EFTA00285909

There, and Back Again 
47 
by anyone to determine whether he or she is moving uniformly or stand-
ing still. But up until Galileo, a state of absolute rest was considered special. 
Aristotle had decided that all objects sought out the state of rest, and the 
Church decided that rest was so special that it should be the state of the 
center of the universe, namely the planet on which God had placed us. 
Like a number of Aristotle's assertions, although by no means all, 
this notion that a state of rest is special is quite intuitive. (For those who 
like to quote Aristotle's wisdom when appealing to his "Prime Mover" 
argument for the existence of God, let us remember that he also claimed 
that women had a different number of teeth than men, presumably 
without bothering to check.) 
Everything we see in our daily lives comes to rest. Everything, that 
is, except the Moon and the planets, which is perhaps one reason that 
these were felt to be special in antiquity, guided by angels or gods. 
However, every sense that we have that we are at rest is an illusion. 
In the example I gave earlier of throwing a ball up and catching it while 
in a moving plane, you will eventually be able to tell that your plane is 
moving when you feel the bouncing of turbulence. But even when the 
plane is on the tarmac, it is not at rest. The airport is moving with the 
Earth at about 3o km/sec around the Sun, and the Sun is moving about 
zoo km/sec around the galaxy, and so on. 
Galileo codified this with his famous assertion that the laws of phys-
ics are the same for all observers moving in a uniform state of motion, 
i.e., at a constant velocity in a straight line. (Observers at rest are simply 
a special case, when velocity is zero.) By this he meant that there is no 
experiment you can perform on such an object that can tell you it is not 
at rest. When you look up in the air at an airplane, it is easy to see that 
it is moving relative to you. But, there is no experiment you can perform 
on the ground or on the plane that will distinguish whether the ground 
on which you are standing is moving past the plane, or vice versa. 
While it seems remarkable that it took so long for anyone to rec-
ognize this fundamental fact about the world, it does defy most of our 
2P_Glealer-StoryEverTold_Atirdd 4? 
12/16116 3:06 PIA 
EFTA00285969

48 
THE GREATEST STORY EVER TOLD-SO FAR 
experience. Most, but not all. Galileo used examples of balls rolling 
down inclined planes to demonstrate that what previous philosophers 
thought was fundamental about the world—the retarding force of fric-
tion that makes things eventually settle at rest—was not fundamental at 
all but rather masked an underlying reality. When balls roll down one 
plane and up another, Galileo noted, on smooth surfaces the balls would 
rise back to the same height at which they started. But by considering 
balls rolling up planes of ever-decreasing incline, he showed that the 
balls would have to roll farther to reach their same original height. He 
then reasoned that if the second incline disappeared entirely, the balls 
would continue rolling at the same speed forever. 
This realization was profoundly important and fundamentally 
changed much about the way we think about the world. It is often sim-
ply called the Law of Inertia, and it set up Newton's law of motion, relat-
ing the magnitude of an external force to the observed acceleration of 
an object. Once Galileo recognized that it took no force to keep some-
thing moving at a constant velocity, Newton could make the natural 
leap to propose that it took a force to change its velocity. 
The heavens and the Earth were no longer fundamentally different. 
The hidden reality underlying the motion of everyday objects also made 
clear that the unending motion of astronomical objects was not super-
natural, setting the stage for Newton's Universal Law of Gravity, further 
demoting the need for angels or other entities to play a role in the cosmos. 
Galileo's discovery was thus fundamental to establishing physics as 
we know it today. But so was Maxwell's later brilliant unification of elec-
tric and magnetic forces, which established the mathematical frame-
work on which all of current theoretical physics is built. 
As Albert Einstein began his journey in this rich intellectual landscape, 
he quickly spied a deep and irreconcilable chasm running through it: 
both Galileo and Maxwell could not be right at the same time. 
2P_Glealer-StoryEverTold_Atincld J8 
12/16116 3:06 PIA 
EFTA00285970

