Corrections?  What say you seek out a resident of Hiroshima and ask them if we can do what we clearly did?

For the correct equation and explanation of it refer to:

http://www.physicsforums.com/showthread.php?p=156726#post156726

See Post #18 or read the entire thread, if you're interested in a correction and clarification of the popular misnomer of: E=mc2 and the maening of the correct equation.

(If the link doesn't work, you might need to join the Board AND then signnon to view the thread / URL... it's a spam free Board and it's free to join).

e = mc² has obvious correspondences to the ordinary, classic equation for the energy represented by a moving body, its kinetic energy, which can be defined as the amount of energy required to accelerate it to its current speed: e = ¹/₂ mv².

IOW Einstein showed that the energy equivalent of the rest mass of an object is twice the amount of energy that classical physics would say would be required to accelerate that mass to the 'cosmic speed limit'.

So if you have a problem with Einstein's equation because of "c²", you should have the same problem with ordinary Newtonian mechanics.

Oh dear. Well, first of all, I don't know if Nagasaki or Hiroshima actually "proved" E=mc2, seeing as Rutherford was already performing collisions that would have lead to the bomb without the theoretical structure of the equivalence of mass and energy.

You're actually asking a very involved question, whether you know it or not. The answer is a very long course in the relationship between mathematical physics and experimental physics. I recommend the following:

Walter Lewin's Course on Classical Mechanics

Walter Lewin's Course on Electromagnetism

Walter Lewin's Course on Waves

And I'm not kidding, or being dismissive. You need to have a good mathematical base before getting into Einstein's math, and understanding the relationship between his math and the math that came before it is absolutely crucial in understanding what he means when he concludes that E=mc2.

The short version: saying that E=mc2 is "unproven" is completely and utterly false. It is as proven as anything has ever been. What you're maybe thinking is "confirmed", which it has been, by thousands of experiments in particle accelerators.

"The speed of light squared" is not a speed, just like the square of the length of the side of a square is not a length. In that case we can match it to an everyday concept, ie 'area'.

So of course we can't "achieve" it. That makes no sense, any more than trying to measure area with the simple ruler we use to measure length.

I don't think we can assign a simple interpretation of velocity squared, but mass X velocity squared can, as I showed, be matched to 'energy'.

Force is defined mathematically as "mass x acceleration" - the force of gravity acting on a mass m is precisely sufficient to cause it to accelerate towards the center of the Earth at 32 feet per second per second.

Energy is defined mathematically as "force x distance". IOW, 1 joule of energy is the amount of energy required to move something through a distance of one meter against a force of one Newton (the force required to accelerate one kilogram from rest to a speed of 1 meter per second in one second).

If you combine these definitions, Energy = (mass x distance per second per second) x distance

The distance an object will cover when subject to a constant acceleration from rest is equal to its average velocity since it started multplied by the elapsed time since it started to move.

An object of mass M that has reached a velocity of V after time T, from rest under constant acceleration of V/T will have had an average velocity of ¹/₂V, so will cover a distance ¹/₂V x T.

The constant force F required to do this is

F = M x acceleration = M x (V/T).

The distance covered is

D = ¹/₂ x V x T

so Energy E = F x D =  M x V /T x ¹/₂ x V x T = ¹/₂ x M x V x V x T/T = ¹/₂ x M x V²

Hope this clarifies the concepts and the math, in the spirit implied by the title "Science 101". 

Forgive if I don't work through the argument justifying " e = m c²", but I hope you can see some connection there, at least in terms of how we go from mass and velocity to energy.

I wasn't quite sure just what your background knowledge was - once I saw the response to my first post, I decided I needed to post a more thorough explanation.

Treat2:

E=mc^2 is not part of general relativity. GR was published in 1918 and SR was published in 1905. The mass energy equivalence was from the fourth paper that Einstein published in 1905 and therefore it is part of SR.

SR is an extension of classical mechanics or what you like to call Newtonian Physics. Also, classical mechanics includes both Lagrangian and Hamiltonian mechanic as well as the work by Newton. Newton's work is taught in high school because it is based on mathematics that you don't need to go to college to learn.

GR is a unification of SR and classical mechanics, specifically gravitation. This had to happen because SR does not include gravitation in it's model.

Quantum mechanics also has roots in classical mechanics but then develops in directions that are quite unlike the classical works. It is mostly inconsistent with SR and GR.

String theory is consistent with both quantum mechanics and SR/GR. It is inconsistent with, well, itself. The fact is that prior to the development of M theory, there were five string theories and they were inconsistent with each other. M theory is a follow on to the five string theories that unifies them into a single theory.

Before you start posting in science threads, I suggest that you read a book (or fifty) on science. Preferably books that are written by scientists and not something that you saw when you were in line at the supermarket checkout.

Let me rephrase into terms more traditional. There is no such thing as energy in a pure for as SciFi appears to be talking about. It always comes in some form. The units of energy are mass x length x length / time x time. The temperature of water is determined by the mass of the molecules and the speed with which they bounce off of each other. Speed is length / time. Perform a little magic to come up with the amount of mass and square the velocity and you get the energy in the water. For the same amount of energy the smaller the amount of water the higher the temperature. Thus a bathtub of ice water has more heat than a cup of boiling water. (I refuse to talk about "global warming" with anyone who cannot tell me the difference between heat and temperature because I have yet to find a melter who knows the difference so they are always talking nonsense.)

What several people before Einstein noted was that the rest mass could be represented as energy. Despite it being the only equation most people know, it was not original with Einstein. He demonstrated that known result fell out of his special relativity formulation more as a confirmation that his approach lead to the same conclusions as others.

Anyway there is no need to invoke Hiroshima or get things going that fast to show it. It explains the energy of particle interactions and decays. Otherwise it explained only handful of anomalies which were largely unknown outside of the scientific community. So one does not have to blow up a city to test it. Measuring the total mass an energy in a neutron decay works as well and is much less wasteful of cities. The resulting proton and electron have less mass than a neutron but their velocities are greater than that of the neutron. When a positron and an electron annialate the resulting two gamma rays, which have no mass, have energy equivalent to the mass of the two electrons which disappeared.

The other major question it answers is if nothing can go faster than light where does the energy that speeds is up go? Energy has to be conserved. It goes into making the object more massive. The equation that E=mc^2 falls out of describes the rate at which energy goes into increased mass instead of increased velocity.

Above where I use mass length and time is from a more general idea of dimensional analysis. Energy is always and only M*L*L/T*T. Velocity is always L/T. Acceleration is always L/T*T. Photons have energy but no mass BUT every calculation regarding photons there is an M a unit of mass in the calculation. The mass that isn't there. But the units are always conserved. There are always the same units going into a reaction as coming out of it. Conservation of energy is a special case of conservation of dimensions.

Rotation is also a dimension. Some particle reactions do not balance unless rotation is conserved even though they do not rotate any more than photons have mass. The conserved rotation is called spin. Now you know the rest of the story. But it confused people. So what quarks came along up, down, strange and charm were conserved. The things to be conserved started geting out of hand. So if these things to be conserved are just information about the particle then one can talk about the conservation of information. Then Shannon's information theory can be applied.

Shannon is also an outstanding whisky whch is the source of inspiration for much of the above.

OK treat2, if you are so all knowing in the ways of science, do please tell us who the guy in my avatar is and wht his role in the question at had was...

If you can.

You don't have many friends do you?

Wait, you understand what he's saying?