[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.)
The press is full of excitement today at the news that anti-matter — hydrogen anti-atoms, specifically, made from positrons and anti-protons instead of electrons and protons — falls down rather than rising up. This has been shown in the ALPHA experiment at CERN. But no theoretical physicist is surprised. Today I’ll explain one of many reasons that no one in the halls of theoretical physics even blinked.
One basic point is that “anti-particle” is not a category but a relationship. We do not say “electrons are particles” and “positrons are anti-particles”, nor do we say “quarks are particles” and “anti-quarks are anti-particles.” Such statements would be inconsistent. Instead we say “quarks and anti-quarks are each others’ anti-particles.” (It’s like the term “opponent” in a football match.) That’s because some particles are their own anti-particles, including photons. If we tried to divide all the types of particles into two categories, it wouldn’t be clear where photons would go; we couldn’t say either that they are particles or that they are anti-particles.
“Anti-particle” is a relationship, exchanging electrons with positrons and leaving photons unchanged. It is not a category; there are no objects that can be said to be “antiparticles”. (If there were, would photons be particles or would they be anti-particles?)
Because of this, we can’t hope that all the types of particles separate into two groups, particles which fall and anti-particle which rise. At best, we would have to guess what would happen to particles that are their own anti-particles. Fortunately, this is easy. There is such a thing as a positronium atom, an exotic atom made from an electron and positron co-orbiting one other. A positronium atom is its own anti-particle; if we flip every particle for its anti-particle, the positronium atom’s electron and positron simply switch places. If indeed gravity pulls down on electrons and pushes up by the same amount on positrons, then gravity’s pull on a positronium atom would cancel. This atom would neither rise nor fall; it would float, feeling no net gravity.
This example would then lead us to expect that particles that are their own anti-particles will float. The logic would apply to photons; they would feel no gravity.
Electrons and quarks make up atoms and are known to fall. If the positrons and anti-quarks that make up anti-atoms were to rise instead, then positronium atoms would float. This would imply that photons float too. But experiments have shown for a century that photons fall.
This would be a consistent picture. But experimentally, it is false: photons do feel gravity. The Sun bends the path of light, a fact that made Einstein famous in 1919, and an object’s strong gravity can create a gravitational lens that completely distorts the appearances of objects behind it. Photons can even orbit black holes. So experiment would force us to accept the picture shown below, if we want positrons to rise. Unfortunately, it is logically inconsistent.
Since photons fall too, we would have to believe either that positronium floats even though photons fall, or that positrons rise even though positronium falls. Neither makes any sense either conceptually or mathematically.
The only consistent picture, then, is that everything falls. Are there any loopholes in this argument? Sure; perhaps the gravity of the Earth, made of atoms, causes electrons and quarks to fall rapidly and causes positrons and anti-quarks to rise slowly, so that positronium still falls, just more gently than ordinary atoms do. (The reverse would be true around a planet made of anti-atoms.) This gives us many more possibilities to consider, and we have to get into more complex questions of what experiment has and hasn’t excluded.
But we would still face another serious problem, because there are anti-quarks inside of protons. (One line of evidence for this is shown here.) If quarks and anti-quarks, which have the same inertial mass (the type of mass that determines how they change speed when pushed) had different gravitational mass (which determines how gravity affects them), then protons and neutrons, too, would not have equal inertial and gravitational mass. [The many gluons inside the protons and neutrons could make this even worse.] Since electrons do have equal inertial and gravitational mass, protons and neutrons would then fall at a different rate than electrons do. The consequence would be that different atoms would fall at slightly different rates. High precision experiments clearly say otherwise. This poses additional obstructions to the idea that anti-quarks (and the anti-protons and anti-neutrons that contain them) could rise in Earth’s gravity.
At best, when it comes to mass and gravity, existing experiments only allow for minor differences between atoms and anti-atoms. To look for subtle effects of any such differences is one of the real, long-term goals of the ALPHA experiment. What they’ve done so far is a neat experimental coup, but despite the headlines, it does not change our basic knowledge of anti-particles in general or of anti-atoms in particular. For that, we have a few years to wait.
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.”*
Today a reader asked me “Out of the quantum fields which have mass, do any of them also have weight?” I thought other readers would be interested in my answer, so I’m putting it here. (Some of what is discussed below is covered in greater detail in my upcoming book.)
Before we start, we need to rephrase the question, because fields do not have mass.
Continuing with the supplementary material for the book, from its Chapter 2. This is in reference to Galileo’s principle of relativity, a central pillar of modern science. This principle states that perfectly steady motion in a straight line is indistinguishable from no motion at all, and thus cannot be felt. This is why we don’t feel our rapid motion around the Earth and Sun; over minutes, that motion is almost steady and straight. I wrote
. . . Our planet rotates and roams the heavens, but our motion is nearly steady. That makes it nearly undetectable, thanks to Galileo’s principle.
To this I added a brief endnote, since the spin of the Earth can be detected, with some difficulty.
As pointed out by the nineteenth-century French physicist Léon Foucault, the Earth’s rotation, the least steady of our motions, is reflected in the motion of a tall pendulum. Many science museums around the world have such a “Foucault pendulum” on exhibit.
But for those who would want to know more, here’s some information about how to measure the Earth’s spin.
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:
Waves in an Impossible Sea, on the intersection of modern physics with human existence and daily life, is essentially done and edited now — not perfect, of course, but as good as I have had time to make it. Now I await the proofs.
The book is supposed to appear in early March. Here’s the cover art, created by an artist at the publisher, Basic Books. I hope it makes you curious about what might lie inside!
A Harvard physicist takes us on an awe-inspiring journey from relativity to the Higgs field, showing how the universe creates everything from what seems like nothing at all
In my last post I raised a question about the pros and cons of common sense. I left it as a wide-open question, as I was curious to see how readers would react.
Many aspects of common sense affect how we relate to other people, and it’s clear they have considerable value. But the intuitions we have for nature, though sometimes useful, are mostly wrong. These conceptual errors pose obstacles for students who are learning science for the first time.
It’s also interesting that once these students learn first chemistry and then Newtonian-era physics, they gain new intuitions for the natural world, a sort of classical-physics common sense. Much of this newfound common sense also turns out to be wrong: it badly misrepresents how the cosmos really works. This is a difficulty not only for students but also for many adults. If you’ve read about or even taken a class in basic astronomy or physics, it can then be challenging to make sense of twentieth-century physics, where Newtonian intuition can fail badly.
