Astronomy

Heads Up — Northern Lights Possible in Next 24 Hours

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[Note added: the predicted storm has begun, as of about 1000 UTC, 5:00 AM NYC time; good for early birds on the west coast and those in Asia.] If you live in Canada, Europe or the northern half of the US, keep an eye to the north late tonight and possibly tomorrow night. A series … Read more

Is Einstein’s Theory of General Relativity Truly Elegant?

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  • 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.

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What [Really] Causes our Twice-Daily Ocean Tides?

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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.

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The Impossible Commentary: Is Gravity a Force? Is it an Illusion?

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[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.

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The Impossible Commentary: Newton, Gravity, and the Speed of the Moon

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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.)

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Beyond the Book: The Ambiguities of Scientific Language

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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.”*

Why might one not view them as matter?

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How to Tell that the Earth Spins

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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.

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Beyond the Book (and What the Greeks Knew About the Earth)

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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:

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