Relativity in the rough

From: Alan Boyle (alan.boyle_at_msnbc.com)
Date: 03/01/05 

Date: Tue, 1 Mar 2005 11:24:57 -0800

Howdy to the group: I'm Alan Boyle, science editor at MSNBC.com... We're in
the midst of putting together a graphic introduction to relativity in honor
of the Einstein centenary, and I thought I would try to put out a first
rough draft of the "script" so that if there are glaring problems, we can
fix them *before* we do all the Flash magic and publish it. This is just a
rough outline, and there may be incomplete references to things that would
be included in the app... but if you see anything glaringly miscast, please
write alan.boyle@msnbc.comBUTNOSPAM ... Probably should put "Rough
Relativity" in the subject line so I can distinguish it from the Nigerian
investment opportunities. Many thanks...

The roots of relativity

I. Introduction: Einstein's relativity theories predict
some weird effects, such as black holes, a kind of time travel and bending
light waves. But Einstein didn't go out looking for the weirdness; rather,
the grand achievement of his theories was to demonstrate that the laws of
physics work the way we think they should, even in weird circumstances.
Einstein's view of the world is actually the one that best fits our everyday
experience. Click through this graphic to find out why.

II. Before Einstein.

a. Galilean relativity: The idea of relativity goes back to Galileo's
day in the mid-1500s. If you're playing a game of tennis on the deck of a
smoothly sailing cruise ship, would you have to change your game completely
just because you're traveling across a calm ocean at 25 mph? Of course not.
That illustrates the Galilean concept of relativity, that the laws of
physics work equally well in any reference frame, even if one frame is
moving with respect to another frame. By adding together forces and
velocities, you could figure out exactly how that tennis ball would move, on
land or on the cruise ship.

b. The problem of electrodynamics: What about light waves? In the
mid-1800s, physicist James Clark Maxwell determined that electromagnetism -
including electricity, magnetism and even light - propagated through space
as waves. These waves were thought to ripple through a substance that filled
the universe, known as the ether, just as sound waves propagated though air.
That implied that the speed of those electromagnetic waves through a vacuum*
would vary, depending on whether you were at rest with respect to the ether,
or moving through the ether, just as the speed of sound waves varied. And
that, in turn, implied that not all reference frames would be the same when
it came to light and other electromagnetic waves. Physicists conducted
increasingly precise experiments to look for variations in the speed of
light that could reveal how fast Earth was moving through this universal
ether - but every time they looked, the speed of light was exactly the same.
(Climax came with the 1887 Michelson-Morley experiment, one of the most
famous experiments in physics)

(* When we're talking about speed of light, we're always talking about its
maximum speed in a vacuum. Light waves can always move more slowly in a
medium such as water or glass. In fact, physicists have designed some
ultra-cold environments where light seems to stop altogether.)

III. Special relativity: Clocks and yardsticks

a. Einstein instinctively knew there was something wrong with the way
physicists were thinking about the problem. Even at the age of 16, he
daydreamed about matching the speed of a light wave and seeing it frozen in
space. Such an idea would lead to bizarre effects: For example, if you held
a mirror in front of your face, the light reflected from your face could
never catch up with the mirror, meaning the glass would be blank.

b. A decade later, in 1905, Einstein put forth the claim that
electromagnetic waves obeyed the same principle of relativity Galileo put
forth for the motion of objects more than three centuries earlier: The laws
of physics are the same in all smoothly moving reference fields. Einstein
said that also meant that the speed of light was constant, even if that idea
might seem "apparently irreconcilable" with the principle of relativity.

c. How did Einstein reconcile those two ideas? He made the radical
assertion that because the speed of light the same in all reference frames,
it must be our measurements of distance and time that vary between reference
frames.

d. Light clock illustration:

1. Set up Al's light clock: Box with a light pulse flashing up and
down, and a counter for each beat. A

2. Set up Bert's light clock: Moving with respect to the first.

3. Pre-Einsteinian view: Light pulse moves up and down at the same
beat. But since the light pulse takes a diagonal path for Bert's clock, it
has to move faster to keep the same beat. More than a century's worth of
experiments, however, have shown that this isn't the case. (Poof!)

4. Einsteinian view: Light pulse moves at a constant speed, meaning
that it appears slower for Bert's clock. (2 or 3 beats for Bert's clock, 4
beats for Al's clock)

5. It gets even stranger: We've shown that from Al's point of view,
Bert's clock seems to be ticking more slowly. But from Bert's point of view,
it's Al's clock that's the slow one.

e. This phenomenon has sparked the phrase "moving clocks run slow" .
but physicists say that phrase can be misleading. As we've just seen, either
Al's or Bert's clock could be considered the "moving" clock. Physicist
Richard Wolfson suggests a more "relative" description of the relativity in
time measurement: "The time between two events is shorter when measured by a
single clock that's present at both events than it is when measured by two
separate clocks."

f. And if time gets "squishy" between reference frames that are
moving with respect to each other, measurements of distance gets squishy
also. It turns out that your measurements of objects that are moving through
your reference frame get shorter in the direction of the motion. (Shrinking
yardstick.)

