omenti

beyond 3d

Ask a physicist, biologist or chemist what got them interested in science and chances are they'll talk about a dramatic single moment - some refer to it as a calling.  I've written about mine on Sulphur Mountain in Banff.  Two young physicists took the time to try and explain their cosmic ray telescope.  Much of it was beyond me but the idea that something from outside our solar system slammed into the upper atmosphere and created a shower of other particles stuck.  And that these wouldn't live long enough to make it from the upper atmosphere to their telescope unless time was different for them.  I had no idea how that worked, but the fact that they could show that universal time - a master clock for the universe - didn't exist ate at me for nearly two years.  I didn't know it but I was about to become a physics student.

 

Somehow I found two correspondence mentors who taught me a little physics and more math.  Two years after Sulphur Mountain I finally understood why time ran more slowly for those speeding muons than for me.  That and what E =mc² really meant and how Einstein figured it out.  Einstein figuring it out was extraordinary, but more extraordinary is Special Relativity is simple and clear - beautiful - even if the results seem odd.  A high school student could read his paper and follow everything with just basic algebra and trigonometry.  

 

There are more than a few explanations in print and online.  To really learn it you need to puzzle it out for yourself with pencil and paper guided by a good textbook and problems.  Instead I'll talk about how he came to that flash of insight. 

 

Around the age of sixteen Einstein had been kicked out of the German school system.  He moved to Switzerland and spent a year at a school that put a premium on visualization and individualism.  There he learned about electromagnetism - light was just oscillating electric and magnetic fields that traveled at the speed of light. He found himself wondering what it would be like to run alongside a beam of light. Could he visualize what these fields looked like?

 

Maxwell's equations said that electromagnetic radiation - light - travels at 300,000,000 meters per second in a vacuum.   If he was going that fast the fields would vanish.  That didn't work.  Since Galileo physics was built on the idea of relativity.  The laws of physics didn't depend on how fast you are traveling.  All you can measure is the velocity of one object relative to another.  He had run directly into a wall.

 

For a decade Einstein kept at the problem.  Finally he went with a crazy idea (to be fair he tried a few crazy ideas).  What if the speed of light was the same for all observers no matter how fast they were moving? If you were on a train traveling at 80% the speed of light and pointed a flashlight forward, you'd measure the speed of light from the flashlight as 300,000,000 meters per second, as would a stationary observer watching from the ground as your train sped past.

 

The way out of this paradox was the person on the train and the observer on the ground experienced time differently.  Two events can happen simultaneously for one observer and at different times for another and both could be right.  Understanding exactly how that works requires learning about special relativity and you can't avoid the math and some sketches.    

 

Einstein offered the following gedankenexperiment (thought experiment):  An observer near a train track watches a speeding train go by.  Exactly as the midpoint of the train goes by two bolts of lighting strike the train - one at the front, the other at the back.   The distance from each strike to her is exactly the same and she says the lightning strikes were simultaneous. 

 

A passenger is sitting at the train's exact midpoint.   Because the train is moving the light from the pulse at the back has to travel a bit further than the pulse from the front. He says the strike at the front of the train came first.  They weren't simultaneous.  The key is it's simultaneity that's relative.  Once you understand that the algebra is simple.  The construction you are left with is space and time are intimately connected in a four dimensioned coordinate system called spacetime.  Spacetime doesn't change, but objects in the 3d world we perceive and time have different measurements for observers who are moving relative to each other.

 

I remember the amazing feeling when it came together in my mind.  It was early June around sunrise.  I got on my ten speed and rode as fast as I could.

 

 

 

 

lessons

Recently Om wrote an excellent piece on Derek Jeter’s career and some lessons one might draw from it. Even if you don’t like baseball, it’s worth reading.

 

Consistency, finding opportunity, leading by example .. and the ultimate goal.

 

One of my heroes is Ray Davis. I got to know him when I was a grad student and postdoc at Brookhaven National Laboratories. He was an experimental physical chemist who was doing some interesting solar physics. He was also of those people who mentored those more junior by example. I sailed with him on his homemade sailboat and joined him on numerous nature walks around the BNL installation as he photographed almost everything. He’d show up on Mondays with bandages from whatever home repair he had attempted. 

 

It’s worth reading a personal statement he made in 2002

 

also check out how people recognized him at the bottom. I’m sure he didn’t put that in himself. He was exceptionally humble.

 

His statement doesn’t go into the controversy and drama of the Homestake Gold Mine experiment. By 1960 physicists had a good idea how fusion took place in the Sun. It’s a somewhat complicated multistep process and different from how manmade fusion machines or bombs work. Some of the energy is released in the form of neutrinos. You may have head about neutrinos. They have a very small mass and barely interact with matter. A standard comment is more than half the neutrinos that strike a piece of lead a light year thick will travel though as if it didn’t exist. But the Sun was making a lot of electron neutrinos and a few will interact. In the late 60s Ray decided to count them and nail down what was going on in the Sun’s core.

 

He was exceptionally careful. Every month he was able to count about three dozen argon37 atoms They started out as chlorine37 but were turned into argon37 when an electron neutrino struck them. Ray spent years making sure hhis results were accurate. His numbers were very consistent… and about a third of what everyone knew was required for the Sun to shine like we see it. It seemed eithre Ray was wrong or the solar models were wrong. Ray persisted. People were in awe of how careful he was. The solar models were also holding up in other tests.

