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David vs. Goliath: What a tiny electron can tell us about the structure of the universe December 22, 2018

Posted by apetrov in Blogroll, Particle Physics, Physics, Science, Uncategorized.
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File 20181128 32230 mojlgr.jpg?ixlib=rb 1.1
An artist’s impression of electrons orbiting the nucleus.
Roman Sigaev/ Shutterstock.com

Alexey Petrov, Wayne State University

What is the shape of an electron? If you recall pictures from your high school science books, the answer seems quite clear: an electron is a small ball of negative charge that is smaller than an atom. This, however, is quite far from the truth.

A simple model of an atom with the nucleus of made of protons, which have a positive charge, and neutrons, which are neutral. The electrons, which have a negative charge, orbit the nucleus.
Vector FX / Shutterstock.com

The electron is commonly known as one of the main components of atoms making up the world around us. It is the electrons surrounding the nucleus of every atom that determine how chemical reactions proceed. Their uses in industry are abundant: from electronics and welding to imaging and advanced particle accelerators. Recently, however, a physics experiment called Advanced Cold Molecule Electron EDM (ACME) put an electron on the center stage of scientific inquiry. The question that the ACME collaboration tried to address was deceptively simple: What is the shape of an electron?

Classical and quantum shapes?

As far as physicists currently know, electrons have no internal structure – and thus no shape in the classical meaning of this word. In the modern language of particle physics, which tackles the behavior of objects smaller than an atomic nucleus, the fundamental blocks of matter are continuous fluid-like substances known as “quantum fields” that permeate the whole space around us. In this language, an electron is perceived as a quantum, or a particle, of the “electron field.” Knowing this, does it even make sense to talk about an electron’s shape if we cannot see it directly in a microscope – or any other optical device for that matter?

To answer this question we must adapt our definition of shape so it can be used at incredibly small distances, or in other words, in the realm of quantum physics. Seeing different shapes in our macroscopic world really means detecting, with our eyes, the rays of light bouncing off different objects around us.

Simply put, we define shapes by seeing how objects react when we shine light onto them. While this might be a weird way to think about the shapes, it becomes very useful in the subatomic world of quantum particles. It gives us a way to define an electron’s properties such that they mimic how we describe shapes in the classical world.

What replaces the concept of shape in the micro world? Since light is nothing but a combination of oscillating electric and magnetic fields, it would be useful to define quantum properties of an electron that carry information about how it responds to applied electric and magnetic fields. Let’s do that.

This is the apparatus the physicists used to perform the ACME experiment.
Harvard Department of Physics, CC BY-NC-SA

Electrons in electric and magnetic fields

As an example, consider the simplest property of an electron: its electric charge. It describes the force – and ultimately, the acceleration the electron would experience – if placed in some external electric field. A similar reaction would be expected from a negatively charged marble – hence the “charged ball” analogy of an electron that is in elementary physics books. This property of an electron – its charge – survives in the quantum world.

Likewise, another “surviving” property of an electron is called the magnetic dipole moment. It tells us how an electron would react to a magnetic field. In this respect, an electron behaves just like a tiny bar magnet, trying to orient itself along the direction of the magnetic field. While it is important to remember not to take those analogies too far, they do help us see why physicists are interested in measuring those quantum properties as accurately as possible.

What quantum property describes the electron’s shape? There are, in fact, several of them. The simplest – and the most useful for physicists – is the one called the electric dipole moment, or EDM.

In classical physics, EDM arises when there is a spatial separation of charges. An electrically charged sphere, which has no separation of charges, has an EDM of zero. But imagine a dumbbell whose weights are oppositely charged, with one side positive and the other negative. In the macroscopic world, this dumbbell would have a non-zero electric dipole moment. If the shape of an object reflects the distribution of its electric charge, it would also imply that the object’s shape would have to be different from spherical. Thus, naively, the EDM would quantify the “dumbbellness” of a macroscopic object.

