Category Archives: black holes

Black Holes, Mercury, and Einstein: The Role of Dimensional Analysis

In last week’s posts we looked at basic astronomy and Einstein’s famous E=mc2 through the lens of the secret weapon of theoretical physicists, “dimensional analysis”, which imposes a simple consistency check on any known or proposed physics equation.  For instance, E=mc2 (with E being some kind of energy, m some kind of mass, and c the cosmic speed limit [also the speed of light]) passes this consistency condition.

But what about E=mc or E=mc4 or E=m2c3 ? These equations are obviously impossible! Energy has dimensions of mass * length2 / time2. If an equation sets energy equal to something, that something has to have the same dimensions as energy. That rules out m2c3, which has dimensions of mass2 * length3 / time3. In fact it rules out anything other than E = # mc2 (where # represents an ordinary number, which is not necessarily 1). All other relations fail to be consistent.

That’s why physicists were thinking about equations like E = # mc2 even before Einstein was born. 

The same kind of reasoning can teach us (as it did Einstein) about his theory of gravity, “general relativity”, and one of its children, black holes.  But again, Einstein’s era wasn’t first to ask the question.   It goes back to the late 18th century. And why not? It’s just a matter of dimensional analysis.

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Coordinate Independence, Kepler, and Planetary Orbits

Could you, merely by changing coordinates, argue that the Sun gravitationally orbits the Earth?  And could Einstein’s theory of gravity, which works equally well in all coordinate systems, allow you to do that?  

Despite some claims to the contrary — that all Copernicus really did was choose better coordinates than the ancient Greek astronomers — the answer is: No Way. 

How badly does the Sun’s path, nearly circular in Earth-centered (geocentric) coordinates, violate the Earth’s version of Kepler’s law?  (Kepler’s third law is the relation T=R3/2 between the period T of a gravitational orbit and the distance R, which is half the long axis of the ellipse that the orbit forms.)   Since the Moon takes about a month to orbit the Earth, and the Sun is about 400 = 202 times further from Earth than the Moon, the period of the Sun would be 4003/2 = 8000 times longer than the Moon’s, i.e. about 600 years, not 1 year. 

But is this statement coordinate-independent? Can it serve to prove, even in Einstein’s theory, that the Earth orbits the Sun and the Sun does not orbit the Earth? Yes, it is, and yes, it does. That’s what I claimed last time, and will argue more carefully today.

Of course the question of “Does X orbit Y?” is already complicated in Newtonian gravity.  There are many situations in which the question could be ambiguous (as when X and Y have almost equal mass), or when they form part of a cluster of large mass made from many objects of small mass (as with stars within a galaxy.)  But this kind of ambiguity is not what’s in question here.  Professor Muller of the University of California Berkeley claimed that what is uncomplicated in Newtonian gravity is ambiguous in Einsteinian gravity.  And we’ll see now that this is false.

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Black Hole Announcement Expected Thursday

In 2019, the first image of the surroundings of a black hole was produced, to great fanfare, by the astronomers at the Event Horizon Telescope (EHT). The black hole in question was the enormous one at the center of the galaxy M87.

The “image” of the surroundings of a black hole in galaxy M87. What does it actually show? It is most likely an image (in radio waves) of an “accretion disk” of material around the black hole, its radio emissions somewhat distorted by the warped geometry around the black hole.

At the time, there was also hope that the EHT would produce an image of the region around the black hole at the center of our own galaxy, the Milky Way. That black hole is thousands of times smaller, but also thousands of times closer, than the one in M87, and so appears about the same size on the sky (just as the Moon and Sun appear the same size, despite the Sun being much further away.)

However, the measurements of the Milky Way’s black hole proved somewhat more challenging, precisely because it is smaller. EHT takes about a day to gather the information needed for an image. M87’s black hole is so large that it takes days and weeks for it to change substantially — even light takes many days to cross from one side of the accretion disk to the other — so EHT’s image is like a short-exposure photo and the image of M87 is relatively clear. But the Milky Way’s galaxy’s black hole can change on the times scale of minutes and hours, so EHT is making a long-exposure image, somewhat like taking a 1-second exposure of a tree on a windy day. Things get blurred out, and it can be difficult to determine the true shape of what was captured in the image.

Apparently, the EHT scientists have now met these challenges, at least in part. We will learn new things about our own galaxy’s black hole on Thursday morning; links to the press conferences are here.

