Category Archives: LHC News

A Big Think Made of Straw: Bad Arguments Against Future Colliders

Here’s a tip.  If you read an argument either for or against a successor to the Large Hadron Collider (LHC) in which the words “string theory” or “string theorists” form a central part of the argument, then you can conclude that the author (a) doesn’t understand the science of particle physics, and (b) has an absurd caricature in mind concerning the community of high energy physicists.  String theory and string theorists have nothing to do with whether such a collider should or should not be built.

Such an article has appeared on Big Think. It’s written by a certain Thomas Hartsfield.  My impression, from his writing and from what I can find online, is that most of what he knows about particle physics comes from reading people like Ethan Siegel and Sabine Hossenfelder. I think Dr. Hartsfield would have done better to leave the argument to them. 

An Army Made of Straw

Dr. Hartsfield’s article sets up one straw person after another. 

  • The “100 billion” cost is just the first.  (No one is going to propose, much less build, a machine that costs 100 billion in today’s dollars.)  
  • It refers to “string theorists” as though they form the core of high-energy theoretical physics; you’d think that everyone who does theoretical particle physics is a slavish, mindless believer in the string theory god and its demigod assistant, supersymmetry.  (Many theoretical particle physicists don’t work on either one, and very few ever do string theory. Among those who do some supersymmetry research, it’s often just one in a wide variety of topics that they study. Supersymmetry zealots do exist, but they aren’t as central to the field as some would like you to believe.)
  • It makes loud but tired claims, such as “A giant particle collider cannot truly test supersymmetry, which can evolve to fit nearly anything.”  (Is this supposed to be shocking? It’s obvious to any expert. The same is true of dark matter, the origin of neutrino masses, and a whole host of other topics. Its not unusual for an idea to come with a parameter which can be made extremely small. Such an idea can be discovered, or made obsolete by other discoveries, but excluding it may take centuries. In fact this is pretty typical; so deal with it!)
  • “$100 billion could fund (quite literally) 100,000 smaller physics experiments.”  (Aside from the fact that this plays sleight-of-hand, mixing future dollars with present dollars, the argument is crude. When the Superconducting Supercollider was cancelled, did the money that was saved flow into thousands of physics experiments, or other scientific experiments?  No.  Congress sent it all over the place.)  
  • And then it concludes with my favorite, a true laugher: “The only good argument for the [machine] might be employment for smart people. And for string theorists.”  (Honestly, employment for string theorists!?!  What bu… rubbish. It might have been a good idea to do some research into how funding actually works in the field, before saying something so patently silly.)

Meanwhile, the article never once mentions the particle physics experimentalists and accelerator physicists.  Remember them?  The ones who actually build and run these machines, and actually discover things?  The ones without whom the whole enterprise is all just math?

Although they mostly don’t appear in the article, there are strong arguments both for and against building such a machine; see below.  Keep in mind, though, that any decision is still years off, and we may have quite a different perspective by the time we get to that point, depending on whether discoveries are made at the LHC or at other experimental facilities.  No one actually needs to be making this decision at the moment, so I’m not sure why Dr. Hartsfield feels it’s so crucial to take an indefensible position now.

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Long Live LLPs!

Particle physics news today...

I’ve been spending my mornings this week at the 11th Long-Lived Particle Workshop, a Zoom-based gathering of experts on the subject.  A “long-lived particle” (LLP), in this context, is either

  • a detectable particle that might exist forever, or
  • a particle that, after traveling a macroscopic, measurable distance — something between 0.1 millimeters and 100 meters — decays to detectable particles

Many Standard Model particles are in these classes (e.g. electrons and protons in the first category, charged pions and bottom quarks in the second).

Typical distances traveled by some of the elementary particles and some of the hadrons in the Standard Model; any above 10-4 on the vertical axis count as long-lived particles. Credit: Prof. Brian Shuve

But the focus of the workshop, naturally, is on looking for new ones… especially ones that can be created at current and future particle accelerators like the Large Hadron Collider (LHC).

Back in the late 1990s, when many theorists were thinking about these issues carefully, the designs of the LHC’s detectors — specifically ATLAS, CMS and LHCb — were already mostly set. These detectors can certainly observe LLPs, but many design choices in both hardware and software initially made searching for signs of LLPs very challenging. In particular, the trigger systems and the techniques used to interpret and store the data were significant obstructions, and those of us interested in the subject had to constantly deal with awkward work-arounds. (Here’s an example of one of the challenges... an older article, so it leaves out many recent developments, but the ideas are still relevant.)

