Since the upcoming book is basically done, it’s time for me to launch the next phase of the project — the supplementary material, which will be placed here, on this website.
Any science book has to leave out many details of the subjects it covers, and omit many important topics. While my book has endnotes that help flesh out the main text, I know that some readers will want even more information. That’s what I’ll be building here over the coming months. I’ll continue to develop this material even after the book is published, as additional readers explore it. For a time, then, this will be a living, growing extension to the written text.
As I create this supplementary material, I’ll first post it on this blog, looking for your feedback in terms of its clarity and accuracy, and hoping to get a sense from you as to whether there are other questions that I ought to address. Let’s try this out today with a first example; I look forward to your comments.
In Chapter 2 of the book, I have written
Over two thousand years ago, Greek thinkers became experts in geometry and found clever tricks for estimating the Earth’s shape and size.
This sentence then refers to an endnote, in which I state
The shadow that the Earth casts on the Moon during a lunar eclipse is always disk-shaped, no matter the time of day, which can be true only for a spherical planet. Earth’s size is revealed by comparing the lengths of shadows of two identical objects, separated by a known north-south distance, measured at noon on the same day.*
Obviously this is very terse, and I’m sure some readers will want an explanation of the endnote. Here’s the explanation that I’ll post on this website:
Once we clear away the hype (see the previous posts 1, 2, 3, 4), and realize that no one is doing anything as potentially dangerous as making real wormholes (ones you could actually fall into) in a lab, or studying how to send dogs across the galaxy, we are left with a question. Why bother to do wormhole research at all?
The answer is that it has nothing to do with actually making wormholes… at least, not in the sense of science fiction portals that you and I could use to travel from here to some faraway place across the universe. It has to do with potentially gaining new insight into the quantum physics of gravity, space and time.
How Do We Study Black Holes, and Why?
Why do scientists do research on black holes? There are at least two very different reasons.
Large black holes can be observed in nature. These black holes, which astronomers and gravitational wave experimenters study, are well-described by non-quantum physics — “classical” physics, where the future is (in principle) truly predictable from the past.
Small black holes are a window into quantum gravity — the unknown quantum physics of spacetime, where space itself is governed by the uncertainty principle, meaning that the very shape of spacetime can’t be precisely specified. This is relevant for black holes far too small for us to discover using astronomy, yet far too difficult for us to produce experimentally. They are important because they pose conceptual problems and puzzles for quantum gravity. Theoretical physicists think about black holes, and study their math, in hopes of uncovering quantum gravity’s secrets.
To gain more insight into their workings, scientists also simulate black holes on computers, and study analogues to black holes in laboratories.
Why Wormholes?
In contrast to black holes, there may be no wormholes worthy of the name anywhere in our universe. Though recent research clearly shows that there’s no principle that forbids wormholes from existing, it also shows it’s unlikely that large wormholes can be produced or can endure in our universe. While black holes are a generic outcome of the collapse of a huge star, wormholes are relatively delicate, and difficult to create and maintain.
But wormholes may be even more interesting than black holes for the problems of quantum gravity. This was only appreciated, slowly at first, over the past 10 years.
It’s hard to define the quantum state of a black hole. [In quantum physics, objects don’t just have locations and motions; roughly speaking, they have “states”, in which they have a combination of many locations and motions all at once.] The basic obstacle is entropy, a measure of missing information. The air in your room has entropy, because although you may know its temperature and pressure, you do not know where every atom of air is; that’s missing information. It turns out that a black hole has entropy too, which means that our usual description of a black hole is intrinsically missing some crucial information. That prevents us from knowing precisely what its state is.
But surprisingly, in some circumstances the quantum state of a wormhole can be sharply defined — in which case its entropy is zero. (Such a wormhole is not missing any information. But if you take either half of this wormhole and ignore the other half, you find a black hole. That black hole has entropy precisely because you’re ignoring all the information included in the other half of the wormhole!) To obtain and understand such a wormhole involves giving it two apparently different but actually interchangeable descriptions, one in terms of space-time and gravity, where the wormhole’s geometric shape is clear, and one in terms of what one might call a gravity-independent auxiliary quantum system, in which its quantum state is precisely defined.
