Special Relativity

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www.perimeterinstitute.ca/powerofideas
What’s the big idea?
Einstein figured out that everything always moves at the speed of light, not through space, but through 
spacetime. For example, even if you’re just sitting in a chair, and it seems like you’re not moving, in fact 
you’re moving through time—hurtling into the future at the speed of light. Einstein unified the ideas 
of motion through space, and motion through time, ultimately leading to E=mc2. This understanding 
of the equivalence of energy and mass might one day provide abundant, clean energy for the rest of 
humankind’s existence on earth. Explore the wonder and power of Einstein’s ideas!
You measure space with a ruler and time with 
a clock. Einstein’s special relativity idea unified 
space and time into something called spacetime. 
Like different sides of a cube, space and time are 
now understood as just different sides of a single 
thing—spacetime. To see this unity, consider that 
both space and time can be measured with the 
same instrument—a clock. How do you measure 
space with a clock? Just time how long it takes 
light to travel from here to there, and multiply 
by the speed of light. For example, one light-
second is the distance light travels in one second. 
If you think this is trivial, you’re right. Until you 
throw in the idea that our universe has a speed 
limit, and that light always moves at this maximum 
possible speed. 
A speed limit? Nonsense! If you’re in a spaceship 
zipping past a speed limit sign at almost the 
speed of light, and I’m doing the same but in the 
opposite direction, surely we will see each other 
zip by at faster than the speed limit! Actually, 
we won’t, and that’s because space and time are 
relative. This means that, because of our relative 
motion, I will experience your “spacetime cube” 
as rotated relative to mine. What’s space for me 
will be space and time for you, and vice versa, in 
a remarkable way that guarantees that nothing 
ever exceeds Einstein’s universal speed limit.
For example, let’s think of the Special Relativity 
animation as showing me zipping past you, from 
your point of view. The two clocks in my hands 
are synchronized—they read the same time for 
me, but not for you (I’m not kidding). As they 
zip by, if you were to momentarily touch my two 
clock faces at the same instant for you, the clock 
you touch with your left hand would be in my 
future, relative to the clock you touch with your 
right hand. I would see you touch the clock in my 
left hand first, then a short time later, the clock in 
my right hand. And you would actually feel, with 
your fingers, the different positions of the hands 
of my two clocks. This is not an optical (or any 
other kind) of illusion. 
You would also notice that at the instant you 
touched both of my clocks, your hands would 
be unusually close together. I would physically 
occupy less of your space than my own space 
(notice in the animation how my width is 
contracted). What’s space for you—the distance 
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What’s it good for?
between your hands, is space and time for me: 
space as in the distance between your hands 
from my point of view (which is contracted by 
the same factor by which you see my width 
contracted!), and time as in the delay between 
when your hands touch my left and right clocks.
This remarkable unification of space and time 
quickly led Einstein to an even more surprising 
unification: energy and mass are, in essence, 
the same thing, as is expressed in his famous 
equation E=mc2. This equation explains, for 
example, the fusion process at the heart of 
how the sun and stars work. It thus provides 
the basic knowhow to construct an artificial 
sun, a potential future technology that may one 
day help solve the world’s energy and related 
environmental problems once and for all. This is 
the power of ideas!
to burning fossil fuels. But it is not until the mass-
energy conversions involve the nucleus of an 
atom that the true power of Einstein’s idea shows 
itself clearly. Fission—the splitting of large atomic 
nuclei—is one example of this idea in action, 
currently providing energy for cities all over 
the world. Fusion—the joining of small atomic 
nuclei—is another, and may one day help solve 
the world’s energy and related environmental 
problems. Small idea. Big impact!
National Lab System
During the early years of the 20th century 
theoretical physics underwent a revolution, and 
the implications of that revolution—in particular 
special relativity and E=mc2—led to a new 
model for how successful science can be done. 
The Manhattan Project to build the world’s 
first atomic bomb brought together some of 
the greatest physics minds of the time. It was 
a government-funded high concentration of 
intellectual and experimental resources. And 
it worked. After the war, it eventually led to the 
national laboratory system in the United States, 
one of the largest scientific research systems 
in the world. The research covers a wide range 
of questions in physics, chemistry, materials 
science, and other areas of the physical sciences, 
for instance finding solutions to the world’s 
energy and environmental problems, two of the 
most important concerns facing humanity today.
Expanding Research Opportunities
Three hundred thousand kilometres in one 
second—that is the speed limit of our universe, 
and the idea at the heart of the unification of 
space and time. Interesting things happen when 
particles like electrons are accelerated to close 
to this speed. For instance, at the Canadian 
Light Source, electrons whizzing around a large 
ring at 99.999687% the speed of light emit a 
special type of light called synchrotron radiation. 
Pouring out from as many as 19 “faucets,” this 
extremely bright light is supplying industry, 
academic, and government researchers with 
an exceptionally fine-tuned probe to answer 
questions in medicine, mining, and advanced 
materials. Designing a research tool like this, 
with twice as many control points as a nuclear 
Candu reactor, relies on innovative engineering 
and the physics of special relativity. Imagine: 
Einstein’s ideas about space and time have led 
to the creation of a machine that generates 
beams of light billions of times brighter than 
sunlight, a tool that’s helping researchers create 
a brighter tomorrow. 
Mass and Energy
E=mc2. This simple mathematical statement 
has profound implications—energy and mass 
are, in essence, the same. It means that a cup 
of hot coffee weighs more than the same 
cup after it has cooled, giving off some of its 
energy, even though the mass difference in 
our coffee example is too small to measure. 
The same mass-energy conversion happens in 
every chemical reaction, from baking cookies