Tuesday, April 13, 2010

Some Things to Know About Quantum Mechanics

Sometimes throwing the word "quantum" around makes you look smart.

In the right company, of course, it has the opposite effect, at least if you use it incorrectly.  See my rant on the book, The Secret.

Quantum mechanics, the branch of physics that deals with things on a small scale--but not to be confused with particle physics, which deals with things on an even smaller scale--has the property of seeming out-there, highly subjective, and sometimes even mystical, because the set of rules and physical processes being described are really better understood by staring at math equations than by trying to use declarative sentences.   As a result, different physicists might describe the same thing with disparate analogies, yet when they get into the nerdy details together, they both understand what's going on.

So, to make your life a little more interesting at parties, I'm going to share some insights into the magical, mystical world of quantum, with the disclaimer that to really understand, you have to have had a fair amount of training in calculus and linear algebra.

And if you think you're too un-smart to understand calculus and linear algebra, I say you might not be, you should try it some time.  Some people would call mathematics a precisely reasoned logic system.  I would call it a very precise language, which describes the universe quite elegantly.

First, quantum mechanics is, like any branch of physics, a set of rules.

Now, a general set of rules is something we are all well familiar with.  The rules governing things here on Earth are things we know intuitively because we can see them and experience them:  force, mass, inertia, gravity, etc and the rules of their relationships are referred to by we physics types as classical mechanics.

Well, it turns out that quantum mechanics--dealing principally with the protons, neutrons, and electrons that all classical objects are made up of when you get down to it--works here on Earth as well as anywhere else, and a good thing too, but we can't see quantum mechanics working because all of those protons, neutrons, and electrons doing their thing together aggregates into what we actually observe, which is classical mechanics.  If you never bothered to delve deeper you'd never know that classical mechanics wasn't the only set of rules in play, and for thousands of years, we didn't know, because we didn't have the technology and hadn't done the thought experiments.

So quantum mechanics--one set of rules, and classical mechanics--another, don't necessarily conflict, so much as provide different frameworks to understand what is happening.  Each has it's appropriate place to be used, just like you'd look through sunglasses when your outside, and normal glasses, (if you need glasses) when you're inside.  Both are correct when used in the right place.  So while quantum may seem magical and mystical, it is in fact happening right now, right in front of your nose--you just don't have the tools to see it, and odds are to accomplish most things you don't need to anyway.

In the case of classical mechanics, as I said, everybody knows about it, because everybody can see it.  Even if you've never taken a physics class, you intuitively use classical mechanics every time you do most anything, expecting a certain result.  We developed math and things like Newton's Laws, to describe what was always expect to happen and called it 'physics', and tortured students with what they already knew, darn it, for years.  Oh, and refining of our knowledge of it helped us build things like cars, skyscrapers, rockets, and satellites.

Quantum mechanics was sort of the opposite.  On a very generalized level, the math that describes quantum mechanics, namely, calculus (nasty integrals, and symbolically unsolvable differential equations, to be precise) and linear algebra, already existed.  Scientists noticed a number of things that no longer made any sense if you just used classical mechanics to look at them, and as it turned out most of these things had to do with the behavior of the sub-atomic particles involved.  Smart people began piecing these puzzles together.  Math had proven a useful too thus far, so they used math to create a set of rules, describing how really tiny things act.   The set of rules was refined to matched reality well, and with more evidence better, and better still.  We don't know that they are true, and we probably never can.  But the rules work so well in so many cases, that the likelihood of their truth is no longer in dispute by most scientists.  (Some few are still proponents of the 'hidden variables' explanation, something Einstein himself proposed, not liking the un-pin-down-able nature of quantum mechanics.)

So, what are the rules?

Unfortunately the "real" rules are pretty much inseparable from the math.  In this case, the math makes it way easier to get a handle on what's happening.  One line for each, verses the paragraphs I go into below.

But they go something like this.  I'm going to state them out of order, because that is the way that they make the most sense.

Rule 3:  A system can be represented by a state function, called a wave-funciton.