Additionally, this type of physics was widely seen as exotic and unmotivated at the beginning of the LHC run, so only a small handful of specialists focused on these phenomena in the first few years (2010-2014ish).  As a result, searches for LLPs were woefully limited at first, and the possibility of missing a new phenomenon remained high.

More recently, though, this has changed. Perhaps this is because of an increased appreciation that LLPs are a common prediction in theories of dark matter (as well as other contexts).  The number of new searches, new techniques, and entirely new proposed experiments has ballooned, as has the number of people participating. Many of the LLP-related problems with the LHC detectors have been solved or mitigated. This makes this year’s workshop, in my opinion, the most exciting one so far.  All sorts of possibilities that aficionados could only dream of fifteen years ago are becoming a reality. I’ll try to find time to explore just a few of them in future posts.

  But before we get to that, there’s an interesting excess in one of the latest measurements… more on that next time.

Just a few of the unusual signatures that can arise from long-lived particles; (Credit: Prof. Heather Russell)

Third step in the Triplet Model is up.

Advanced particle physics today:

Today I’m continuing the reader-requested explanation of the “triplet model,”  (a classic and simple variation on the Standard Model of particle physics, in which the W boson mass can be raised slightly relative to Standard Model predictions without affecting other current experiments.) The math required is pre-university level, just algebra this time.

The third webpage, showing how to combine knowledge from the first page and second page of the series into a more complete cartoon of the triplet model, is ready. It illustrates, in rough form, how a small modification of the Higgs mechanism of the Standard Model can shift a “W” particle’s mass upward.

Future pages will seek to explain why the triplet model resembles this cartoon closely, and also to explore the implications for the Higgs boson. 

Please send your comments and suggestions!

Triplet Model: Second Webpage Complete

Advanced particle physics today:

I’m continuing the reader-requested explanation of the “triplet model,” a classic and simple variation on the Standard Model of particle physics, in which the W boson mass can be raised slightly relative to Standard Model predictions without affecting other current experiments.

The math required is pre-university level, mostly algebra and graphing.

The second webpage, describing what particles are in field theory, and how the particles of one field can obtain mass from a second field, is ready now. In other words, the so-called “Higgs mechanism” for mass generation is sketched on the new page.

Meanwhile the first page (describing what the vacuum of a field theory is and how to find it in simple examples) is here. 

Please send your comments and suggestions, as I will continue to revise the pages in order to improve their clarity.

The W Boson Isn’t Behaving

The mass of the W boson, one of the fundamental particles within the Standard Model of particle physics, is apparently not what the Higgs boson, top quark, and the rest of the Standard Model say it should be.  Such is the claim from the CDF experiment, from the long-ago-closed but not forgotten Tevatron.  Analysis of their old data, carried out with extreme care, and including both more data and improved techniques, calibrations, and modeling, has led to the conclusion that the W boson mass is off by 1/10 of one percent (by about 80 MeV/c2 out of about 80,400 MeV/c2).  That may not sound like much, but it’s seven times larger than what is believed to be the accuracy of the theoretical calculation.

  • New CDF Result: 80,443.5 ± 9.4 MeV/c2
  • SM Calculation: 80,357± 4 [inputs]± 4[theory] MeV/c2
The new measurement of the W mass and its uncertainty (bottom point) versus previous ones, and the current Standard Model prediction (grey band.)

What could cause this discrepancy of 7 standard deviations (7 “sigma”), far above the criteria for a discovery?  Unfortunately we must always consider the possibility of an error.  But let’s set that aside for today.  (And we should expect the experiments at the Large Hadron Collider to weigh in over time with their own better measurements, not quite as good as this one but still good enough to test its plausibility.) 

A shift in the W boson mass could occur through a wide variety of possible effects.  If you add new fields (and their particles) to the Standard Model, the interactions between the Standard Model particles and the new fields will induce small indirect effects, including tiny shifts in the various masses.  That, in turn, will cause the relation between the W boson mass, top quark mass, and Higgs boson mass to come into conflict with what the Standard Model predicts. So there are lots of possibilities. Many of these possible new particles would have been seen already at the Large Hadron Collider, or affected other experiments, and so are ruled out. But this is clearly not true in all cases, especially if one is conservative in interpreting the new result. Theorists will be busy even now trying to figure out which possibilities are still allowed.