There, and Back Again 
49 
More than twenty years ago, when my daughter was an infant, I first 
began to think about how to explain the paradox that young Einstein 
struggled with, and a good example literally hit me on the head while 
driving her in my car when she was an infant. 
Galileo had demonstrated that as long as I am driving safely and at 
a constant speed and not accelerating suddenly, the laws of physics in 
our car should be indistinguishable from the laws of physics that would 
be measured in the laboratories in the physics building to which I was 
driving to work. If my daughter was playing with a toy in the backseat, 
she could throw the toy up in the air and expect to catch it without any 
surprises. The intuition her body had built up to play at home would 
have served her well in the car. 
However, riding in the car did not lull her to sleep like many young chil-
dren, but rather made her anxious and uncomfortable. During our trip, she 
got sick and projectile-vomited, and the vomit followed a trajectory well 
described by Newton, with an initial speed of, say, fifteen miles per hour, 
and a nice parabolic trajectory in the air, ending on the back of my head. 
Say my car was coasting to a red light at this time at a relatively slow 
speed, say, ten miles per hour. Someone on the ground watching all of 
this would see the vomit traveling at 2.5 miles per hour, the speed of the 
car relative to them (io mph) plus the speed of the vomit (is mph), and 
its trajectory would be well described by Newton again, with this higher 
speed (zs mph) as it traveled toward my (now moving) head. 
So far so good. Here's the problem, however. Now that my daughter is 
older, she loves to drive. Say she is driving behind a friend's car and dials 
him on her cell phone (hands-free, for safety) to tell him to turn right to 
get to the place they are both going. As she talks into the phone, elec-
trons in the phone jiggle back and forth producing an electromagnetic 
wave (in the microwave band). That wave travels to the cell phone of her 
friend at the speed of light (actually it travels up to a satellite and then 
gets beamed down to her friend, but let's ignore that complication for 
the moment) and is received in time for him to make the correct turn. 
2P_Glealer-StoryEverTold_Atirdd 49 
12/16116 3:06 PIA 
EFTA00285971

50 
THE GREATEST STORY EVER TOLD-SO FAR 
Now, what would a person on the ground measure? Common sense 
would suggest that the microwave signal would travel from my daugh-
ter's car to her friend's car at a speed equal to the speed of light, as might 
be measured by a detector in my daughter's car (label it with the symbol 
c), plus the speed of the car. 
But common sense is deceptive precisely because it is based on com-
mon experience. In everyday life we do not measure the time it takes 
light, or microwaves, to travel from one side of the room to another or 
from one phone to a nearby phone. If common sense applied here, that 
would mean someone on the ground (with a sophisticated measuring 
apparatus) would measure the electrons in my daughter's phone jiggling 
back and forth and observe the emanation of a microwave signal, which 
would be traveling at a speed c plus, say, ten miles per hour. 
However, the great triumph of Maxwell was to show that he could 
calculate the speed of electromagnetic waves emanated by an oscillat-
ing charge purely by measuring the strength of electricity and magne-
tism. Therefore if the person on the ground observed the waves having 
speed c plus io mph, then for that person the strength of electricity and 
magnetism would have to be different from the values that my daughter 
would observe, for whom the waves were moving at a speed c. 
But Galileo tells us this is impossible. If the measured strengths of 
electricity and magnetism differed between the two observers, then it 
would be possible to know who was moving and who was not, because 
the laws of physics—in this case electromagnetism—would take on dif-
ferent values for each observer. 
So, either Galileo or Maxwell had to be right, but not both of them. 
Perhaps because Galileo had been working when physics was more 
primitive, most physicists came down closer to the side of Maxwell. 
They decided that the universe must have some absolute rest frame 
and that Maxwell's calculations applied in that frame only. All observ-
ers moving with respect to that frame would measure electromagnetic 
2P_Glealer-StoryEverTold_Atind0 50 
12/16116 3:06 PIA 
EFTA00285972

