Black hole questions

 Who knew that, a dozen years after I wrote something trying to explain a bit about black holes, people would still be reading it?  I get questions from time to time from readers, and I’m happy to try to answer them.  As long as I’m writing answers anyway, I’ll go ahead and post them here in case anyone else is interested.

This batch is from a high school student named Brandon Thrush.

 1. I have a good idea of what the event horizon is, but I do not know what you mean when you say that it is actually moving outward at the speed of light; does this mean that the whole entire black hole is moving at the
speed of light?

This is a very subtle and potentially confusing idea.

Suppose that you dropped a flashlight into the black hole, and at the exact moment it crossed the horizon, it emitted a photon (that is, a little burst of light) in a direction straight out, away from the black hole.  That photon would be stuck on the horizon, never falling into the black hole but never getting further away either.  Now, one of the main ideas of relativity is that light always travels at the same speed (the speed of light, naturally!) no matter how it’s measured or by whom.  So that photon is, by definition, traveling at the speed of light, and yet
it’s staying right on the horizon.  The logical conclusion is that the horizon is moving at the speed of light.

You might say that this is just a silly word game: Why do I say the horizon is moving outwards, rather than saying that the photon is sitting still?  The answer is just that the idea that the speed of light is always
the same (which means that photons never sit still) is so powerful and useful that physicists hate to give it up.  We’d rather say that the horizon is moving at the speed of light — even though it never gets anywhere!  — than give up on that idea.

At this point, it’s customary to mention the quote from Lewis Carroll’s Through the Looking Glass, in which the Red Queen says something like “Here it takes all the running you can do just to stay in the same place.
If you want to get anywhere, you’ll have to go a great deal faster than that!”

2. When you give examples of two black holes, one smaller than the other, you say that in the smaller black hole you would be torn apart before you even reach the horizon, but in the larger one, you would not be torn apart until after you reach the horizon.  How can this be?

The reason is that the thing that tears you up is the “tidal force,” which has to do with the difference in the strength of the gravitational pull between one end of you and the other end.  If every atom in your body is
being pulled on (and hence accelerated) by gravity in the same way, you won’t feel any ill effects, but if one part of you is being pulled more strongly than the other, you will.  For a large black hole, the scale of everything is so big that there’s no real difference between the pull on your head and the pull on your feet: both are huge, but they’re essentially the same.  For a smaller black hole, each of those pulls is smaller, but they’re different, and that’s what matters.

3. When a black hole is formed, it is because of a dying star, but does the star suddenly collapse under its own gravitational force and what is left is its gravitational force field, called the black hole, or does the star gradually collapse into its own force field?

I think I like the first way of saying it better. Certainly “suddenly” is better than “gradually”: although the leadup to the final collapse is gradual, once the final collapse gets started, it’s very quick.

There’s another obligatory literary reference here, by the way: “Gradually and then suddenly” is the way Hemingway describes going bankrupt in The Sun Also Rises.
The big idea is that, before it collapses, a star exists in an equilibrium, in which the pressure caused by the star’s particles (nuclei and electrons) balances the pull of gravity.  When a black hole forms, the reason is that that balance couldn’t be sustained, and gravity won.  The particles get pulled in closer and closer to the center.  After that process is complete, all that an outside observer can detect is the gravitational field (which we often prefer to call the “curvature of spacetime.”)

4. When the star is collapsing into the center, what happens to the particles while reaching the center?  What is their fate?

Once they get very near the center, we have to admit that we just don’t know.  Everything we say about what happens to particles inside the horizon of a black hole is based on theory, not observation, since we never see the interior.  But at first (that is, immediately after crossing the horizon) we can have pretty high confidence in our descriptions of the process: the physical conditions at first are very similar to situations we see in other places, so we think we understand them.  But near the center, the densities and temperatures get very high, eventually passing out of the range where we think we understand the physics.

So here’s what we can say: during the collapse, the particles that are falling in towards the center get compressed to higher and higher densities and higher and higher temperatures until, at some point, …. we don’t really know.

5. When a large black hole, such as a stellar-mass black hole, constantly grows, does the gravitational field extend farther and farther?  If so, would not the black hole eventually consume everything in the universe?