The Power of Duality: A Rosetta Stone for Quantum Gravity
One physical object, two quantum descriptions — one with gravity, one without; the first with more space dimensions than the latter. It’s like being able to read the same text in two completely different languages. It’s an example of what physicists often call “a duality.” (I’ve gone into more detail about this in recent posts here and here.)
This is the message of what goes by the mantra of “ER=EPR”, referring to two famous and apparently unrelated papers from 1935 by Einstein and Rosen, with the second having Podolsky as a co-author. ER=EPR asserts that two apparently different things,
a tangible bridge across curved, extra-dimensional space between two regions, and
a less tangible bridge, established with quantum entanglement between objects in the same two regions, without any use of gravity,
are literally the same thing.
An conceptual illustration of the proposal that two perfectly entangled quantum systems (EPR) are equivalent to a wormhole connecting the locations of those systems (ER), and represent two languages for describing exactly the same thing. The wormhole is empty; the slabs shown merely indicate how distances are shrinking as one proceeds to the wormhole’s midpoint. Not shown is that the wormhole changes shape over time; for the situation in this picture, this wormhole is “non-traversable”, because there’s insufficient time to cross from one side of the bridge to the other before it shrinks down to nothing.
Discovering that spacetime is related to quantum entanglement, and that ER and EPR involve the same issues, is somewhat like discovering that two poorly understood and partially readable texts in completely different languages are actually two translations of exactly the same document. It’s a Rosetta stone. Parts of the document can easily be read in one language, other parts in the second language; and putting them together, we find we can read more and more.
Similarly, the math of a wormhole (ER) looks completely different from the math of two quantum-entangled non-gravitational systems (EPR). But in particular cases, Juan Maldacena and Lenny Susskind argued, they are two languages describing the same object. We can combine these two partial views of this single object to learn more and more about it.
Moreover, because we’re using math, not text, we can go a step further. Even in regimes where we cannot “read the document” in either language, we can use computers to explore. Scientists can try to simulate the math of the entangled auxiliary quantum systems on a computer, ideally a quantum computer so that it keeps track of all quantum effects, to learn more about the wormhole’s behavior in regimes where we have no idea how it works — in regions where the quantum uncertainty principle affects space and time.
Even more remarkable would be to actually make — not merely simulate — this entangled pair of auxiliary quantum systems. Then we would be closer to making a wormhole, with laws of nature different from ours and with its own gravity, that connects on to our world. But that’s a long ways off, and not the story for the present.
From ER=EPR to Traversable Wormholes
A further breakthrough, beyond the original ER=EPR idea, came with the work of Gao, Jafferis and Wall (see also here and here) in which it was demonstrated for the first time that “traversable wormholes” — ones that can truly serve as bridges across which objects can be transported — do make physical sense. Astonishingly, they are related by duality to an important and exciting research area in quantum information, called “quantum teleportation.” That’s the process by which, using two entangled quantum systems, quantum information can be brought to one of the systems, destroyed in that system, and recreated in that second system some distance away. Again, don’t expect anyone to be teleporting your dog, but simple information and ultra-microscopic objects might be transportable.
Be warned though; the teleportation only works if additional non-quantum information is traded between the two systems. In the wormhole language, that means you can only get through the wormhole if information is also passed outside the wormhole from the departure region to the arrival region. This makes it impossible to go someplace that you haven’t already been sending messages to, and to use any such wormhole as a shortcut — i.e., to get to your destination faster than could a near-light-speed spacecraft traveling outside the wormhole. Not only do portals to ultra-distant places remain science fiction, they now seem even more likely to stay that way.
Still, with these caveats, there’s still something amazing here: we can now imagine using the Rosetta stone of duality to simulate a traversable wormhole, and learn how it works in quantum gravity. That would be fantastic!
The Dream of Simulating Quantum Gravity
This is a dream, yet to be fulfilled. Computers are nowhere near being able to handle the questions we’d like to answer about the gravity we live with in our “four-dimensional space-time” (our familiar three space dimensions, plus one more for time). But by simplifying the problem in several steps (see the last figure of this post), we can at least hope to answer some early questions in a much simpler sort of wormhole in a simpler sort of gravity. This is what I’d prefer to call an artificially-simulated cartoon wormhole— rather than a “baby” wormhole, because unlike a baby, it isn’t a small version of an adult, nor has it any hope of growing into one. It’s more like a stick figure. It’s in two-dimensional space-time — one space and one time. That’s a big simplification — there’s nothing like normal gravity there! [Worse, we don’t have an exact duality in that case; the auxiliary quantum system we need isn’t really the same “text” as the wormhole. These are two systems, not one, with a limited but useful overlap.]
