# Energy-mass equivalence question

• Charlie G
In summary, Charlie is trying to understand the math behind the energy-mass equivalence equation and is having trouble understanding why 1/2 the mass was dropped in the equation for an object moving at relativistic speeds. The book he is reading is a fictional conversation between Newton and Einstein and is a good read in his opinion.
Charlie G
The book I'm reading on special relativity is a ficitonal conversation between Newton and Einstein. Einstein is explaining relativity to Newton. Its a very good book in my unprofessional opinion, but one thing I'm having problems with is energy-mass equivalence.

I'm not having trouble with the concept, but the equation. In the chapter, Newton has just learned of relativistic mass increase, so he is trying to modify his old energy equation E=1/2mv squared (sorry I don't know how to make the squared sign lol, could anyone tell me how to do that as well) to work for objects moving at relativistic speeds. In the next chapter Newton comes into talk about his work he had done during the night, he says that he believes the equation for the energy of an object moving at relativistic speeds is E=Mc squared, where M is the moving mass and the objects speed is so close to c at relativistic speeds he calls the objects speed c.

Now the problem I'm having is the book doesn't really explain the math (it was meant for the layman like myself, though I really wanted alittle more detail). It did go on to E=myc squared, and ultimatly E=mc squared for an object at rest. But why, in the equation, was 1/2 the mass dropped for the entire mass? Speed squared was kept but the mass portion of the equation changed. I was hoping someone could tell me why this was done.

Charlie G said:
The book I'm reading on special relativity is a ficitonal conversation between Newton and Einstein. Einstein is explaining relativity to Newton. Its a very good book in my unprofessional opinion, but one thing I'm having problems with is energy-mass equivalence.

I'm not having trouble with the concept, but the equation. In the chapter, Newton has just learned of relativistic mass increase, so he is trying to modify his old energy equation E=1/2mv squared (sorry I don't know how to make the squared sign lol, could anyone tell me how to do that as well) to work for objects moving at relativistic speeds. In the next chapter Newton comes into talk about his work he had done during the night, he says that he believes the equation for the energy of an object moving at relativistic speeds is E=Mc squared, where M is the moving mass and the objects speed is so close to c at relativistic speeds he calls the objects speed c.

Now the problem I'm having is the book doesn't really explain the math (it was meant for the layman like myself, though I really wanted alittle more detail). It did go on to E=myc squared, and ultimatly E=mc squared for an object at rest. But why, in the equation, was 1/2 the mass dropped for the entire mass? Speed squared was kept but the mass portion of the equation changed. I was hoping someone could tell me why this was done.
Many textbooks propose the following approach to the link you are looking for.
Start with m=m(0)/sqr(1-bb) ; b=v/c. For small v/c we can expand m as a series of powers of b
m=m(0)(1+bb/2+...) (1)
Multiply (1) by cc in order to obtain
mcc=m(0)cc+m(0)vv/2 (2)
in which Newton recognizes his kinetic energy m(0)v^2/2...

Hi Charlie,

The mass energy equivalence formula can be derived from the fact that photons have momentum which is proportional to their frequency. Basically, if an object emits two photons of equal and opposite momentum in its rest frame then it remains at rest. Transforming that to a frame where the object is moving then one photon is redshifted and the other is blueshifted. The one that is blueshifted carries more momentum than the one that is redshifted and so, to conserve momentum, the mass of the object must have gone down. When you work out how much mass was lost you get m=E/c²

You can also read Einstein's own discussion for the general public at

http://www.bartleby.com/173/ chapter 15 of RELATIVITY, The Special and General Theory.

Thx for all the replies, the bartelby website was really helpful:)

## 1. What is energy-mass equivalence?

Energy-mass equivalence is a principle in physics that states that energy and mass are interchangeable and equivalent forms of each other. This principle is described by Albert Einstein's famous equation, E=mc^2, where E represents energy, m represents mass, and c is the speed of light.

## 2. How does energy-mass equivalence work?

The principle of energy-mass equivalence is based on the concept that all matter is made up of atoms, which contain particles such as protons, neutrons, and electrons. These particles have both mass and energy, and the total energy of a system is equal to the sum of its mass and energy. This means that under certain conditions, mass can be converted into energy, and vice versa.

## 3. What are the implications of energy-mass equivalence?

The implications of energy-mass equivalence are far-reaching, and have had a significant impact on our understanding of the universe. This principle has been used to develop technologies such as nuclear power and nuclear weapons, and has also helped us understand the behavior of particles at the subatomic level. It has also led to the development of theories such as the Big Bang Theory and the theory of relativity.

## 4. Can energy-mass equivalence be observed in everyday life?

While the concept of energy-mass equivalence may seem abstract, it can be observed in everyday life. One common example is the process of nuclear fission, where the conversion of a small amount of matter into energy produces a large amount of energy. This principle also applies to the functioning of stars, where nuclear fusion reactions convert mass into energy, allowing stars to emit light and heat.

## 5. Is energy-mass equivalence a proven concept?

Yes, energy-mass equivalence is a well-established principle in physics and has been proven through numerous experiments and observations. This concept has been validated by the success of theories such as the theory of relativity and has been used in various practical applications. Its accuracy has been confirmed time and time again, making it a fundamental concept in our understanding of the physical world.

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