 

It turned out new physics was afoot. Ray was only sensitive to one type of neutrino - the electron neutrino - the type the Sun had to generate. What they found, when another observatory was built that detected another type was neutrinos oscillated from one type to another as they sped along. It was as if your Ford changed into a Chevy and then a Toyota regularly. You owned a “car” that was an admixture of these different brands. Startling new physics. Ray had peered into the core of the Sun with a tank of chlorine about a mile underground in South Dakota and by not giving up when the numbers seemed wrong, found Nature was answering with a new question

 

Ray was sprinkled with Swedish holy water in 2002 for his work.

 

It is remarkable that his institution - BNL - gave him that level of freedom. It’s also remarkable how he stuck with it and impressed all of us with the beauty of his work.

 

lessons…

connecting the titanic, sputnik and dealing with forgetfulness

1955, Fred Whipple had just been appointed to head the Smithsonian Astrophysical Observatory in Cambridge.  The International Geophysical Year was less than two years away and he wanted to involve citizen scientists as much as possible.  Whipple was one of the few who realized a satellite was likely and set about creating a web of radio operators to monitor and relay transmissions from satellites along with groups of amateur astronomers who could optically track their orbits.  Operation Moonwatch was formed and by Sputnik's launch over 200 teams were in place. 

 

Tracking a satellite was done with a clock and a low power telescopes that could read azimuth and declination.  The National Bureau of Standards time signal broadcast on WWV in Fort Collins, Colorado used as the reference clock and most people into amateur astronomy had a shortwave radio. Readings from stations separated by hundreds of miles were sent by amateur radio operators to a computer at MIT that gave the project a bit of its precious time.  More clusters of readings would come in from around the world and a model of the satellite's orbit generated an ephemerides - predictions of where it would be. Later specialized cameras were developed by Bell Labs to automatically generate satellite ephemerides as well as tracking ICBM tests, but Moonwatch was a success and lit the imagination of a few people.  

 

In physics it's common to turn a problem on its head to gain a bit of insight.  Operation Moonwatch used known positions on earth and an accurate clock to measure a position in orbit.  What if you put synchronized clocks in space and measured how long it took radio signals to reach a position on earth?  With enough satellites with synchronized clocks you could triangulate a position anywhere on the Earth's surface.  The technical details were difficult details, but the basic idea was simple.  

 

It turns out accurate navigation is very difficult and expensive and a limiting factor in fighting the cold war.  It was so difficult that as technology progressed ARPA decided to push ahead with a satellite based global positioning system - the inverse of Operation Moonwatch.  It was a bargain for what it gave to the military.  Finally a good enough signal was made available to civilians and navigation changed.¹ 

 

GPS doesn't work everywhere.  It would be nice to track things indoors and at a lower cost. Bluetooth and WiFi are currently used -  usually measuring signal strength from several transmitting beacons and triangulate a position.  Sometimes it's just proximity to a single beacon - a lighthouse model.   The approaches aren't very accurate - three to ten meters is common.  Good enough to track your phone as you move around, say, in a mall or subway, but doing better would be nice.

 

This is where the Titanic comes in..

 

On April 15, 1912 the Titanic struck an iceberg.  Frantic radio signals went out, but there was confusion among rescue vessels and people on land trying to coordinate the rescue effort.  Sometimes it takes a disaster to create order and an effort to regulate radio frequencies began soon after. Transmitters were assigned narrow swaths of the electromagnetic spectrum that were large enough to effectively communicate with receivers that could tune to those frequencies. Regulations changed as larger chunks of this resource were needed - AM radio required more than Morse Code, FM radio even more and television much more. Government would parcel out these increasingly scarce resources, but power was also regulated and it was possible to give much larger chunks to low power short range communications - WiFi and Bluetooth are examples.  Most of radio engineering tried to pack as much information into as little spectrum as possible and to build transmitters and receivers that could be accurately tuned to specific frequency ranges  If you waited for some technology to catch up there was another way (actually several, but I'll only mention one) way to do radio.

 

You may have heard about ultrawideband (UWB).  In the mid 2000s it was supposed to be a good way to send large amounts of information over short distances.  Cheaper and higher bandwidth than the WiFi of the day. Often existing technologies are improved with scale and an embedded base making it difficult for new players.  Sophisticated coding technologies and enormous penetration (WiFi has greater penetration than smartphones) cemented WiFi as the prime high bandwidth low range wireless connection.  In a few years UWB went from redundant to lagging. Many thought it was dead, but it had a few advantages in some use cases.   

 

Here's how it works.  Rather than sending out a precisely tuned narrow band frequency, UWB sends out narrow (in time) digital pulses that "splash" over a very wide frequency range.  The signals are usually only one or two billionths of a second long and aren't sent that often - a hundred thousand to ten million a second are common rates. The frequency range is so wide that usually at least some of it can pass through objects that block signals like GPS and WiFi.  It's also so weak that narrowband communication can't detect it.²

 

 Imagine scattering a few UWB transmitters around where you know their location with some accuracy.  Now start transmitting synchronized pulses.  A receiver notices the time of arrival of each signal and, using the fact that light travels about 30 centimeters in a billionth of a second, can triangulate it's own position.  Accuracy is about ten centimeters - about four inches.

 

A use case I'm familiar with is finding the locations of players in a beach volleyball game.  In international FIVB games a very small (less than a half ounce) UWB device goes in the back of each player's  shirt or sports bra.  Their positions are tracked within ten centimeters about a hundred times a second and accelerometers and a compass send out rotation and orientation information on the UWB signal that the announcers, coaches and sports science people use.  Four transmitters are used and all four players are easily tracked.

