum).

The black holes were each about 100 miles in diameter before merging, and less than two minutes before their merger this binary black hole system was spiraling at almost the speed of light at a distance of about 600 miles (a disk of space about the size of Alaska).

The power of the gravitational waves emitted by the extraordinary event that LIGO observed was greater than the combined power of the light emitted by every star in the universe at that moment.  By comparison, the gravitational waves emitted by the entire solar system have a power of about 200 watts (two ordinary light bulbs). The final ping of gravity waves when the black holes finally merged had a frequency roughly the same as the sound wave of a middle D note on a piano.

For a matter of seconds or minutes after the merger, the black hole would have been a bit "bumpy" by the combined force of gravity would swiftly smooth it out into an equilibrium smoothly curved shape.

The statistical significance of the detection event was 5.1 sigma (i.e. 5.1 standard deviations in excess of the null hypothesis that no gravitational wave event was detected) which rates as a scientific discovery. It is the first direct observation of gravity waves (which had previously been inferred from the behavior of binary star systems observed with telescopes) and the most direct observation to date that has been made of black holes.

Gravity Wave Detectors

The LIGO experiment detects gravity waves by looking at the interference pattern generated by two laser beams traveling about 4 kilometers each and back at right angles to each other at two locations, one in Washington State and the other in Louisiana, which are screened out for all manner of forms of background noise.

The LIGO experiment is sensitive to distortions of space-time on a scale of 1/1000th of the diameter of an atom, something made possible only by the immense precision with which we understand and can measure electromagnetic phenomena using the Standard Model.  What LIGO detected was a distortion in the actual physical distance from the two detectors to the four reference points of about that magnitude in a pattern that identified the strength and direction of the source generating the gravity waves.  The gravity wave event that was detected was not accompanied by a surge in cosmic neutrinos (which are associated with supernovas and star collision/mergers, but not with black hole mergers).

About half a dozen other gravity wave detection experiments are set to come on line over the next few years.  Some are space-based, one more is land based, and one uses continuous observations of pulsars in the Milky Way to great, in effect, a galaxy sized gravity wave telescope.

The experiments are largely complementary to each other rather than being competitors.  Each experiment is sensitive to a different range of gravity wave frequencies, with LIGO measuring only the highest frequency gravity waves.  For example, the LISA gravity wave experiment (in space) would not have been able to detect this event because the gravity wave was too large for its instrumentation which is tuned to less dramatic gravity waves to see.

Scientists had doubted that LIGO would be the first to detect gravity waves because it takes such an extraordinary event for it to receive a signal that it can confirm is a gravity wave with the 5 sigma significance needed to constitute a discovery.  These events were predicted to be rare and LIGO simply got lucky in having such an event occur at the right time.  Lower frequency gravitational waves are suspected to be more frequent because less dramatic events can create them.  But, LIGO has also detected several more potential gravitational wave events during its several year existence, although those detections were less statistically significant.


Twelve papers were generated by LIGO based upon the experiment.  The most notable for my purposes was the one examining the extent to which the observed gravitational waves matched the predictions of General Relativity in strong gravitational fields.

Strong gravitational fields have been the subject of a great deal of speculations about ways that general relativity could be tweaked while still remaining consistent with general relativity, in part, because experimental evidence did not constrain deviations from general relativity very strictly.

A couple of recent papers, one 95 pages long, and one four pages long, have examined how observations form LIGO could test alternatives to General Relativity, which make different predictions about the kinds of strong field gravity waves that would be generated by events like this one.

The ultra-precision LIGO results are consistent with General Relativity up to the limits of its margin of error with no real tension between theory and experiment, and accordingly, greatly constrain the parameter space of alternative theories of gravity that can still be consistent with experimental observations.  For example, these experiments place an experimental bound on how heavy gravitons can be in a "massive graviton" theory.

Similarly, direct experimental observations of gravitational waves, by providing a direct observation of the mechanism by which gravity is transmitted, powerfully disfavors alternative theories of gravity in which gravitational effects are non-local or transmitted instantaneously.  These limits may become even more power when gravity wave detectors capable to seeing the weaker gravity waves generated by events involving stars that allow gravitational wave measurements to be correlated with evidence from telescopes that see photons, cosmic ray detectors and neutrino detectors from the same event.

Understanding strong gravitational fields is relevant to understanding gravitational singularities like the Big Bang, cosmological inflation, black holes, galaxy formation, and the way that galactic clusters work.

