Invariant mass is comparable to rest energy, while relativistic mass is equivalent to relativistic energy, according to the idea of mass-energy equivalence (also called total energy). Relativistic mass is not the same as classical mass because they represent different concepts. Classical mass is defined as the quantity of matter that has a gravity force acting on it; thus, it is an intrinsic property of the matter itself. In special relativity, mass and energy are treated as equivalents, so the term "mass" can be used to describe either type of entity.
Rest energy is the energy of an object at rest. It is equal to one-half of the mass times the velocity squared (E = mc²), where m is the mass and c is the speed of light in vacuum. So, two objects with equal mass but different velocities will have equal amounts of rest energy but different amounts of kinetic energy. Rest energy is always conserved: If an object has no net external forces acting on it, then its mass cannot change. And if its mass does not change, then its rest energy must also not change.
Mass is also conserved when there are external forces acting on an object.
While current physics has abandoned the phrase "conservation of mass," under earlier language, relativistic mass may also be characterized as being comparable to the energy of a moving system, allowing for relativistic mass conservation. In other words, it is possible for there to be more massive systems than non-relativistic ones of equal energy content.
In general relativity, the total mass M of an object is defined in terms of its gravitational field by the expression:
Where G is the universal constant of gravity and c is the speed of light in vacuum. If we assume that the mass inside the radius r of an object is proportional to its volume (a good approximation for large objects), then we can write:
Where V is the volume of the object. Now if we take the limit as r goes to infinity in both equations above, we find that the mass must always be equal to the energy of the object.
This result was first discovered by Albert Einstein in his paper "Über die Entwicklung des Relativitätsprinzips" (On the development of the principle of relativity). The paper was published in 1916 while he was working on his theory of general relativity.
E0 = mc2, which means that mass is a kind of energy. When energy is stored in an item, its mass grows. The relativistic total energy E and the relativistic momentum p are related by the equation E2 = (pc) 2 + (mc2) 2. At extremely high speeds, the rest energy mc2 vanishes, and E = pc. This means that light can travel infinitely far if it is not slowed down by anything.
Mass is defined as the amount of matter inside an object. For example, the mass of the Sun is about M?! =1.9891×1030 kg. Its energy is therefore E⊕=1.987×1030 J. The mass of the Earth is 5.972×1024 kg. So the mass of the Earth is about 5.972×1024 J. The mass of a human being is 70 kg. A car has a mass of about 1000 kg. A bus has a mass of about 15000 kg. An airplane has a mass up to about 20000 kg. A spacecraft like Apollo has a mass of about 175 kg. A ton of metal has a mass of about 10000 kg. A ton of coal has a mass of about 22000 kg. A ton of oil has a mass of about 27700 kg. A ton of nuclear fuel has a mass of about 60000 kg.
The rest energy formula says that the total energy E of an object is equal to the product of its mass and the speed of light squared, divided by 2.
According to mass-energy equivalence, mass is concentrated energy. Einstein developed the equation E=mc2 in his theory of special relativity. Mass contains a significant quantity of energy. Because of the mass changes, nuclear processes may be understood to release far more energy than chemical ones. The overall effect is that all matter is destructible, and nothing is immune to change.
All forms of matter are equally subject to gravity. If mass could be created or destroyed, then so would gravity. This would have important implications for physics as we know it today. Gravity is one of the four fundamental forces of nature along with the strong force, electroweak force, and electromagnetism. As far as we know, they are all part of a single underlying field. There is no reason why this field should not exist without gravity.
The fact that all matter is destructible does not mean that everything is interchangeable. You can't simply replace a cup of water without affecting the environment and the people in it. Mass differs from matter in that it can be transformed into other types of matter, but not necessarily everywhere at once. For example, when you burn gasoline, it breaks down into carbon dioxide, oxygen, and heat. All of these substances are elements, and therefore matter. But because there's less amount of gasoline than there was before, you could say that it has been converted into something else.
Mass can be eliminated in order to liberate energy. We usually don't notice when an object's mass changes since the change in mass is so little for such a significant gain in energy. But the fact remains that energy can be transformed from one form to another.
The rest energy of an object is the minimum amount of energy required to accelerate it through a vacuum to 1 cm per second. Since no physical process can create or destroy energy, this number must be equal to the energy available in matter and radiation at any given time. For example, the total energy in the Earth is about 1022 joules, but the rest energy of the Earth is much less than this because most of the energy is stored in the Sun rather than within the Earth itself.
We can calculate the rest energy of the Earth using Einstein's famous equation E=mc2. If we assume that the Earth has a density of 5500 kg/m3 and a mass of 6*1021 kg, then the total energy is:
E = 545 * 1030 J = 5.5 * 1014 Teva Joules