 

It would also be useful for augmented reality and Apple has included an UWB chip in every iPhone 11 - the greatest deployment of the technology so far.  For now it's being used for data transfer, but wait a bit.  Someone could also make very cheap ($10 or less) postage stamp devices that might be powered by available light that could be location tags.  Put them on your keys, glasses, remote control .. anything you tend to lose track of.  We went through trying to manage dementia with my mother.  I would have paid a lot for this capability.  And thousands of other uses from amateur sports to tracking boxes accurately in warehouses.

 

There are probably some bad things that can be done with it.  We need to be thinking these things through, but our track record isn't exactly good. 

__________

¹ It also gives a very good frequency standard and a timing signal.  Without this our mobile phone system, high frequency trading and a host of other core technologies we depend on would break.  This is an issue as GPS is vulnerable to attack and we've done almost nothing on backup technologies. 

² The FCC defines it as taking up at least 500 MHz of spectrum somewhere from 3.1 to 10.6 GHz.  Power is under -41.3 dBm/MHz .. or 75 nanowatts.  Since it only deposits a tiny bit of power in any narrowband frequency, it's just below the noise floor of a narrowband receiver.  Fortunately it's straightforward to build a receiver that can detect the signal. 

hacking creativity and collaboration

A recent Bell Labs reunion celebrating the 50^th anniversary of Unix gave me a chance to visit with old friends I hadn't seen in a long time.  Some of the people had moved into industry (Google was a popular landing place) and others found university posts.  I found myself thinking about the differences between the evaluation process of major research universities and the old Bell Laboratories.

 

In a run that lasted about five decades Bell Laboratories - call it Bell Labs Classic - was arguably the most applied research organization in the world.  There were certainly warts and missed opportunities and it effectively came to an end about five years after the mid 80s breakup of AT&T, but it was an astonishing place while it lasted.  I'm continually been struck by differences between that institution and almost everything else I've run into.

 

In universities hiring and promotion (tenure and beyond) is strongly connected to ten or so recommendation letters from leaders of the field in different universities. The authors are almost always experts in the same subspecialty as the junior researcher.  Bell Labs was different. There was an internal ranking that extended throughout the research organization. A department head would rank their people and the results were merged with the rankings from the other department heads in the same center. These rankings would then go through the same process for the next two levels up until a ranking of the entire institution existed. An expert in a field might receive fantastic marks inside their department, but do poorly further up in the process as others might be unaware of them. Interdisciplinary work would stand out and the highest ranked people tended to have one solid speciality along with work in centers far removed from their own.

 

I entered the Labs as an experimental particle physicist. There were a number of physics groups, but no particle physics. I was initially assigned to an applied physics group and found myself working with a number of other groups as I scrambled to find my way. In the process I made connections inside and outside the center and found some encouragement to trade help with others.   All researchers were given the title of  MTS  - member of the technical staff.  It resulted in a certain equality that made approaching others easy.  

 

Most researchers weren't interested in management, but there was one small step up.   If you were in the top ten percent or so for a number of years you became a distinguished member of the technical staff and given more freedom. In my case I was initially given a day a week and resources to do anything I wanted.  Those projects were all collaborations far from my home organization. 

 

Guaranteed funding for pure and applied research went away about five years after AT&T's breakup and folks had to attach their work to business units. It’s what killed Bell Labs, but realistically it was the only logical path for the company at the time. Bell Labs Classic could only exist as part of a regulated monopoly, but that’s another story.  

 

Some universities are playing around with this kind of ranking to stimulate interdisciplinary work. I don’t think it works in industrial applied research.. at least not at scale, but it might be worth considering.  Of course there are different mechanisms in other organizations - places like Pixar - but the difference between Bell Labs Classic and research universities is quite possibly the result of collaboration encouraged by a simple ranking process.

 

mad science

It seems Apple released a new smartphone yesterday. This one has several reasons to make me want to upgrade, but the most drool-worthy is its power as a computational camera.  I'll leave it to other to write the reviews and compare it to Google's efforts - a new iPhone isn't in my budget this year.  But perhaps a few words on computational photography are relevant.

 

Computational photography has been around for over sixty years.¹  In particle physics you slam particles into each other and carefully study the wreckage that emerges from the collision. About sixty years ago bubble chambers came into use.  The idea was to record the wreckage in three dimensions.  A chamber was filled with a transparent liquid like liquid hydrogen, kept just below its boiling point. Just before a fast moving particle entered the chamber a piston at the bottom of the chamber was dropped suddenly causing  the liquid to superheat. The incoming particle collides with a particle in the liquid - usually a proton if the liquid is hydrogen - and charged particles from the collision leave a trail of tiny bubbles in the sensitized superheated liquid.   Three cameras at right angles to each other simultaneously captured three views of the bubble tracks and the piston is moved back into position waiting for the next collision.  

 

A large magnet surrounds the chamber causing the particles to bend one way or another depending on their charge.  The slower a charged particle moves, the more it curls.  The photographic sheets are developed and "girls" - it was considered women's work - would trace the tracks by hand with digitizers creating lists of coordinates for each track that a computer program could use to compute the fundamentals of each collision.²  This type of computing was the most demanding of the day.   In the late sixties and beyond recording the collisions directly in digital form using a variety of "counters" took over and the scale of experiments and necessary computation exploded.