It may end up being important to understanding quantum gravity theories which generally predict that many singularities in general relativity (a non-quantum "classical" theory of physics) which means circumstances in which infinities show up as results in equations, actually just produce very large numbers that are not infinite when quantum effects are considered.  Some quantum gravity theories also reproduce general relativity in the classical limit in the medium sized gravitational fields, while deviating from general relativity somewhat in the extreme strong field and extreme weak field limits. So, quantum gravity theories that differ from general relativity in the strong field limit can be constrained.

Extensive measurements of general relativity at work in the strong field limit may also provide insights to quantum gravity researchers who are looking for some additional, experimentally supported axiom to address the problem of the non-renormalizability of naive quantum gravity theories.  For example, if gravity wave observations in the strong field limit become precise enough, the possibility that the gravitational constant G runs or does not run with energy scale in the way that the Standard Model coupling constants do, this could provide an axiom that could be used to formula workable quantum gravity theories.  But, the LIGO observation, while ultra-precise, isn't sufficiently precise to place strong bounds on that possibility.

What it does not tell us.

On the other hand, not all ill understood aspects of gravitational phenomena in which gravity are important can better understood by looking at the strong field of general relativity that govern black holes and the Big Bang.

Phenomena like dark matter and dark energy are relevant only in the context of extremely weak gravitational fields.  An improved understanding of gravitational strong fields only limits resolution of dark matter and dark energy phenomena to the extent that a solution to this weak field issues has a side effect that would have phenomenological effect in the strong field regime as well.

Also, it is important to note that the what LIGO has seen is completely different from the effects of tensor modes of primordial gravitational B waves which the BICEP-2 experiment reported that it had seen signs of in the cosmic background radiation (which later proved to be unsupported by the available data).

Searches like those at BICEP-2 are looking for patterns in the overall distribution of matter and energy in the universe that are associated with particular cosmological inflation scenarios in the early moments after the Big Bang, rather than the gravity wave produced by a single, more recent event in one particular part of the universe that experiments like LIGO and LISA are designed to detect.

Impact Of Future Gravity Wave Observations

Gravity wave telescopes provide a new way to conduct astronomy, to supplement telescopes that look at electromagnetic waves in wavelengths on the infrared side as low as cosmic background radiation and radio waves and on the ultraviolet side to frequencies a bit beyond the blue of visual light. Cosmic ray telescopes and neutrino telescopes detect tiny bits of matter like electrons or neutrinos or individual interstellar gas or dust atoms or molecules that are hurled across the universe at high speeds from distant stars  (the term "cosmic rays" is misnomer since cosmic rays generally don't involve mere photons).

Over the next few decades, as more events are observed at a wider range of frequencies as the new gravitational wave detection experiments come on line, these constraints on the strong field behavior of Nature relative to General Relativity will become much more tight.

Footnotes Regarding Black Holes

* It is not uncommon to say that black holes are the most dense objects in the universe, and that this is why light cannot escape them.  Density means matter divided by volume.  And, for the most conventional definition of the volume of a black hole, i.e. the volume within its "event horizon" which which light cannot escape, this is not true except for the smallest of black holes. All, but the smallest of black holes are not the most dense objects in the universe, and necessarily, the reason that light cannot escape a black hole is not that it is the most dense object in the universe.

For example, photons routinely escape from neutron stars and from atomic nuclei which are more dense than all but the smallest of black holes.  Yet, we routinely directly observe the light from neutron stars with telescopes, and the photons emitted from atomic nuclei are what keep the electrons that are moving in a cloud around those atomic nuclei from flying away.

Neutron stars, which have a mass just under the threshold for them to gravitationally collapse into a black hole can have a mass of about 3 times the Sun packed into a density roughly the same as an atomic nucleus before they collapse to form black holes.  The most dense objects in the universe are black holes just over this threshold.

But, the volume of a black hole, as measured by its event horizon, grows more rapidly than its mass, due to the non-linear nature of gravity in general relativity.  As a result, black holes that are significantly heavier than the neutron star-black hole threshold, such as the roughly 30 times the Sun mass black holes seen by LIGO are significantly less dense in mass per event horizon contained volume than neutron stars or atomic nuclei.  The density of the supermassive black holes at the center of galaxies like the Milky Way and its satellite galaxies, measured in mass per event horizon contained volume, is on the order of the density of liquid water or ordinary Earth rocks.