There, and Back Again 
51 
waves to have a different speed relative to themselves than Maxwell had 
calculated. 
A long scientific tradition gave physical support to this idea. After 
all, if light was an electromagnetic disturbance, what was it a distur-
bance of? For thousands of years, philosophers had speculated about 
an "ether," some invisible background material filling all of space, and 
it became natural to suspect that electromagnetic waves were traveling 
in this medium, just as sound waves travel in water or air. Electromag-
netic waves would travel with some fixed, characteristic speed in this 
medium (the speed calculated by Maxwell), and observers moving with 
respect to this background would observe the waves as faster or slower, 
depending on their relative motion. 
While intuitively sensible, this notion was a cop-out, because if you 
think back to Maxwell's analysis, it would mean that these different ob-
servers in relative motion would measure the strength of electricity and 
magnetism to be different. Perhaps it was deemed to be acceptable be-
cause all speeds obtainable at the time were so small compared to the 
speed of light that any such differences would have been minute at best 
and would certainly have escaped detection. 
The actor Alan Alda once turned the tables on conventional wisdom 
at a public event I attended by saying that art requires hard work, and 
science requires creativity. While both require both, what I like about 
his version is that it stresses the creative, artistic side of science. I would 
add to this statement that both endeavors require intellectual bravery. 
Creativity alone amounts to nothing if it is not implemented. Novel ideas 
generally stagnate and die without the courage to implement them. 
I bring this up here because perhaps the true mark of Einstein's ge-
nius was not his mathematical prowess (although, contrary to conven-
tional wisdom, he was mathematically talented), but his creativity and 
his intellectual confidence, which fueled his persistence. 
The challenge that faced Einstein was how to accommodate two con-
2P_Glealer-StoryEverrold_AC.irdd Si 
12/16116 3:06 PIA 
EFTA00285973

52 
THE GREATEST STORY EVER TOLD-SO FAR 
tradictory ideas. Throwing one out is the easy way. Figuring out a way to 
remove the contradiction required creativity. 
Einstein's solution was not complex, but that does not mean it was 
easy. I am reminded of an apocryphal story about Christopher Colum-
bus, who got a free drink in a bar before departing to find the New 
World by claiming he could balance an egg upright on top of the bar. 
After the barman accepted the bet, Columbus broke the tip off the egg 
and placed it easily upright on the counter. He never mentioned not 
cracking it, after all. 
Einstein's resolution of the Galileo-Maxwell paradox was not that 
different. Because, if both Maxwell and Galileo were right, then some-
thing else had to be broken to fix the picture. 
But what could it be? For both Maxwell and Galileo to be right re-
quired something that was clearly crazy: in the example I gave, both 
observers would have to measure the velocity of the microwave emitted 
by my daughter's cell phone to be the same relative to them, instead of 
measuring values differing by the speed of the car. 
However, Einstein asked himself an interesting question, What does 
it mean to measure the velocity of light, after all? Velocity is determined 
by measuring the distance something travels in a certain time. So Ein-
stein reasoned as follows: it is possible for two observers to measure the 
same speed for the microwave relative to each of them, as long as the 
distance each measures the ray to travel relative to themselves during a 
fixed time interval (e.g., say, one second, as measured by each of them in 
their own frame of reference) is the same. 
But this too is a little crazy. Consider the simpler example of the 
projectile vomit. Remember that in my frame it travels from her mouth 
in the backseat to hit my head, say, three feet away, in about one-quarter 
second. But for someone on the ground the car is traveling at 10 miles 
per hour during this period, which is about 14.5 feet per second. Thus for 
the person on the ground, in one-quarter second the vomit travels about 
3.6 feet plus 3 feet, or a total 6.6 feet. 
2P_Glealer-StoryEverTold_Aairdd 52 
12/16116 3:06 PIA 
EFTA00285974