But cartoons aren’t to be mocked. Don’t underestimate them; cartoons are a powerful tool for educators everywhere, and subversive political cartoons have helped take down governments. For decades, famous physicists — Schwinger, ‘t Hooft, Gross and Neveu, Kogut and Susskind, and many more — have studied cartoon versions of real physics, especially ones in which our four space-time dimensions are replaced with just two. They’ve often learned interesting lessons from doing so, sometimes even profound ones.
[Note: Stick figure physics also can be a very good description of real stick-figure systems, for example a one-dimensional chain of atoms inside a material.]
I hasten to caution you that this technique does not always work. Not all of the lessons learned from stick-figure physics turn out to apply to the corresponding real-world problem. But this method has had enough success that we should take cartoon studies seriously.
This is why exploration of one-dimensional wormholes, and of some sort of auxiliary quantum problem to which they might be approximately related, may be worthwhile. And this is why it’s important to learn to simulate these auxiliary quantum systems on quantum computers, as was done in the paper that generated all the hype, based on proposals made in this paper and this one. Even if we can’t hope soon to understand how three-dimensional quantum space emerges from quantum entanglement, we can perhaps hope to learn more about one-dimensional quantum space, using quantum computer simulation. Maybe what we learn there would already teach us a deep and universal truth about quantum gravity, or at least suggest new ways to think about its subtleties.
The experiment done in the recent paper is a baby step in this direction. Others have attempted something along similar lines, but this is the first experiment that seems to have focused on the truly wormhole-like regime, and found some evidence for what was expected already of wormholes (from direct calculation and from classical computers…I’ll write about those details in a future post.) That seems like a real step forward. But let’s keep things in perspective. No new knowledge was created by this experiment; its achievements were technical and technological. It’s not a conceptual breakthrough. (I’m not alone in this view; Lenny Susskind, Dan Harlow and Scott Aaronson all expressed the same opinion in the New York Times and elsewhere.)
But nevertheless, this experiment represents a little arrow that points to a possible big future… not a future of a new Elon Musk, building wormholes for fun and profit, but one of a future Einstein, comprehending the quantum nature of spacetime itself.
The fusing of small atomic nuclei into larger ones, with the associated release of particles carrying a lot of motion-energy, is the mechanism that powers the Sun’s furnace, and that of other stars. This was first suspected in the 1920’s, and confirmed in the 1930s.
Nuclear fission (the breaking of larger atomic nuclei into smaller pieces) was discovered in the 1930s, and used to generate energy in 1942. Work on fission in settings both uncontrolled (i.e. bombs) and controlled (ie. power plants) proceeded rapidly; bombs unfortunately were quickly designed and built during World War II, while useful power plants were already operating by 1951. Meanwhile work on fusion also proceeded rapidly; in the uncontrolled setting, the first bomb using fusion (triggered by a fission bomb!) was already made in 1951, and in a flash of a decade, huge numbers of hydrogen bombs filled the arsenals of superpowers large and small. But controlled fusion for power plants… Ah.
Had it been as easy to control fusion as it was to control fission, we’d have fusion plants everywhere; fossil fuels would be consigned only to certain forms of transportation, and the climate crisis would be far less serious than it is right now. But unfortunately, it has been 70 years of mostly bad news — tragic news, really, for the planet.
But finally we have a little glimmer of hope. On December 5th, somebody finally managed, without using a bomb, to get more fusion-generated energy out of an object than the energy they had to put into it.
[UPDATE: Not really. Though this was a success and a milestone, it wasn’t nearly as good as advertised. Yes, more energy came out of the fusing material than was put into the fusing material. But it took far more energy to make the necessary laser light in the first place — 300 megajoules of energy off the electricity grid, compared to a gain from the fusing material of about 1 megajoule. So overall it was still a big net loss, even though locally, at the fusing material, it was a net gain. See thislink, in particular the third figure, which shows that the largest energy cost was electricity from the grid to run the lasers. In short, well, it’s still a good day for fusion, but we are even further from power plants than we were led to believe today.]
