Of Particular Significance

Tag: geology

If you’re of a certain age, you know Alan Alda from his wonderful acting in television shows and in movies. But you may not know of his long-standing interest in science communication and his podcast Clear and Vivid (named for the characteristics that he feels all communication should have.)

Alda and I had a great conversation about the idea that we are made of waves, and what it means for our relationship to the universe. A slimmed-down version of that discussion is now available on his podcast. I hope you enjoy it!

Separately, as promised: to my last post, which covered various ways of depicting and interpreting wave functions, I’ve added explanations of the two quantum wave functions that I placed at the end. Tomorrow I’ll take a step back and consider wave functions from a larger point of view, taking a brief look at what they are (and aren’t), what’s “wavy” (and not) about them, and at their roles in contexts ranging from pre-quantum physics of the 19th century to quantum field theory of the 21st.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 18, 2025

Before we knew about quantum physics, humans thought that if we had a system of two small objects, we could always know where they were located — the first at some position x1, the second at some position x2. And after Isaac Newton’s breakthroughs in the late 17th century, we believed that by combining this information with knowledge of the objects’ motions and the forces acting upon them, we could calculate where they would be in the future.

But in our quantum world, this turns out not to be the case. Instead, in Erwin Schrödinger’s 1925 view of quantum physics, our system of two objects has a wave function which, for every possible x1 and x2 that the objects could have, gives us a complex number Ψ(x1, x2). The absolute-value-squared of that number, |Ψ(x1, x2)|2, is proportional to the probability for finding the first object at position x1 and the second at position x2 — if we actually choose to measure their positions right away. If instead we wait, the wave function will change over time, following Schrödinger’s wave equation. The updated wave function’s square will again tell us the probabilities, at that later time, for finding the objects at those particular positions.

The set of all possible object locations x1 and x2 is what I am calling the “space of possibilities” (also known as the “configuration space”), and the wave function Ψ(x1, x2) is a function on that space of possibilities. In fact, the wave function for any system is a function on the space of that system’s possibilities: for any possible arrangement X of the system, the wave function will give us a complex number Ψ(X).

Drawing a wave function can be tricky. I’ve done it in different ways in different contexts. Interpreting a drawing of a wave function can also be tricky. But it’s helpful to learn how to do it. So in today’s post, I’ll give you three different approaches to depicting the wave function for one of the simplest physical systems: a single object moving along a line. In coming weeks, I’ll give you more examples that you can try to interpret. Once you can read a wave function correctly, then you know your understanding of quantum physics has a good foundation.

For now, everything I’ll do today is in the language of 1920s quantum physics, Schrödinger style. But soon we’ll put this same strategy to work on quantum field theory, the modern language of particle physics — and then many things will change. Familiarity with the more commonly discussed 1920s methods will help you appreciate the differences.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 17, 2025

Pioneer Works is “an artist and scientist-led cultural center in Red Hook, Brooklyn that fosters innovative thinking through the visual and performing arts, technology, music, and science.” It’s a cool place: if you’re in the New York area, check them out! Among many other activities, they host a series called “Picture This,” in which scientists ruminate over scientific images that they particularly like. My own contribution to this series has just come out, in which I expound upon the importance and meaning of this graph from the CMS experimental collaboration at the Large Hadron Collider [LHC]. (The ATLAS experimental collaboration at the LHC has made essentially identical images.)

The point of the article is to emphasize the relation between the spikes seen in this graph and the images of musical frequencies that one might see in a recording studio (as in this image from this paper). The similarity is not an accident.

Each of the two biggest spikes is a sign of an elementary “particle”; the Z boson is the left-most spike, and the Higgs boson is the central spike. What is spiking is the probability of creating such a particle as a function of the energy of some sort of physical process (specifically, a collision of objects that are found inside protons), plotted along the horizontal axis. But energy E is related to the mass m of the “particle” (via E=mc2) and it is simultaneously related to the frequency f of the vibration of the “particle” (via the Planck-Einstein equation E = hf)… and so this really is a plot of frequencies, with spikes reflecting cosmic resonances analogous to the resonances of musical instruments. [If you find this interesting and would like more details, it was a major topic in my book.]

The title of the article refers to the fact that the Z boson and Higgs boson frequencies are out of tune, in the sense that if you slowed down their frequencies and turned them into sound, they’d be dissonant, and not very nice to listen to. The same goes for all the other frequencies of the elementary “particles”; they’re not at all in tune. We don’t know why, because we really have no idea where any of these frequencies come from. The Higgs field has a major role to play in this story, but so do other important aspects of the universe that remain completely mysterious. And so this image, which shows astonishingly good agreement between theoretical predictions (colored regions) and LHC data (black dots), also reveals how much we still don’t understand about the cosmos.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 13, 2025

[An immediate continuation of Part 1, which you should definitely read first; today’s post is not stand-alone.]