It will be quite some time before the experimental and theoretical dust settles.  The implications are not yet obvious and they depend on the degree to which we trust the details.  Even if this discrepancy is real, it still might be quite a bit smaller than CDF’s result implies, due to statistical flukes or small errors.  [After all, if someone tells you they find a 7 sigma deviation from expectation, that would be statistically compatible with the truth being only a 4 or 5 sigma deviation.] I expect many papers over the coming days and weeks trying to make sense of not only this deviation but one or more of the other ones that are hanging about (such as this one.)

Clearly this will require follow-up posts.

Note added: To give you a sense of just how difficult this measurement is, please see this discussion by someone who knows much more about the nitty-gritty than a theorist like me ever could.

A Prediction from String Theory

(An advanced particle physics topic today…)

There have been various intellectual wars over string theory since before I was a graduate student. (Many people in my generation got caught in the crossfire.) But I’ve always taken the point of view that string theory is first and foremost a tool for understanding the universe, and it should be applied just like any other tool: as best as one can, to the widest variety of situations in which it is applicable. 

And it is a powerful tool, one that most certainly makes experimental predictions… even ones for the Large Hadron Collider (LHC).

These predictions have nothing to do with whether string theory will someday turn out to be the “theory of everything.” (That’s a grandiose term that means something far less grand, namely a “complete set of equations that captures the behavior of spacetime and all its types of particles and fields,” or something like that; it’s certainly not a theory of biology or economics, or even of semiconductors or proteins.)  Such a theory would, presumably, resolve the conceptual divide between quantum physics and general relativity, Einstein’s theory of gravity, and explain a number of other features of the world. But to focus only on this possible application of string theory is to take an unjustifiably narrow view of its value and role.

The issue for today involves the behavior of particles in an unfamiliar context, one which might someday show up (or may already have shown up and been missed) at the LHC or elsewhere. It’s a context that, until 1998 or so, no one had ever thought to ask about, and even if someone had, they’d have been stymied because traditional methods are useless. But then string theory drew our attention to this regime, and showed us that it has unusual features. There are entirely unexpected phenomena that occur there, ones that we can look for in experiments.

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The Earth’s Shape and Size? You Can Measure it Yourself — Part 3

In the first post in this series, I showed, using pressure spikes in barometers from around the world, that the pressure wave from the volcano that exploded in the Kingdom of Tonga earlier this month circled the Earth about once every 36 hours (accurate to within 5% or so, which is about two hours). It required only grade school arithmetic to do it, too! That the round-trip time is the same in many different directions provides evidence that the Earth is a sphere, obtained without the need for photographs, expensive travel or even geography!

But as I showed in my second post, it’s too quick to view it as proof of a spherical Earth. There’s a loophole.

What the direction-independence of the pressure wave’s round-trip time proves is that the Earth has some amount of symmetry: if you are standing at the volcano, then no matter in which direction you look, the Earth has the same shape (to within 5% or so). But there are many shapes that have this symmetry, not just a sphere. For instance, an ellipsoid, a gourd, a flat disk or an inverted bowl would all have this symmetry, as long as the Tonga volcano were centrally located: at one end of the ellipsoid or gourd, or in the center of the flat disk or bowl. Even though it’s unlikely that the Tonga volcano would be at such a very special point on a non-spherical Earth, we can’t prove that it’s not the case without more information.

If the Tonga Volcano were located at the end of an ellipsoid, or at the center of a disk or bowl with reflective edges, it would have created pressure spikes with the same pattern as if it were on a sphere. (Image created with Mathematica 11.3.)

As I pointed out, though, the pressure wave from a second volcanic blast of a similar nature, arising from another point on the Earth, wouldn’t show the same independence of direction unless either

  • the Earth’s a sphere, or
  • the Earth’s not a sphere, but the second volcano is located at the exact opposite side of the Earth from the Tonga volcano.

The second possibility is extremely unlikely, especially as the relevant location, southern Algeria, has no volcanoes! So if the round-trip times for a second natural explosion are the same in all directions, that proves the Earth’s a sphere.

Such powerful and dangerous eruptions are rare, fortunately, and so it might seem that we will have to wait a long time to close this loophole. But in fact, we can look to the past, where the famous 1883 explosion of Krakatoa, between the islands of Sumatra and Java in Indonesia, fits the bill. The same types of pressure spikes were observed then as we have observed this month. The only challenge is to find that century-old data.