Poster Child for Particle Physics
In the Sun and similar stars, fusion proceeds through several processes in which protons (the nuclei of the simplest form of hydrogen) are converted to neutrons and combine with other protons to form mainly helium nuclei (two protons and two neutrons). Other important nuclei are deuterium D (a version of hydrogen with a proton and neutron stuck together), tritium T (another version with a proton plus two neutrons — which is unstable, typically lasting about 12 years), and Helium-3 (two protons plus one neutron.)
Fusion is a fascinating process, because all four of the famous forces of nature are needed. [The fifth, the Higgs force, plays no role, though as is so often the case, the Higgs field is secretly crucial.] In a sense, it’s a poster child for our understanding of how the cosmos works. Consider sunshine:
We need gravity to hold the Sun together, and to crush its center to the point that its temperature reaches well over ten million degrees.
We need electromagnetism to produce the light that carries energy to the Sun’s surface and sunshine to Earth.
We need the strong nuclear force to make protons and neutrons, and to combine them into other simple nuclei such as deuterium, tritium and helium.
We need the weak nuclear force to convert the abundant protons into neutrons (along with a positron [i.e. an anti-electron] and a neutrino.)
How can we be sure this really happens inside the Sun? There are quite a few ways, but perhaps the most direct is that we observe the neutrinos, which (unlike everything else that’s made in the process) escape from the Sun’s core in vast numbers. Though very difficult to detect on Earth, they are occasionally observed. By now, studies of these neutrinos, as here by the Borexino experiment, are definitive. Everything checks out.
In the recent experiment on Earth, gravity’s role is a little more indirect — obviously we wouldn’t have a planet on which to live and laboratories in which to do experiments without it. But it’s electromagnetism which does the holding and crushing of the material. The role of the strong and weak nuclear forces is similar, though instead of starting with mostly protons, the method that made fusion this week uses the weak nuclear force long before the experiment to make the neutrons needed in deuterium and tritium. The actual moment of fusion involves the strong nuclear force, in which
D + T –> He + n
i.e. one deuterium nucleus plus one tritium nucleus (a total of two protons and three neutrons) are recombined to make one helium nucleus and one neutron, which come out with more motion-energy than the initial D and T nuclei start with.
The Promise of Endless Cheap Safe[r] Power?
The breakthrough this week? Finally, after decades of promises and disappointments, workers at a US lab, Lawrence Livermore Laboratory in California, working at the National Ignition Facility, have gotten significantly more energy out of fusion than they put in. How this works is described by the lab here. The steps are: make a pellet stocked with D and T; fire up a set of lasers and amplify them to enormous power; aim them into a chamber containing the pellet, heating the chamber to millions of degrees and causing it to emit X-rays (high-energy photons); the blast of X-rays blows off the outer layer of the pellet, which [action-reaction!] causes the inner core of the pellet to greatly compress; in the high temperature and density of the pellet’s core, fusion spontaneously begins and heats the rest of the pellet, causing even more fusion.
Not as easy as it sounds. For a long time they’ve been getting a dud, or just a little fusion. But finally, the energy from fusion has exceeded the energy of the initial lasers by a substantial amount — 50%.
This one momentary success is far from a power plant. But you can’t make a power plant without first making power. So December 5th, eighty years and three days after fission’s first good day, was a good day for fusion on Earth, maybe the first one ever.
If this strategy for making fusion will ever lead to a power plant, this process will have to repeated over and over very rapidly, with the high-energy particles that are created along the way being directed somewhere where they can heat water and turn a steam turbine, from which electric current can be created as it is in many power plants. Leaving aside the major technical challenges, one should understand that this does not come without radioactive pollution; the walls of the container vessel in which the nuclear reactions take place, and other materials inside, will become radioactive over time, and will have to be disposed of with care, as with any radioactive waste. But it’s still vastly safer than a fission power plant, such as are widespread today. Why?
