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| Albert Einstein's famous equation is both powerful and complex as well as simple, when boiled down to its essence. |
E=mc2
Why Does E=mc2?
By Paul Sutter,
The Ohio State University
Let's play a game! The speed of light
is just a number, right?
If you define your units, for example,
what a "meter" and a "second" are, you can say that the
speed of light is around 300,000,000 meters per second.
Or 670,000,000 "miles" per
"hour," whatever those are.
What if, instead,
we just said the speed of light was
equal to…1. Just 1.
So, 1 what? I said: just 1. No miles,
no seconds, no fortnights, no leagues. Just…1.
We're allowed to do it, because it's
just a number, and we're picking a system where speed has no units.
In this system, a jet airliner cruises
at a snail's pace of 0.000001, or 0.0001 percent of the speed of light.
Two of the fastest human-made objects,
the Helios probes, zoomed around the solar system at a whopping 0.00025! Look
at them go!
Now that we've
defined the speed of light to be 1, let's look at the most famous equation in
physics: E = mc2.
We know all the
bits, but let's refresh: E is for
energy, m is for mass and c is the constant
speed of light.
But in our newfangled unit system
(called, for the technically minded, geometrized units), c equals 1, and that famous
equation boils down to its essence:
E = m.
I'll even spell it
out:
Energy = mass.
It doesn't get any
clearer than that, folks.
Energy is mass. Mass is energy. They
are equivalent; they are equal. They are the same thing.
Wait, wait, wait,
you say as you look at me suspiciously. What about light?
Photons don't have any mass, but they
sure do have plenty of energy. How else do plants eat?
And momentum has energy. But where's
the momentum in E=m? It's looking
like we don't have enough letters to cram it in.
The confusion
comes about from the "m" used in E=m.
We normally think of "mass"
as something concrete and simple. Hold a rock in your hand; it has mass. Throw
it, and it has mass and momentum.
But that's not the "m" in E=m.
Instead, when Einstein wrote that
equation down, he meant something different, usually referred to as "relativistic
mass."
That term isn't used so much nowadays,
because it causes so much head-scratching.
Let's take a step
back and see what Einstein was thinking.
You remember kindergarten-level special relativity, and
hearing things like "it's impossible
to move at the speed of light, because the faster something goes, the more mass
it has. To get to the speed of light, it has infinite mass, so it would be
impossible to push!"
Yeah, well now it's time for
first-grade-level special relativity.
A fundamental
aspect of our universe is that there's a universal (and I really mean universal)
speed limit: the same speed that light goes.
No matter what, you can never crack
that speed. Let's see how that plays out in practice:
Let's say I give
you a nice, solid shove and send you flying away at 0.9 — that is, 9/10th the
speed of light.
What if I catch up to you and give you the
exact same shove, again.
You won't be going 18/10th the speed of
light, because that's not allowed. You'll get closer to
the speed of light, but never cross it.
So for the exact same force that I
impact on your hopeless self, I don't move you as fast. I get less bang for the
buck.
And the closer you
get to the speed of light, the less effective my shoves will be: the first one
may get you to 0.9, then the second to 0.99, then 0.999, then 0.9999.
Diminishing returns every time. In
fact, it's as
if you were getting
more massive. That's exactly what more mass means: You get harder to push.
So what's going
on? The answer is energy.
You still have the same old normal,
everyday, rest mass that you always had.
But you're going really, really fast. And that speed has an energy
associated with it – kinetic energy.
So it's like all that kinetic energy is acting like extra mass; either way I count
it, you get harder to push, because of that fundamental speed limit.
In other words,
you can say that energy is mass. Huh, whaddaya know.
Back to the
"m" in E=m.
When physicists first started playing
with those equations, they were well aware of the universal speed limit and its
nonintuitive consequence that you get harder to push the faster you go.
So they encapsulated that concept into
a single variable: the relativistic mass, which combines both the normal,
everyday mass and the "effective" mass you gain from having loads of
kinetic energy.
When we break up
"m" into its different parts, we get:
E2 = m2 + p2
Or bringing back
our friend c:
E2 = m2c4 + p2c2
And we have
another character joining the party: p, for momentum.
Photons don't have mass, but they do
have momentum, so they still get energy.
In this view, mass
is a kind of energy. But I just said above that energy acts like mass. What's
the deal? Are we just talking in circles?
No. Mass is
energy. Energy is mass. You can count things energywise or masswise. It doesn't
matter. They’re
the same thing.
A hot cup of
coffee literally weighs more than a cold cup.
A fast-moving spaceship literally
weighs more than a slow one.
A rock — or an atomic nucleus — is a
compact, bundled-up ball of energy, and sometimes we can tease some of that
energy out for a big boom.
Follow all of the Expert Voices
issues and debates — and become part of the discussion — on Facebook, Twitter and Google+. The views
expressed are those of the author and do not necessarily reflect the views of
the publisher. This version of the article was originally published on Live Science.
Paul
Sutter is an astrophysicist at The Ohio State
University and
the chief scientist at COSI Science Center. Sutter is
also host of the podcastsAsk a Spaceman and RealSpace, and the YouTube series Space In Your
Face. Sutter contributed this article to Live
Science's Expert Voices: Op-Ed &
Insights.
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