What?  In math, remember, a function is an equation of two variables.  It describes the relationship between those variables.  Example:  y=x.  If you plotted that, you'd get a diagonal line, because the x and y values of that line, no matter what they are, are always the same.

Rule 3 says that there exists a function that describes every system.  An electron floating around has a function that describes it.  An atom has a function.  A person, consisting of millions and millions of atoms, does too. Are those functions hella complicated?  Yeah.  They're called wave-functions because they usually always have a sine in them somewhere, and if you've ever looked at a graph of y=sin(x), you'll see a line that goes up and down in a repeated pattern.  That's a wave.  There are some implications, of course, to everything being described as a wave, and I might explain some of those in a later entry.

Furthermore, any system at any instant in time has a wave-function, and the information describing the system is contained in that function.  This is a pretty profound rule.  It says that things are describable by math.

Rules number 1 and 2 are closely related.

Rule 1: For an observable value, say, momentum of a particle, you can do math on the wave-function that results in that wave-function being multiplied by that observable value.

Okay, I told you this is just too math-y to use good old declarative sentences.  Basically, say the energy of an electron is equal to 2 Joules.  I just made that number up, I don't think electrons ever have that much energy.  But in my example the electron has a certain energy at a certain instant in time, and that is 2 Joules.  From Rule 3, we know that the electron at that moment in time can be described by a function, probably a complicated one.  Whatever it is, the objective of Rule 1 is to obtain the result: (electron function, whatever it is) multiplied by 2.  That would go on one side of the equals sign.  On the other, you would Do Math, but the result of the math you are doing would give you the electron's Rule 3 function multiplied by 2, and 2 is the energy of the electron at that point in time.

What math do you do?  That depends.  You do certain math for each observable value.  There's certain math you do for momentum, certain math you do for energy, position, etc.  So rule number 1 is stating that Math Exists that you can do, for any observable you want to measure.  Once you've done that math, you will have the wave-function multiplied by the value of the thing you want to measure.   Momentum Math on the wave-function gives you the wave-function multiplied by the momentum of the system.  Position Math gives you the wave-function multiplied by the position of the system.

The implication of this is that you can find out these things about the system, not by measuring the energy, the momentum, the position, but by doing math.  And it gives you an exact result. (Assuming you know what the wave-function is, of course.) In the case of our example, applying Rule 1 told us that the electron has 2 joules.  Not 2.5, not 2.01, not 2.001, not 2 and some error inherent in measuring.  2.  Exactly.  "Quantum" comes form "Quantized", or "quanta", meaning, discrete, exact value.  Not a range, but a yes or a no.

Rule 2 Is closely related.  It says that if you do decide to measure an observable value, again, something like energy, momentum, or position, of a system, then the wave-function of that system, at the instant you take a measurement, will be equal to the wave-function required to make Rule # 1 work for whatever value you get from your measurement.

I'll use a tiny bit of algebra to demonstrate, because you can do algebra with numbers, but you can also do algebra with functions.

y=4x.   We know what y is from Rule 1, that's the Math that Exists that you Do, to get the value of the observable multiplied by the wave-function.  Say 4 is value of the observable, and x represents the wave-function, whatever hella complicated thing it is.  Y is something that doesn't change, remember that there is certain math to measure energy, certain math to measure momentum, certain math to measure each thing that you want to measure.  So if we are trying to measure the energy of an electron at a specific moment in time, then y is the Energy Math, and 4 is what we got when we took the measurement.   Just for simplicity, I will say y is equal to 2.  You know two parts of the equation, and two are all you need to solve it:

2=4x.  If this is so, we can figure out what x is.  x is equal to 1/2.

So you can figure out the wave-function.  It has to be the wave-function that make the algebraic expression above work.  That is the only wave-function it could be at that instant.