There, and Back Again 
53 
Hence for the two observers, the distances traveled by the vomit in 
the same time is noticeably different. How could it be that for the micro-
wave the distances both observers measure could be the same? 
The first hint that perhaps such craziness is possible is that electro-
magnetic waves travel so fast that in the time it takes the microwaves to 
get from one car to another, each car has moved hardly at all. Thus any 
possible difference in measured distance traveled during this time for 
the two observers would be essentially imperceptible. 
But Einstein turned this argument around. He realized that both 
observers had not actually measured the distances traveled by the mi-
crowaves over human-scale distances, because the relevant times ap-
propriate for light to travel over human-scale distances were so short 
that no one could have measured them at the time. And similarly, on 
human timescales light would travel such large distances that no one 
could measure those distances directly either. Thus, who was to say that 
such crazy behavior couldn't really happen? 
The question then became, What is required for it to actually occur? 
Einstein reasoned that for this seemingly impossible result to be pos-
sible, the two different observers must measure distances and/or times 
differently from each other in just such a way that light, at least, would 
traverse the same measured distance in the same measured time for 
both observers. Thus, for example, it would be as if the observer on the 
ground in the vomit case were to measure the vomit traversing 6.6 feet, 
but would somehow also infer the time interval over which this hap-
pened to be larger than I would measure it inside my car, so that the in-
ferred speed of the vomit would be the same relative to him as I measure 
it to be relative to me. 
Einstein then made the bold assertion that something like this does 
happen, that both Maxwell and Galileo were correct, and that all ob-
servers, regardless of their relative state of motion, would measure any 
light ray to travel at the same speed, c, relative to them. 
Of course, Einstein was a scientist, not a prophet, so he didn't just 
2P_Glealer-StoryEverTold_Aairdd 53 
12/16116 3:06 PIA 
EFTA00285975

54 
THE GREATEST STORY EVER TOLD-SO FAR 
claim something outlandish on the basis of authority. He explored the 
consequences of his claim and made predictions that could be tested to 
verify it. 
In doing so he moved the playing field of our story from the domain 
of light to the domain of intimate human experience. He not only for-
ever changed the meaning of space and time, but also the very events 
that govern our lives. 
2P_Glealer-StoryEverTold_Atirdd 54 
12/16116 3:06 PIA 
EFTA00285976

Chapter 5 
A STITCH IN TIME 
He stretcheth out the north over the empty place, 
and hangeth the earth upon nothing. 
-JOB 26:7 
The great epic stories of ancient Greece and Rome revolve 
around heroes such as Odysseus and Aeneas, who challenged the gods 
and often outwitted them. Things have not changed that much for more 
modern epic heroes. 
Einstein overcame thousands of years of misplaced human percep-
tion by showing that even the God of Spinoza could not impose his 
absolute will on space and time, and that each of us evades those imagi-
nary shackles every time we look around us and view new wonders amid 
the stars above. Einstein emulated artistic geniuses such as Vincent van 
Gogh and reasoned with the parsimony of Ernest Hemingway. 
Van Gogh died fifteen years before Einstein developed his ideas on 
space and time, but his paintings make it clear that our perceptions of the 
world are subjective. Picasso may have had the chutzpah to claim that he 
painted what he saw, even as he produced representations of disjointed 
people with body parts pointing in different directions, but van Gogh's 
55 
2P_Glealer-StoryEverrold_Aairdd 55 
12/16116 3:06 PIA 
EFTA00285977