The internal mass distribution of matter within a black hole is unknown and may be unknowable.  In general relativity, all of the observable properties of a Kerr black hole in equilibrium, such as the one created upon the merger that LIGO observed a few minutes to a few years or so after the merger, can be determined from its mass and its angular momentum.  (The fact that this is possible is a problem for quantum gravity theories for which the law that information cannot be created or destroyed is an axiom that requires considerable theoretical attention.)

The observational reality that there is a well known maximum density of matter approximately equal to the density of an atomic nucleus, neutron star or small stellar mass black hole is generally considered to be a mere empirical fact that emerges from other physical laws.  But, one can imagine a Copernican revolution arising from a theory in which a maximum density of mass-energy per volume (appropriately defined) is a law of nature.  The black hole-neutron star transition point also provides a physical calibration point which is ultimately a function of an equilibrium between a function of the gravitational constant G and a function of the strong force coupling constant of the Standard Model.

** It is theoretically possible for a black hole of less than 3 solar masses to exist, either because it is created by means other than being created exclusively from self-generated gravitational collapse, or because it was once larger and evaporated via Hawking radiation (because actually, what escapes from black holes is not nothing, but merely almost nothing with a little bit of Hawking radiation escaping).  Generally speaking, cosmic background radiation adds more mass to a stellar or larger black hole than Hawking radiation takes away.  But, in principal, at some point in time when this wasn't the case, a stellar black hole could evaporate to less than 3 solar masses while retaining its black hole status.

In real life, no one has ever observed a black hole of this kind which would be called a "primordial black hole" and most primordial black holes created around the time of the Big Bang probably would have evaporated via Hawking radiation by now, but primordial black holes of 10^14 kg or more would not have evaporated and primordial black holds of 10^23 kg or less can't be excluded by gravitational lensing observations.

Thus, primordial black holes, if they did exist, would have masses comparable to asteroids and have been proposed as dark matter candidates (although few dark matter theorists view them as a very serious dark matter candidate for a variety of reasons).

Primordial black holes would have a radius of 145 femto-meters (the size of several tightly packed uranium atoms sitting side by side) to 0.145 millimeters (the thickness of a strand or hair or one coat of paint).


Ryan said...

This ~62 solar mass black hole would be the largest stellar mass black hole observed by a factor of 4 or so would it not? LIGO may have been lucky, but how lucky could it possibly have been? Does this merger happening at all tell us something new about the formation if intermediate mass black holes?

You mentioned the effects of different modifications in very large acceleration cases (ie black holes) and very low acceleration cases (ie galaxies). I'd just like to mention that the M-sigma relationship implies to me at least that the two are linked, and that a complete understanding of gravity and/or dark matter will likely solve both.

Nirjhar007 said...

Great to see you back Andrew, how are things?.
Indeed a great discovery, this perhaps will help to achieve more significant findings. also nice to see India's part in the quest.

andrew said...

@Ryan. Yes. The largest observed stellar mass black hole was previously about 15 stellar masses and the smallest definitively observed supermassive black hole is about 10^5 stellar masses. So, both of the black holes in the binary system were larger than the largest previously observed black hole by roughly a factor of two and the combined final black hole larger than any stellar black hole previously observed by a factor of four.

There have been a number of suspected intermediate sized black holes, but none has been definitively observed, although it is widely assumed that mergers of black holes play an important role in the formation of supermassive black holes. At 62 stellar masses it is arguably an intermediate mass black hole already, there are not real definitive standards by which to draw lines, except that arguably the definition of "stellar black hole" ought to be limited to black holes formed directly from the collapse of a star without mergers with other black holes, in which case this would be an intermediate black hole rather than a stellar black hole, by definition.

The M-sigma relationship is an important and under-explained phenomena but my guess is that it largely flows from an understanding of weak fields (and perhaps from the likely reality that black holes are generally Kerr black holes with angular momentum rather than Schwartzchild black holes that do not rotate) rather than depending much upon the details of the merger of black holes in the strong field limit.

@Nirjhar007, things are O.K., taking it slow.

AFAIK, India's space program is currently focused on solar system physics like sending a probe to Mars, which is an entirely worthwhile thing to do, but if India really wants to make a big impact on the quest to understand fundamental physics, an investment in space based astronomy observation apparatus (in the days of gravitational, cosmic ray and neutrino observatories, you can no longer call them telescopes), would be their best best.

