Quote: . . . the Higgs field exhibits the most inelegant of the known laws governing fields and particles. There’s an amusing tendency for those who tout beauty to ignore this, as though it were an inconvenient family member, and to focus instead on Einstein’s elegant theory of gravity. Yet even that theory has its issues.
Endnote: Einstein’s theory of gravity is amazingly elegant as long as one ignores the puzzle of “dark energy,” which would have been easier to do had it been exactly zero, and as long as gravity is a very weak force, as its weakness leads to extremely simple equations. In string theory, Einstein’s equations become much more complex, and the elegant simplicity of the math shifts to the level of the strings themselves . . . perhaps.
I’ll expound below upon the second bullet point, hoping to draw attention to general questions concerning aesthetics in theoretical physics.
More about tidal forces today (see also yesterday’s post) and the conceptual point underlying Earth’s ocean tides.
(Quote) Because gravity dwindles at greater distances, the Moon’s pull is stronger on the near side of the Earth and weaker on the far side than it is on the Earth’s center. This uneven pull stretches our planet’s oceans slightly, resulting in a small bulge of water, not much taller than a human, both on the Earth’s side facing the Moon and on the opposite side, too.
(Endnote) To explain why gravity leads to a water bulge on both sides of the Earth is too complex for a footnote, and I’d rather not repeat the most commonly heard explanations, which are misleading. One can see a hint of the cause as follows: if one drops a water balloon in constant gravity, it will fall as a sphere, whereas if it is pulled more strongly at the bottom than at the top, it will stretch into an oval as it falls.
Here I’ll explain this last observation more carefully.
[This is a tricky one… it’s easy to make confusing statements about Einstein’s theory of gravity (general relativity), and so I am especially hopeful of getting readers’ feedback on this subtle issue, to make sure what follows is 100% clear and correctly stated.]
(Quote) On Earth’s surface, we are roughly 4,000 miles from Earth’s center. But if you ascended another 22,000 miles, where you’d find the GOES weather satellites that monitor Earth’s weather patterns, you’d find your weight (but not your mass!) reduced to one-fortieth of what it is on Earth… And if you traveled out into deep space, far from any large object, you’d weigh virtually nothing. Yet all the while, your body’s mass—the difficulty I would face if I tried to speed you up or slow you down—would never change.
(Endnote) Confusingly, astronauts orbiting Earth inside nearby space stations appear to float as though weightless. From Newton’s perspective, they are not truly weightless; if they were, they’d coast, leaving the Earth’s vicinity and moving rapidly into deep space. Instead, they and their spaceship are pulled by gravity into a common orbit around the Earth. Since they travel on the same path as their container and as the camera which films them, they seem and feel weightless. (This subtle issue is turned on its head in Einstein’s view of gravity.)
Astronauts in a space station seem to float, as though they are weightless. Are they truly weightless? Or are they only apparently weightless?
The same issues arise for people in a freely falling elevator, accelerating downward with ever greater speed. They will feel weightless, too. But are they?
Newton would have said they are apparently weightless, subject to gravity but all falling together along with their vehicle. A naive (but instructive!) reading of Einstein might lead us to say that they are truly weightless… that the gravity that Newton claims is present is a pure illusion, a fictitious force. But a precise Einsteinian would say they are almost but not quite weightless — and the lack of perfect weightlessness is a clue, a smoking gun in fact, that they are indeed subject to gravity.
Additional supplementary material for the upcoming book; your comments/corrections are welcome. This entry has to do with how Newton realized that weight and mass aren’t the same thing — that the pull of Earth’s gravity depends on how far you are from the Earth’s center.
(Quote) Newton knew right away that if the force of gravity were as powerful out by the Moon as it is at Earth’s surface—if the Moon accelerated toward the Earth at the same rate that your dropped keys do—then motion and gravity would be wildly out of balance[and so the Moon would have fallen and crashed into the Earth.]
(Endnote) To avoid disaster, the Moon’s orbital speed would need to be 40 miles per second, leading it to circle Earth twice a day.
Here I’ll explain why this is true, using a little math. (If you already know something about Kepler’s laws of planetary orbits, additional relevant discussion can be found in this post from 2022.)
Personally, I think that popular science books ought to devote more pages to the issue of how language is used in science. The words scientists choose are central to communication and miscommunication both among researchers and between scientists and non-scientists. The problem is that all language is full of misnomers and contradictory definitions, and scientific language is no exception.
One especially problematic scientific word is “matter.” It has multiple and partly contradictory meanings within particle physics, astronomy and cosmology. For instance,
(Quote) It’s not even clear that “dark matter,” a term used widely by astronomers and particle physicists alike, is actually matter.
(Endnote) Among possible dark matter particles are axions and dark photons, neither of which would obviously qualify as “matter.”*
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:
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.
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.