Rule 2 two helps us understand a last important thing about quantum mechanics, which is that even though the rules are set it up so that things are exact, the applications tend to be probabilistic.  This is because these wave-functions are not simple numbers, like 1/2, but very complicated beasts, consisting of multiple variables.  Rules 1 and 2 always apply:  if you Do the Math that Exists, you get an exact value and a matching wave-function.  But often instead of something simple, like an electron floating around in space, there are complications, like, an electron within an atom, a bunch of atoms together in a molecule.  In these case, there are many possible states.  An electron within at atom could be in one orbit, or another.  There may be two electrons, and the proton matters too.  In this case, the wave-function is often what we call a superposition of possibilities. Superposition is a term describing how waves interact with each other:  unlike matter, waves can occupy the same space at once, they are superimposed on each other.  The wave-function for a complex system is often a superposition of all the many, many allowed states that the system could be in.

In this case the wave-function does not tell us which possibility is reality, it just tells us the probability of each one.   When you make the measurement (assuming, in a situation like this, that you could), you get one of these possibilities, and the wave-function becomes the function which describes that reality over any other.  But until you make the measurement, there may be multiple possibilities for the state of the system, with different probabilities, and the wave-function will reflect that.

So A, B, and C, may all be options.  Because of the Rules, we know that "sorta A sorta B", is not an option, or A.5, or however you want to look at it.  It will be A, B, or C, when you take your measurement.  Until you do, the wave-function, could it be determined, would tell you something like A is 50% probable, B is 45%, and C is 5%.  If you take 100 measurements, you will measure A 50 times, B 45 times, and C 5 times.

And this is how it works in the world of the small.  There are only certain ways to be.  But there are also probabilities of being there, which govern how everything actually is.

What do these rules enables us to do and say about the universe? There are so many implications, and so many successful applications of quantum mechanics.  The periodic table, all that stuff you might have learned and hated in chemistry about the strange shapes of electron orbits--all of that can be solved precisely with quantum mechanics.  I will take the remainder of your reading attention to explain just one, particularly important example.

We owe a functioning sun, and in fact all stars, to quantum mechanics.  It turns out that even inside the very hot sun, the collisions of all the protons are not energetic enough to enact the heating mechanism of the sun, in which two protons get close enough to overcome the Electrostatic force that usually repels like charges, are sucked together by the stronger but shorter-distance Strong Nuclear Force, and start the quark-swapping chain of events known as nuclear fusion. It just isn't hot enough.   Yet we know for a fact that fusion does happen, and it's a pretty good thing for us that it does.

There happens to be a quantum behavior, called tunneling, in which--even though the energy required to create fusion is much higher than the energy of protons colliding at 15 million Kelvins--because of the probabilistic, rather than deterministic, rules of QM, there is a very, very small probability that the protons will "tunnel through the energy barrier", or, despite not having enough energy to fuse, will fuse anyway.  This is kind of like how quantum mechanics says that if you throw yourself at the wall enough times, there IS a tiny probability that you will go through it.   But go throw yourself into the wall, and I guarantee that even if you did it your entire life, you will not go through it, because that probability is so incredibly tiny.  You can't take enough measurements to make that wave-function the reality.

The probability of two protons fusing anyway is also very, very small.  Thing is, in the sun, there are, let us just say, a lot of protons.  The sun is, after all, 300,000 times bigger than the Earth, and a proton is inconceivably small even when compared to an ant.  Furthermore, it's darn hot in the center of the sun, meaning the protons there have loads of kinetic energy and are zipping around at incredible speeds.  Lots of things in a a finite space moving very quickly means that those things are going to run into each other.  Many millions of collisions per second, in fact.  And so even if the probability for a single collision resulting in fusion is tiny, there are so many collisions happening, enough that yes, fusion does occur, the sun does shine, and life on Earth does reap considerable benefit.

So yeah.  Try that out at a party sometime.  "Did you know that fusion is due to the improbable possibility of proton tunneling within the sun?"

Friday, April 9, 2010

Nerves and Muscle Memory

Of all the things I may be good at, music, or getting up in front of people--or maybe it's the combination--are not among them.

I can be okay with that.

I prefer not to be the center of attention, I prefer to quietly observe in a situation, until I feel comfortable.  So performing on stage, even though I had my high school acting phase (but in that situation you're somebody else, so who cares?) is not usually my first impulse.

Yet I actually like giving presentations, like the one I have to give tonight.

