E=mc^2

In the equation;

E=mc²

E is energy, m is mass (specifically "rest mass"), and c is the speed of light.

Basically the equation is saying that matter (objects with mass) is a form of energy. That energy is proportional to the speed of light squared. In the equation above, the energy isn't of an object in motion, but an object at rest. Here's an example:

An electron at rest has mass = 9.1 x 10^-31 kilograms.

The "Rest Energy" of that Electron is;

E=(9 x 10-³¹ kg)(3 x 10⁸ m/s)²= 81 x 10^-15 kg·m²/s²= 81 femtojoules (10^-15 joules)

A positron has the same energy since it has the same mass as an electron.

When a positron and electron annihilate each other, 2 x 81 femtojoules of energy is released (in the form of two photons).

Hopefully this gives you an idea of rest energy, if you're looking for more, you can visit the rest energy section in Wikipedia.

Hi Elika. Albert Einstein and Stephen Hopkins are of 2 schools of thoughts. Albert is pro creation and Hopkins is pro evolution. I tends to side with Einstein.

Now the answer. When Einstein started in his search his intention was to understand "How has GOD created the world". In my opinion he did discover that. Einstein is a Jewish. He knew when GOD created the whole world GOD spoke and eveything came into existance. So E=mc^2 which mean m=c^2/E. Charges is a form of energy which means that with enough energy under proper control we can make things, physical items like minerals and chemicals even cells and tissues.

Proves. Atomic and nucleus scientists started off to make bigger radio active molecules by bombarding smaller radio molecules into big molecules like plotonium and uranium. To their surprise they broke down the bigger molecules to form smaller molecules and giving off great amount of energy. That is how the basic idea of atomic and nucleus bombs was accidentally discovered.

My opionin is: E=mc^2 stands and true. Man is only given the ability to break down and to create belongs to GOD alone.

Quoting elika: "… c=(E/m)^1/2 … thus, if one were to achieve the speed of light, the mass of the object, must be invariably small, but the energy should be phenomenally large."

As Roger pointed out, the equation E = mc² represents the rest energy of an object, meaning it is stationary. When it moves, the energy equation is:

E = mc²/sqrt(1-(v/c)²)

This energy tends to infinity when v tends to c, which some people interpret as meaning that the mass of the object tends to infinity (also referred to as relativistic mass or moving mass). The modern trend is to speak only of rest mass and relativistic energy.

Interestingly, if one approximates the energy equation for speeds (v) very much smaller than the speed of light (c), then it can be expressed as:

E = mc² + 1/2 mv²,

which is Einstein's rest energy + Newton's kinetic energy!

Hi Jorrie

Does your equation means that the gravitational force exerted by Earth on a rotating disk or two counter rotating disks with vertical axis would not increase on increasing the angular speed, as you said in a past letter?

Jaime Soto

Chile

Nope, sorry Jaime. The more kinetic energy, the stronger the pull of gravity on the object, i.e., the heavier it becomes on Earth's surface. Energy has weight!

If you could spin a disk so fast that its perimeter speed approaches "c", without destroying it, the disk will become extremely heavy. The energy needed to spin it up would also be extreme!

"If you could spin a disk so fast that its perimeter speed approaches "c", without destroying it, the disk will become extremely heavy."

I just want to specify the "name" of that experience, it is called inertia, the more the object has either mass or energy the more it is difficult to modify its state. That is one main reason why we cannot bring anything to the speed of light, it would take more than all the universe energy (maybe less, I didn't calculate the universe energy yet) to make the step from 99.95% speed of light to 99.99% speed of light and even more to bring it to 100% speed of light because the inertia has increased. Inertia is at first about mass but due to this relation E=mc^2, inertia has become energy too.

Correct me if I'm wrong.

Antoine Lacerte

Student in Mechanical Engineering (Québec)

Hi Antoine, you wrote: "I just want to specify the "name" of that experience, it is called inertia, the more the object has either mass or energy the more it is difficult to modify its state."

I agree - inertial mass/energy and gravitational mass/energy are equivalent to each other - this is one of the fundamentals of general relativity. When I said "energy is heavy", or something to that effect, that meant the same thing!

Okay, nice

Just wanted to see if what I was thinking of it was right or not.

Thank you.

Antoine

Actually, modern special relativity tries to get away from the concept of relativistic mass (m = m0/sqrt(1-v²/c²)) in favor of just describing a particles' energy as the quadrature addition of its (rest) mass energy (mc²) and its kinetic energy pc (p is the momentum) Thus the total energy of a moving particle is E = sqrt(m²c⁴+p²c²).

For small speeds (pc<<mc²), a Taylor series expansion gives the 1/2 mv² term familiar from Newtonian dynamics.

Conversely, as the momentum term increases, the energy approaches pc, and the rest mass is negligable.

Daggett Beaver, I fully agree with you on "relativistic mass".

Your E = sqrt(m²c⁴+p²c²) and my E = mc²/sqrt(1-v²/c²), where m is the rest mass and momentum p = mv/sqrt(1-v²/c²), are equivalent.

I still tend to cling to the second expression, due to its "velocity time dilation effect on momentum and energy" interpretation. I try not to talk "relativistic mass" however. Graphically, the first expression is however more intuitive!

Jorrie

It is the velocity of light SQUARED not the velocity of light. At some point there is a theroretical problem with time but that is only caused by the physics of measurement devices. So far, we can't decribe the effects of MLV because we barely understand a scale we cant test. We have nothing that will move that fast even as a significant partial velocity simulation.

Mark Howell

Explanation how we arrive from E_c=mv²/2 to the Einstein's eqⁿ: E=mc², is very simple shown in the book "Subcuantic Universe", on-line published (free downloading) from: www.adslexpress.ro/soma

Iulian Somacescu

Quote: "Explanation how we arrive from E_c=mv²/2 to the Einstein's eqⁿ: E=mc², is very simple shown in the book "Subcuantic Universe"..."

If you mean that "E_c=mv²/2" is equivalent to "E=mc^2", then you, and/or the book are mistaken! I must confess, I haven't read the book, but this sounds very WRONG! E_c=mv²/2 is kinetic energy and E=mc² is rest energy, which are not equivalents.

Jorrie