What is E=MC2?

Question

What does E=MC2 actually mean? How does it work? Also, does it have anything to do with Einstien's theory that time can be slowed (maybe even stopped)?

Do you know of any websites where I can learn more about this?

Answer 1

This formula proposes that when a body has a mass, it has a certain energy equivalence, even "at rest". This is opposed to the Newtonian mechanics, in which a massive body at rest has no kinetic energy, and may or may not have other (relatively small) amounts of internal stored energy (such as chemical energy or thermal energy), in addition to any potential energy it may have from its position in a field of force. That is why a body's rest mass, in Einstein's theory, is often called the rest energy of the body. The E of the formula can be seen as the total energy of the body, which is proportional to the mass of the body.

Conversely, a single photon travelling in empty space cannot be considered to have an effective mass, m, according to the above equation. The reason is that such a photon cannot be measured in any way to be at "rest" and the formula above applies only to single particles when they are at rest, and also systems at rest (i.e., systems when seen from their center of mass frame). Individual photons are generally considered to be "massless," (that is, they have no rest mass or invariant mass) even though they have varying amounts of energy and relativistic mass. Systems of two or more photons moving in different directions (as for example from an electron-positron annihilation) will have an invariant mass, and the above equation will then apply to them, as a system, if the invariant mass is used.

This formula also gives the quantitative relation of the quantity of mass lost from a resting body or a resting system (a system with no net momentum, where invariant mass and relativistic mass are equal), when energy is removed from it, such as in a chemical or a nuclear reaction where heat and light are removed. Then this E could be seen as the energy released or removed, corresponding with a certain amount of relativistic or invariant mass m which is lost, and which corresponds with the removed heat or light. In those cases, the energy released and removed is equal in quantity to the mass lost, times the speed of light squared. Similarly, when energy of any kind is added to a resting body, the increase in the resting mass of the body will be the energy added, divided by the speed of light squared.

The equivalence or inter-convertibility of energy and matter was first enunciated, in approximate form, in 1717 by Isaac Newton, in "Query 30" of the Opticks, where he states:

“ Are not the gross bodies and light convertible into one another, and may not bodies receive much of their activity from the particles of light which enter their composition. ”

The exact formula for the mass-energy equivalence, however, was derived by Albert Einstein based on his 1905 inquiry into the behavior of objects moving at nearly the speed of light. The famous conclusion he drew from this inquiry is that the mass of a body is actually a measure of its energy content. Conversely, the equation suggests (see below) that all of the energies present in closed systems affect the system's resting mass.



According to the equation, the maximum amount of energy "obtainable" from an object to do active work, is the mass of the object multiplied by the square of the speed of light.

It was actually Max Planck who first pointed out that Einstein's equation implied that bound systems would have a mass less than the sum of their constituents, once the binding energy had been allowed to escape. However, Planck was thinking in terms of chemical reactions, which have binding energies too small for the measurement to be practical. Early experimenters also realized that the very high binding energies of the atomic nuclei should allow calculation of their binding energies from mass differences, however it was not until the discovery of the neutron in 1932, and the measurement of the free neutron rest mass, that this calculation could actually be performed (see nuclear binding energy for example calculation). Very shortly thereafter, the first transmutation reactions (such as ) were able to verify the correctness of Einstein's equation to an accuracy of 1%.

This equation was used in the development of the atomic bomb. By measuring the mass of different atomic nuclei and subtracting from that number the total mass of the protons and neutrons as they would weigh separately, one could obtain an estimate of the binding energy available within an atomic nucleus. This could be (and was) used in estimating the energy released in the nuclear reaction, by comparing the binding energy of the nuclei that enter and exit the reaction.


[edit] Practical examples
A gram of mass could (theoretically) be converted entirely into approximately:

90,000,000,000,000 Joules (90 terajoules)
25,000,000 kilowatt-hours
The energy in 21 kilotons of TNT
Approximately 0.0000850 Quads (quadrillion British thermal units)
It is important to note that practical conversions of "mass" to energy are rarely 100 percent efficient. One theoretically perfect conversion would result from a collision of matter and antimatter (e.g. in positronium experiments); for most cases, byproducts are produced instead of energy, and therefore very little mass is actually converted. For example, in nuclear fission roughly 0.1% of the mass of fissioned atoms is converted to energy. In turn, the mass of fissioned atoms is only part of the mass of the fissionable material: e.g. in a nuclear fission weapon, the efficiency is 40% at most. In nuclear fusion roughly 0.3% of the mass of fused atoms is converted to energy. In actual thermonuclear weapons (see nuclear weapon yield) some of the total bomb mass is casing and non-reacting components, so the efficiency in converting passive energy to active energy, at 7 kilotons/kg, does not exceed 0.03% of the bomb mass.