 

By the late 70s people were beginning to categorize medical x-rays and ultrasounds computationally and resonance imaging began to emerge.  The computational requirements were stiff in the day, but your phone could easily handle the computing required for your MRI.  It has been argued that this form of computational photography has had the largest impact on human health of any form of computation.

 

Playing with photographic images from telescopes and microscopes was  necessary in science, but the techniques quickly migrated to computer science labs.  Just as the Utah Teapot was the universal test for 3d imaging, a photo known as Lenna was the ubiquitous test for imaging algorithm research in male dominated CS departments during the 70s and 80s.  It wasn't unusual to see her image appear in several papers in a single journal issue.  Journal images today aren't as sexist.

 

Some of what went into academic image processing made its way into Photoshop in the late eighties.  Photoshop went on to be a preferred platform for creative artists to do computational post-processing of their images.  Take a photo on your camera and play with it on your computer.

 

But what if the camera and computer could be combined into something that could redefine imaging?  I'd argue that took place in science some time ago as the imaging part of telescopes, microscopes and particle detectors had began to require built-in computation.  It's been in the past few years we've seen the emergence of a new type of photography in handheld cameras.  Smartphones, with vast development resources, are leading the way and we're on the verge of an explosion of new techniques and ideas.

 

At this point it would make sense to talk a bit about the basics of 2d fourier transforms to get a sense of how that's done.  Here's a short non-technical introduction that gives a sense of a basic function.

 

 

The computational power of the latest smartphones is staggering and, at least in Apple's case, a good deal of it can be devoted to computational photography.  Currently much of it is used to improve snapshots that would otherwise be unusable.  Noise can be reduced while still keeping important detail - often using psychological models of human perception, the dynamic range of an image can be extended by taking a number of shots and bringing out detail in dark areas and suppressing burned out overexposed regions, realtime video can be overlayed with other information creating a computation synesthesia of sorts, machine learning is becoming useful in many ways,  .. the list goes on and on.  

 

I'll offer one that could appear in about a year with the next generation of smartphones.  Time of flight image sensing is now sort of practical for a smartphone and will probably be a feature in high volume phones like the iPhone next year. Basically a pulse of infrared laser light is sent out to an object and the time it takes to go out and return is used to calculate the distance.  This is done for a somewhat smaller image than your camera takes - a few hundred thousand to a million pixels. But these pixels now have distance information in addition to enough image information that it can be used to create a distance map for the full image from the main sensor.   This could be very useful in augmented reality, but here's one I'd like to see.  Take two or three phones on tripods and point them at a dancer, athlete or someone getting physical therapy.  A very accurate motion capture video could be quickly made and you wouldn't have to spend $50k and up on specialized equipment.  Coaches and physical therapists would be delighted. 

 

A thousand other uses will emerge we haven't thought about. Independent of their platforms there are strong reasons why Apple needs a great computational camera.  What will separate winners from losers will be usefulness, playfulness, and great user interfaces and experiences.  That's the hard part. 

 

For the best photos a good photographer is still required and the tiny lenses and sensors on smartphones are limited by basic physics.  But always having a camera with you and one that can correct basic mistakes is a serious plus.  That and there are emerging capabilities that will take photography in new directions.  

__________

¹ digital computational photography.  I won't go into details here, but optical computation has been around even longer.  If you're interested in the subject realize a lens is an optical computer capable of creating a Fourier transform.

² I like this example as a neutrino slams into a protron bangnig the vacuum hard enough that a D⁺ (d plus meson) appears.  It is composed of two quarks:  charm and anti-down.  I have a fondness for charm quarks:-)  Also this was made during the twilight of bubble chambers in the late 70s. 

 

 

 

abigail van allen's layer cake - catalyst for the last half of the 20th century

I was in my second year of grad school and had gone to dinner at my advisor's house.  These dinners were always interesting and the deserts were a near match.  That night we had a wonderful homemade cake.  A layer cake rolled in the shape of a log, filled with fresh fruit and coated with a thin layer of bitter chocolate.  One of the guests - James Van Allen - yes the guy the Van Allen belts are named after - remarked on the cake and told us the story about Sputnik starting the space race was all wrong.  The real beginning came years earlier in his living room over his wife's excellent layer cake.  Reality is often more fascinating than the recent history we hear in school.

 

It was around 1953.  Van Allen and a group of physicists were at his home after a formal meeting.  This night a critical step was taken.  After talking about new learnings from balloon and sounding rocket explorations of the ionosphere.  Someone suggested maybe an Earth orbiting satellite would be possible soon.  After all - this von Braun guy was making a lot of noise about space travel being practical.

 

Indeed Wernher von Braun had been trying to popularize space travel.  He had teamed up with science fiction writers and later with Disney and Collier's trying to convince the public. Although von Braun was charismatic, he wasn't taken that seriously.  The only thing the government wanted him for was leading the Army's program to be rockets that could deliver nuclear weapons.

 

Enjoying the excellent cake was someone who could make a difference.  Lloyd Berkner was one of the most respected scientists in the United States.  He had the ear of generals and even the President.  He made an interesting suggestion.  Maybe the way to learn more about near space would be a multination collaboration like one that explored Antarctica.   Given global tensions it could be useful for political reasons and would spread the costs. Larger sounding rockets could be built along with expeditions to the poles.  Maybe even a satellite.   Everyone at the dinner loved the idea and the International Geophysical Year was proposed soon afterwards.  Ultimately dozens of countries and hundreds of scientists were involved.  The target year would be 1957.