56 
THE GREATEST STORY EVER TOLD-SO FAR 
masterpieces demonstrate that the world can look very different to dif-
ferent people. 
So too, Einstein explicitly argued, for the first time as far as I know 
in the history of physics, that "here" and "now" are observer-dependent 
concepts and not universal ones. 
His argument was simple, based on the equally simple fact that we 
cannot be in two places at once. 
We are accustomed to feeling that we share the same reality with those 
around us because we appear to share the same experiences as we look 
about together. But that is an illusion created by the fast speed of light. 
When I observe something happening now, say, a car crash down the 
street or two lovers kissing under a lamppost as I walk nearby, neither of 
these events happened now, but rather then. The light that enters my eye 
was reflected off the car or the people just a little bit earlier. 
Similarly when I take a photo of a beautiful landscape, as I just did in 
Northern Ireland where I began writing this chapter, the scene I captured 
is not a scene merely spread out in space, but rather in space and time. 
The light from the distant pillared cliffs at Giant's Causeway perhaps a 
kilometer away left those cliffs well before (perhaps thirty-millionths of 
a second before) the light from the people in the foreground scrambling 
over the hexagonal lava pods left to reach my camera at the same time. 
With this realization, Einstein asked himself what two events that 
one observer views as happening at the same time in two different loca-
tions would look like for another observer moving with respect to the 
first observer while the observations were being made. The example he 
considered involved a train, because he lived in Switzerland at a time 
when a train was leaving about every five minutes for somewhere in the 
country from virtually any other place in the country. 
Imagine the picture shown below in which lightning hits two points 
beside either end of a train that are equidistant from observer A, who is at 
rest with respect to those points, and observer B on a moving train, who 
passes by A at the instant A later determines the lightning bolts struck: 
2P_Glealer-StoryEverTold_Atirdd 58 
12 /18/16 3:06 PIA 
EFTA00285978

A Shich in Time 
57 
lightning hits 
B 
A 
a little while later 
A little while later A will see both lightning flashes reaching him at 
the same time. B, however, will have moved during this time. Therefore 
the light wave bringing the information that a flash occurred on the 
right will already have passed B, and the light bringing the information 
about the flash on the left will not yet have reached him. 
B sees the light coming from either end of his train, and indeed the 
flash at the front end occurs before the flash at the rear end. Since he 
measures the light as traveling toward him at speed c, and since he is in 
the middle of his train, he concludes therefore that the right-hand flash 
must have occurred before the left-hand flash. 
Who is right here? Einstein had the temerity to suggest that both ob-
servers were right. If the speed of light were like other speeds, then B would 
of course see one wave before the other, but he would see them traveling 
toward him at different speeds (the one he was moving toward would be 
faster and the one from which he was moving away would be slower), and 
he would therefore infer that the events happened at the same time. But 
because both light rays are measured by B to be traveling toward him at 
the same speed, c, the reality he infers is completely different. 
As Einstein pointed out, when defining what we mean by different 
physical quantities, measurement is everything. Imagining a reality that 
is independent of measurement might be an interesting philosophical ex-
ercise, but from a scientific perspective it is a sterile line of inquiry. If both 
A and B are located at the same place at the same time, they must both 
measure the same thing at that instant, but if they are in remote locations, 
almost all bets are off. Every measurement that B can make tells him that 
2P_Glealer-StoryEverrold_Atirdd Si 
12/16116 3:06 PIA 
EFTA00285979

58 
THE GREATEST STORY EVER TOLD-SO FAR 
the event at the forward end of his train happened before the next, while 
every measurement that A makes tells him the events were simultaneous. 
Since neither A nor B can be at both places at the same time, their mea-
surement of time at remote locations depends upon remote observations, 
and if those remote observations are built on interpreting what light from 
those events reveals, they will differ on their determination of which re-
mote events are simultaneous, and they will both be correct. 
Here and now is only universal for here and now, not there and then. 
• 
• 
• 
I wrote "almost all" bets are off for a reason. For as strange as the example I 
just gave might seem, it can actually be far stranger. Another observer, C, 
traveling on a train moving in the opposite direction from B on a third track 
beside A and B will infer that the event on the left side (the forward part of 
his train) occurred before the event on the right-hand side. In other words, 
the order of the events seen by the two observers B and C will be completely 
reversed. One person's "before" will be the other's "after." 
This presents a big apparent problem. In the world in which most of us 
believe we live, causes happen before effects. But if "before" and "after" can 
be observer dependent, then what happens to cause and effect? 
Remarkably, the universe has a sort of built-in catch-n, which ends up 
ensuring that while we need to keep an open mind about reality, we don't 
have to keep it so open that our brains fall out, as the publisher of the New 
York Times used to say. In this case, Einstein demonstrated that a reversal 
of the time ordering of distant events brought about by the constancy 
of light is only possible if the events are far enough apart so that a light 
ray will take longer to travel between them than the inferred time differ-
ence between the two events. Then, if nothing can travel faster than light 
(which turns out to be another consequence of Einstein's effort to coordi-
nate Galileo and Maxwell), no signal from one event could ever arrive in 
time to affect the other, so one event could not be the cause of the other. 
But what about two different events that occur some time apart at 
2P_Glealer-Storgverrold_Atirdd 58 
12/16116 3:06 PIA 
EFTA00285980