USS Enterprise, Long Beach and Bainbridge in formation in the Mediterranean, 18 June 1964. Enterprise crewmembers spelled out Einstein's famous equation on the flight deck to commemorate the first all-nuclear battle formation.In the equation, mass is energy, but for the sake of brevity, the word "converted" also is used; in practice, one kind of energy is converted to another, but it continues to contribute mass to systems so long as it is trapped in them (active energy is associated with mass also, as seen by single observers). Thus, the total mass of any system is conserved and remains unchanged (for any single observer) unless energy (such as heat, light, or other radiation) is allowed to escape the system. In any cases, the use of the phrase "converted" is intended to signify energy which has gone from passive potential energy, into heat or kinetic energy which can be used to do work (as in a nuclear reactor or even in a heat-producing chemical reaction). To use the quantitative examples above, if a kilogram of rest mass was converted to 90 PJ of light, heat, or other forms of kinetic energy, it would still continue to weigh one kilogram, so long as it was trapped in any system which allowed it to be weighed.

The equivalence or inter-convertibility of energy and matter was first enunciated, in approximate form, in 1717 by Isaac Newton, in "Query 30" of the Opticks, where he states:

“ Are not the gross bodies and light convertible into one another, and may not bodies receive much of their activity from the particles of light which enter their composition. ”

The exact formula for the mass-energy equivalence, however, was derived by Albert Einstein based on his 1905 inquiry into the behavior of objects moving at nearly the speed of light. The famous conclusion he drew from this inquiry is that the mass of a body is actually a measure of its energy content. Conversely, the equation suggests (see below) that all of the energies present in closed systems affect the system's resting mass.

E = mc² where m stands for rest mass (invariant mass), applies to all objects or systems with mass but no net momentum. Thus, it applies most simply to particles which are not in motion. However, in a more general case, it also applies to particle systems (such as ordinary objects) in which particles are moving but in different directions so as to cancel momentums. In the latter case, both the mass and energy of the object include contributions from heat and particle motion, but the equation continues to hold.

The equation is a special case of a more general equation in which both energy and net momentum are taken into account. This equation always applies to a particle that is not moving as seen from a reference point, but this same particle can be moving from the standpoint of other frames of reference (where it has a net momentum). In such cases, the equation (if the mass used is invariant mass) becomes more complicated as the energy changes, since momentum-containing terms must be added so that the invariant mass remains constant from any reference frame (as it must, given the definition of invariant mass).

Alternative formulations of relativity, see below, allow the mass to vary with energy and simply ignore momentum, but this involves use of a second definition of mass, called relativistic mass because it causes mass (which is now relativistic mass, not invariant mass) to differ in different reference frames.

A key point to understand is that there may be two different meanings used here for the word "mass". In one sense, mass refers to the usual mass that someone would measure if sitting still next to the mass, for example. This is the concept of rest mass, which is often denoted m0. It is also called invariant mass. In relativity, this type of mass does not change with the observer, but it is computed using both energy and momentum, and (unless momentum happens to be zero) the equation E = mc2 is not in general correct for it, if the total energy is wanted. (In other words, if this equation is used with constant invariant mass or rest mass of the object, the E given by the equation will always be the rest energy of the object, and will change with the object's internal energy, such as heating, but will not change with the object's overall motion).

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


with v being the relative velocity. This can be shown to be equivalent to


with p being the relativistic momentum (ie. p = γp0 = mrel * v).

When v = 0, then p = 0, and both formulas above reduce to E = m0c2, with E now representing the rest energy, E0. This can be compared with the kinetic energy in newtonian mechanics:

,
where E0 = 0 (in Newtonian mechanics only kinetic energy is treated, and thus "rest energy" is zero).

Answer 2

This is Einstain's famous equation from the special theory of relativity (which also addresses the slowing down of clocks moving at high speeds). It indicates that mass can be converted into energy, and vice versa; the theory was vindicated at the expense of inhabitants of Hiroshima and Nagasaki in 1945. The sun is powered by fusing of hydrogen into helium; because the helium weighs a bit less, the difference appears as energy, to give you your next suntan.

Answer 3

E is energy that any mass has at rest
M is mass
C is the speed of light

The relationship between energy and mass is to key to understanding why and how energy is released in nuclear reactions.

Answer 4

it is the mass energy equation, that, in basic English, says that energy and mass are directly related.

it was derived from relativity but isn't directly related to time dilation.

any physics website should give you more information on it.

Answer 5

try to relate that to black holes and i think you will have a better understanding. i learned about it in astronomy the other day. its too complicated to explain so ill let you do some research!