Pressure spikes, similar to those seen around the world in mid-January, observed in late August 1883 from the Krakatoa blast.

It actually isn’t much of a challenge. The Royal Society, an organization based in London with an outsized role in the history of modern science, spent the years following the blast collecting all the data that we might ever want. And as I realized on Monday night, the full Royal Society report from 1888 is available online, via Google Books and perhaps other sources. It took me five minutes to find the pressure data, and thirty seconds to find the tables that I needed to close the loophole and prove, once and for all, that the Earth’s a nice round ball.

That’s worth thinking about. The Royal Society’s experts had to collect all this data by sending letters to keepers of weather records, located in remote places all around the world. Not only did they need all the details of atmospheric pressure over time following the Krakatoa eruption, they also had to be very careful that they interpreted the timing correctly. In those days, time zones were very new, and weren’t universally adopted, so it would have been very easy to mistake the meaning of any local time marked on the pressure charts. It must have been hard work, prone to errors. On top of this, they couldn’t know exactly when the biggest explosion happened — there were no satellites there to see it, and of the few eyewitnesses, none apparently had a precise clock — so they had to infer the timing of the blast from the pressure data itself.

Meanwhile, while some experts were studying the pressure spikes, other experts were collecting other information about the eruption: the tsunamis, the eruptive history, the materials ejected by the volcano, the optical and electromagnetic effects and the eyewitness reports. By the time everything was collated and ready for public distribution, it was 1888 — over four years later. Copies of the Royal Society report were buried in large public and university libraries, but this 600 page document wasn’t necessarily something you could find at your small town bookstore. Even a few decades ago, it wasn’t the easiest information to obtain quickly.

But that has changed in the era of the internet and of projects such as Google Books. Indeed, what took the Royal Society four years for Krakatoa now takes almost no time at all. For the Tonga volcano, pressure data from many places, including weather stations owned by ordinary people, was reported almost in real time via social media and various websites. That made it easy to show the Earth is probably a sphere within a few days, almost as soon as the data came in. Closing the last loopholes, to really prove the Earth’s a sphere, simply required a short visit to the Great Library in the Cloud. All this can be done by pretty much anyone, including internet-enabled schoolchildren with a science teacher who provides guidance as to what to do and why.

The Krakatoa Report’s Data and the Round Trip Time

So let’s open the pages of the Royal Society report, and see what it contains.

In my first post in this series (and also in the post before that) I pointed out that if you have the pressure data from a certain city and can see the spikes that were generated by the volcano’s pressure wave, then it is simple arithmetic to determine the round-trip travel time T of that bit of pressure wave that traveled from the volcano to that city. If the Earth’s really (approximately) a sphere and the pressure wave moves at an (approximately) constant speed, then the pressure wave will travel uniformly around the Earth, and every location in the world will find the same time T, no matter how far or in what direction relative to the volcano.

More specifically, I pointed out that if you observed, say, four pressure spikes that occurred after the blast by times T1, T2, T3, T4, then there are three ways to measure T. (If you only saw three spikes, then you get two measurements; if only two, as is the most common, then you still get one shot at T.)

  • T3 – T1 = T
  • T4 – T2 = T
  • T1 + T2 = T

The first two relations are easy to understand: T1 is the first pass of the outbound pressure wave, and T3 is the second pass of the outbound wave (while T2 and T4 are the first and second pass of the inbound wave), so the time between T3 and T1 is just the round-trip time T, and the same is true for T4 and T2. The last one is trickier, and I point you to the relevant section of the first post in this series.

For the Tonga volcano explosion, I collected data from nine locations around the world and ended up with about twenty measurements of T, all of which fell between 34 3/4 and 36 3/4 hours. It’s not surprising that there’s some variation. First, it can be hard to say exactly when a pressure spike happened; often each spike is really multiple spikes very close together (for instance, see the second figure here) as the wave goes by, so should you choose the largest spike, or the leading spike, for the timing? The difference can be as big as an hour. The data can also be clouded (heh) by local weather, which can move the pressure around for other reasons, and make the start of the spiking hard to identify. Second, the wave’s speed was surely not exactly constant; it probably varied by a few percent due to temperature variations and other effects that I don’t personally understand. Third, we know the Earth’s not a perfect sphere; it’s slightly squashed at the poles, by about 2 percent — though two percent of 36 hours is about twenty minutes, so that’s relatively small effect. So the fact that the answers are all consistent within a two hour range is actually pretty solid evidence that the Earth’s symmetrical in all directions around Tonga, and probably a sphere.

