*. . . 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.

————

The spin of the Earth was first detected through what is known as the Coriolis effect, which causes objects far from the equator and moving in long paths to seem to curve gently. The reasons for the apparent curved paths, as well as the consequent impacts on navigation and weather, are discussed in this post from 2022, one of a series in which I showed how you can confirm basic facts of astronomy for yourself.

*(Regarding the Coriolis effect: there’s a famous tourist trap in which trained professionals cause water to spin down drains in opposite directions, depending on which side of the equator they are standing on. But this is a magician’s trick, intended to obtain a nice tip from impressed travelers. The Coriolis effect is tiny on the scale of a sink; it’s only easy to observe on scales of miles (kilometers). It is even tinier right near the equator* *— that’s why there are no hurricanes at very low latitudes — and so it has no effect on the trickster’s draining water. Here’s someone’s webpage devoted to this issue.)*

In the same post, I described the basics of a Foucault pendulum, the simplest device that can visibly demonstrate the Earth’s rotation. It’s really nothing more than an ordinary pendulum, but very tall, heavy, and carefully suspended. Unfortunately, although such a pendulum is easy to observe and is common in science museums, it is conceptually confusing. It is easily understood only at the Earth’s poles, where it swings in a fixed plane; then the Earth rotates “underneath” it, making it to appear to spectators that it rotates exactly once a day. But at lower latitudes, the pendulum appears to rotate more slowly, and at the equator it seems not to rotate at all (because, again, there’s no Coriolis effect near the equator.) Depending on how close the pendulum is to the equator, it may take weeks, months or years to rotate completely. To understand these details is not straightforward, even for physics students.

A better device for measuring the Earth’s rotation, which Foucault was well aware of and which I discussed in the next post in that same series, is a gyroscope — for example, a spinning top, or indeed any symmetrical, rapidly spinning object. Conceptually, a gyroscope is extremely simple, because its pointing direction stays fixed in space no matter what happens around it. Once pointed at a star, the gyroscope will continue to aim at that star even as the Earth turns, and so it will appear to rotate once a day no matter where it is located on Earth.

So why don’t science museums display gyroscopes instead of Foucault pendula? Unfortunately, even today, it is still impossible to build a mechanical gyroscope that is stable enough over a full day to demonstrate the Earth’s rotation. Ring laser gyroscopes, which use interference effects between light waves, are much more stable, and they can do the job well (as a flat-earther discovered to his embarrassment — see the last final section of that same post.) But their workings are invisible and nonintuitive, making them less useful at a science museum or in a physics classroom.

Now here’s something worth thinking about. Imagine a intelligent species living forever underground, perhaps without vision, never having seen the sky. Many such species may exist in the universe, far more than on planetary surfaces that are subject to potentially sterilizing solar flares and other catastrophes. Despite complete ignorance of their astronomical surroundings, these creatures too can prove their planet rotates, using nothing more than a swinging pendulum or a spinning top.

]]>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:

By the time that ancient Rome’s power was expanding, Greek scholars understood the basics of solar and lunar eclipses. Noting the relation between the phases of the Moon and the positions of the Sun and Moon, they recognized that the Moon’s light is reflected sunlight. They were aware that New Moon occurs when the Sun and Moon are on the same side of the Earth, while Full Moon occurs when they are on the opposite sides. And they knew that a lunar eclipse occurs when the Earth lies between the Sun and Moon, so that the Earth blocks the Sun’s light and casts a shadow on the Moon. This is illustrated (not to scale) in Fig. 1.

From these shadows, they confirmed the Earth was a sphere. Clearly, if the Earth had the shape of an X, it could cast an X-shaped shadow.

If Earth were a flat disk like a coin, then depending on the Moon’s location in the sky, the Earth’s shadow might be circular or might be oval. The important point is **the shadow of a circular disk is not always a circular disk**. You can confirm this with a coin and a light bulb.

The only shape which always creates a circular, disk-like shadow, from any angle and from any place and at any time, is a sphere, as you can confirm with a ball and a light bulb.

This is consistent with what is actually observed in eclipses, as in Fig. 4. The circular shadow of the Earth is shown especially clearly when sets of photos taken during an eclipse are carefully aligned.