A Stitch in Time 
59 
the same place. Will different observers disagree about them? To ana-
lyze this situation Einstein imagined an idealized clock on a train. The 
ticks of the clock occur each time a light ray sent from a clock on one 
side of the train reflects off a mirror located on the other side and re-
turns to the clock on the original side of the train (see below). 
minor 
clock 
Let us say each round-trip (tick) is a millionth of a second. Now con-
sider an observer on the ground watching the same round-trip. Because 
the train is moving, the light ray travels on the trajectory shown below, 
with the clock and mirror having moved between the time of emission 
and reception. 
mirror 
4 
clock 
clock 
Clearly this light ray traverses a greater distance relative to the observer 
on the ground than it does relative to the clock on the train. However, the 
light ray is measured to be traveling at the same speed, c. Thus, the round-
trip takes longer. As a result, the one-millionth-of-a-second click of the 
clock on the train is observed on the ground to take, say, two-millionths of 
a second. The clock on the train is therefore ticking at half the rate of a clock 
on the ground. Time has slowed down for the clock on the train. 
Stranger still, the effect is completely reciprocal. Someone aboard the 
train will observe a clock on the ground as ticking at half the rate of their 
2P_Glealer-StoryEverTold_Atincld 59 
12/16116 3:06 PIA 
EFTA00285981

60 
THE GREATEST STORY EVER TOLD-SO FAR 
clock on the train, as the figure would look identical for someone on the 
train watching a light travel between mirrors placed on the ground. 
This may make it seem like the slowing of clocks is merely an illusion, 
but once again, measurement equals reality, although in this case a little 
more subtly than for the case of simultaneity. To compare clocks later to 
see which, if any, of the observers clocks has really slowed down, at least 
one of the observers will have to return to join the other. That observer 
will have to change his or her uniform motion, either by slowing down 
and reversing, or by speeding up from (apparent) rest and catching up 
with the other observer. 
This makes the two observers no longer equivalent. It turns out that the 
observer who does the accelerating or the decelerating will find, when she 
arrives back at the starting position, that she has actually aged far less than 
her counterpart, who has been in uniform motion during the whole time. 
This sounds like science fiction, and indeed it has provided the fod-
der for a great deal of science fiction, both good and bad, because in 
principle it allows for precisely the kind of space travel around the gal-
axy that is envisaged in so many movies. There are a few rather signifi-
cant glitches, however. While it does make it possible in principle for a 
spacecraft to travel around the galaxy in a single human lifetime, so that 
Jean-Luc Picard could have his Star Trek adventures, those back at Star 
Fleet command would have a hard time exerting command and control 
over any sort of federation. The mission of ships such as the USS Enter-
prise might be five years long for the crew on board, but each round-trip 
from Earth to the center of the galaxy of a ship at near light speed would 
take sixty thousand years or so as experienced by society back home. To 
make matters worse, it would take more fuel than there is mass in the 
galaxy to power a single such voyage, at least using conventional rockets 
of the type now in use. 
Nevertheless, science fiction woes aside, "time dilation"—as the rel-
ativistic slowing of clocks is called with regard to moving objects—is 
very much real, and very much experienced every day here on Earth. 
2P_Glealer-StoryEverTold_Atirdd 60 
12/16116 3:06 PIA 
EFTA00285982

