Polarization in Light and Politics

The essence of an electromagnetic (EM) wave is defined by two key parameters: its frequency and the strength (amplitude) of its electric field (E).  The strength of the magnetic field (B) is not a 'free variable' - it is given by E/c, where c is the speed of light.  Light is just one variety of EM wave.  It, like all others, is self-sustaining because the oscillating electric field produces an oscillating magnetic field and vice versa.  The relationship between the orientations of these fields and the direction of wave travel is shown below:

Figure 1: EM Wave Field Orientations (courtesy of: astronomy.swin.edu.au)

Here, the wave propagates in the x-direction, the electric field oscillates in the z-direction, and the magnetic field oscillates in the y-direction.  The electric and magnetic field vectors are always perpendicular to one another and exist in a plane that is itself perpendicular to the direction of travel of the light wave.  If the light wave is headed towards you, then you can be sure that the magnetic and electric field vectors span a plane that faces you.  The field vectors are separated by a right angle.

Wikipedia, a Surprisingly Reliable Science Resource

At first, an active encyclopedia written by and large on a volunteer basis sounds like an ill-conceived plan.  Considering that so much content on the internet is incorrect, the Wikipedia experiment was bound to fail.  But then, something strange happened: it actually worked.

The internet community, which can always be counted on for lewd YouTube comments dripping of ignorance and disrespect, somehow came together to compile a mass of information that is almost always factual (obviously, different parts of the community are at play here).  Yes, some donor money goes to pay tens of employees to overlook things, and do some fact-checking, but Wikipedia remains a database composed by tens of thousands of anonymous members of our global village, and is perhaps one of the best things to come out of the internet age.

Written mostly by amateurs, who have free time to spare, the volume of information grows at a staggering rate: thousands of pages per hour.  This kind of productivity at no cost, but reasonable quality, helps to explain why Wikipedia has flourished and the Encyclopedia Britannica has become all but irrelevant; oh, and did I mention it's free?

But here is the million-dollar question: "Do I encourage my science students to use Wikipedia?"

What Kind of Star are you?

Despite constituting the vast majority of the matter in the universe, stars are surprisingly simplistic.  A star spends nearly all of its life in hydrostatic equilibrium, whereby gravity pulls it inward as thermal pressure pushes it outward.  This state is known as the main sequence, during which countless Hydrogen atoms fuse to form Helium ones, and release energy in the process.

OK, that might not seem simple.  But, a star is simplistic in the sense that its entire future is quite predictable given its mass when this thermonuclear fusion process begins.  We can predict how long this steady radiation will endure based on this mass.  One might think that more massive stars have more fuel to burn, and will burn for longer as a result.  Though more mass does mean more fuel, it also means higher temperature and pressure, which means a greater fusion rate.  Massive stars actually live a far shorter life than less massive ones - lifetime is roughly proportional to M^(-2.5), where M is mass.

In the graph shown below, the approximate time a star spends in its main sequence is shown as a function of its mass ratio to the Sun.

 

What if There Were no Moon?

On one late drive home last week, I looked up at the full moon in the early night sky, and just marveled at its beauty.  And I asked myself the question, "How much different would life on Earth be if there were no moon orbiting around us?"

This may sound like an arbitrary question, but it is a very legitimate one.  Trying to imagine life without the Sun would be a rather pointless exercise, because without a star to govern our orbit and act as a steady energy source, there would be no life.  The same cannot be said for the one celestial body that orbits around the Earth.   

For all of its beauty, the Moon, our singular natural satellite that orbits us roughly once per month, is, for lack of a better word, unnecessary.  Some planets have no moons, some have many (the other night, I looked at Jupiter through a telescope and beheld its four moons) - a moon is, in a way, a planetary afterthought.  If the Moon were to mysteriously disappear tomorrow, the resulting physical changes on Earth would be minimal.
 

Keeping our Heads in the Face of Tragedy

My heart is filled with sadness.  Yesterday's Boston Marathon Bombing is at the front of my mind as it is no doubt for you and everyone you know.  I don't know anyone killed or injured on a personal level, but it is the kind of event that breaks the heart of humanity, and for this reason I feel the need to mourn.

When ugliness becomes so apparent in the world, we feel the need to make sense of it.  I imagine a work of art, so carefully painted by an artist over the course of days or weeks.  The beautiful result can be destroyed in seconds by a vandal with a can of spray paint.  It is so much easier to undo something than to do it.  It is a manifestation of the second law of thermodynamics.  Chaos has a tendency to increase.

When an event that aims to lift the spirits of a city is marked by the sinister act of one or a few rogue individuals, some feel as though we should just give up.  It seems there will always be these bad seeds.  We must remember that such cowards form the tiniest portion of humanity, and in no way represent us.  They succeed in wreaking havoc because it is vastly easier to rain on a parade than to assemble one.

In this dark hour, let us keep our heads, mourn the individuals directly affected, and honour them with our persistence.  We must keep celebrating life despite such acts.  In many ways, life is like a marathon; we must keep running, even when the terrain is so terribly unforgiving.

Unraveling the Mechanics of Spider-Man's Web

My three-year-old has an obsession with Spider-Man.  She has been putting bad guys in jail for the past week with the help of her Spider-Man action figure.  So, being who I am, I could only resist conducting a mechanical assessment of the fictitious hero's web for so long.