Electric dipole moment in the quantum world

The story of EDM, however, is very different in the quantum world. There the vacuum around an electron is not empty and still. Rather it is populated by various subatomic particles zapping into virtual existence for short periods of time.

The Standard Model of particle physics has correctly predicted all of these particles. If the ACME experiment discovered that the electron had an EDM, it would suggest there were other particles that had not yet been discovered.
Designua/Shutterstock.com

These virtual particles form a “cloud” around an electron. If we shine light onto the electron, some of the light could bounce off the virtual particles in the cloud instead of the electron itself.

This would change the numerical values of the electron’s charge and magnetic and electric dipole moments. Performing very accurate measurements of those quantum properties would tell us how these elusive virtual particles behave when they interact with the electron and if they alter the electron’s EDM.

Most intriguing, among those virtual particles there could be new, unknown species of particles that we have not yet encountered. To see their effect on the electron’s electric dipole moment, we need to compare the result of the measurement to theoretical predictions of the size of the EDM calculated in the currently accepted theory of the Universe, the Standard Model.

So far, the Standard Model accurately described all laboratory measurements that have ever been performed. Yet, it is unable to address many of the most fundamental questions, such as why matter dominates over antimatter throughout the universe. The Standard Model makes a prediction for the electron’s EDM too: it requires it to be so small that ACME would have had no chance of measuring it. But what would have happened if ACME actually detected a non-zero value for the electric dipole moment of the electron?

View of the Large Hadron Collider in its tunnel near Geneva, Switzerland. In the LHC two counter-rotating beams of protons are accelerated and forced to collide, generating various particles.
AP Photo/KEYSTONE/Martial Trezzini

Patching the holes in the Standard Model

Theoretical models have been proposed that fix shortcomings of the Standard Model, predicting the existence of new heavy particles. These models may fill in the gaps in our understanding of the universe. To verify such models we need to prove the existence of those new heavy particles. This could be done through large experiments, such as those at the international Large Hadron Collider (LHC) by directly producing new particles in high-energy collisions.

Alternatively, we could see how those new particles alter the charge distribution in the “cloud” and their effect on electron’s EDM. Thus, unambiguous observation of electron’s dipole moment in ACME experiment would prove that new particles are in fact present. That was the goal of the ACME experiment.

This is the reason why a recent article in Nature about the electron caught my attention. Theorists like myself use the results of the measurements of electron’s EDM – along with other measurements of properties of other elementary particles – to help to identify the new particles and make predictions of how they can be better studied. This is done to clarify the role of such particles in our current understanding of the universe.

What should be done to measure the electric dipole moment? We need to find a source of very strong electric field to test an electron’s reaction. One possible source of such fields can be found inside molecules such as thorium monoxide. This is the molecule that ACME used in their experiment. Shining carefully tuned lasers at these molecules, a reading of an electron’s electric dipole moment could be obtained, provided it is not too small.

However, as it turned out, it is. Physicists of the ACME collaboration did not observe the electric dipole moment of an electron – which suggests that its value is too small for their experimental apparatus to detect. This fact has important implications for our understanding of what we could expect from the Large Hadron Collider experiments in the future.

Interestingly, the fact that the ACME collaboration did not observe an EDM actually rules out the existence of heavy new particles that could have been easiest to detect at the LHC. This is a remarkable result for a tabletop-sized experiment that affects both how we would plan direct searches for new particles at the giant Large Hadron Collider, and how we construct theories that describe nature. It is quite amazing that studying something as small as an electron could tell us a lot about the universe.

A short animation describing the physics behind EDM and ACME collaboration’s findings.

Alexey Petrov, Professor of Physics, Wayne State University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

The Conversation

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Rapid-response (non-linear) teaching: report January 25, 2018

Posted by apetrov in Blogroll, Education, Near Physics, Physics, Science.
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Some of you might remember my previous post about non-linear teaching, where I described a new teaching strategy that I came up with and was about to implement in teaching my undergraduate Classical Mechanics I class. Here I want to report on the outcomes of this experiment and share some of my impressions on teaching.