What about Krakatoa? The Royal Society managed to obtain over forty measurements of pressure readings, most of them with multiple spikes and some with as many as seven. These are arranged in two tables, one showing the odd-numbered spikes (the outgoing pressure wave) and one showing the even-numbered spikes (the returning pressure wave). Careful: the times in their raw data are shown relative to midnight Greenwich Mean Time, not to the Krakatoa blast, which occurred very close to 3:00 Greenwich Mean Time (best estimate being 2:56), so you need to subtract about three hours to obtain T1, T2, etc. That will be important at the end of this section.

Then the authors of this section of the report calculated T3 – T1 (and T5 – T3, etc., which measure later round-trip times) and put that in a table, shown below. (I’ve crossed out a few entries, because the Royal Society questioned the data quality for those cases.) And what did they find for T, the round-trip time for the Krakatoa pressure wave? In location after location, they found something close to 35 – 36 hours — a little more here, a little less there, but essentially the same as what one finds for the Tonga volcano pressure wave.

In the green-boxed columns are the round trip times (for the first, second, and third trips where available) for the outbound pressure wave, as measured in many locations around the world. Note that they show hours with two decimal places, not hours and minutes. I crossed out entries where the Royal Society judged the measurement data (listed elsewhere in the report) to be problematic.

Next the authors calculated T4 – T2 (and T6 – T4, when available) and put that in a table also. Of course they find something close to 35 – 36 hours again, though sometimes a bit less.

Same as the previous figure, but now for the inbound (returning) pressure wave.

The authors then used the data to figure out the timing of the big explosion; if you’re curious how they did that, also just using arithmetic, see this post. We’ll just accept their timing, and with the risk of a small amount of logical circularity, we can calculate T1 + T2, which the Royal Society didn’t do. Let’s look at an example of how this is done from the report’s timing tables.

A small fraction of the timing data tables of the report, showing the times of wave passages relative to midnight Greenwich Mean Time (GMT, or UTC nowadays); the volcano exploded around 2:56 GMT

The Melbourne weather observatory saw the first spike at 8:14 GMT, but since the volcano exploded around 2:56 GMT, we should subtract 2:56 from this number to get T1 = 5:18 . The second spike (the first column of the second table) was at 34:25, and so T2 = 34:25 – 2:56 = 31:29. Adding these two numbers together gives T1 + T2 = 36:47 = 36.78 hours. Repeating this for all the locations with two reliable spikes, we again find 35 – 36 hours, plus or minus an hour or so.

The round-trip times that I obtained by adding the Royal Society’s recorded times for the first and second pressure spikes; locations with data marked as questionable in the report are not shown here, but give similar answers.

Implications

In these results, there is some amount of variation, especially in data from North America. The Royal Society authors noticed this, of course, and spent quite a few pages of their report trying to understand it. Apparently the pressure wave moved a little faster in some directions than others, though with variation no more than 10%. Why did this happen? (And why, so far, have we seen no sign of such a large variation in this month’s pressure wave?) I’m certainly not expert enough to say. In fact, I have the impression that atmospheric scientists have been debating the implications of this variation ever since, at least as recently as 2010.

In fact one of the possible advantages of using T1 + T2 to calculate T, aside from the fact that many sites measured two pressure spikes but not as many measured three or more, is that these variations may have tended to cancel out. (For instance, if a northward-moving part of the wave moved faster than average and the southward-moving part moved slower by an equal amount, that would shift T3 – T1 and T4 – T2 but not T1 + T2.) You can see there’s somewhat greater uniformity in my numbers than in the round-trips as calculated in the Royal Society’s tables; but still, round trip times as measured in North America are longer by a few percent.

Nevertheless, for our current purposes, the differences are small. To within 10%, both Tonga and Krakatoa pressure waves indicate that they are at symmetric points on the Earth — and since they’re not on opposite ends of the Earth, this proves the Earth’s a sphere, to 10% or better. Flat Earths are flat out, as are bowl Earths, gourd Earths and highly elliptical Earths.

