MATT STRASSLER
Of Particular Significance

Category: Particle Physics

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.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON April 7, 2022

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Why Didn’t Copernicus Figure Out Kepler’s Third Law Decades Earlier?

Kepler’s third law is so simple to state that (as shown last time) it is something that any grade school kid, armed with Copernicus’s data and a calculator, can verify. Yet it was 75 years from Copernicus’s publication til Kepler discovered this formula! Why did it take Kepler until 1618, nearly 50 years of age, to recognize such a simple relationship? Were people just dumber than high-school students back then?

Here’s a clue. We take all sorts of math for granted that didn’t exist four hundred years ago, and calculations which take an instant now could easily take an hour or even all day. (Imagine computing the cube root of 4972.64 to part-per-million accuracy by hand.) In particular, one thing that did not exist in Copernicus’ time, and not even through much of Kepler’s, was the modern notion of a logarithm.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON April 7, 2022

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Breakthrough! Do-it-Yourself Astronomy Pays Off: A Law of Nature (and a Bonus)

In recent posts (here and here), I showed you methods that anyone can use for estimating the planets’ distances from the Sun; it just takes high-school trigonometry. And even more recently I showed how, using just algebra, you can easily obtain the planets’ orbital periods from their cycles as we see them from Earth, starting with one solar conjunction and ending at the next.

Much of this work was done by Nicolai Copernicus himself, the most famous of those philosophers who argued for a Sun-centered universe rather than an Earth-centered universe during the millennia before modern science. He had all the ingredients we have, minus knowledge of Uranus and Neptune, and minus the clues we obtain from telescopes, which would have confirmed he was correct.

Copernicus knew, therefore, that although the planetary distances from the Sun and their cycles in the sky (which astrologers [not astronomers] have focused on for centuries) don’t seem to be related, the distances and their orbital times around the Sun are much more closely related. That’s what we saw in the last post.

Let me put these distances and times, relative to the Earth-Sun distance and the Earth year, onto a two-dimensional plot. [Here the labels are for Mercury (Me), Venus (V), Mars (Ma), Jupiter (J), Saturn (S), Uranus (U) and Neptune (N).] The first figure shows the planets out to Saturn (the ones known to Copernicus).

Figure 1: The planets’ distances from the Sun (in units of the Earth-Sun distance) versus the time it takes them to complete an orbit (in Earth-years). Shown are the planets known since antiquity: Mercury (Me), Venus (V), Mars (M), Jupiter (J) and Saturn (S).

The second shows them out to Neptune, though it bunches up the inner planets to the point that you can’t really see them well.

Figure 2: Same as Figure 1, but now showing Uranus (U) and Neptune (N) as well.

You can see the planets all lie along a curve that steadily bends down and to the right.

Copernicus knew all of the numbers that go into Figure 1, with pretty moderate precision. But there’s something he didn’t recognize, which becomes obvious if we use the right trick. In the last post, we sometimes used a logarithmic axis to look at the distances and the times. Now let’s replot Figure 2 using a logarithmic axis for both the distances and the times.

Figure 3: Same as Figure 2, but now with both axes in logarithmic form.

Oh wow. (I’m sure that’s the equivalent of what Kepler said in 1618, when he first painstakingly calculated the equivalent of this plot.)

It looks like a straight line. Is it as straight as it looks?

Figure 4: Same as Figure 3, but with a blue line added to show how well a straight line describes the distance/time relationship of the planets, and with a grid added that passes through 1, 10, 100, 1000 Earth-years and distances equal to 1, 10, 100 Earth-Sun distances.

And now we see three truly remarkable things about this graph:

  • First, the planet’s distances to the Sun and orbital times lie on a very straight line on a logarithmic plot.
  • Second, the slope of the line is 2/3 (2 grid steps up for every 3 steps right) rather than, say, 7.248193 .
  • Third, the line goes right through the point (1,1), where the first horizontal and first vertical lines cross.

What do they mean?