First, the waste from a fission plant is suitable for making nuclear weapons; it has to be not only buried safely but also guarded. Waste from a fusion plant, though still radioactive, is not useful for that purpose.
Second, if a fission plant malfunctions, its nuclear chain-reaction can start running away, getting hotter and hotter until the fuel melts, breaks through the vessel that contains it, and contaminates ground, air and water. By contrast, if a fusion plant malfunctions, its nuclear reactions just… stop.
And third, mining for uranium is bad for the environment (and uranium itself can be turned into a fuel for nuclear weapons.) Mining for hydrogen involves taking some water and passing electric current through it. Admittedly it’s a bit more complicated than that to get the deuterium and especially the tritium you need — the tritium be obtained from lithium, which does require mining — but still, less digging giant holes into mountains and contaminating groundwater with heavy metals.
Meanwhile, both forms of nuclear power have the advantage that they don’t dump loads of carbon into the atmosphere, and avoid the kind of oil spills we saw this week in Kansas.
So even though we are a long way from having nuclear fusion as a power source, and even though there will be some nuclear waste to deal with, there are good reasons to note this day. Someday we might look back on it as the beginning of a transformed economy, a cleaner atmosphere, and a saved planet.
A break from all these wormholes and strings; let’s take a moment to look at the sky. In the US, sadly, most of the country will be under cloud, but for those who aren’t, you have a spectacle tonight, at around 10-11pm Eastern Time in the US, roughly 5-6 am UT in Northern Europe.
It’s not terribly unusual for the Moon to pass in front of a planet and block it, from the point of view of some of us on Earth. This time it is Mars’ turn. You’ll be able to see the Moon eclipsing Mars (a “lunar occultation” of Mars), weather permitting, in the region shown below. This map is taken from in-the-sky.org, where you can enter your location and find out exactly when you’ll see Mars disappear behind the Moon and then reappear.
Visibility of tonight’s occultation of Mars by the Moon. See in-the-sky.org for more details.
This should be fun even with the naked eye — Mars won’t disappear in an instant but will do so gradually — but it will be better with binoculars, and great in a small telescope. It will give you a chance to see that yes, the Moon is in slow, steady motion in the sky relative to the planets, which (being further) seem to move more slowly. Lunar and solar eclipses provide a similar opportunity to observe this motion, but I think occultations provide the clearest sense of it.
The Full Moon can be seen from south to north across the Earth. Why isn’t the occultation visible everywhere? It is because the Moon is smaller than the Earth, as I explained here as part of my series on “Do It Yourself Astronomy”. In a sense, the light of Mars effectively (though not literally) casts the Moon’s shadow onto the Earth, and the shadow’s width — the width of the region over which the occultation is visible — would be the same as the diameter of the Moon, were the occultation visible close to the Earth’s equator. (As I pointed out, you can use this fact to measure the Moon’s size without ever leaving the Earth.) Because tonight’s occultation is visible closer to the poles, the region of visibility on the Earth’s surface is distorted by the Earth’s curvature, making it larger than the Moon by about 50% — about 3000 miles (5000 km) or so. (That’s yet more evidence that the Earth’s not flat, in case you needed some.)
Finally, there’s something quite remarkable about this occultation. It occurs close to two special moments:
almost at full Moon (within a few hours);
almost at “Mars opposition” (within a few hours) — when Mars is (nearly) closest, brightest and highest in the midnight sky, as brilliant as it gets over its cycle.
Since (1) happens once a month, and (2) happens once every two years, and occultations don’t occur all the time, this seems like quite a coincidence!
Only… it’s not as big a coincidence as it looks. A puzzler for you: why isn’t it a coincidence that (1) and (2) happen at the same time? That is, if there’s an lunar occultation of Mars at full Moon, why must Mars be nearly at opposition? [Hint: it’s just geometry.]
Sadly, the LunaH-MAP mini-satellite (or “CubeSat”) that I wrote about a couple of days ago, describing how it would use particle physics to map out the water-ice in lunar soil, has had a serious setback and may not be able to carry out its mission. A stuck valve is the most likely reason that its thruster did not fire when instructed to do so, and so it has sailed past the Moon instead of going into the correct orbit. There’s still some hope that the situation can be salvaged, but it will take some luck. I feel badly for the scientists involved, who worked so hard and now face great disappointment.