Next, one you are aware that the Earth’s a sphere (and, as the Greeks also knew, that the Sun is far away ), it’s not hard to learn the size of the Earth. Imagine two vertical towers sitting on flat ground in two different cities. To keep things especially simple, let’s imagine one city is due north of the other, and the distance between them — call it “D” — is already known.

In each city, a person observes their tower’s shadow at exactly noon. (No clock is needed, because one can watch the shadow over time, and noon is when the shadow is shortest.) The end of the shadow and the tower’s base and top form the points of a right-angle triangle, as in Fig. 5, whose other angles we can call ⍺ and 𝜃. For a person squatting at the shadow’s end, the angle ⍺ is easily measured: it is the angle formed by the tower’s silhouette against the sky. Because this is a right-angle triangle, the angle 𝜃 is 90 degrees minus ⍺, so each observer can easily determine 𝜃 for their city’s tower. We’ll call their two measurements 𝜃_{1} and 𝜃_{2}. Knowing these angles and their distance D, they know everything we need to determine the size of the Earth.

The key observation is that **the difference in these angles is the same as the difference in the latitude between the two cities**. To see this, examine Fig. 6 below. The paths of sunlight (the orange dashed lines in Figs. 5 and 6) are parallel to the Earth-Sun line. [This (almost-exact) parallelism is only true because the Sun’s distance from Earth is much larger than the Earth’s size — which the Greeks knew.] Meanwhile the line from the Earth’s center to the first tower (call it L1) is a continuation of the line from that tower’s base to its top. Because (a) L1 forms an angle 𝜃_{1} with the sunlight, as shown in Fig. 5, and (b) the sunlight line and Earth-Sun line are parallel, as shown in Fig. 6, the intersection of L1 with the Earth-Sun line is also 𝜃_{1}! Similarly, the line from the Earth’s center to tower 2 forms the angle 𝜃_{2} with the Earth-Sun line. As can be seen in Fig. 6, it follows that **the angle between the two lines connecting the Earth’s center to the two towers is 𝜃 _{2} – 𝜃_{1}** , the difference in the noon-time sun angles as seen by the two observers!

Now, however, the observers can use the fact that they know D, the distance between the cities. In particular, the distance D is to the Earth’s circumference C just as 𝜃_{2} – 𝜃_{1} is to 360 degrees (or, in radians, to 2ℼ). In formulas

- D/C = (𝜃
_{2}– 𝜃_{1})/360°

So (dividing and multiplying on both sides) the Earth’s circumference is simply

- C = D [360° / (𝜃
_{2}– 𝜃_{1}) ]

and since they know both D and 𝜃_{2} – 𝜃_{1} , they now know the Earth’s circumference. (Note this correctly says that if the angle were 90 degrees = 2ℼ/4, then D would be C/4.)

Eratosthenes made this measurement (in a slightly different way) around 240 B.C.E. Reports by classical historians do not quite agree on what he found, but in the most optimistic interpretation of the historical record, he was well within 1 percent of the correct answer. And why not? Once you’ve realized what you should do, this is a relatively simple measurement; it’s one that you and a distant friend could carry out yourselves.

Note: You might prefer to see the answer in radians instead of degrees; since 360° = 2ℼ radians, we can write

- C = D [2ℼ / (𝜃
_{2}– 𝜃_{1}) ] (in radians)

and since C = 2ℼR, where R is the Earth’s radius, that gives us a particularly simple formula

- R = D / (𝜃
_{2}– 𝜃_{1}) ( in radians)

Note: If the two cities are not due north-south of one another, this poses no problem. Measure tower 1’s shadow at the first city’s noon, and tower 2’s shadow at the second city’s noon on the same day; then take D not to be the distance between the two cities but instead the distance between their latitude lines. Practically speaking, we can make a triangle with one side being the distance between the cities and the other two sides aligned north-south and east-west; then D is the length of the north-south line, as in Fig. 7. With this definition of D, the formulas above are still valid.

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!