 

Van Allen and the other near space guys kept proposing satellites with no luck.  Then, a few years later, Berkner found the key.  President Eisenhower was focused on avoiding WWIII and countering the Soviets.  Something like a satellite for science was nothing but a distraction.  Berkner had used the "it will shock the other side" argument without luck.  Then he changed gears and suggested it could lead to spy satellites.

 

Eisenhower was a general.   Having great surveillance is deeply embedded in military DNA.  Spies on the ground, high altitude aircraft, code breakers .. whatever it took.  The only trick with a satellite, Berkner said, would be to establish Earth orbit as neutral territory.  A small scientific satellite could set a precedent.   Eisenhower agreed and the Navy ultimately won a competition to work on Project Vanguard - a satellite to be instrumented by Van Allen's team. 

 

The Soviet Union's ICBM project was led by a scientist more interested in space flight than ICBMs.  He realized an ICBM would make a dandy satellite launcher and when Khrushchev took power managed to convince him on an ICBM program and added an Earth orbiting satellite would have a great political impact.  Khrushchev agreed, but what he really wanted was a big ICBM.

 

Through the International Geophysical Year interactions it had become clear that the Soviets were building a satellite - indeed that it would launch in the Fall of 1957.  It seemed like a fantastic cap to the year, but the knowledge and excitement didn't go beyond far that group.

 

When Sputnik (fellow traveler) launched it was mostly ignored by the Americans - certainly the government.  The New York Times made a big announcement and people went out to look.  Satellite tracking became almost a hobby for some (that was the genesis for a global positioning system, but that's another story), but America wasn't quaking in fear.

 

The American government was happy - perhaps delighted.  They weren't first, but this little Soviet metal sphere orbited over American territory several times a day.  Precedent had been established. It would take time, but the Americans would get their spy satellites.

 

The story most of us know came from Texas.  Lyndon Banes Johnson worried whoever controlled space could control Earth - an old sci-fi trope.  LBJ also happened to be the Senate Majority Leader.  He gave impassioned speeches about falling behind.  His words resonated with the public and early American rocket failures only increased public anxiety.  

 

And what about Van Allen and the other scientists?  Johnson managed to open the serious money spigot.  It became clear that ICBMs made great satellite launchers with modest changes.  The scientific study of space was a dandy idea to help prove in new rocket technology.    STEM education in the public schools sprang up largely out of Berkeley and MIT.  The world was changing.

 

The Van Allen Belts?  They were discovered using the early Explorer series of satellites in 1958.  The interaction of the Earth's magnetic field and the solar wind was beginning to sort out. 

 

So that's the secret .. really good layer cake.

 

why revolutions sometimes need astonishing simplicity

Physics is, by far, the simplest science.

 

I probably have said it too much and it can raise eyebrows. It may not seem that way as we have a reasonably deep understanding and the required knowledge can seem esoteric, but that complexity isn't central and misses the point. What is astonishing is that you can often make seemingly absurd simplifications - spherical bodies, frictionless surfaces, planets that behave as if they were points - and get not only a pretty good answer, but a deep understanding of what is really going on - a hint of how Nature really works.

 

Galileo Galilei was said to have dropped balls of similar size, but different weights from the Leaning Tower of Pizza and summarized that they fell at the same rate.  In fact he probably never did the experiment.  Instead he rolled balls down inclined planes showing their acceleration depended on the angle of the plane rather than their mass.   He suggested a very high angle (vertical) was equivalent to balls of different weights falling at the same rate.   The acceleration from gravity was more important than friction against the plane and air resistance. Assuming you understood air resistance and friction against the plane you could add these effects later and get a better answer.  His insight is probably the most important idea in physics.

 

This realization that physics was fundamentally simple brought together ideas from a variety of sources and led to an idea that went beyond revolutionizing physics to revolutionizing how we think about our place in the Universe - the conversation of momentum as articulated in Newtonian physics.

 

Before Newton and Galileo Aristotle's physics was grounded on natures and causes. Whenever something moved there had to be a mover.  When it stopped it was because the mover gave up.  There were four elements- air, fire, water and earth.  Earth and water's nature was moving down, air and fire went up.  All transformations had some underlying cause.  Push a cup on your desk and it moves.  Stop pushing and it stops.   The conservation of momentum would say give it a push and it starts moving until opposed.  In fact friction opposes its motion. For many of the things people did the Aristotle's model was fine - in fact we often think about the world that way.  But look more closely and it fails to predict what's going on. 

 

It would be natural at this point to talk about Newton and the marriage of math to physics as it started to become a science. I'll skip that and move to someone you may or may not be aware of - Laplace.

 

Pierre-Simon Laplace came about a century after Newton.  Newton was deeply religious, but his God was not as interventionist as earlier thinking required.  God created Heaven and Earth and started everything moving.  Then, thanks to the conversation of momentum, simple things like the motion of the planets went on without any intervention.  He noted there might be some problems every  once and awhile that would demand attention, but God could kick back and do other things.

 

Laplace was probably the first person to understand Newtonian physics at a deep level - certainly much deeper than Newton.  As he advanced the math and physics he had a remarkable insight.  He knew how to answer the question "what determines what happens next?"  The answer appears to be more philosophy than physics, but it's deeply rooted in the later.   It's also simple - "the state of the universe precisely now."