The first rule to remember is that a black hole of a certain mass has just the same gravitational pull as any other object of that mass.  So, for instance, a black hole the mass of the Sun attracts outside objects just as much as the Sun does, and no more.

Now, it’s true that as a black hole sucks in more stuff, its mass grows, and so does its gravitational pull.  But after the black hole has gotten all of the stuff near to it, it stops adding new matter at any significant rate, and so it stays pretty much the same after that.

In principle, every black hole in the universe is slowly adding more mass and hence pulling more strongly, but it’s important to emphasize the word “slowly.”  A typical black hole, after it’s had some time to clean out its immediate surroundings, grows at such a slow rate that even over the lifetime of the Universe we wouldn’t expect its mass to grow very much.

6. You refer to a large black hole as a “stellar-mass” black hole, but what are the different names given to the different sizes of black holes?  What are they from the smallest to the largest?

I have to admit that I’m not up-to-date on the subject of classification of black holes.  The last time I paid much attention to the subject, two main categories of black holes were thought to exist:

  1. Black holes that formed from the collapse of stars.  These typically have masses of about 10 times the mass of the Sun (plus or minus quite a bit).
  2. Black holes at the centers of galaxies.  A typical mass for these is  a million times the mass of the Sun.  The conventional wisdom seems to be that most large galaxies have one of these, and that they formed along with the galaxy itself.

When I talk about stellar-mass black holes, I mean the first category.  The other kind are most often called supermassive black holes.

It’s perfectly possible for black holes to exist with other masses. People have talked seriously about the possibility of microscopic black holes, for instance. But the black hole candidates that people have found in the
sky mostly fall into those two categories.  (I think that some black hole candidates have been found with masses in between the two categories — say around a thousand times the mass of the Sun — but I don’t know much
about that.)

Nate Silver on “climategate”

One more thing on this whole business of the “trick” perpetrated in a graph in a climate-change paper.  Nate Silver says this:

Actually, what you have is a scientist, Dr. Jones, talking candidly about sexing up a graph to make his conclusions more persuasive. This is not a good thing thing to do — I’d go so far as to call it unethical — and Jones deserves some of the loss of face that he will suffer. Unfortunately, this is the sort of thing that happens all the time in both academia and the private sector — have you ever looked at the graphs in the annual report of a company which had a bad year? And it seems to happen all too often on both sides of the global warming debate (I’d include some of the graphics from An Inconvenient Truth in this category, FWIW.)

But let’s be clear: Jones is talking to his colleagues about making a prettier picture out of his data, and not about manipulating the data itself. Again, I’m not trying to excuse what he did — we make a lot of charts here and 538 and make every effort to ensure that they fairly and accurately reflect the underlying data (in addition to being aesthetically appealing.) I wish everybody would abide by that standard.

Silver’s clearly a really smart guy and knows a lot about how to handle data, but boy is this wrong. A graph in a scientific paper, or for that matter a blog post, is a part of an overall argument and is designed to convey certain information and not other information.  The person who makes such a graph has to make choices about what to include and what not to include, and those choices necessarily involve consideration of how the graph fits into the larger argument.

Silver seems to imagine that a graph is an objective representation of The Way Things Are, but it just isn’t.  I’m not saying merely that this notion of objectivity is an ideal that can never be fully achieved: I don’t even think it’s meaningful as an ideal to strive for.  Any graph you make will be selective.  Deal with it.

Of course, I’m not saying that anything goes: you can’t fake your data, and you can’t be deliberately deceptive.  But as far as I can tell, there’s precisely no evidence that Jones did anything like that.  In his use of words like “sexing up” and “unethical,” Silver is making a serious accusation without supplying evidence.  He should know better.

Another great accomplishment by a Berkeley grad student.

I know it’s just about Thanksgiving, but check out the runner-up in Wired’s contest for best Halloween costume:


She’s the cosmic microwave background radiation! Her name is Jessica Kirpatrick, and she’s a graduate student at U.C. Berkeley, working with my old friend and former housemate David Schlegel.

One or two Halloweens from now, this costume will be out of date: there should be a much better CMB map.

Thanks to Ken Ganga for passing this along.


Apparently that’s what some people are calling the revelations found in a bunch of emails by climate scientists that were hacked into and made public by climate change deniers.  Stephen “Freakonomics” Dubner gets the vapors, talking about how this exposes the “very ugly side” of climate science.  For a less heated discussion, check out Andrew Revkin’s summary of the controversy, and for the mainstream climate science point of view, go to RealClimate.

