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Einstein's E=mc² 2009

Page history last edited by Sally Hair 15 years ago

By Cynthia L.

 

"If my theory of relativity is proven successful, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew." - Albert Einstein ( 1879 - 1955 )

Picture: http://farm4.static.flickr.com/3345/3186806743_6da686afc5.jpg

 

When you hear the name Albert Einstein you think of E=mc². Everyone knows a few general facts about this famous equation: who it's by and how it is a rather important concept, but what does this equation actually mean? And where did it come from?

 

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Is the theory of relativity complex? or can it be explained is simple terms? Einstein seems to find it simple so lets figure it out. Picture at:  http://www.cartoonstock.com/newscartoons/cartoonists/rma/lowres/rman701l.jpg

 

 

A little Background info.

Einstein's equation explains relativity. There are actually two types of relativity: general and special. Since Einstein's special relativity equation will be broken up, this will give a brief summery of general relativity.

General relativity is a geometric theory, also by Einstein, that unifies special relativity and Newton's law of universal relativity. It describes gravity as a property of geometric space and time. 

 

What does it mean?

Literally speaking, the formula E=mc2 means "an object's mass is a form of energy and energy carries mass. Mass and energy are two forms of the same thing," but what does that mean? Well it is basically saying that energy can be converted to mass, and vice versa, with the right conditions. It tells us the amount of energy a given quantity of mass would be equivalent to if it were suddenly turned into energy. Still, what does the E, m, and c2 stand for and how does this theory work? Lets start by breaking up the formula.

 

Breaking down the formula

Lets start with the variables in the formula. E represents energy, m for mass and c for the speed of light in a vacuum (about 3x 10^8 m/sec). The total energy is the sum of kinetic energy and rest energy, so energy equals mass multiplied by the speed of light squared. E is in joules,  is in kilograms and c in m/s. If we to write this out it would be E joules= m kg x (299,792,448 m/s)^2.

You may be wondering what is this formula used for? And although the variables of the formula are explained how do they work in the equation and for what reason?

The E

Newton's 1st law, also know as the law of conservation of energy, tells us that energy can only transformed from one form to another; it can never be created or destroyed. The universe was "born" with a specific quantity of energy and that amount can't be changed. The law of conservation of mass says that the mass of a closed system will remain constant regardless of the processes acting inside the system. Mass cannot be destroyed but it can be rearranged in space or changed into different types of particles. This implies that, in a closed system, the mass or the reactants must equal the mass of the product. Einstein unifies these two concepts in his equation (which is why it is called the conservation of mass-energy or mass-energy equivalence).

M for Matter 

Mass, which is the degree of acceleration an object acquires when subjected to a force, is the amount of matter in an object (different from your weight which is the measure of gravitational force on an object). The equation states that when energy is put equal to mass multiplied by the square of the velosity of mass shows that with a small amount of mass you can have a large amount of energy.  In this equation, mass is what we are converting, or setting equal to, to energy. This is important to show that matter and energy are equivalent- mass can be turned into energy and energy into math. Special relativity uses Einstein's equation to say that even energy has mass. 

 

C to the second power

Why is the speed of light squared? In relativity, all the energy that moves along with an object adds up to the total energy of the object. Even a single photon, the unit for light, traveling in empty space has a relativistic mass (m= E/c2). Lets set up an example.

Say you have a box of ideal mirrors. This box contains light. The mass of the box is increased by the energy of light since the total energy of the box is its mass. 

Still, why c2? Einstein's equation tells us that E and mc2 are interchangeable. The c2 is actually the conversion factor tellling you how they are linked. When you convert inches to centimeters, both measuring length, the conversion factor is 2.5. When you convert mass into energy of energy into mass, the conversion factor is the square of the speed of light. Because c is so large (about 300,000 k/sec) and its square much larger (90,000,000,000 k/sec), a tiny amount of mass can be converted into a huge amount of energy- which is the point of Einstein's equation. 

Just in case, here's the math:

 

 

In developing special relativity, Einstein found that the kinetic energy of a moving body is

 

K.E.=\frac{m_0 c^2}\sqrt{1-\frac{v^2}{c^2}} - m_0 c^2,

 

with v the velocity, and m0 the rest mass.

He included the second term on the right to make sure that for small velocities, the energy would be the same as in classical mechanics:

 

K.E.=\frac{1}{2}m_0 v^2 + ...

 

Without this second term, there would be an additional contribution in the energy when the particle is not moving.

Einstein found that the total momentum of a moving particle is:

 

P=\frac{m_0 v}\sqrt{1-\frac{v^2}{c^2}}.

 

and it is this quantity which is conserved in collisions. The ratio of the momentum to the velocity is the relativistic mass, m.

 

m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}

 

And the relativistic mass and the relativistic kinetic energy are related by the formula:

 

K.E.=m c^2 - m_0 c^2. \,

 

Einstein wanted to omit the unnatural second term on the right-hand side, whose only purpose is to make the energy at rest zero, and to declare that the particle has a total energy which obeys:

 

 E=m c^2 \,

 

which is a sum of the rest energy m0c2 and the kinetic energy. This total energy is mathematically more elegant, and fits better with the momentum in relativity. But to come to this conclusion, Einstein needed to think carefully about collisions. This expression for the energy implied that matter at rest has a huge amount of energy, and it is not clear whether this energy is physically real, or just a mathematical artifact with no physical meaning.

 

Sources and links:

http://en.wikipedia.org/wiki/E%3Dmc2

http://en.wikipedia.org/wiki/Special_relativity

http://www.relativitycalculator.com/E=mc2.shtml 

http://www.allyoulike.com/?p=20146

Einstein for Dummies. Calle, Charlos I. Wiley publishing Inc. 2005. Indianapolis, Indiana. 

 

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