Elements of Relativity

I'm pleased to announce the publication of my textbook on relativity for beginners, The Elements of Relativity.

Relativity is one of the greatest achievements of 20th-century physics, yet we physicists are reluctant to teach it to anyone but advanced students. This is a missed opportunity because lots of people are interested in relativity and there are few real barriers for beginners. You don't need much prior knowledge of math or physics (only some basic geometry and algebra) to gain a complete a complete understanding of special relativity (which includes topics such as how we can travel into the future faster, and E=mc²). Mostly you need to practice disciplined thinking in terms of reasoning from assumptions to conclusions, and being able to identify why an apparently counterintuitive conclusion does not actually violate your assumptions. And that's what makes it a great college course for general education.

General relativity (GR, which includes black holes and gravitational waves) does require a lot of math for a complete understanding, but this does not justify leaving GR entirely out of a general education course on relativity.  For GR a conceptual understanding is goal enough, and the important concepts can be taught in a way that builds on (and reinforces understanding of) special relativity.

In 2009 I decided to teach a course like this. There was no textbook that really matched the course, so I used bits of various textbooks and resources. I soon realized that I needed a unified textbook, so I started writing one. I taught the course several more times with different drafts of my book, and after many years The Elements of Relativity is finally ready for public consumption.

Although the book is for beginners, it is not fluff; it makes you think. If you enjoy thinking and you're interested in relativity, this book is for you. The book would also help physics majors solidify their understanding, if their formal training has emphasized mathematical over conceptual understanding.

You can order the book directly from Oxford University Press, or from Amazon.

"Just" a Theory?

A recently published letter to the New York Times reminds us that relativity is "just a theory" and so is the Big Bang.  Scientists and science educators need to set the record straight on this "just a theory" meme any time we get a chance to discuss science with kids and grown-up nonscientists.  So here's my shot at it.

A good analogy is to think of facts as being like bricks: solid and dependable, but one or a few bricks are not very useful by themselves ("an electron passed through my detector at 11:58:32.01" or "the high temperature in Davis, CA on September 1, 2013 was 96 F").  Only when we assemble lots (lots) of bricks into a coherent structure do we get the benefits of having a building (the theory of relativity, or a climate model).  Not only is an isolated brick rather useless, but the building can easily survive the removal of a few bricks here and there.  A good theory integrates millions or billions of observations into a coherent whole.  Calling relativity "just a theory" is like calling the Great Wall of China "just a fence," the Panama Canal "just a ditch," or the Golden Gate Bridge "just a road."

There's a reason that calling the Great Wall of China "just a fence" sounds more outrageous than calling relativity "just a theory"---I used the word fence which connotes something less important than a wall.  There's a rich vocabulary to describe to describe barriers: from weak to strong we might use tape, rope, cordon, railing, fence, and wall. But most people don't use a similarly rich vocabulary to describe levels of sophistication of mental models.  From weak to strong I might suggest educated guess, working hypothesis, model, and theory, but most people in practice indiscriminately use the word theory for any of these.  So it's our duty as scientists to make clear that well-accepted scientific theories integrate an incredible range of observations into a structure which is so coherent that it is difficult to imagine all those pieces fitting into any other structure.  Maybe a better analogy to calling relativity "just a theory" is calling an assembled jigsaw puzzle "just one way to fit the pieces together."

Gotcha, the just-a-theory crowd says,  by making that analogy you are showing that you are rigid in your thinking and unwilling to accept alternative explanations.  Nonsense. Scientists are constantly trying to prove accepted theories wrong.  Anyone who succeeds in disproving relativity, the Big Bang, or evolution will win a Nobel Prize and eternal fame, so we'd be happy to do so.  But we know from experience that the most likely explanation for an isolated fact that seems to contradict relativity, the Big Bang, or evolution is that the fact itself was taken out of context or is not being properly interpreted, rather than that an extremely well-tested theory is wrong.

This doesn't mean that we will twist any fact to make it fit into our well-accepted theories. It does mean that surprising facts may end up extending the theory rather than replacing it.  For example, Newton's theory of gravity explains a ton of observations about the motions of the planets and stars, but in a few extreme circumstances (such as very close to the Sun) it doesn't predict exactly what is observed.  Einstein developed a theory of gravity (general relativity) which does correctly predict these situations. Einstein's theory is more complicated than Newton's, but in most situations the complicated parts of Einstein's theory have very little quantitative effect so we can simplify it a great deal and in those cases it turns out to be identical to....Newton's theory!  This almost had to be the case, because Newton's theory accounted so well for so many observations that it would be hard to imagine that it was wrong rather than incomplete. 