Course description

Our Classical Mechanics class is a gateway class for our physics majors. It is the first class they take after they are done with general physics lectures. So the students are already familiar with the (simpler version of the) material they are going to be taught. The goal of this class is to start molding physicists out of physics students. It is a rather small class (max allowed enrollment is 20 students; I had 22 in my class), which makes professor-student interaction rather easy.

Rapid-response (non-linear) teaching: generalities

To motivate the method that I proposed, I looked at some studies in experimental psychology, in particular in memory and learning studies. What I was curious about is how much is currently known about the process of learning and what suggestions I can take from the psychologists who know something about the way our brain works in retaining the knowledge we receive.

As it turns out, there are some studies on this subject (I have references, if you are interested). The earliest ones go back to 1880’s when German psychologist Hermann Ebbinghaus hypothesized the way our brain retains information over time. The “forgetting curve” that he introduced gives approximate representation of information retention as a function of time. His studies have been replicated with similar conclusions in recent experiments.

EbbinghausCurveThe upshot of these studies is that loss of learned information is pretty much exponential; as can be seen from the figure on the left, in about a day we only retain about 40% of what we learned.

Psychologists also learned that one of the ways to overcome the loss of information is to (meaningfully) retrieve it: this is how learning  happens. Retrieval is critical for robust, durable, and long-term learning. It appears that every time we retrieve learned information, it becomes more accessible in the future. It is, however, important how we retrieve that stored information: simple re-reading of notes or looking through the examples will not be as effective as re-working the lecture material. It is also important how often we retrieve the stored info.

So, here is what I decided to change in the way I teach my class in light of the above-mentioned information (no pun intended).

Rapid-response (non-linear) teaching: details

To counter the single-day information loss, I changed the way homework is assigned: instead of assigning homework sets with 3-4-5 problems per week, I introduced two types of homework assignments: short homeworks and projects.

Short homework assignments are single-problem assignments given after each class that must be done by the next class. They are designed such that a student needs to re-derive material that was discussed previously in class (with small new twist added). For example, if the block-down-to-incline problem was discussed in class, the short assignment asks to redo the problem with a different choice of coordinate axes. This way, instead of doing an assignment in the last minute at the end of the week, the students are forced to work out what they just learned in class every day (meaningful retrieval)!

The second type of assignments, project homework assignments are designed to develop understanding of how topics in a given chapter relate to each other. There are as many project assignments as there are chapters. Students get two weeks to complete them.

At the end, the students get to solve approximately the same number of problems over the course of the semester.

For a professor, the introduction of short homework assignments changes the way class material is presented. Depending on how students performed on the previous short homework, I adjusted the material (both speed and volume) that we discussed in class. I also designed examples for the future sections in such a way that I could repeat parts of the topic that posed some difficulties in comprehension. Overall, instead of a usual “linear” propagation of the course, we moved along something akin to helical motion, returning and spending more time on topics that students found more difficult (hence “rapid-response or non-linear” teaching).

Other things were easy to introduce: for instance, using Socrates’ method in doing examples. The lecture itself was an open discussion between the prof and students.

Outcomes

So, I have implemented this method in teaching Classical Mechanics I class in Fall 2017 semester. It was not an easy exercise, mostly because it was the first time I was teaching GraphNonlinearTeachingthis class and had no grader help. I would say the results confirmed my expectations: introduction of short homework assignments helps students to perform better on the exams. Now, my statistics is still limited: I only had 20 students in my class. Yet, among students there were several who decided to either largely ignore short homework assignments or did them irregularly. They were given zero points for each missed short assignment. All students generally did well on their project assignments, yet there appears some correlation (see graph above) between the total number of points acquired on short homework assignments and exam performance (measured by a total score on the Final and two midterms). This makes me thing that short assignments were beneficial for students. I plan to teach this course again next year, which will increase my statistics.