 

Many see this as a contradiction to free will, but it applies to systems simple enough that we have enough information about them.  That happens to include a lot of fundamental physics.   Biology and sociology are far too complex for us to deal with exactly.  Classical physics is, at its core, non-teleological.  What happens is not determined by final goals or causes.  In fact we don't have to know about the past either - just the now.  The fly in the ointment is you have to know a lot of information.  All the relevant information for every point in the Universe.  This led to the idea of fields being important - information attached to every point - which is at the foundation of modern physics. 

 

This insight is often called the conservative of information.  Words are loaded and easily misused out of context and this is a very specialized.  It's the exact state of everything at a given instant of time.  Conservation implies the information that exists is exactly what is needed to determine the next moment allowing you to move ahead in time. 

 

The conservation of momentum and information are deep ideas with an enormous impact on how we think about Nature and all of physics, not to mention the technological byproducts that have changed how we live.  All of this was set in motion by understanding physics - the study of  matter and motion - can be stripped down to a bare simplicity if you're sufficiently clever.  

 

This way of thinking - stripping down to simple enough - is part of the playfulness of the sport. The approach can be useful in some other areas, but only if you have a handle on local limitations. 

 

why are we here?

The professor drew a box around the words and added "do not erase" at the bottom.  That marked the opening of a two semester course in General Relativity.  He never commented directly, but its presence was anything but subtle . 

 

The circumstances under which Karl Schwarzchild wrote three significant papers in 1915 were a mixture of ideal and and anything but.  An artillery lieutenant in the German army on the Russian front, he had contracted a disease that would kill him a year later  Before the war he was a physicist and astronomer.   In the army he managed to find access to current papers and had become fascinated with Albert Einstein's brand new General Theory of Relativity.   The formula for General Relativity had written looks simple, but each symbol represents some very complex mathematical objects.  Einstein was unable to solve them exactly and his prediction of the precession of the perihelion of Mercury's orbit was only an approximation.

 

It seems strange that Einstein, with his beautiful geometric approach to General Relativity, tried to solve the problem in rectangular coordinates.  In a few months Schwarzschild created a novel coordinate system and was able to solve a simple system exactly with what is now known as the Schwarzschild metric.  Schwarzschild sent it to Einstein for comments with this preface.

 

As you see, the war treated me kindly enough, in spite of the heavy gunfire, to allow me to get away from it all and take this walk in the land of your ideas.

Einstein was delighted

I have read your paper with the utmost interest. I had not expected that one could formulate the exact solution of the problem in such a simple way. I liked very much your mathematical treatment of the subject. Next Thursday I shall present the work to the Academy with a few words of explanation.

 

The simple case was simple indeed - a non-rotating spherically symmetric mass.   Still there were remarkable conclusions.  At long distances it reduced to Newton's gravitation equation, but close to a large mass there was a point where nothing - not even light - could escape from its surface.  Any number of crazy things would happen as you neared this event horizon. Inside everything would collapse to a point - a singularity.  Furthermore any initial configuration of matter (dust for example) would gravitationally attract and, if there was enough of it, collapse into a black hole.

 

About two weeks into the course we had enough differential geometry under our belts to look at the Schwarzschild metric.  I remember looking up at the words on the upper right hand corner of the board and wondering why our Universe hadn't collapsed into a black hole - like almost instantly after it was formed.  Wasn't there an enormous mass in a tiny space?  I worked out the Schwartzschild radius for a mass the size of the universe in my notebook margin.  Why didn't this happen?

 

The next week it became apparent why.  The metric was for a static universe. General Relativity had a lot to say about non-static universes although that wasn't accepted until the next decade.  There are a number of other metrics that apply to more complex, eg. realistic, universes that do things like expand or contract.  One of these had major contributions from a Catholic priest who basically laid out the mathematical underpinnings of the expanding universe Hubble discovered in 1929, but that's another story.

 

Now it was easy to rule out a static universe .. immediately after the Big Bang (which turns out not to be the beginning) the new universe would find itself within a black hole and would have collapsed into itself.    Or so I thought

 

There's something interesting about General Relativity - you've probably heard the presence of energy and matter curves spacetime.  It turns out there's more -  it also impacts the evolution of spacetime itself.  There are three possibilities that depend on the initial expansion rate.  

 

Too small for the amount of matter and energy and the universe would expand for awhile - perhaps the tiniest fraction of a second - and then collapse on itself.  It's tempting to call it a black hole, but it's worse. Spacetime itself would collapse with it.  Not very promising for life. 

 If the expansion rate was too high, matter would separate so quickly stars wouldn't form.. in fact atoms wouldn't form either.  It's a bad sign if you can't make it to chemistry.   Not good if you want life down the road.

 There's an intermediate case.  There's an exceedingly fine line between collapse into nothingness or expansion into a nearly void.  Here the expansion rate eventually drops to zero with stars, galaxies, planets an us developing along the way.  You want this one.

 

What we now know is a bit more complex.  It's the third case, the goldilocks universe, but dark energy which is causing an accelerating expansion.   It has been slow enough to allow the formation of everything we have.  What really astounds me is the balance.  The fine tuning of the right amount of expansion for the amount of mass energy is precise..   If there had been an extra hydrogen nucleus it would have collapsed.  One less and the infinite expansion would have prevented the formation of complexity.  The words on the blackboard seem much deeper to me now than they did at the time.

 

And if your name becomes associated with something in the public imagination there are always the joke.  Einstein and Schrödinger both mentioned cats so...

northward and beyond!