I know nothing at all about climate science (although I share 1/2 of my genes with someone who does), so I won’t say anything about the scientific merits of the issues.  But I have been a scientist for quite a while, so naturally I’ve spent a lot of time talking to and emailing other scientists.  As far as I can tell, what’s in this trove of emails is exactly what you’d expect to find if you listened in on the private conversations of a bunch of scientists discussing any remotely controversial subject.  Personally, I rarely call people who disagree with me “idiots,” for instance, but I’ve certainly heard that, and a lot worse, from colleagues.  If this is as “ugly” as it gets, things are just fine.

One supposed smoking gun in the emails is the scientist Phil Jones’s statement  that he used a “trick” in a graph to “hide the decline” in temperature in a time series.  From Revkin’s article,

Dr. Mann, a professor at Pennsylvania State University, confirmed in an interview that the e-mail message was real. He said the choice of words by his colleague was poor but noted that scientists often used the word "trick" to refer to a good way to solve a problem, "and not something secret."

That’s exactly true. In my experience,  scientists use “trick” very often to mean simply “good idea,” not anything underhanded. If you’re going to worry about anything in that quote, it should be the bit about “hiding”:  science isn’t supposed to be about hiding things, right?  So let’s look at that.  Here’s the full quote from the email (via RealClimate):

 I've just completed Mike's Nature trick of adding in the real temps to each series for the last 20 years (ie from 1981 onwards) and from 1961 for Keith's to hide the decline.

In other words, the “trick” in question consisted of plotting the supposedly problematic data in plain sight, while comparing it with another data set.  No actual hiding was done — in fact, apparently the paper explicitly displays the supposedly “hidden”material. I don’t know which of his own papers Jones is referring to, but the original source of the “trick” is Figure 5b in this Nature paper, in which the supposedly “hidden” data are right there in view.

So here’s what Jones is guilty of: behaving in a completely scientifically appropriate manner, and then describing that he did somewhat inaccurately in a private email exchange later.

Let me repeat that I’m not qualified to make judgments on the science: this just isn’t my field.  But here’s what I can say.  Some climate change deniers claim essentially that the mainstream community is engaged in a massive conspiracy to suppress the truth.  If they were right, this trove of hacked emails would prove it.  But from everything I’ve seen, what’s contained in them is pretty much exactly what you’d expect under the opposite hypothesis — that the climate science community is behaving like a normal, healthy scientific community.  Rather than bolstering the conspiracy theorists’ claims, the new data provides strong evidence falsifying them.

Carbon offsets and personal virtuousness

Here’s the opening of an article in the New York Times:

In 2002 Responsible Travel became one of the first travel companies to offer customers the option of buying so-called carbon offsets to counter the planet-warming emissions generated by their airline flights.

But last month Responsible Travel canceled the program, saying that while it might help travelers feel virtuous, it was not helping to reduce global emissions. In fact, company officials said, it might even encourage some people to travel or consume more.

A bit later, we find

For Mr. Francis of Responsible Travel, the final straw came when he noticed that carbon offsets were being offered by private jet companies and helicopter tour operators, which generate very high emissions per passenger. "The message was, €˜Don't worry, you can offset the emissions,' " he said. "But you don't really need to see Sydney from the air, do you? And you can travel in a commercial airliner."

Skepticism about carbon offsets is certainly warranted, mostly because it’s hard to verify whether the emission reduction being paid for is actually occurring.  But that’s not the objection being raised here: what the above seems to be saying is that regardless of whether the offsets work, they’re bad if they don’t cause people to fly less.  That’s nonsense.  If buying the offsets really does offset the carbon emission of flying, then it’s OK (from a carbon emission point of view) to buy the offsets and fly. In fact, not flying would then be no more “virtuous” than flying.

Let me be 100% clear about one thing: the “If” in that last paragraph is a big “If.”  It’s quite possible that offsets don’t work, in which case people shouldn’t use them.   In fact, that possibility seems quite likely to me.