To give one simple example, sending two Hubble-like space telescopes to opposite ends of the solar system (which wouldn't be all that expensive now that that the technology is so well proven) would dramatically improve our ability to do parallax measurements of stellar distances (because it would extend the base of the triangle from ca. 16,000 miles to ca. 200 AU, that could in turn be used to calibrate all other telescope based measurements improving their precision by two or three orders of magnitude.

andrew said...

The Fermi gamma ray monitor saw a burst of gamma rays 0.4 seconds after the gravitational wave was observed. The odds of this being a false positive are 0.2%.

Ryan said...

@Andrew - the models I've seen for SMBH formation (and I admit I haven't kept up to date on this) produce large numbers of "orphan" IMBHs out there, which have been conspicuously missing. Until now at least.

Actually, do you know any decent papers on SMBH formation under MOND / modified gravity to check out? It strikes me that the papers I read generally assumed the presence of a dark matter halo.

Maju said...

Why would the volume of a black hole be defined by the event horizon? Shouldn't it be defined by the singularity instead, whose volume is infinitesimal? The event horizon is an effect of the black hole, not the black hole itself!

andrew said...

@Ryan. I can't recall seeing any such papers recently.

@Maju. Because the singularity extends all of the way up to the event horizon. Within the event horizon we really have no theory to guide us regarding how matter is internally distributed although it is assumed to be symmetrical.

Maju said...

I'm familiar with the notion that a singularity should be a 1D point in a non-rotating black hole and a 2D ring in a rotating one, which are the actually documented ones. But maybe that's only a particular theory. In any case I have never read or watched before anyone who claims that the singularity and event horizon are or can even be the same, on the opposite: the event horizon is just the place of no return for anything.

Talking of "matter" inside a black hole, at least at singularity level, sounds extremely odd for me, as the dimensional reality of a singularity is not enough for even the smallest particle to exist anymore (all them have non-zero size and exist in an Einstenian 3+i dimensional reality, which does not exist anymore in the black hole (singularity)).

BTW, I was just thinking (one thing brings to the other) that gravitons do not seem to behave like photons (not affected by the curvature of space-time, else black holes would be impossible: self-denying, as they would not allow their own emitted gravitons to escape), so maybe they cannot exist at all, else they'd be affected by the curvature of space-time just like the other massless particles. Or am I missing something re. the hypothetical gravity particle?

Ryan said...

@Maju - It may be that a more complete understanding of gravity will demonstrate that the singularities do not exist at all.

Maju said...

Well, Einstein has been proven right once and again: he's probably right in that too, even if he disliked the idea himself. In fact he disliked black holes and hoped that Nature, somehow, would not allow for them, but we now know better: black holes do exist, we orbit one, and, if they do exist, they should behave as the theory that correctly predicted them to begin with and be singularities.

Basically I'm discounting gravitons right now: they seem to be totally wrong. And therefore I'm wondering if, somehow, QM can be explained in relativistic terms, rather than the opposite.

Ryan said...

" black holes do exist, we orbit one, and, if they do exist, they should behave as the theory that correctly predicted them to begin with and be singularities. "

Why? Our direct observations of black holes are pretty much non-existent.

Maju said...

So what is Sagittarius A*? There's a black hole there: we see that we don't see a compact massive object around which stars orbit, that's a black hole! If I could insert an image here I'd insert this one or its equivalent animation (see: here). Even Hawking paid his bet against the existence of black holes after this discoverym which is already more than a decade old.

Oh, OK, you're trying to trick me with the word "direct". Well, not a single subatomic particle has been "directly" observed either. So good for QM if we want to go nit-picky. "Direct" observation requires of the "direct" use of some of our five senses, usually sight, so that's a no-no. There's a point where you have to go "indirect" and begin inferring. Meh, Newtonian-minded-people!

Ryan said...

Maju - What I'm getting at is we know very little about the nature of black holes.

Maju said...

We know very little about the very nature of the universe, matter included. Most people, scientists even, take matter and energy, space and time for granted. But modern science has shown that they are all but that simple. I'm nowadays personally very tempted to think that matter (incl. massless "particles" like the photon) is little more than warping of space-time but I can't find a known theory that holds this idea: all theories I know of (incl. string theories) try to integrate Relativity into QM and my suspicion is that it is the wrong approach, that maybe trying to integrate QM into Relativity, by means of deconstructing its "belief in particles", in "matter", holds more promise. But it's just a hunch I have.

andrew said...

More analysis regarding why LIGO is unlikely to say much about quantum gravity from Sabine.