I must like it for the challenge though, because even when I think that I'm calm and that by god I do have confidence, my body still sweats double and shakes and my heart flutters and I end up doing whatever I'm doing in front of people at about twice normal speed.  But yes, I do like a challenge.

So, I've been trying to play George Winston's variation on Pachabel's Cannon in D for about four months.  Merely competently, of course, not with all the flourishes.  Even so it is somewhat above my level, but I can manage it on the home piano when nobody is around.  Loving the challenge, I set myself a goal:  I will perform this song at the no-pressure just-for-fun math recital of my alma matter.  Since I'm a graduate, most people won't know me anyway.  I practiced and got, oh, I dunno, 90% correct most of the time, so I figured I had, a tiny shot at it anyway.

Leading up to my turn, I tried to act like it was no big deal.  It was a math department recital:  half the acts involved juggling or calculus jokes or math-adapted lyrics to popular songs.  I had played the song hundreds of times, and when I was taking lessons, oh, ten years ago, I'd always managed competence at the obligatory biannual recital.  I'm not generally lacking in confidence, not anymore, so I should have been able to walk up there with the self-assuredness of someone who is quite happy with herself and her abilities.

Yet my hands shook wildly, the sweat poured out, and as soon as I sat down and began I knew I was wrong.  For one thing, the seat was too short, so my muscle memory was slightly fooled, used to going through the desired sequence with my hands a little lower than that, thank you.  But I did okay, until I didn't, until I missed a note and couldn't just plow through because the muscle memory flow was interrupted, and even though I'd always been 100% on that sequence, I suddenly had no idea where my hand was supposed to go.  I said, "oh no!", got mutters of sympathy from the audience, and just started at the beginning of that sequence.  But my nerves were done for by then (I was sitting too far to the left too, I daresay, having been too nervous to take the time to get comfortable before starting) so I had to pause a few more times throughout, skip some parts completely that I knew I couldn't land in the state I was in, and plow through a succession of not-right-at-all flubs just to get to the end.

So I had set a goal for myself.   Learn a song, play it at the talent show.  And I followed through with that goal.  And then, I wouldn't say I failed miserably, because I did play it, after all, rather than chicken out.  I don't even wish I hadn't done it, because I wanted that challenge. 

I had thought myself better at mastering nerves than that, however.  

Tuesday, April 6, 2010

Particle Physics, Climate Change, and Dinner With Vera Rubin, Part III: Dinner With Vera Rubin

 Read Part I here.
Read Part II here.

Read article full text on the SPS website, and see a photo of Dr. Rubin and the author.

One of the benefits of being an undergraduate at this meeting was the opportunity to interact with renowned astronomer Dr. Vera Rubin.  She gave a presentation on her work to the undergraduates attending the meeting, and played on my team in Physics Jeopardy (we lost).  At 82 years of age, Dr. Rubin's presentation on her work studying the rotation of galaxies was both interesting and anecdotal:  with a colleague, it was her observation that the stars in other galaxies complete their rotation much faster than predicted by Newton's law of gravitation. It was this observation that that led to the postulation of dark matter!

Several of the students, myself included, were invited to a special dinner on the town with Dr. Rubin as our guest of honor.  We piled into a circular table at a nice Italian restaurant.  I had the privilege of sitting next to Dr. Rubin for the first half of the meal, and she was very eager to hear our stories and share her own.  She spoke candidly about both her joys and struggles in astronomy:  from the advisor who told her she would not be allowed to present her research at a conference, but that he could present it for her in his name; to the lone scientist at that conference who, instead of making a big deal about the disaster of her presence, asked enlightening questions and offered to help her publish her work in her own name.  She said she knew she wanted to be an astronomer from the time she was a little girl and could stare at the stars from the window of her bedroom—back when she believed that everything in the world could be learned from books.  Discovering that everything could not be learned from books only increased her desire to learn more, and through hard work and undaunted determination, with the help of a supportive husband and family, she succeeded at receiving her PhD, making important contribution to our knowledge of galaxies, and raising four children.