I have deconstructed the physics of superheroes before.  My approach is to ignore the mutation aspect - to accept the background story that gave the hero his or her powers.  My concern is instead, given such powers, is the rest reasonable?  For Spider-Man, I'd like to focus on the web that he shoots from his wrist to the buildings of New York City as a principal means of transportation.  Can a thin web realistically sustain the tension that manifests within it when Spider-Man swings through the city?

Consider the awesome illustration below (mad 'Paint' skills) that shows the famous web-slinger swinging from the top of a building using web length 'R'.

If Spider-Man is initially at rest (at 1), then a simple energy conversion analysis (gravitational potential energy converts to kinetic energy) shows that at the bottom of his swing (at 2), his speed v is given by (2gR)^0.5, where g is the surface gravity.  Here, aerodynamic effects were ignored as were any elastic or visco-elastic effects associated with the web.  A free body diagram for Spider-Man is drawn in the figure at the instant the web is vertical (at 2).  The tension in the web points up while the gravitational force points downward.  Applying Newton's Second Law in the normal (n) direction gives the following (note that there is an upward acceleration associated with this circular path):

Ft - Fg = ma

 

where m is Spider-Man's mass.  This becomes:

 

Ft = m(g + v^2/R) = m(g + 2g) = 3mg

Do we Really Improve with Age?

There is no debate as to whether a person's physical well-being improves with age: it does not.  When I was ten years old, and I got a cut or a bruise, it was gone without a trace within days.  Now, at the age of thirty-one, small bumps and bruises linger for weeks, even months.  It is as though my physiology has stopped trying.

When adults confront this reality, they may look on the bright side: as we grow older, we gain experience, and get smarter.  But, is there any evidence of this?  I am beginning to notice that the longer we are around, the more resistant we become to change.  And, if this is so, then our age actually becomes a deterrent for self-improvement.  A relative of mine recently pointed out that as adults age, they simply become more exaggerated versions of themselves.  Think of the seniors in your family - you may find that there is much truth to this statement.

Why do we become set in our ways?  Many reasons.  For one, the effort to improve has a smaller return on investment as we age, as there is simply less time remaining.  Another reason is that change implies we have been doing it wrong, and, the longer we have been around, the harder it becomes to face such a reality.  But, the bottom line is that change is hard because learning is hard.  Seeing the world in a new way - accepting that something is not how you always thought it was - is daunting.  It is something that students are asked to do every day, and it is so clear to me which ones wish to accept this challenge and which do not.

A Talk About the Future

This Thursday, March 14, 2013, I will be giving a talk at Vanier College in the auditorium (room A103) entitled "Robo Sapiens" at 2:30 pm.  The one hour presentation is about the reasonably near-term future of mankind: the next three decades.  It deals specifically with physiological enhancement by way of robotics and biomedical engineering as well as artificial intelligence and the technological singularity.

As most of my readers will not be in attendance, I will briefly discuss some of the content below.

In particular, I want to address the very notion of predicting the future.  Perhaps you have heard the term 'futurist' or 'futurologist' - such a designation befits a person whose predictions for the future are sought by industry, world leaders, and members of society.  It is a sweet gig: state what you think is going to happen in the world of technology, the economy, societies, and our civilization at large some time from now, and no one will fault you if you turn out to be wrong.  Who will bother to look it up?  Rather than dwell on the past, people will still wish for insight into the future.

What process does one use to predict the future anyway?  One usually examines historical trends, takes a close look at the current state of things and the directions in which they are currently headed, and then extrapolates forward.  The result is a guess, but an educated one.

Staying in 'Contact' with Carl Sagan

Though one of my personal heroes has been deceased for many years, he still touches base with me every so often through the amazing body of work that he left behind.  Carl Sagan, science guru extraordinaire, penned some tremendous science non-fiction, from Cosmos to Demon-Haunted World, but also a fair bit of science fiction.  I just finished reading Contact (1985), his first novel, which would eventually become a feature film (1997, the year after he passed) that I have yet to see.

Contact is a tremendous novel by many standards, but one measure is the extent to which it has permeated my consciousness, and it has a great deal.  While reading this tale of a message from an alien civilization and an eventual visit, and in the weeks since, I have stared a bit longer at the stars at night, captivated by the scale of the universe.  I wonder if there are beings on another planet looking up in similar awe at a view not so different from mine.

Stuck in Traffic? Pass the Time with Physics

When I find myself stuck in traffic, my mind first turns to the shortcomings of public transit for my typical commute - a part of me wishes I still lived downtown.  The next place my mind often wanders to is physics; a surprising number of seemingly abstract scenarios actually describe the motion (or lack thereof) of one's car in a system of interconnected streets.

One such analogy is that of a system of interconnected springs and masses:

Imagine that you are the sixth car waiting, single file, at a red light.  The moment that the light turns green, the first car begins to accelerate, but you do not move.  Each car must wait for the car in front of them to displace in order to proceed forward.  It is the same for the system of masses.

If a force is imparted on the first mass, there will be a time delay before the effect of this force is felt by the tenth mass.  We can think of the springs like spaces between cars, and the masses as the cars themselves.  This analogy is far from perfect.  For one thing, cars are more independent than this model would suggest.  Car 1 is unaffected by all those behind it, whereas the motion of mass 1 is greatly affected by the motion of those behind it.