In preparation for Thursday, you might find my non-expert’s guide to a black hole “silhouette” useful. This was written just before the 2019 announcement, when we didn’t yet know what EHT’s first image would show. The title is a double-entendre, because I myself wasn’t entirely expert yet when I wrote it. The vast majority of it, however, is correct, so I still recommend it if you want to be prepared for Thursday’s presentation.

The only thing that’s not correct in the guide (and the offending sections are clearly marked as such) are the statements about the “photon ring”. It took me until my third follow-up post, two months later, to get it straight; that post is accurate, but it is long and very detailed. Most readers probably won’t want to go into that much detail, so what I’ll do here is summarize the correct parts of what I wrote in the weeks following the announcement, repeating a few of the figures that I made at the time, and then tell you about a couple of new things that have been learned since then about M87’s black hole. Hopefully you’ll find this both interesting on its own and useful for Thursday.

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A Ring of Controversy Around a Black Hole Photo

[Note Added: Thanks to some great comments I’ve received, I’m continuing to add clarifying remarks to this post.  You’ll find them in green.]

It’s been a couple of months since the `photo’ (a false-color image created to show the intensity of radio waves, not visible light) of the black hole at the center of the galaxy M87, taken by the Event Horizon Telescope (EHT) collaboration, was made public. Before it was shown, I wrote an introductory post explaining what the ‘photo’ is and isn’t. There I cautioned readers that I thought it might be difficult to interpret the image, and controversies about it might erupt.EHTDiscoveryM87

So far, the claim that the image shows the vicinity of M87’s black hole (which I’ll call `M87bh’ for short) has not been challenged, and I’m not expecting it to be. But what and where exactly is the material that is emitting the radio waves and thus creating the glow in the image? And what exactly determines the size of the dark region at the center of the image? These have been problematic issues from the beginning, but discussion is starting to heat up. And it’s important: it has implications for the measurement of the black hole’s mass (which EHT claims is that of 6.5 billion Suns, with an uncertainty of about 15%), and for any attempt to estimate its rotation rate. Continue reading

The Black Hole `Photo’: Seeing More Clearly


Ok, after yesterday’s post, in which I told you what I still didn’t understand about the Event Horizon Telescope (EHT) black hole image (see also the pre-photo blog post in which I explained pedagogically what the image was likely to show and why), today I can tell you that quite a few of the gaps in my understanding are filling in (thanks mainly to conversations with Harvard postdoc Alex Lupsasca and science journalist Davide Castelvecchi, and to direct answers from professor Heino Falcke, who leads the Event Horizon Telescope Science Council and co-wrote a founding paper in this subject).  And I can give you an update to yesterday’s very tentative figure.

First: a very important point, to which I will return in a future post, is that as I suspected, it’s not at all clear what the EHT image really shows.   More precisely, assuming Einstein’s theory of gravity is correct in this context:

  • The image itself clearly shows a black hole’s quasi-silhouette (called a `shadow’ in expert jargon) and its bright photon-sphere where photons [particles of light — of all electromagnetic waves, including radio waves] can be gathered and focused.
  • However, all the light (including the observed radio waves) coming from the photon-sphere was emitted from material well outside the photon-sphere; and the image itself does not tell you where that material is located.  (To quote Falcke: this is `a blessing and a curse’; insensitivity to the illumination source makes it easy to interpret the black hole’s role in the image but hard to learn much about the material near the black hole.) It’s a bit analogous to seeing a brightly shining metal ball while not being able to see what it’s being lit by… except that the photon-sphere isn’t an object.  It’s just a result of the play of the light [well, radio waves] directed by the bending effects of gravity.  More on that in a future post.
  • When you see a picture of an accretion disk and jets drawn to illustrate where the radio waves may come from, keep in mind that it involves additional assumptions — educated assumptions that combine many other measurements of M87’s black hole with simulations of matter, gravity and magnetic fields interacting near a black hole.  But we should be cautious: perhaps not all the assumptions are right.  The image shows no conflicts with those assumptions, but neither does it confirm them on its own.

Just to indicate the importance of these assumptions, let me highlight a remark made at the press conference that the black hole is rotating quickly, clockwise from our perspective.  But (as the EHT papers state) if one doesn’t make some of the above-mentioned assumptions, one cannot conclude from the image alone that the black hole is actually rotating.  The interplay of these assumptions is something I’m still trying to get straight.

Second, if you buy all the assumptions, then the picture I drew in yesterday’s post is mostly correct except (a) the jets are far too narrow, and shown overly disconnected from the disk, and (b) they are slightly mis-oriented relative to the orientation of the image.  Below is an improved version of this picture, probably still not the final one.  The new features: the jets (now pointing in the right directions relative to the photo) are fatter and not entirely disconnected from the accretion disk.  This is important because the dominant source of illumination of the photon-sphere might come from the region where the disk and jets meet.