Perhaps inspired by the Pope decor, Dr. Rubin told another story as the evening came to a close.  She told us about a time when she was able to meet the Pope, as an astronomer selected to be a member of the Pontifical Academy of Sciences.  (As a member of that organization, Dr. Rubin shares an honor with such notable scientists as Steven Hawking, Werner Heisenberg and Paul Dirac.)  Apparently, members receive elaborate jewelry as indication of their membership, which Dr. Rubin had not thought to wear on her evening in the Vatican.  She was expecting, along with the other members of the Academy present, to have an opportunity to meet with the Pope, an opportunity that was extended to members alone and not to their families.  Because she had not brought her jewelry identifying her as a member, and because she was one of the few female members of the Academy of Sciences, she was stopped by three separate Cardinals during the course of her ascent, and told that only members would be allowed to see the Pope.  By the time it was her turn to speak to the Pope and shake his hand, she laughed to recall that she was very angry.

"I told him that I was one of five female members of the Pontifical Academy," said Dr. Rubin, "and that was all I said." 

In response, the Pope looked thoughtful, said, "Oh?" and paused.  "Is that all?" he asked, to which she replied, stonily, "Yes."

"Well, there will be more," replied the Pope, and that concluded the interview.

Over the course of the evening, Dr. Rubin was inducted into Sigma Pi Sigma, joining many of the students present who were also members of the SPS honor society.  When she accepted her certificate and pin, she told us how envious she was of all of us, because we would go on to learn and discover the things she did not yet know.

And that—whether you got into science because you can see the stars from your bedroom window, or because, like me, your parents watched at lot of Star Trek—sums up both the privilege and the bane of being a scientist.  We do, especially at conferences like these, get to experience something of the breadth of what human beings have learned about our world and our universe, which grows steadily year by year, and encompasses more fascinating things than one lifetime alone could spend in awe over discovering.  And yet the more we discover, the more we realize what remains that we don't yet know, what we won't be able to know until more scientists and fresh insight come along to uncover it.  I wonder, and I certainly hope, that the mysteries of dark matter are solved, the elusive Higgs found, and any potential climate crises averted with new and more sustainable technology, within my lifetime.  Yet by the time any new discoveries come to pass, I'm sure there will be even more fascinating questions to explore.

Saturday, April 3, 2010

Yours Truly Presenting -An Evening At PARI

Here's the official press release (written by PARI staff):

"Rosman, NC (March 24, 2010) – The public is invited to a special presentation concerning solar energy Friday, April 9 at the Pisgah Astronomical Research Institute (PARI). The evening’s activities will include a tour of the PARI campus and celestial observations using PARI’s optical or radio telescopes.

The program is part of PARI’s monthly Evening at PARI series and will feature presentations by PARI Chief Information Officer Lamar Owen and Alternative Energy Intern Leigha Dickens, a student at UNC-Asheville. “With support from NASA, PARI has become one of the first observatories in the world to make a large-scale commitment to alternative energy,” said Owen. “We have designed and constructed solar arrays that power the telescopes and scientific instruments on our optical ridge. In addition to providing clean alternative energy our arrays serve as a solar energy lab, allowing us to demonstrate to students, teachers, engineers and scientists how to build and use such a system. We’re now inviting the public to share that information and see how it works.”

The Evening at PARI program will begin at 7:00 p.m. with a site tour, followed by the presentation and observing session. Each participant will also have the opportunity to have a photo taken with a PARI telescope and will receive a subscription to the PARI newsletter and a 10% discount on PARI merchandise.

About PARI
The Pisgah Astronomical Research Institute (PARI) is a not-for-profit 501 (c)(3) foundation established in 1998. Located in the Pisgah Forest 30 miles southwest of Asheville, NC, the PARI campus is a dark sky location for astronomy and was selected in 1962 by NASA as the site for one of the first U.S. satellite tracking facilities. Today, the 200 acre campus houses radio and optical telescopes, earth science instruments, 30 buildings, a fulltime staff and all the infrastructure necessary to support STEM (science, technology, engineering and math) education and research. PARI offers educational programs at all levels, from K-12 through post-graduate research. The institute is a member of the NC Grassroots Museum Collaborative, a partner in NC OPT-ED and is affiliated with the 16-campus University of North Carolina system through PARSEC, a UNC Center hosted at PARI. For more information about PARI and its programs, visit www.pari.edu.