What I’m objecting to (again) is the very common notion that even if things like offsets do work there’s something morally unsavory about them.  In fact, people quite often make the comparison with virtue and sin explicit, derisively referring to things like carbon offsets as “buying indulgences.”  Personally, I think that this attitude is unhelpful. When it comes to figuring out what to do about carbon emissions and climate change, all that matters is what works; there is no separate notion of “virtue” to be considered.

To be fair, the rest of the article does raise the real issues, suggesting doubt that the offsets currently on offer really do sufficiently reduce carbon emissions by the claimed amount, and claiming that ones that did do so would be priced much higher than those on offer.  I just wish we could have this discussion without mixing it all up with ill-considered moralizing.  For one thing, figuring out what works is a hard enough problem without that distraction.  For another thing, you may have noticed that people really don’t like being lectured to about their morals.  Casting the debate in simplistic moralizing terms is not likely to be politically effective, it seems to me.

The zeal of the convert

My brother Andy pointed me to this climate science blog.  I don’t know much about climate science, but I do know about probability and data modeling, and I like the way this guy writes about them.  For instance, he has a really nice piece illustrating how you can model the climate at a variety of levels of complexity from very simple up to  massively complex simulations.  The point of this post is to debunk the notion, which seems to be widespread, that the only reason scientists believe in climate change is because of complicated black-box simulation codes.  He illustrates how  you can see the big picture very easily from much simpler models.

His most recent post is about his born-again Bayesianism.   It’s generally very sensible and worth reading, although I want to point out one important distinction that I think he blurs a bit.  The word Bayesian can describe two different (but overlapping) kinds of people:it can refer to

  1. People who use a specific set of statistical techniques, or
  2. People who have a certain philosophical stance about the meaning of probability.

Personally, I think that you absolutely have to be a Bayesian in the second sense of the term: the frequentist notion of probability strikes me as utterly incoherent.  But I think you should be completely agnostic as far as the first point is concerned.  Bayesian and frequentist statistical techniques are just tools.  They’re both perfectly sensible, and you should use whichever tool is more convenient for the problem you’re trying to solve at the moment.

I think that some people think that being a Bayesian in sense 2 means that you have to be a strict Bayesian in sense 1 — that is, that you can never calculate a confidence interval again.  Fortunately, it just isn’t so. For instance, I cowrote a paper quite a while ago in which we analyzed the same data set from both Bayesian and frequentist points of view to illustrate the relation between the two.

What Arnold Schwarzenegger and the microwave background have in common

Governor Schwarzenegger sent a letter to the California assembly along with his veto of a recent bill.  The first letters of each line of the message spell out a certain vulgar phrase.  The Governor’s office says it’s a coincidence, but apparently lots of people don’t believe them.

This has a lot in common with the subject of a colloquium I gave here at the Université Paris last week.  (If you really want to, you can see the slides for this talk.)  My talk was about several unexpected patterns that have been observed in maps of the microwave background: there are a number of things that should, according to the standard theory, be random but that look non-random.  There’s a lot of controversy over whether these patterns are significant.  The problem is that after you’ve noticed a pattern, it’s very hard to quantify just how unlikely that pattern is, and hence whether it demands an explanation.

Human beings are really good at pattern-finding.  Maybe what we’re seeing is a chance fluctuation, and we’re just fooling ourselves into thinking it’s a pattern with an underlying cause.

The probability of this particular phrase being spelled out in this particular way in Schwarzenegger’s letter are something like one in a trillion.  But if you want to decide whether you think an explanation is required (i.e., that someone did it on purpose), that one-in-a-trillion number isn’t the right one to use: you should  try to figure the probability of something like this happening, rather than the probability of this particular thing happening.

Suppose that you read in the paper that Mary Jones won the lottery.  You’re not likely to be astonished by that fact, even though the probability of this particular person winning the lottery is very small. The reason is simple: the probability of someone winning the lottery is quite large.

So in the cases of both the microwave background and the vulgar acrostic, we should ask how unlikely is it that some similarly unusual pattern would show up.  The problem is that it’s very hard to phrase that question precisely enough that it has a meaningful answer.

So what should we do?  In Schwarzenegger’s case, we should get whatever juvenile amusement we can out of the situation, then decide that it just doesn’t matter and move on.  In the case of the microwave background, things are a bit different: if these patterns are real, then they may be telling us something scientifically very important.  So we should try to figure out new data sets that will shed light on the question.  Unfortunately, that’s hard to do.