g. Al and Bert twin-paradox calculator (* The fact that Al ages more
than Bert might seem to contradict relativity theory. From Al's point of
view, shouldn't it equally be the case that Bert would seem younger? No: The
reason Al's the one who ages more slowly is because he's in a shifting
reference frame. For an alternate explanation, stay tuned for general
relativity.)

h. One of the implications of the theory is that it would be
impossible for an object to be accelerated all the way up to the speed of
light. If you were to measure the dimensions of an object moving at
99.999999 percent of the speed of light, relative to your reference frame,
that moving light clock would slow to a near-stop, the object would seem to
shrink to near-nothingness, but its measured mass would come close to
infinity. It would take an infinite amount of energy to give the object that
extra little push to light speed - which is the root of Einstein's most
famous equation, E=mc2.

i. All this can get confusing: Observers in different frames of
reference might not agree on what happens when, or even which events come
first and which come later. (Mishmash of moving clocks, yardsticks, trains,
rocket ships, etc., on overlapping grids.) So does that mean that everything's
relative? Are we lost in space and time? Thankfully, no. Einstein's special
theory of relativity includes equations that help physicists work out
consistent coordinates for events, using measurements that incorporate space
as well as time - a four-dimensional view of the cosmos known as spacetime.
(Grids shift to align the patterns of clocks, etc., into one picture that
points the way to the next section on "warps in spacetime".)

IV. General relativity: Warps in spacetime

a. In the world of clocks and yardsticks, we've been talking about
reference frames that move uniformly in relation to each other. But that's
actually a very rare and special scenario - that's why the theory is called
"special" relativity. Einstein realized that if he was going to have a
coherent explanation for how the electromagnetic realm worked, he'd have to
account for scenarios in which there was acceleration, including the force
of gravity. And that meant he'd have to take on an even bigger challenge:
the Newtonian view of the universe.

b. Problem for Einstein: Newton's claims that there was an "absolute
time," and that gravity acted instantaneously on distant objects. Both those
claims contradict special relativity.

c. In 1907, Einstein had what he later called the "happiest thought in
my life": that gravity and powered acceleration were equivalent for any
local reference frame. Nine years later, the insight yielded what is now
known as the general theory of relativity, Einstein's crowning achievement.

d. In thinking about the Principle of Equivalence, Einstein visualized
the experience of a man falling off a roof. But for our purposes, let's
consider a sealed elevator car in Earth's gravity field, as well as a rocket
ship in zero-gravity:

1. Elevator car in free fall (left) (Newton in the left car, Einstein
in the right)

2. Rocket ship in zero-gravity (right)

3. Elevator car comes to rest (left)

4. Rocket ship accelerates at 32 ft/sec2 (right)

5. Laser light (another Einstein-based innovation) turns on in rocket
ship (right)

6. Lantern with focused beam turns on in elevator car (left)

7. Conclusion: Light bends in a gravity field! (Einstein smiles,
Newton frowns)

e. Newton's theories did not account for the bending of light waves,
which have no mass. The bending of light led Einstein to propose that
gravity was not a mysterious "action-at-a-distance" force that acted on
mass. Rather, gravity arose from the way concentrations of mass warped the
fabric of spacetime itself, and objects as well as light waves simply
followed the path of least resistance through those warps. Physicist Richard
Wolfson calls this a case of "cosmic laziness."

f. The greater the mass, the more curvature there is. One way to
measure that curvature would be to have a setup of three powerful lasers and
light sensors around a huge star. If the star is relatively light, the
angles of this cosmic triangle would add up to about 180 degrees. The more
massive it is, the higher the sum would be. Add or subtract mass to this
star to see how space curves. (The ball-on-rubber-*** model. In the
extreme case of a black hole, the sum would go up to 1,080 degrees . three
times 360.)

g. Remember how outside observations of time and space vary between
reference frames that are in smooth motion with respect to each other? This
effect applies to accelerated reference frames as well. For example, if you
were to send a clock and a yardstick from Earth to Jupiter, the clock would
seem to tick slower and the yardstick would shrink slightly in the stronger
gravitational field. When the clock was brought back to Earth, it would
still be out of sync. That provides an alternate explanation for the
phenomenon in the twin paradox: Al is the one who goes through acceleration
and deceleration, while Bert isn't subjected to as many forces during Al's
trip. Thus, Al is the one who ages less.

V. Proving Einstein right: At first, Einstein's theories
weren't given much credence. But as years and decades went by, the evidence
in support of those theories grew - and believe it or not, scientists would
find it hard to function without them. Here are some of the key phenomena
confirming the theories:

a. Precession of Mercury (check)

b. Bending of light during eclipse (check)

c. Subatomic particle decay and E=mc2 (check)

d. Spacetime frame dragging (check) . including GPS (cf. Scientific
American): GPS satellites have to be adjusted by 38 microseconds every day
to account for the relativity effect.

e. Black holes (semi-check)

f. Gravity waves (question mark)

Sources: "Simply Einstein" by Richard Wolfson; "Einstein for Beginners" by
Joseph Schwartz and Michael McGuinness; Scientific American; Physics FAQ