Yesterday a friend asked for comments on a piece about the recent movement of the magnetic north pole.  The article referred to an update to officially published information about the Earth's magnetic field.  Unfortunately it was both confusing and inaccurate so I typed out a reply on my iPhone.  He suggested I turn it into a blog post.  I'm leaving it unedited and adding a bit on the North Star.

 

This is poorly written. The model is not used for GPS, but rather for compasses… smartphones and cars have compasses, but the accuracy is poor- a few degrees.. this wander is, at middle latitudes, only a fraction of a degree. There are folks who need very accurate compasses (submarines for example) and using them at high latitudes demands a very accurate map. Also GPS denial is a major worry of the military.

The standard model for the planet’s magnetic field is fairly well accepted, but some aspects are not well known.

It’s exceptionally important.. our form of life certainly wouldn’t exist without it as it builds a shield that keeps energetic particles largely from the Sun from reaching the surface. The core of the Earth is mostly iron and a few other heavy elements. It’s about the size of the moon and very hot - about 5700°C if memory serves - but under enormous pressure so it’s a solid. . Just outside is a 1500 or so thick liquid that is mostly iron with a good deal of nickel. This is also a hot zone, although not quite as hellish, and the pressure is now low enough that it’s a non-homogeneous fluid. There’s a lot of movement - in very very slow motion - with slightly warmer plumes rising and the cooling and falling and getting mixed put into circular motions as from the Earth’s rotation (the Coriolis force). The flow of the hot liquid iron generates huge electric currents which, in turn, make magnetic fields. These separate magnetic field regions roughly align along the Earth’s spin axis and produce the planet’s magnetic field.

The motion of the poles is caused by large scale flows going on deep below. To our time scale it appears slow, but it’s been going since the formation of the planet.

Something dramatic takes place every half million years or so although the timing is statistically random. The poles swap. The last was about 700 or 800k years ago (I could be wrong… the number sticks with me) and probably happened very quickly — in a few hundred years or less. There have been short lived reversals since then.. one was during the last glacial period and only lasted for a few hundred years. The Earth’s field dropped to a very low level - like under 10% of the current level - and filled for awhile before going back to something stable.

The strength of the field has been dropping for a few hundred years and there is speculation it might lead to one of these mini events or perhaps even a complete reversal. There are people who feel it is very likely in the “near” future — like the next 5,000 or 10,000 years.

 

On dark and starry nights most people can find Ursa Major - the constellation know as The Big Dipper.  Fewer can find Polaris - the North Star.  The trick is to use the outermost stars of the Little Dipper's bowl as a pointer.  Extend the end of the bowl upwards five times its length and the bright star is Polaris.  It's close to the north celestial pole - the point in the sky you'd find if you extended the axis the Earth spins on straight up.  Polaris is within a degree - roughly the width of your little finger at arm's length and close enough for simple navigation.¹ 

 

Finding North is fundamentally important to navigation.  If you want to be accurate with a compass you need the magnetic corrections.  And to navigate  by the stars you need the celestial north pole.   Literature is full of references.

But I am constant as the northern star,
Of whose true-fixed and resting quality
There is no fellow in the firmament.  (Julius Caesar III i)

A guiding star is mentioned in Iceland sagas 800 years ago.  But it hasn't always been Polaris.  

 

You've probably played with toy gyroscopes.  Spin one up and points in one direction even when you move it around.  But perturb it you  and it can wobble in a circle.  Its spin axis is said to be precessing. The Earth's slightly  non-spherical shape and the gravitational influence of the Sun and Moon conspire to give the Earth a wobble that takes about 25,800 years to complete.   Polaris has been roughy the north star for about a thousand years and is currently about as close to the celestial pole as it gets.  Vikings were navigating in the 8th and 9th century used Polaris even though it was about seven degrees off - enough for large errors if they didn't make corrections.  At the time of Christ a collection of stars in the Little Dipper was used and it was about three degrees off for Columbus.   Shakespeare's Julius Caesar was using a bad metaphor - the North Star isn't North over time.   But it's even less reliable in another way and that makes it fascinating.

 

Polaris is a bright and fat yellow star about two thousand times brighter than the Sun and nearly fifty times the Sun's diameter.  There are two smaller companion stars making it wobble back and forth a bit..  If you can make accurate position measurements it isn't steady.  Even more dramatic is the fact that its brightness changes on a regular basis . well, sort of regular. (did I mention it was fascinating?)

 

A bit over a hundred years ago Henrietta Swan Leavitt made a discovery that revolutionized astrophysics and astronomy.  She showed the intrinsic brightness of a certain type of variable stars called Cepheids was directly related to the time it took to change brightness.  She ha given astronomers an important method to measure stellar distances.  The fact she didn't receive a Nobel Prize is an astonishing example of sexism. As Nobels go this would have been one of the more important.

 

Polaris is about 450 light years away - the closest Cepheid.  Think of it as a nuclear powered internal combustion reciprocating engine (although technically there isn't any combustion).  In Cepheids a carbon core is surround by thin shells of fusing helium and hydrogen.  The cycle starts with the helium  being singly ionized - the temperature is such that one electron is missing (He^-) . Gravity pulls the shell inward compressing and heating it.  Enough heat that the second electron is stripped away.  Doubly ionized helium  (He^{- -}) is more opaque to heat transfer than the singly ionized variety so it heats up in a hurry.  As it heats it expands beginning to cool in the process.  Finally it's cold enough that electrons from the plasma soup in the layer re-attach and He^{- -} is becoming the He^- variety. Radiation now flows more easily and the star gets brighter as it expands.  But now enough radiation is getting through that gravity begins to pull in the He^- and the cycle repeats.  A huge engine chugging away.  When the largest engines on Earth were at around ten thousand horsepower, Henrietta had worked out the secret of vastly larger engines.