Moreover, because the round trip times are essentially the same for both eruptions, the Earth apparently hasn’t grown or shrunk, nor have the speeds of pressure waves significantly changed, during the past 140 years. In all that time, only the speed of information has changed, which is why I can write this post within two weeks of the explosion, before the ash has even settled on the ground.

Looking Ahead

We now know, without any loopholes, the shape of the Earth; but what of its size? Since we know the round-trip time T, all we need to determine the Earth’s circumference C is the speed v with which the pressure waves were traveling:

  • C = v T.

We could guess the waves were traveling at sound speed, but apparently that’s really not the right way to think about these huge waves; and in any case sound speed varies with pressure and thus with altitude, and so it’s not at all clear which value for sound speed we would want to use. It would be better to actually measure v directly from the pressure data. We can do this, without assuming the Earth’s a sphere, by looking at how quickly the pressure wave crossed small parts of the world. For the recent explosion, that data is available too, and we’ll use it next time to find v.

(to be continued)

As reproduced in the Royal Society report, one of six drawings of the sunset just west of London on November 26th, 1883, three months after Krakatoa’s eruption. Created by Mr. W. Ascroft.

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The Earth’s Shape and Size? You Can Measure it Yourself — Part 2

In my last post, I showed, using only simple arithmetic, that the observed atmospheric effects from the January 15th volcanic explosion in the Kingdom on Tonga are consistent with a round Earth. From the timing of the observed spikes in pressure, seen around the world, one can work out how long the pressure wave took to do a round-trip of our planet. It’s clear that the pressure wave from the eruption moved outward and circled the Earth, moving in all directions over the same amount of time (35-36 hours, to within 5% or so). This uniformity is what we would expect if the Earth’s approximately a sphere and the pressure wave had a roughly constant speed.

But at the end of the post I pointed out that this isn’t yet a proof that the Earth’s spherical; there are loopholes, involving possibilities such as an ellipsoidal Earth with the Tonga eruption at one end. And there’s even a flat version of Earth that we can’t rule out with this data!

So in this post, we’ll look at why most shapes for the Earth are ruled out, see why there’s a loophole — why a small number of non-spherical shapes are still consistent with the data — and look at how we might close that loophole.

A Square Earth

Flat Earth’s aren’t plausible, but they are easy to draw and visualize, so I’m going to start by showing why most (but not quite all) flat Earth’s are inconsistent with the data I used in the last post. Once you see the origins of the inconsistencies, the same principles will apply to other shapes that would be much harder to visualize if you didn’t already know what to look for.

Let’s start with a square Earth (yes, square, not a cube — though a cube would have similar problems). This Earth has edges, and we have to figure out what happens to the pressure wave when it gets there. Leaving aside the obvious difficulty that we have no idea how a square planet would hold on to its atmosphere at the edges, there are three easy options for what happens to the pressure wave at the edge:

  • It disappears.
  • It bounces back (i.e., it reflects).
  • It somehow goes round to the back side, crosses it, and reappears.

Disappearance is ruled out immediately, because then the pressure wave would pass each point on Earth once, whereas the data shows it appears multiple times. So let’s focus on the second possibility, the reflecting square. The problems we’ll find here will also affect the third possibility.

There’s another question we have to answer: where is the volcano inside this square? Well, let’s start with the simplest case, where the volcano is dead center. After we see what’s wrong with that, it will be easy to see that an off-center volcano is even worse.

On a square with reflections, the pressure wave expands and then bounces back from the walls, rather than going all the way around as on a sphere. In other words, a round trip from the volcano to a chosen location and back to the volcano involves some reflections instead of a continuous trip. That’s okay in principle, but what’s not okay can be seen in the Figure below. Trips north-south and east-west have the same length, but trips northeast-southwest and northwest-southeast are longer by a square root of 2, about 40% longer. We would certainly have seen this in the pressure spike data; if north-south trips took 36 hours, then northeast-southwest trips would have taken almost 51 hours.

(Left) On a square Earth with reflective edges and a central volcano, round trip times are different for diagonal paths than for horizontal or vertical paths. (Right) In fact round trips can be extremely long at certain angles.

And actually it’s worse than this, because the reflections would make a total mess of the pressure wave. You can get a little intuition for this by tracing the path of the bit of wave that moves west-southwest. It bounces around several times before returning to the volcano!