The other five scientists who contributed are

- Jon Butterworth, a senior physicist at the ATLAS experiment at the Large Hadron Collider (LHC), well-known for his public outreach in the UK, and the author of several books for general readers about physics;
- Adam Keshavarzi, a physicist at the g-2 experiment measuring the magnetic properties of the muon (and finding a result that deviates slightly from the current Standard Model prediction);
- Clare Burrage, Surjeet Rajendran and Emily Adlam, three accomplished theoretical physicists with highly creative and wide-ranging approaches to the problems of the Standard Model. They’re younger and much more involved in the details of possible solutions than I am, so keep an eye on what they’re doing.

The experimenters, of course, are hoping their experiments will shed some new light on the puzzles that the Standard Model leaves open. I don’t want to get into those details today, but I’ll come back to the g-2 experiment at some point soon.

In my brief contribution to the feature, I make simple points concerning the following issue. So far, other than the Higgs boson, the LHC hasn’t discovered any new elementary particles or other dramatic unexpected effects. This poses a conceptual crisis, because there were strong arguments (based on quantum field theory and on experiments) that Higgs bosons shouldn’t appear alone. That crisis both justifies and motivates the work by professors Burrage, Rajendran and Adlam, along with other young physicists.

In their articles, the other theorists discuss their approaches. Rajendran, whose work has covered many research areas, examines the potential role of new experiments aimed at finding evidence of particles whose interactions with all known particles are extremely weak. Burrage, thinking along similar lines, describes a subtle form of new force whose effects depend on the environment that it is in, and which can’t be observed without specially designed experiments, including ones that she and her colleagues have proposed. Adlam has a more radical and more speculative proposal: that not only is our way of thinking about time wrong (which by itself is plausible, given how confusing time is to us), our misunderstanding of it may have an impact even on the Standard Model.

As of yet, neither they nor anyone else seems to have an exceptionally compelling idea. But out of these new lines of thought, intriguing proposals for entirely new types of experiments are emerging. This all to the good; as is often said, we should never let a crisis go to waste. If our current confusion leads to a novel set of experimental questions about the world, that’s real progress. And if one of those new experiments turns up something no one (or almost no one) was expecting, that’s priceless.

]]>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.

Let’s take just one example. Any child who has tried to move a heavy box by sliding it along a floor knows that if you want to keep it moving at a constant speed, you have to keep pushing it; and the heavier the box, the harder you have to push it. It also seems harder to push it at a high speed than at a low speed. For this reason, the natural expectation of any reasonable person who hasn’t taken a physics course is that the amount of force required to push the box grows with the **speed** *v* at which you want to push it and with the **weight** *W* of the box.

Such a person might then imagine, incorrectly, that this is true for any object in any circumstance, at least on Earth. It’s common sense.

Misconceptions of this sort *(which arise from not recognizing the crucial role of friction) *were typical for centuries, even among highly intelligent, thoughtful scholars. * *It wasn’t until Isaac Newton that the veils were entirely lifted, with his laws of motion, of which the second reads * F = m a*. This equation implies

- that no force at all is required to make an object move at a fixed speed and direction,
- that the force
required to change the speed or direction of an object is proportional to its*F***mass***m*(not its weight) and the object’s**acceleration**(not its speed,) and**a** - the direction of the object’s acceleration is the same as the direction of the force applied to the object.

And yet no sooner has a student spent months learning and internalizing this law, developing a detailed intuition for it, than it is undermined by the 20th century, first by Einstein’s relativity and then by quantum physics. That’s unfortunate for people who take only one year of physics, because those advanced subjects are either not covered, or are covered in a cursory way that does not allow for a new intuition to take hold. Worse, incoherent statements about these topics are not uncommon in first-year textbooks.

In Einstein’s theory of motion, the analogue of * F = m a* is a much more complex equation, as you can find in the 2nd, 4th and 5th sections of https://en.wikipedia.org/wiki/Acceleration_(special_relativity) . Worse, the intuition for what is meant by force and acceleration in this context are not straightforward. Textbooks and courses rarely consider them with care.