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON April 5, 2022

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How You Can Determine Each Planet’s Year from its Distances and Cycles

Whether you’re a die-hard who insists on measuring the distances between the planets and the Sun yourself (which I’ve shown you how to do here and here), or you are willing to accept what other people tell you about them, it’s interesting to look at the pattern among these distances. They are shown at right, starting with the smallest — Mercury (Me) — and proceeding to Venus (V), Mars (Ma), Jupiter (J), Saturn (S), Uranus (U) and Neptune (N), nearly 100 times further out than Mercury. The inner planets up to Mars are very close together, all bunched within 1.5 times the Earth-Sun distance, whereas the outer planets are much further apart.

Figure 1: (Left) the planet-Sun distances relative to the Earth-Sun distance; (Right) the time between solar conjunctions, when the planet disappears (roughly) behind the Sun from Earth’s perspective; “>” indicates the planet moves into the morning sky (east) after conjunction, whereas “<” means it moves into the evening sky (west).

Also shown in the figure are the lengths of the planet’s cycles. Remember, a cycle starts when a planet reappears from behind the Sun and ends when a planet again disappears behind the Sun… the moment of “solar conjunction,” or just “conjunction” for short in this post. Some planets have short cycles, others have long ones. Interestingly, now it is the outer planets that all bunch up together, with their cycles just a bit longer than an Earth year, whereas Mercury, Venus and Mars have wildly different cycles ranging from a third of an Earth-year to two Earth-years. In the figure I’m also keeping track of something that I didn’t mention before. As their cycles begin, Mercury and Venus initially move into the evening sky, in the west, setting just after sunset. I’ve indicated that with a “<” Meanwhile Mars, Jupiter and Saturn move into the eastern morning sky, rising just before sunrise, as indicated with a “>”. (Mars, Jupiter and Saturn just reappeared from behind the Sun this winter; that’s why they’re all in the morning sky right now.) This difference is going to prove important in a moment.

Before going on, let me make another version of the same figure, easier to read. This involves making a “logarithmic plot”. Instead of showing the step from 1 to 2 as the same as the step from 0 to 1, as we usually do, we replot the information so that the step along the axis from 1 to 10 is the same as the step from 0.1 to 1. It’s gives exactly the same information as the Figure 1, but now the planet-Sun distances don’t bunch up as much.

Orbits Vs. Cycles

Figure 2: exactly the same as Figure 1, but with the vertical axis in “log-plot” form.

Now, the cycles from one solar conjunction to the next, long beloved of astrologers, are not beloved of astronomers, because they involve a combination of two physically unrelated motions. A solar conjunction happens when a planet disappears behind the Sun from Earth’s perspective, so the time between one conjunction and the next combines:

  • the orbital motion of the planet around the Sun;
  • the yearly rotation of the line between the Sun and the Earth. (So far, we haven’t found evidence as to whether the Sun moves around the Earth or the Earth moves around the Sun — and we’ll remain agnostic about that today.)

So what astronomers want to know is the orbital period of each planet — it’s own year. That is, how long does it takes each planet to orbit the Sun, from the planet’s perspective, or from the Sun’s perspective. This is the time that an observer on the Sun would see for the planet to complete a circle relative to the fixed stars, and vice versa. (Remember we gathered evidence that the stars are fixed, or extremely slowly drifting from the perspective of the Earth, using a gyroscope, whereas either or both the Sun or the Earth are rotating relative to one another by about one degree per day. We also know the stars are much further than the Sun from our two measurements of the Moon’s radius.)

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON March 31, 2022

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Alert — Aurora (Northern Lights) Possible Tonight

There was a big solar flare on Monday, which as often happens created a flash of X-rays (travel time to Earth 8.5 minutes), a blast of high speed protons and electrons (travel time minutes to hours), and a “Coronal Mass Ejection” (CME) of slower subatomic particles (travel time 1 to 3 days.) It’s the CME that is one of the main triggers for auroras borealis (north) and australis (south).