More generally, what is happening is that the wave is becoming very complex as it reflects multiple times. In the animation below I’ve shown what would happen to a pressure wave on a square. There’s no way we would have seen a simple pattern of spikes in the data around the world had it been square.

On a square Earth with a reflective edge, a circular blast from a centrally located volcano would lead to a very complicated pattern of pressure spikes that do not correspond to what is observed.

Is there any way out of this argument? So far I’ve assumed that the wave travels at a constant speed as it moves away from the volcano. What if it didn’t? What if, instead of forming a circle, it formed a square, which could move out uniformly and bounce back uniformly from the edges, so that all round trips were of the same duration? This would require that the wave’s speed heading toward the corners of the square is 40% faster than it’s speed heading north, south, east and west. That’s a clever idea, and so far, what I’ve told you doesn’t exclude it. But in a later post we’ll use pressure spike data to measure the wave’s speed in various directions, and we won’t see such large variation; so we will rule this out soon enough.

The spike patterns would be at least as complicated, and generally worse, if

  1. the volcano were not dead center on the reflecting square (making the pattern of reflections even more complex — see the figure below);
  2. the pressure wave went round the back of the square Earth;
  3. the square was instead a rectangle with sides of different length; or
  4. the square was instead a triangle, hexagon, parallelogram, a five-pointed star, a crescent, or some irregular shape;

In short, a flat Earth is completely excluded — ruled out by the data — except for one very special shape.

On a square Earth with a reflective edge, a circular blast from a non-centrally located volcano would lead to an even more complicated pattern of pressure spikes.

The Flat Disk Earth

Imagine the Earth’s a flat disk, and put the volcano at the exact center. Then, you can get exactly the same pressure spike data as we actually observe. Let’s see why.

If a pressure wave moves off at a constant speed from an explosion at the center of a disk, it will form a ring that moves outward, reflects off the walls, and comes right back to the volcano. And it will do this over and over again. In all directions from the volcano, the out-and-back trips all take the same amount of time; and at each location on Earth, the pressure wave will pass twice during this out-and-back trip. You can go further and check that the equations I used to determine the round-trip time on a spherical Earth will work for a disk Earth too, where T is now the out-and-back time. The spike pattern from a volcano centered on a disk looks identical to that of a volcano on a sphere.

On a disk-shaped Earth with a reflective edge, a blast from a central volcano would reproduce the pressure spikes observed following this month’s explosion.

This is only if the volcano is dead center, however. For example, in the figure below, the trip to the right is longer than the trip to the left; and yet again, because the volcano’s not in the center, the reflections off the edges will quickly make the wave extremely complex and lead to a highly irregular pattern of spikes around the world. So an off-center volcano is ruled out. (The situation is no better if the waves, rather than reflecting off the edges, somehow go round the back.)

A disk Earth with a volcanic blast away from the center will not have equal round-trip times; the full pattern is very complex, but just the two paths shown are enough to give different round-trip times, not seen in the actual pressure spike data.

So the only way to interpret our data, if the Earth is flat, is to conclude that Tonga sits in the very middle of a flat disk. But this is quite a loophole! How can we prove the Earth is not flat?


The Flat-Earthers’ Flat Earth

By the way, what I’ve just told you means that the pressure spike data rules out the flat-disk Earth most popular with flat Earthers. That silly model of Earth puts the north pole at the center and stretches the south pole out into a circle tens of thousands of miles around, with the idea that no one ever actually flies over the south pole to check it out.

The flat earth with north pole at center, popular with a certain set, with a red dot showing the far-off-center location of the Tonga volcano. Pressure waves from that location could not have created the observed pressure spikes.

Well, let’s leave aside the fact that many scientists, including personal friends of mine, have experiments (Ice Cube, BICEP, South Pole Telescope, and many more…) running within a mile or so of the south pole, and they (and the pilots who fly them there) can confirm it is a point, not an arc tens of thousands of miles wide. But we now have an argument that’s not hearsay: given where the Tonga volcano is located on this flat-disk Earth, an explosion there would never have been able to generate the observed regular and simple pattern of pressure spikes. A 12-year-old can prove the flat-earthers’ model of Earth is definitively ruled out.