In fact at least four and perhaps five of the ten CubeSats launched along with NASA’s Artemis mission have apparently failed in one way or another. This includes the Near-Earth Asteroid Scout and Team Miles, both of which were intended to test and use new technologies for space travel but with whom communication has not been established, and OMOTENASHI, which is intended to study the particle physics environment around the Moon and land a mini-craft on the surface, but which has had communication issues and will not be able to deploy its lander. It’s not clear what’s happening with Lunar-IR either.
One has to wonder whether this very high failure rate is due to the long delays suffered by the Artemis mission. The original launch date was at the end of August; batteries do degrade, and even satellites designed for the rigors of outer space can suffer in Florida’s heat and moisture.
The recent launch of NASA’s new moon mission, Artemis 1, is mostly intended to demonstrate that NASA’s incredibly expensive new rocket system will actually work and be safe for humans to travel in. But along the way, a little science will be done. The Orion spacecraft at the top of the giant rocket, which will actually make the trip to the Moon and back and will carry astronauts in future missions, has a few scientific instruments of its own. Not surprisingly, though, most are aimed at monitoring the environment that future astronauts will encounter. But meanwhile the mission is delivering ten shoe-box-sized satellites (“CubeSats“) which will carry out various other scientific and/or technological investigations. A number of these involve physics, and a few directly employ particle physics.
The use of particle physics detectors for the purpose of studying the not-so-empty space around the Moon and Earth is no surprise. Near any star like the Sun, what we think of as the vacuum of space (and biologically speaking, it is vacuum: no air and hardly any atoms, making it unsurvivable as well as silent) is actually swarming with subatomic particles. Well, perhaps “swarming” is an overstatement. But nevertheless, if you want to understand the challenges to humans and equipment in the areas beyond the Earth, you’ll inevitably be doing particle physics. That’s what a couple of the CubeSats will be studying, entirely or in part.
What’s more of a surprise is that one of the best ways to find water on the Moon without actually landing on it involves putting particle physics to use. Although the technique is not new, it’s not so obvious or widely known, so I thought I’d draw your attention to it.
A week or so ago, I wrote about my skepticism concerning the claim of a “detection” of the photon ring that’s widely expected to lie hidden within the image of a black hole. A nice article in Science News appeared today outlining the current controversy, with some quotes from scientists with differing views (including a dissenter from the EHT itself). It’s a good read: to the point, well-written, and with high standards.
Figure 1: Image of the accretion disk surrounding M87’s black hole [Credit : EHT collaboration]
Background: The image in Figure 1, created by the Event Horizon Telescope (EHT) in 2019, shows the “accretion disk” of material circling and eventually falling into the giant black hole at the center of the galaxy M87. But the image is too blurry to easily reveal the photon ring, whose appearance in a perfect telescope might look like that in Figure 2, which shows a simulation of the region around a black hole.
Unlike the accretion disk, the photon ring would be an effect purely of curved space-time around the black hole, which is expected to lens and focus light from the accretion disk into a narrow circlet. As such, the ring would be a smoking-gun signature of Einstein’s gravity at work. That’s why any claim of detection, using fancy image processing or any other method, merits both attention and critique.
Figure 2: A simulation of what a perfect telescope image might reveal, with a narrow bright ring appearing withing a swirling inhomogeneous disk. [Credit A. Chael]
Back in 2019, the Event Horizon Telescope (EHT) made history as its scientists used it to create an image of a huge black hole — or rather, of the “accretion disk” of material surrounding a black hole — at the center of the galaxy M87. The dark central gap reveals where the disk’s material vanishes from view, as it presumably flows toward and disappears into the black hole.
EHT’s image of the M87 galaxy’s black hole’s accretion disk, created from radio-wave measurements. [How do we know there’s a black hole there? I left an answer in the comments.]
What the image actually shows is a bit complicated, because there is not only “light” (actually, radio waves, an invisible form of light, which is what EHT measures) from the disk that travels directly to us but also (see the Figure below) light that travels around the back of the black hole. That light ends up focused into a sharp ring, an indirect image of the accretion disk. (This is an oversimplication, as there are additional rings, dimmer and close together, from light that goes round the black hole multiple times. But it will be a decade before we can hope to image anything other than the first ring.)