Update 23:00 Eastern Time (0300 UT): the CME has arrived in the past hour. There are northern lights going on, but so far they are still quite far north compared to predictions. This could change, but it will soon be too late for me to report on it, and it’s pretty cloudy here so I’m unlikely to stay up late hoping. Checking “northern lights” or “aurora” on Twitter is a good way to get real-time information, and there are some webcams on https://aurora.live/camera/ .

Aurora forecasts are not very reliable yet, because of a lack of data about the CMEs themselves and the ever-changing environment between the Sun and the Earth through which they are moving. So neither timing of arrival nor strength of impact can be predicted with great confidence. With that caveat, it seems likely that the flare will arrive late tonight or early in the morning in Europe, late afternoon to evening in the United States. Its effects could be as strong as any we’ve seen in a number of years; auroras may well be visible well into central Europe and the northern third of the United States, or even further south than that, on and off over a period of many hours. Fingers crossed.

We will have mostly cloudy skies here, so I probably won’t see this one. But I hope many of you are lucky enough to see a spectacle tonight!

Update: Also today, an even stronger flare occurred. If this one also created a CME that’s aimed toward Earth, we may have another round of strong auroras within a couple of days. See the data below showing X-rays detected from today’s flare, and from Monday’s earlier flare.

Measurements by two of our geostationary weather satellites of X-rays coming from the Sun; large peaks are caused by solar flares which produce X-rays in great abundance. The more X-rays, the stronger the flare.

Oh, and by the way, sometime soon I’ll show you how to use solar flares and CMEs to solve one of the hardest problems in do-it-yourself astronomy. If only the Greeks had known!

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON March 30, 2022

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How to Estimate the Distance to the Outer Planets Yourself

Now, the last step in mapping out the other planets, before heading for more intriguing territory.

In a previous post I showed you how you can measure the distance between Venus and the Sun, RVS, relative to the distance between Earth and the Sun, RES. Under the assumption that Venus’s orbit around the Sun is circular (or nearly so), you can use the fact that when the angle between Venus and the Sun reaches its maximum (the moment of greatest elongation, and also approximately the moment when Venus appears half lit by the Sun), there’s a simple right-angle triangle in play. High school trigonometry then gives you the answer: RVS/RES ≈ 0.72 ≈ 1/√2. The same trick works for Mercury, which, like Venus, is a near Sun-orbiting planet, closer to the Sun than Earth.

But there’s no maximum angle for Mars, Jupiter, or the other far planets. These planets are further out than Earth and can even appear overhead at midnight, when they are 180 degrees away from the Sun. Fortunately there’s another right triangle we can use, again under the assumption of a (almost-)circular orbit, and that can give us a decent estimate.

The Triangle for the Far Sun-Orbiting Planets

Let’s focus on Mars first, although the same technique will work on the outer planets. Mars has a cycle in which it disappears behind the Sun, from Earth’s perspective, on average every 780 days. (That start of the cycle is called “solar conjunction,” or just “conjunction” when the context is clear.) About half a cycle later, after on average 390 days, it is at “opposition”: closest to Earth, largest in a telescope, appearing overhead at midnight, and at its brightest. But if we wait only a quarter cycle, on average 195 days after conjunction, then the Mars-Sun line is at a 90 degree angle to the Earth-Sun line. That means that Mars, Earth and the Sun form a right-angle triangle with the right angle at the location of the Sun.

So on the day of first quarter we should measure the angle on the sky between Mars and the Sun. That’s the angle A on the figure below. Then the Mars-Sun distance RMS and the Earth-Sun distance RES are the two sides of a right-angle triangle. That means they are related by the tangent function:

  • RMS/RES = tan A.
For a planet whose distance RPS from the Sun is greater than Earth’s, an estimate of its distance compared to the Earth-Sun distance RES can be made using the fact that (were its orbit perfectly circular) it would make a right-angle triangle after the first or third quarter of its cycle, with the right angle located at the Sun. Sizes of Earth, Sun and planet not shown to scale.
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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON March 28, 2022

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