 

Polaris isn't exactly your garden variety Cepheid.  In addition it's getting brighter - ten percent brighter in the last century.  (this would be a true disaster if it happened to the Sun..  most life would be snuffed out in a hundred years and the oceans would boil away a hundred years later)  To make things more interesting the change in brightness throughout the star's period got much weaker almost vanishing in the 1990s - but now it's returning. There are some interesting hints and more than a few conjectures, but it's still a mysterious object. Curiously it was discovered to be emitting X-rays.  That usually implies a super hot atmosphere driven by an extremely strong magnetic field.  Where it would come from is still a mystery,.

 

It's humbling to realize how much we can learn by looking at these tiny points of light in the sky and asking really good questions.

__________

¹ As seen from Earth the Moon is about thirty minutes of arc in diameter - a half degree.  Here are some rules of thumb that are close enough for most people.  If you're really tall with long arms your hands and fingers are usually a bit larger.  If you like you can calibrate your hand.  These are all at arms length

1 degree - the width of your little finger

5 degrees - the width of your three middle fingers side by side

10 degrees - make a fist and hold it with the back of your hand facing you.  

25 degrees -  stretch your thumb and little finger as far away from each other as they'll go. Tip to tip is about 25 degrees

15 degrees - a bit out of order .. like the 25 degree measurement, but between your index and middle finger.

 

smoke rings, sports and beyond

Canals saw explosive growth in England during the first few decades of the Industrial Revolution allowing raw materials like iron and coal to fall in price by as much as eighty percent.   Improving canals became a major industry - they became straighter with locks and aqueducts coming into wide-spread use to deal with changes in elevation.  Then, around 1840, railroads became the thing and many of the canals were purchased for their right of way.  The expansion of railways led to two of the more dramatic financial bubbles in history, but that's another story.  The story here is about something really interesting that happened just before the railroads started taking over.

 

James Scott Russell found himself working on a large canal near Edinburgh, Scotland.  A newly minted engineer, he had been hired to investigate the movement of barges in the hope of making them more efficient.  Russell spent a lot of time observing and making measurements.  One day the tow rope between the mules and the barge snapped and the barge came to a sudden stop.  He watched in amazement watching mass of water in front of the barge's front bow 

“I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat sud- denly stoppednot so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course ong the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beau- tiful phenomenon which I have called the Wave of Translation.”

Afterwards he built a tank in a laboratory to conduct controlled experiments. In 1844 he published his results noting four things about these solitons.

° The waves are stable, and can travel over very large distances (normal waves tend to either flatten or steepen and topple.

° The speed depends on the size of the wave, and its width on the depth of water.

° The waves do not merge, larger waves overtake smaller ones rather than combining.

° If a wave is too big for the depth of water, it splits into two waves, one big and one small.

A few decades later  physicists began to work out the physics leading off in unimaginable directions.  But back to that wave moving down the canal.  If it was large enough you could surf on it.  And, with enough study and money you could build very repeatable waves to your liking.  It turns out a surfer named Kelly Slater did just that.  The December 17^th, 2018 issue of The New Yorker has a great article. 

 

It turns out solitons exist throughout the physical world - smoke rings, packets of light in fiber optic strands and much more.  On light packets - high speed data communication using optical fibers simply wouldn't work without solitons - the bits of information would blur into a muddle at high data rates. The math is a tad beyond the level of this blog - you'd see it in a second year undergrad physics class.  As people continued to work out why it is stable some insight came from that radical moment in 1953 when the computer went beyond a bicycle for the mind to becoming both a telescope and microscope.

 

Physics 101 classes usually have a vortex ring demonstration to illustrate some of the properties of vortex ring solitons.  Smoke ring guns are a lot of fun and fairly easy to build.  Turning them into a really great demonstration takes some effort. Dianna Cowern recently posted her version.  Her enthusiasm is pure wonderfulness.

Recipe Corner

 

The return of recipe corner - at least for today.  This was great last night

 Roasted Brussels Sprouts

 

Ingredients

° 1 pound Brussels sprouts - remove the outer leaves

° 1 medium sized onion - I had a sweet onion (Vidalia)

° 1 largish baking apple (Granny Smith) cut into half inch chunks 

° 1 tbl olive oil (doesn't have to be a great EVOO)

° 1/2 tsp grated nutmeg

° salt

° ground black pepper

° 1 cup apple cider

° 2 tsp butter

° 1 tsp brown sugar

Technique

° preheat oven to 350°F

° everything through the olive oil into a large baking pan.  salt and pepper to taste and toss to coat.  Cover with aluminum foil. 

° roast for about 25 minutes, uncover and stir

° temp up to 375°F and roast with no foil 'til the sprouts brown a bit - 10 minutes for me

° when the roasting begins bring the cider to a boil in a sauce pan over medium-high heat.  Add butter and brown sugar and stir 'til dissolved. Cook at a boil until it is reduced to the consistency of a syrup .. about 15 minutes for me.  I had about 4 tbl remaining. 

° Put the Brussels sprouts into a serving bowl, add the syrup and toss.. you probably need to adjust salt and pepper a bit before serving.