This example shows that a small number of facts can be critically important and that scientists do pay attention to facts which don't fit the theory.  But we don't modify or overturn theories willy-nilly.  When the planet Uranus didn't move exactly as Newton's theory predicted, modifications of the theory were considered but so was the possibility that some mass other than the Sun and the known planets was pulling on Uranus, and that led to the discovery of Neptune.  If we rejected well-established theories at the first hint of any discrepancy with new observations, we would be giving undue weight to the new observations and too little weight to the vast range of previous observations explained by the theory.  If you want to overthrow a theory because some new observation seems to contradict it, then give us a better theory which explains the new observation while still fitting the previous observations just as well as the old theory.  That latter part seems to be conveniently forgotten by people who want to reject well-established theories.

A closely parallel situation is that of criminal investigators and prosecutors who present their "theory of the crime" to a jury. ("Model of the crime" would better fit my vocabulary hierarchy, but this is the word actually used.)    A lot of facts may be introduced into evidence ("a car with the suspect's license plate was recorded crossing the Tappan Zee Bridge at 2:20am on August 31"), but by themselves they don't mean anything important.  A good theory of the crime provides a coherent explanation of so many different facts that the jury is forced to conclude that it is true beyond a reasonable doubt.  If you want to call it "just a theory" then offer us a different theory which fits the facts just as well.  The defense is given sufficient time and strong motivation to offer a good alternative theory, so failure to present one is damning. 

Turn! Turn! Turn!

This spring I am assigned to work with the Peregrine School 3-4
graders on astronomy, and last Friday was my first day, so I started
with basics like how we know the Earth spins.  We tend to feel
superior to people in the past who believed that the Sun went around
the Earth but, really, how can you use basic observations to show that
it doesn't?  I suspect that most people on the street would be stumped
by this if I didn't allow "satellites" or "NASA" as an answer.

If we only had the observation that the Sun rises and sets every 24
hours, we wouldn't be able to conclude anything.  Each star also rises
and sets in roughly (later we'll see why I say roughly) 24 hours, so
based on pure majority rule, it might be easy to attribute the
apparent motion of the Sun and stars to Earth spinning.  This model
invokes only one thing (Earth) moving, vs the other model invokes a
grand conspiracy of everything else in the universe circling us at an
agreed-upon rate of once every 24 hours.  Sounds like a no-brainer,
but why don't we feel Earth moving?

The kids had lots of ideas in response to this question. It moves so
slowly we can't feel it? No, its circumference is about 24,000 miles
so if it spins in 24 hours its equator must move 1,000 mph.  It moves
so quickly we can't feel it? Gravity?  Centrifugal force? It's so big
we don't feel it move?  There were so many ideas about this that I
decided to explore Galilean relativity: if you are in a laboratory
moving at constant velocity, there is no experiment you can do to
prove you are not actually stationary.  Think about a smooth flight in
an airplane.  If you drop something does it fly backward, indicating
that you are actually traveling at 500 mph?  No, it falls straight
down.  Unless you look out the window, you can't tell that you're
moving---there is NO experiment which will tell you this.  If you do
look out the window, all you can conclude is that you are moving
relative to Earth...there is no experiment you can do that says Earth
is stationary and you are the one who is moving.

This was a pretty new and shocking idea for the kids, so we spent a
long time discussing it.   I remembered a great video I had seen
demonstrating one aspect of this, so I sketched it out and asked them
to predict what would happen.  Say you have a pitching machine which
shoots baseballs at 100 mph, but you mount this machine in the back of
a pickup truck which goes 100 mph the other way.  What will the ball's
speed be, relative to people on the ground? 200 mph? 100 mph?  Zero?
We analyzed this until break time, then after break I showed them the
video.  Mythbusters also did a similar thing, which you can see much more clearly.

The bottom line is that velocities are relative.  So if everything in
your vicinity is moving together at the same speed, it can all be
considered stationary.  This applies to your vicinity on Earth:
although Earth's rotation causes different parts of Earth to move in
different directions and speeds, the part that you experience at any
one time is so small that to high precision it's all moving at the
same speed in the same direction. (When winds move air over hundreds
of miles, that air does eventually feel the effect of Earth's
rotation, the Coriolis effect.)

So not feeling Earth's spin is not a valid argument that it must be
still.  But how do we prove it spins? The Coriolis effect is one way,
but I considered that too advanced for this audience.  Instead, I
explained the Foucault pendulum, which many of them had seen but
probably didn't realize the significance at the time.

Next, we tackled Earth's motion through space.  Spinning is not enough
to explain all our observations, because the stars rise and set every
day slightly faster than the Sun, which means that over time the Sun
loses more and more ground to the stars, and over the course of a year
we see the Sun make one complete circle around the sky relative to the
stars.  What could explain this?  Well, maybe the Sun does go around
Earth, in addition to Earth spinning. But maybe the Earth goes around
the Sun. How could we tell the difference?  I'll get to the bottom of
that next time I visit the school, but for the time being I wanted to
focus on other changes throughout the year and tie them all together
into a coherent model.  I'll post that part of our discussion soon.