Not realizing this, people often apply the following incorrect logic:

- Einstein claimed that no object can move faster than the cosmic speed limit
(also known as the speed of light);**c** - Therefore, the closer an object’s speed to
, the more difficult it must be to accelerate it (and therefore the more force must be applied to do so, for the same acceleration); otherwise its speed could easily be made to exceed**c**;**c** - And so, an object’s mass must grow with its speed, so that a fixed force produces less and less acceleration.
- In fact, as its speed reaches
, the object’s mass must become infinite to assure that that the acceleration correspondingly becomes zero; otherwise it could accelerate past**c**.**c**

This sounds perfectly reasonable, but it is somewhere between misleading and inconsistent. It is an effort to retain Newton’s law, and Newtonian common sense, in the context of Einstein’s relativity. But it’s simply not true that * F = m a*, where

What happens to * F = m a* in quantum physics? Even the idea of such an equation assumes that objects have trajectories — paths across space on which objects travel as time goes by. But what we learned from quantum physics is that real objects in the real world do not, in fact, have trajectories. It’s a long story to see what happens to Newton’s law in that context. (For a glimpse, see https://www.physnet.org/modules/pdf_modules/m248.pdf, but that’s just the beginning.)

In short, not only does our common sense intuition from **before** first-year physics have to be discarded, so does the intuition built up **during** first-year physics! This is a serious challenge for students, teachers and writers. And it raises an interesting question: would it be better, both for those who will someday take a first-year physics class and for those who never will, to try to convey some preliminary, qualitative intuition for how the world really works? Only later would we then teach Newton’s physics for what it is: not as a set of ancestral truths, but merely as an approximation that served (and still serves) as a temporary bridge between ordinary common sense and the universe’s underlying reality.

However, this plan had a problem. The Higgs field would be irrelevant were it not for quantum physics on the one hand and **Einstein’s** relativity on the other, and to comprehend the latter requires some understanding of **Galileo’s** earlier concept of relativity. To show why the Higgs field can give mass (more precisely, rest mass) to certain types of particles requires combining all of these notions together. Each of these topics is daunting, worthy of multiple books, and I knew I couldn’t hope to cover them all in 100,000 words!

To my surprise, resolving this problem wasn’t as difficult as I expected, once I picked out a few crucial elements about each of these subjects that I felt everyone ought to know. Lining up those conceptual points carefully, I found I could give a non-technical yet accurate explanation of how elementary particles can get mass from a Higgs field. (A more mathematical explanation has been given previously on this website, in two series of articles here and here.)

Yet what surprised me even more was that the book’s main subject slowly changed as I wrote it. It became focused on the question of how ordinary life emerges from an extraordinary cosmos. Though a substantial section of the book is devoted to the Higgs field, it is situated in a much wider context than I originally imagined.

This shift of emphasis happened naturally. I had to explain how quantum physics, relativity, and the nature of space are blended together in ** quantum field theory** (our best guide, so far, as to how to describe the basics of the cosmos.) But along the way I had to introduce a slew of counter-intuitive ideas. That task, in turn, required deconstructing human intuition about the world we live in, and replacing it with something deeper and stranger, a child of lessons learned from modern physics.

A key question raised by this replacement is the value of common sense. Under what circumstances is common sense a help, and when is it a hindrance? What are its pros and cons? How has it aided or obstructed science, both historically and in the present day? When should we rely on it, and when should we disregard or distrust it? I’m curious to know what readers think: **are you a fan of common sense, or not?**

In the book, I’ve tried to explain how modern physics intersects with human existence and experience. I hope it will bring a physicist’s perspective on the cosmos, and on humans’ place within it, to a wider range of people. Along the way, it explains clearly and correctly what the Higgs field’s role in nature is, and how it plays that role, to the extent we understand it.

The book is non-technical yet sophisticated; though a layperson with no science background can read it, it’s not a lightweight read. I’ve made the universe as comprehensible as I know how, but I haven’t oversimplified it. Of course I had to leave a lot out; otherwise the book would have been 3500 pages instead of 350. But whatever is covered in the book is covered as carefully as space allows.

Precisely because I’ve had to leave out so many interesting side-topics and technical details, I’ll be providing lots of supplementary material on this website. Some of it will be brief surveys of topics that couldn’t fit in the book; some of it will allow me to discuss subtle points that would have distracted from the flow of the book; and some of it will present some of the underlying math that didn’t belong in a non-technical book, but which I know will interest certain readers of this website. I’ll be writing much of that material in coming months, and as I finish parts of it, I’ll be posting them here. Your comments will be both welcome and essential in making sure that it is comprehensible and comprehensive.

There’s much more to come, so stay tuned.

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