And these considerations also show us why a flat Earth that puts Tonga dead center is ruled out too, though not from the pressure spike data. Just as the flat-earther’s model of Earth, with the north pole at the center, spreads the south pole into an arc tens of thousands of miles long, one with Tonga at the center would spread southern Algeria, the region exactly opposite, into an arc tens of thousands of miles long. But even though that’s in the desert, people live there. There are a few roads and a few towns. Residents there would certainly know if driving to the nearest town took many weeks instead of a few hours.

A flat Earth centered on region of Tonga would spread southern Algeria across tens of thousands of miles; residents of that country would beg to differ.

So that one remaining flat Earth is dead too. Good-bye, and good riddance.

But I went through this argument carefully for a reason. Once we understand why a Tonga-centered flat disk Earth is consistent with the pressure spike data, we can understand all the other loopholes, such as ellipsoidal Earths — and we’ll also see how to rule them out too.

A Symmetry

Why was it that every flat Earth gave the wrong pattern for the spike timing except for the flat disk with the volcano at dead center? What was special about that case?

The study in my last post showed that any bit of the pressure wave, as it started at and headed out from the volcano, took the same amount of time to travel outward and back to its starting point. In other words, as far as the pressure wave was concerned, all directions leading away from Tonga are equivalent to one another. East, north, northwest, south-southwest — it doesn’t matter, the length of the round-trip path was always the same.

A fancier way to say that is that there is a symmetry, a rotational symmetry in particular. If you were to put a spike straight through the Earth starting right at the volcano and going through the Earth’s center, and then you rotated the Earth around the spike, the Earth’s shape would stay the same as you did so. If that weren’t true, then not all directions would look the same, and not all round-trip times would be equal.

So what my analysis of the data actually shows is not that the Earth’s a sphere, but only that it is symmetrical around the Tonga volcano — all directions are equivalent. That’s true of a sphere. But it’s also true of a flat disk with the volcano at its center — or of a bowl. And it’s also true of an ellipsoid with the volcano at one end, or of a gourd shape, or of half a sphere.

So how are we going to check that the right shape for the Earth is truly a sphere?

A pressure wave starting from any point on a sphere, or from a point at either end of an ellipsoid, or from the center of a disk or hemisphere (with reflecting edges), will give a similar pattern to the one observed after the Tonga volcanic explosion. Note this is not true at any other point on the non-spherical surfaces. (Image made with Mathematica 12.)

Special Points vs. Typical Points

The symmetry that I just described requires that either

  • the Tonga volcano is at a very special point on a non-spherical shape, or
  • the Tonga volcano is at a typical point on a sphere.

We already saw this for the flat disk; we could only reproduce the data if the volcano were at the center, and not if it were off-center (as in the flat-earthers’ flat Earth.) And while it’s true for an ellipsoid with a circular cross-section if the volcano is exactly at one end, it wouldn’t be true if the volcano were anywhere else.

That makes all the non-spherical shapes somewhat implausible, because they require that the Tonga volcano be located at a unique, special place — one of at most two on Earth. And what are the chances that the first big volcanic blast of the internet era would occur at such a special location? There are so many other volcanoes — Vesuvius, Mount Rainier, Mount Erebus, Cotopaxi, Taal, Merapi, and hundreds more — any volcano that isn’t on exactly the opposite side of the Earth from the Tonga volcano would have given asymmetric data, with round trip times that vary widely. Only on a sphere is the Tonga volcano at a typical point, with nothing unusual about it.

So a sphere seems much more plausible. But, hey, that’s just a plausibility argument, and coincidences do happen sometimes. If you want to prove the Earth’s a sphere, this argument is not enough.

Fortunately, it’s now clear where proof would come from. We just need to wait for another similarly-sized eruption, from some other volcano, to create another pressure wave that goes round the Earth. Even if the Tonga volcano were somehow located at a special point on Earth, the next big volcanic blast will almost certainly originate from a typical point. It’s very unlikely that it will lie exactly on the opposite side of the Earth from Tonga. If, after this second blast, we do the same measurement of round-trip times using its pressure spikes, and we again find they all show equal round-trip distances in all directions, then we’ll know the Earth is symmetric around that volcano too. And that’s enough, because only a sphere can be rotationally symmetric around two points (unless those two points are exactly at the opposite ends of an ellipsoid or similar shape.)

The only thing that’s too bad (although it’s also quite fortunate) is that explosions this size don’t happen often. We may not be able to close this loophole for quite a few decades to come…

…unless, rather than looking to the future, we look to the past…?

There is, after all, Krakatoa.

(to be continued)