Updated version of yesterday’s figure: main changes are the increased width and more accurate orientation of the jets.  Working backwards: the EHT image (lower right) is interpreted, using mainly Einstein’s theory of gravity, as (upper right) a thin photon-sphere of focused light surrounding a dark patch created by the gravity of the black hole, with a little bit of additional illumination from somewhere.  The dark patch is 2.5 – 5 times larger than the event horizon of the black hole, depending on how fast the black hole is rotating; but the image itself does not tell you how the photon-sphere is illuminated or whether the black hole is rotating.  Using further assumptions, based on previous measurements of various types and computer simulations of material, gravity and magnetic fields, a picture of the black hole’s vicinity (upper left) can be inferred by the experts. It consists of a fat but tenuous accretion disk of material, almost face-on, some of which is funneled into jets, one heading almost toward us, the other in the opposite direction.  The material surrounds but is somewhat separated from a rotating black hole’s event horizon.  At this radio frequency, the jets and disk are too dim in radio waves to see in the image; only at (and perhaps close to) the photon-sphere, where some of the radio waves are collected and focused, are they bright enough to be easily discerned by the Event Horizon Telescope.


The Black Hole `Photo’: What Are We Looking At?

The short answer: I’m really not sure yet.  [This post is now largely superseded by the next one, in which some of the questions raised below have now been answered.]  EVEN THAT POST WAS WRONG ABOUT THE PHOTON-SPHERE AND SHADOW.  SEE THIS POST FROM JUNE 2019 FOR SOME ESSENTIAL CORRECTIONS THAT WERE LEFT OUT OF ALL REPORTING ON THIS SUBJECT.

Neither are some of my colleagues who know more about the black hole geometry than I do. And at this point we still haven’t figured out what the Event Horizon Telescope experts do and don’t know about this question… or whether they agree amongst themselves.

[Note added: last week, a number of people pointed me to a very nice video by Veritasium illustrating some of the features of black holes, accretion disks and the warping of their appearance by the gravity of the black hole.  However, Veritasium’s video illustrates a non-rotating black hole with a thin accretion disk that is edge-on from our perspective; and this is definitely NOT what we are seeing!]

As I emphasized in my pre-photo blog post (in which I described carefully what we were likely to be shown, and the subtleties involved), this is not a simple photograph of what’s `actually there.’ We all agree that what we’re looking at is light from some glowing material around the solar-system-sized black hole at the heart of the galaxy M87.  But that light has been wildly bent on its path toward Earth, and so — just like a room seen through an old, warped window, and a dirty one at that — it’s not simple to interpret what we’re actually seeing. Where, exactly, is the material `in truth’, such that its light appears where it does in the image? Interpretation of the image is potentially ambiguous, and certainly not obvious. Continue reading

A Non-Expert’s Guide to a Black Hole’s Silhouette

[Note added April 16: some minor improvements have been made to this article as my understanding has increased, specifically concerning the photon-sphere, which is the main region from which the radio waves are seen in the recently released image. See later blog posts for the image and its interpretation.]

[Note added June 14: significant misconceptions concerning the photon-sphere and shadow, as relevant to the black hole ‘photo’, dominated reporting in April, and I myself was also subject to them.  I have explained the origin of and correction to these misconceptions, which affect the interpretation of the image, in my post “A Ring of Controversy”.]

About fifteen years ago, when I was a professor at the University of Washington, the particle physics theorists and the astronomer theorists occasionally would arrange to have lunch together, to facilitate an informal exchange of information about our adjacent fields. Among the many enjoyable discussions, one I was particularly excited about — as much as an amateur as a professional — was that in which I learned of the plan to make some sort of image of a black hole. I was told that this incredible feat would likely be achieved by 2020. The time, it seems, has arrived.

The goal of this post is to provide readers with what I hope will be a helpful guide through the foggy swamp that is likely to partly obscure this major scientific result. Over the last days I’ve been reading what both scientists and science journalists are writing in advance of the press conference Wednesday morning, and I’m finding many examples of jargon masquerading as English, terms poorly defined, and phrasing that seems likely to mislead. As I’m increasingly concerned that many non-experts will be unable to understand what is presented tomorrow, and what the pictures do and do not mean, I’m using this post to answer a few questions that many readers (and many of these writers) have perhaps not thought to ask. Continue reading