The Asymmetry Between Location and Motion

We are in the middle of trying to figure out if the electron (or other similar object) could possibly be of infinitesimal size, to match the naive meaning of the words “elementary particle.” In the last post, I described how 1920’s quantum physics would envision an electron (or other object) in a state |P0> of definite momentum or a state |X0> of definite position (shown in Figs. 1 and 2 from last time.)

If it is meaningful to say that “an electron is really is an object whose diameter is zero”, we would naturally expect to be able to put it into a state in which its position is clearly defined and located at some specific point X0 — namely, we should be able to put it into the state |X0>. But do such states actually exist?

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 11, 2025

This is admittedly a provocative title coming from a particle physicist, and you might think it tongue-in-cheek. But it’s really not.

We live in a cosmos with quantum physics, relativity, gravity, and a bunch of elementary fields, whose ripples we call elementary particles. These elementary “particles” include objects like electrons, photons, quarks, Higgs bosons, etc. Now if, in ordinary conversation in English, we heard the words “elementary” and “particle” used together, we would probably first imagine that elementary particles are tiny balls, shrunk down to infinitesimal size, making them indivisible and thus elementary — i.e., they’re not made from anything smaller because they’re as small as could be. As mere points, they would be objects whose diameter is zero.

But that’s not what they are. They can’t be.

I’ll tell this story in stages. In my last post, I emphasized that after the Newtonian view of the world was overthrown in the early 1900s, there emerged the quantum physics of the 1920s, which did a very good job of explaining atomic physics and a variety of other phenomena. In atomic physics, the electron is indeed viewed as a particle, though with behavior that is quite unfamiliar. The particle no longer travels on a path through physical space, and instead its behavior — where it is, and where it is going — is described probabilistically, using a wave function that exists in the space of possibilities.

But as soon became clear, 1920s quantum physics forbids the very existence of elementary particles.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 10, 2025

As expected, the Musk/Trump administration has aimed its guns at the US university system, deciding that universities that get grants from the federal government’s National Institute of Health will have their “overhead” capped at 15%. Overhead is the money that is used to pay for the unsung things that make scientific research at universities and medical schools possible. It pays for staff that keep the university running — administrators and accountants in business offices, machinists who help build experiments, janitorial staff, and so on — as well as the costs for things like building maintenance and development, laboratory support, electricity and heating, computing clusters, and the like.

I have no doubt that the National Science Foundation, NASA, and other scientific funding agencies will soon follow suit.

As special government employee Elon Musk wrote on X this weekend, “Can you believe that universities with tens of billions in endowments were siphoning off 60% of research award money for ‘overhead’? What a ripoff!

The actual number is 38%. Overhead of 60% is measured against the research part of the award, not the total award, and so the calculation is 60%/(100%+60%) = 37.5%, not 60%/100%=60%. This math error is a little worrying, since the entire national budget is under Musk’s personal control. And never mind that a good chunk of that money often comes back to research indirectly, or that “siphon”, a loaded word implying deceit, is inappropriate — the overhead rate for each university isn’t a secret.

Is overhead at some universities too high? A lot of scientific researchers feel that it is. One could reasonably require a significant but gradual reduction of the overhead rate over several years, which would cause limited damage to the nation’s research program. But dropping the rate to 15%, and doing so over a weekend, will simply crush budgets at every major academic research institution in the country, leaving every single one with a significant deficit. Here is one estimate of the impact on some of the United States leading universities; I can’t quickly verify these details myself, but the numbers look to be at the right scale. They are small by Musk standards, but they come to something very roughly like $10000, more or less, per student, per year.

Also, once the overhead rate is too low, having faculty doing scientific research actually costs a university money. Every new grant won by a scientist at the university makes the school’s budget deficit worse. Once that line is crossed, a university may have to limit research… possibly telling some fraction of its professors not to apply for grants and to stop doing research.

It is very sad that Mr. Musk considers the world’s finest medical/scientific research program, many decades in the making and of such enormous value to the nation, to be deserving of this level of disruption. While is difficult to ruin our world-leading medical and scientific research powerhouse overnight, this decision (along with the funding freeze/not-freeze/kinda-freeze from two weeks ago) is a good start. Even if this cut is partially reversed, the consequences on health care and medicine in this country, and on science and engineering more widely, will be significant and long-lasting — because if you were one of the world’s best young medical or scientific researchers, someone who easily could get a job in any country around the globe, would you want to work in the US right now? The threat of irrational chaos that could upend your career at any moment is hardly appealing.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 9, 2025

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