A Stitch in Time 
61 
At high-energy particle accelerators such as the Large Hadron Collider, 
for example, we regularly accelerate elementary particles to speeds of 
99.9999 percent of the speed of light and rely on the effects of relativity 
when exploring what happens. 
But even closer to home, relativistic time dilation has an impact. We 
on Earth are all bombarded every day by cosmic rays from space. If 
you had a Geiger counter and stood out in a field, the counter would 
click at a regular rate every few seconds, as it recorded the impact of 
high-energy particles called muons. These particles are produced where 
high-energy protons in cosmic rays smash into the atmosphere, produc-
ing a shower of other, lighter particles—including muons—which are 
unstable, with a lifetime of about one-millionth of a second, and decay 
into electrons (and my favorite particles, neutrinos). 
If it weren't for time dilation, we would never detect these muon 
cosmic rays on Earth. Because a muon traveling at close to the speed 
of light for a millionth of a second would cover about three hundred 
meters before decaying. But the muons raining down on Earth make it 
twenty kilometers, or about twelve and a half miles or so, from the upper 
atmosphere, in which they are produced, down to our Geiger counter. 
This is possible only if the muons internal "clocks" (which prompt them 
to decay after one-millionth of a second or so) are ticking slowly relative 
to our clocks on Earth, ten to one hundred times more slowly than they 
would be if they were produced at rest here in a laboratory on Earth. 
The last implication of Einstein's realization that the speed of light must 
be constant for all observers appears even more paradoxical than the 
others—in part because it involves changing the physical behavior of 
objects we can see and touch. But it also will help carry us back to our 
beginnings to glimpse a new world beyond the confines of our normal 
earthbound imagination. 
The result is simply stated, even if the consequences may take some 
2P_Glealer-StoryEverTold_Atirdd SI 
12/16116 3:06 PIA 
EFTA00285983

82 
THE GREATEST STORY EVER TOLD-SO FAR 
time to digest. When I am carrying an object such as a ruler, and mov-
ing fast compared to you, my ruler will be measured by you to be smaller 
than it is for me. I might measure it to be to cm, say: 
But to you, it might appear to be merely 6 cm: 
Surely, this is an illusion, you might say, because how could the same 
object have two different lengths? The atoms can't be compressed to-
gether for you, but not for me. 
Once again, we return to the question of what is "real." If every mea-
surement you can perform on my ruler tells you it is 6 cm long, then it 
is 6 cm long. "Length" is not an abstract quantity but requires a mea-
surement. Since measurement is observer dependent, so is length. To 
see this is possible while illuminating another of relativity's slippery 
catch-2zs, consider one of my favorite examples. 
Say I have a car that is twelve feet long, and you have a garage that is 
eight feet deep. My car will clearly not fit in your garage: 
car 
But, relativity implies that if I am driving fast, you will measure my 
car to be only, say, six feet long, and so it should fit in your garage, at 
least while the car is moving: 
car 
4 
garage 
2P_Glealer-StoryEverTold_Atincld 62 
12/16116 3:06 PIA 
EFTA00285984

A Stitch in Time 
63 
However, let's view this from my vantage point. For me, my car is 
twelve feet long, and your garage is moving toward me fast, and it now 
is measured by me to be not eight feet deep, but rather four feet deep: 
car 
garage 
Thus, my car clearly cannot fit in your garage. 
So which is true? Clearly my car cannot both be inside the garage 
and not inside the garage. Or can it? 
Let's first consider your vantage point, and imagine that you have 
fixed big doors on the front of your garage and the back of your garage. 
So that I don't get killed while driving into it, you perform the following. 
You have the back door closed but open the front door so my car can 
drive in. When it is inside, you close the front door: 
However, you then quickly open the back door before the front of my 
car crashes, letting me safely drive out the back: 
Thus, you have demonstrated that my car was inside your garage, 
which of course it was, because it is small enough to fit in it. 
However, remember that, for me, the time ordering of distant events 
can be different. Here is what I will observe. 
I will see your tiny garage heading toward me, and I will see you 
open the front door of the garage in time for the front of my car to pass 
through. 
2P_Glealer-StoryEverTold_Atirdd S3 
12,1&I6 3:06 PIA 
EFTA00285985