I was quite surprised that my students generally liked this way of teaching. In fact, they were disappointed that I decided not to apply this method for the Mechanics II class that I am teaching this semester. They also found that problems assigned in projects were considerably harder than the problems from the short assignments (this is how it was supposed to be).

For me, this was not an easy semester. I had to develop my set of lectures — so big thanks go to my colleagues Joern Putschke and Rob Harr who made their notes available. I spent a lot of time preparing this course, which, I think, affected my research outcome last semester. Yet, most difficulties are mainly Wayne State-specifics: Wayne State does not provide TAs for small classes, so I had to not only design all homework assignments, but also grade them (on top of developing the lectures from the ground up). During the semester, it was important to grade short assignments in the same day I received them to re-tune lectures, this did take a lot of my time. I would say TAs would certainly help to run this course — so I’ll be applying for some internal WSU educational grants to continue development of this method. I plan to employ it again next year to teach Classical Mechanics.

Non-linear teaching October 9, 2017

Posted by apetrov in Blogroll, Physics, Science.
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I wanted to share some ideas about a teaching method I am trying to develop and implement this semester. Please let me know if you’ve heard of someone doing something similar.

This semester I am teaching our undergraduate mechanics class. This is the first time I am teaching it, so I started looking into a possibility to shake things up and maybe apply some new method of teaching. And there are plenty offered: flipped classroom, peer instruction, Just-in-Time teaching, etc.  They all look to “move away from the inefficient old model” where there the professor is lecturing and students are taking notes. I have things to say about that, but not in this post. It suffices to say that most of those approaches are essentially trying to make students work (both with the lecturer and their peers) in class and outside of it. At the same time those methods attempt to “compartmentalize teaching” i.e. make large classes “smaller” by bringing up each individual student’s contribution to class activities (by using “clickers”, small discussion groups, etc). For several reasons those approaches did not fit my goal this semester.

Our Classical Mechanics class is a gateway class for our physics majors. It is the first class they take after they are done with general physics lectures. So the students are already familiar with the (simpler version of the) material they are going to be taught. The goal of this class is to start molding physicists out of students: they learn to simplify problems so physics methods can be properly applied (that’s how “a Ford Mustang improperly parked at the top of the icy hill slides down…” turns into “a block slides down the incline…”), learn to always derive the final formula before plugging in numbers, look at the asymptotics of their solutions as a way to see if the solution makes sense, and many other wonderful things.

So with all that I started doing something I’d like to call non-linear teaching. The gist of it is as follows. I give a lecture (and don’t get me wrong, I do make my students talk and work: I ask questions, we do “duels” (students argue different sides of a question), etc — all of that can be done efficiently in a class of 20 students). But instead of one homework with 3-4 problems per week I have two types of homework assignments for them: short homeworks and projects.

Short homework assignments are single-problem assignments given after each class that must be done by the next class. They are designed such that a student need to re-derive material that we discussed previously in class with small new twist added. For example, in the block-down-to-incline problem discussed in class I ask them to choose coordinate axes in a different way and prove that the result is independent of the choice of the coordinate system. Or ask them to find at which angle one should throw a stone to get the maximal possible range (including air resistance), etc.  This way, instead of doing an assignment in the last minute at the end of the week, students have to work out what they just learned in class every day! More importantly, I get to change how I teach. Depending on how they did on the previous short homework, I adjust the material (both speed and volume) discussed in class. I also  design examples for the future sections in such a way that I can repeat parts of the topic that was hard for the students previously. Hence, instead of a linear propagation of the course, we are moving along something akin to helical motion, returning and spending more time on topics that students find more difficult. That’t why my teaching is “non-linear”.

Project homework assignments are designed to develop understanding of how topics in a given chapter relate to each other. There are as many project assignments as there are chapters. Students get two weeks to complete them.