Photo caption: PARI Alternative Energy Intern Leigha Dickens, shown here at PARI last summer, helped build the solar array on PARI’s optical ridge and will share her experiences during a special presentation at PARI Friday, April 9. PARI CIO Lamar Owen will provide an overview of solar energy and will share details of the design and construction of PARI’s innovative approach to alternative energy. The presentation is open to the public. Contact Christi Whitworth at 828-862-5554 or cwhitworth@pari.edu for more information and reservations."

I add to this that solar power is hot, energy efficiency is cool.  Yeah, that's right. And that if you want to find a, cough, alternative description of PARI, you could always ask the friendly folks at the alien disclosure group.  They're right about PARI having it's own energy source--that being four arrays of solar panels, one of which I installed, that power a network switch, some small telescopes, a mechanical pump, a computer or two. But I clearly don't have high enough security clearance, cause they modified my memory and I don't recall anything else. *snicker.*

Thursday, April 1, 2010

Particle Physics, Climate Change, and Dinner With Vera Rubin, Part II: Perspectives on Minorties in Physics

 Read Part I here.

Read article full text on the SPS website.  

Two other sessions of interest at this meeting [The April meeting of the American Physical Society] were “Perspectives on The Outlook for Women in Physics”, and “Strategies for Improving the Climate for Diversity in Physics Departments.”  In the former, representatives from industry, national laboratories, and academia presented on recent changes and programs put into place to encourage female representation, while in the later, strategies for improving participation among minorities of all kinds were discussed.  I thought the second session was more valuable because it proposed multiple solutions, and was well attended by male and female physicists, students, and industry workers alike.

The speakers explained several programs that have been put into place to address continued low minority participation in physics, especially at the highest levels of physics achievement.  The list included observational site visits to departments requesting them by the APS Committee on the Status of Women in Physics, workshops in which department chairs receive a crash course on issues and strategies for improving the climate of diversity in their departments, and more recently, broad and open conversations brought to the campuses themselves.  Many of these initiatives have been remarkably successful at mitigating some of the more obvious barriers, such as work/life balance issues, the provision of equal support and networking opportunities for all students, regardless of race or gender, and awareness of unconsciously biased behavior.  Many difficult hurdles have been overcome, though many more remain.

A key feature of these sessions was the discussion of best practices for departments and minority studies.  For departments, one of the simplest suggestions was to make lounges an inviting place for students.  If there are inviting, public places to meet and network, all students have an opportunity to be involved, and some of the informal networking that often leaves minorities isolated can be made more inclusive.  This is something that has worked very well in my own undergraduate department, which boasts a very high proportion of female students, as well as a large proportion of students who are constructively involved with department activities.  Other suggestions included celebrating the accomplishments of all students and faculty whenever such accomplishments occur, and never tolerating rudeness and derogatory behavior, especially if one is not a member of the group being singled out.  Advisors and faculty should take care to build in students and colleagues an identity that extends beyond his or her minority status as the "token" member of a particular group.  Finally, the kind of climate that encourages competition for competition's sake, demands extensive after-hours work weeks, and ignores the concerns of the outside world is something that is becoming increasingly undesirable for young women and men who want to balance a rewarding career in physics with a rewarding family life.  Departments and institutions as a whole should take care to observe how policies might inadvertently deter some of their potential talent.

Some of the advice that came up for women and unrepresented groups is to go after networking aggressively, rather than wait for it to come to you, and apply for grants, funding and positions aggressively as well.  As one speaker put it, in reference to general climate and atmosphere, "Have a sense of humor, but don't be a doormat."  It is important to understand situations and to pick the correct battles, but at the same time, there is no need to tolerate discrimination.

Dr. Sherry Yennello, a speaker from Texas A&M University, commented that "physicists are the best problem solvers there are, so let's wrap our heads around this problem."  With all of the ideas, programs, and open dialogue I witnessed at these sessions, a truly inclusive and collaborative environment is something we physicists seem quite capable of building.

Stay tuned for the final installment over the next few days.