Left: A glowing accretion disk (note it does not touch the black hole). Light from the right side of the disk forms a direct, broad image (orange) heading toward us, and also a focused, narrow, indirect image (green) heading toward us from the left side, having gone round the back of the black hole. (Right) From the entire accretion disk, the direct image forms a broad disk, while the indirect image would be seen, with a perfect telescope, as a narrow circle of bright light: the photon ring. Unfortunately, the EHT blurs this picture to the point that the photon ring and the disk’s direct image cannot be distinguished from one another. [Long and careful explanation given here.]
Regrettably, that striking bright and narrow “photon ring” can’t be seen in the EHT image, because EHT, despite its extraordinary capabilities, doesn’t yet have good enough focus for that purpose. Instead, the narrow ring is completely blurred out, and drowned in the direct image of the light from the wider but overall brighter accretion disk. (I should note that EHT originally seemed to claim the image did show the photon ring, but backed off after a controversy.) All that can be observed in the EHT image at the top of this post is a broad, uneven disk with a hole in it.
However, having looked at the paper, I’m skeptical of this claim, at least so far. Here’s why.
Normally, if you claim to have detected something for the first time, you make it clear to what extent you’ve ruled out the possibility it actually isn’t there… i.e., if there’s only a 0.01% chance that it’s absent, that’s a strong argument that it’s present. I don’t see this level of clarity in the paper.
Almost everyone is pretty darn sure that in reality the photon ring is actually present. That introduces a potential bias when you search for it; at least unconsciously, you’re not weighing the present vs. absent options equally. For this reason, it’s important to demonstrate that you’ve eliminated that bias. I don’t see that the authors have done this.
Simulations of black hole surroundings and theoretical estimates both suggest that the photon ring should have significantly less overall brightness than the broad accretion disk. However, the ring measured in this paper has the majority of the total light (60%). The authors explain this by saying this is typical of their method: it combines some of the disk light near the photon ring (i.e., background) with the actual photon ring (i.e. signal). But normally one doesn’t claim to have detected a signal until one has measured and effectively subtracted the background. Without doing so, how can we be sure that the ring that the authors claim to have measured isn’t entirely background, or estimate how statistically significant is their claim of detection?
I’ve included more details on the following section, but the bottom line is that I’d like a lot more information before I’d believe the photon ring’s really been detected.
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.
It’s not widely appreciated how often physicists can guess the answer to a problem before they even start calculating. By combining a basic consistency requirement with scientific reasoning, they can often use a heuristic approach to solving problems that allows them to derive most of a formula without doing any work at all. This week I want to introduce this to you, and show you some of its power.
The trick, called “dimensional analysis” or “unit analysis” or “dimensional reasoning”, involves requiring consistency among units, sometimes called “dimensions.” For instance, the distance from the Earth to the Sun is, obviously, a length. We can state the length in kilometers, or in miles, or in inches; each is a unit of length. But for today’s purposes, it’s irrelevant which one we use. What’s important is this: the Earth-Sun distance has to be expressed in some unit of length, because, well, it’s a length! Or in physics-speak, it has the “dimensions of length.”
For any equation in physics of the form X = Y, the two sides of the equation have to be consistent with one another. If X has dimensions of length, then Y must also have dimensions of length. If X has dimensions of mass, then Y must also. Just as you can’t meaningfully say “I weigh twelve meters” or “I am seventy kilograms old”, physics equations have to make sense, relating weights to weights, or lengths to lengths, or energies to energies. If you see an equation X=Y where X is in meters and Y is in Joules (a measure of energy), then you know there’s a typo or a conceptual mistake in the equation.
In fact, looking for this type of inconsistency is a powerful tool, used by students and professionals alike, in checking calculations for errors. I use it both in my own research and when trying to figure out, when grading, where a student went wrong.
That’s nice, but why is it useful beyond checking for mistakes?
Sometimes, when you have a problem to solve involving a few physical quantities, there might be only one consistent equation relating them — only one way to set an X equal to a Y. And you can guess that equation without doing any work.
Well, that’s pretty abstract; let’s see how it works in a couple of examples.