Overall, students solve exactly the same number of problems they would in a normal lecture class. Yet, those problems are scheduled in a different way. In my way, students are forced to learn by constantly re-working what was just discussed in a lecture. And for me, I can quickly react (by adjusting lecture material and speed) using constant feedback I get from students in the form of short homeworks. Win-win!

I will do benchmarking at the end of the class by comparing my class performance to aggregate data from previous years. I’ll report on it later. But for now I would be interested to hear your comments!

 

Nobel week 2015 October 5, 2015

Posted by apetrov in Blogroll, Physics, Science.
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So, once again, the Nobel week is upon us. And one of the topics of conversations for the “water cooler chat” in physics departments around the world is speculations on who (besides the infamous Hungarian “physicist” — sorry for the insider joke, I can elaborate on that if asked) would get the Nobel Prize in physics this year. What is your prediction?

With invention of various metrics for “measuring scientific performance” one can make educated guesses — and even put predictions on the industrial footage — see Thomson Reuters predictions based on a number of citations (they did get the Englert-Higgs prize right, but are almost always off). Or even try your luck with on-line betting (sorry, no link here — I don’t encourage this). So there is a variety of ways to make you interested.

My predictions for 2015: Vera Rubin for Dark Matter or Deborah Jin for fermionic condensates. But you must remember that my record is no better than that of Thomson Reuters.

So, you want to go on sabbatical… February 5, 2015

Posted by apetrov in Blogroll, Near Physics, Physics, Science.
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Every seven years or so a professor in a US/Canadian University can apply for a sabbatical leave. It’s a very nice thing: your University allows you to catch up on your research, learn new techniques, write a book, etc. That is to say, you become a postdoc again. And in many cases questions arise: should I stay at my University or go somewhere else? In many cases yearlong sabbaticals are not funded by the home University, i.e. you have to find additional sources of funding to keep your salary.

I am on a year-long sabbatical this academic year. So I had to find a way to fund my sabbatical (my University only pays 60% of my salary). I spent Fall 2014 semester at Fermilab and am spending Winter 2015 semester at the University of Michigan, Ann Arbor.

Here are some helpful resources for those who are looking to fund their sabbatical next year. As you could see from the list, they are slightly tilted towards theoretical physics. Yet, there are many resources that are useful for any profession. Of course your success depends on many factors: whether or not you would like to stay in the US or go abroad, competition, etc.

  • General resources:

Guggenheim Foundation
Deadline: September

Fulbright Scholar Program
Deadline: August

  • USA/Canada:

Simons Fellowship
Deadline: September

IAS Princeton (Member/Sabbatical)
Deadline: November

Perimeter Institute:
Visitors
Visiting Professors
Deadline: November

Radcliffe Institute at Harvard University
Deadline: November

FNAL:
URA Visiting Scholar program
Intensity Frontier Fellowships
Deadline: twice a year

  • Europe:

Alexander von Humbuldt:
Friedrich Wilhelm Bessel Research Award
Humboldt Research Award
Deadline: varies

Marie Curie International Incoming Fellowships
Deadline: varies

CERN Short Term visitors
Deadline: varies

Hans Fischer Senior Fellowship (TUM-IAS, Munchen)
Deadline: varies
Some general  info that could also be useful can be found here.

I don’t pretend to have a complete list, but those sites were useful for me. I did not apply to all of those programs — and rather unfortunately, missed a deadline for the Simons Fellowship. Many University also have separate funds for sabbatical visitors. So if there is a University one wants to visit, it’s best to ask.

On a final note, it might be useful to be prepared and figure out, if you get funded, how the money/fellowship will find a way to your University and to you. Also, in many cases “60% of the salary” paid by your University while you are on a sabbatical leave means that you would have to find not only the remaining 40% of your salary, but also fringes that your University would take from your fellowship. So the amount that you’d need to find is more than 40% of your salary. Please don’t make a mistake that I made. 🙂

Good luck!