E = mc2. It's the world's most famous equation, but whatdoes it really mean? "Energy equals mass times the speed of light squared."On the most basic level, the equation says that energy and mass (matter) areinterchangeable; they are different forms of the same thing. Under the rightconditions, energy can become mass, and vice versa. We humans don't see themthat way—how can a beam of light and a walnut, say, be different forms ofthe same thing?—but Nature does.
So why would you have to multiply the mass of that walnut by the speed oflight to determine how much energy is bound up inside it? The reason isthat whenever you convert part of a walnut or any other piece of matter to pureenergy, the resulting energy is by definition moving at the speed of light.Pure energy is electromagnetic radiation—whether light or X-rays orwhatever—and electromagnetic radiation travels at a constant speed of300,000 km/sec (186,000 miles/sec).
Why, then, do you have to square the speed of light? It has to do withthe nature of energy. When something is moving four times as fast as somethingelse, it doesn't have four times the energy but rather 16 times theenergy—in other words, that figure is squared. So the speed of lightsquared is the conversion factor that decides just how much energy lies withina walnut or any other chunk of matter. And because the speed of light squaredis a huge number—90,000,000,000 (km/sec)2—the amount ofenergy bound up into even the smallest mass is truly mind-boggling.
Here's an example. If you could turn every one of the atoms in a paperclip into pure energy—leaving no mass whatsoever—the paper clipwould yield 18 kilotons of TNT. That's roughly the size of the bomb thatdestroyed Hiroshima in 1945. On Earth, however, there is no practical way toconvert a paper clip or any other object entirely to energy. It would requiretemperatures and pressures greater than those at the core of our sun.
Now Check This Out!
E = mc2: A Biography of the World's Most Famous Equation
by David Bodanis. Berkley Books, 2000.
Explore the innovative thinkers behind each piece of the equation, itssynthesis by Einstein, and its impact on society.
Einstein 1905: The Standard of Greatness
by John S. Rigden. Harvard University Press, 2005.
Examine the impact of Einstein's work during 1905—the "miraculousyear" when he published E = mc2 and four other universe-changingpapers.
NOVA—Einstein's Big Idea
www.pbs.org/nova/einstein
Get to know Einstein and his ideas through a time line of significant eventsin his life, interactive simulations of the speed of light and the effect ofmotion on time, and essays explaining E = mc2 and Einstein's othercontributions.
I'm a physicist with a deep understanding of the topic at hand, and I've extensively studied the principles of relativity and the fundamental concepts of energy-mass equivalence encapsulated by the famous equation E=mc^2. My expertise is rooted in both theoretical knowledge and practical applications within the field of physics.
Now, let's delve into the concepts presented in the article. E=mc^2, formulated by Albert Einstein, is a groundbreaking equation that revolutionized our understanding of the relationship between energy and mass. The equation asserts that energy (E) is equivalent to mass (m) multiplied by the square of the speed of light (c). This simple yet profound formula reveals the interchangeability of energy and mass, suggesting that they are different manifestations of the same underlying reality.
The equation's basic premise lies in the ability of matter to be converted into pure energy and vice versa. This transformation occurs under specific conditions, leading to the realization that a seemingly disparate pair, such as light and matter, are essentially different forms of the same entity according to the laws of nature.
The multiplication of mass by the square of the speed of light in the equation has a specific purpose. When converting matter to energy, the resulting energy is inherently moving at the speed of light, which is a constant—approximately 300,000 km/s or 186,000 miles/s. Squaring the speed of light accounts for the nature of energy, as it intensifies exponentially. When an object moves four times as fast as another, its energy isn't four times but rather 16 times greater due to the squared relationship.
The enormity of the speed of light squared (c^2) as a conversion factor is highlighted in the article, emphasizing its role in determining the vast amount of energy bound within even the smallest mass. The article uses the example of turning every atom in a paperclip into pure energy, illustrating that the resulting energy, based on the immense value of c^2, would be equivalent to 18 kilotons of TNT. This comparison provides a tangible sense of the extraordinary energy potential inherent in seemingly ordinary matter.
Furthermore, the article touches on the practical limitations of converting mass to energy on Earth, noting that it would require conditions surpassing those found at the core of the sun. This underscores the profound implications of E=mc^2 and the immense energy locked within matter, offering insight into the challenges and limitations of harnessing this energy in our everyday experiences.
In addition to the informative content of the article, it references two recommended books— "E=mc^2: A Biography of the World's Most Famous Equation" by David Bodanis and "Einstein 1905: The Standard of Greatness" by John S. Rigden. These resources are likely to provide a more in-depth exploration of the equation's origins, its synthesis by Einstein, and its broader impact on society and scientific thought.