84 
THE GREATEST STORY EVER TOLD-SO FAR 
I will then see you kindly open the back door before I crash: 
After that, and after the back of my car is inside the garage, I will see 
you close the front door of your garage: 
As will be clear to me, my car was never inside your garage with both 
doors closed at the same time because that is impossible. Your garage 
is too small. 
"Reality" for each of us is simply based on what we can measure. In 
my frame the car is bigger than the garage. In your frame the garage is 
bigger than my car. Period. The point is that we can only be in one place 
at one time, and reality where we are is unambiguous. But what we infer 
about the real world in other places is based on remote measurements, 
which are observer dependent. 
But the virtue of careful measurement does not stop there. 
The new reality that Einstein unveiled, based as it was on the em-
pirical validity of Galileo's law, and Maxwell's remarkable unification 
2P_Glealer-StoryEverTold_Atincld S4 
12116116 3:06 PM 
EFTA00285986

A Stitch in Time 
66 
of electricity and magnetism, appears on its face to replace any last 
vestige of objective reality with subjective measurement. As Plato 
reminds us, however, the job of the natural philosopher is to probe 
deeper than this. 
It is said that fortune favors the prepared mind. In some sense, Plato's 
cave prepared our minds for Einstein's relativity, though it remained for 
Einstein's former mathematics professor Hermann Minkowski to com-
plete the task. 
Minkowski was a brilliant mathematician, eventually holding a 
chair at the University of Gottingen. But in Zurich, where he was one 
of Einstein's professors, he was a brilliant mathematician whose classes 
Einstein skipped, because while he was a student, Einstein appeared 
to have a great disdain for the significance of pure mathematics. Time 
would change that view. 
Recall that the prisoners in Plato's cave also saw from shadows 
on their wall that length apparently had no objective constancy. The 
shadow of a ruler might at one time look like this, at io cm: 
and, at another time like this, at 6 cm: 
The similarity with the example I presented when discussing relativ-
ity is intentional. In the case of Plato's cave dwellers, however, we rec-
ognized that this length contraction occurred because the cave dwellers 
were merely seeing two-dimensional shadows of an underlying three-
dimensional object. Viewed from above, it can easily be seen that the 
shorter shadow projected on the wall results because the ruler has been 
rotated at an angle to the wall: 
2P_Glealer-StoryEverTold_Atincld 65 
12/16116 3:06 PIA 
EFTA00285987

BB 
THE GREATEST STORY EVER TOLD-SO FAR 
shadow 
And as another Greek philosopher, Pythagoras, taught us, when seen 
this way, the length of the ruler is fixed, but the projections onto the wall 
and a line perpendicular to the wall always combine together to give the 
same length, as shown below: 
shadow 
N 
This yields the famous Pythagorean theorem, L a = 
+ y2, which high 
school students have been subjected to for as long as high schools have 
taught geometry. In three dimensions, this becomes L a = 
+ ya + z1. 
Two years after Einstein wrote his first paper on relativity Minkowski 
recognized that perhaps the unexpected implications of the constancy 
of the speed of light, and the new relations between space and time 
unveiled by Einstein, might also reflect a deeper connection between 
the two. Knowing that a photograph, which we usually picture as a 
two-dimensional representation of three-dimensional space, is really 
an image spread out in both space and time, Minkowski reasoned that 
observers who were moving relative to each other might be observing 
different three-dimensional slices of a four-dimensional universe, one in 
which space and time are treated on an equal footing. 
29_GlealerASIoryEverTold_Atirdd 88 
1'2/1&16 3:06 PIA 
EFTA00285988