What is equivalent mass

Special theory of relativity

The study of heat conduction led to correct results based on the assumption that heat is an indestructible substance that flows from the warmer to the colder substance. It seemed one "Theorem of the Preservation of Heat" to give. On the other hand, experiences have been known since time immemorial, according to which heat is generated through friction (Indian lighter). After physicists had long resisted admitting such a generation of "heat", they finally succeeded in showing that an exactly proportional amount of mechanical energy always has to be expended to generate an amount of heat through friction. For example with the pendulum, the mechanical energy of which is gradually transformed into heat through friction. This merged the principles of the conservation of mechanical and thermal energy into a single sentence. At this point, the physicists were forced to believe that this law of conservation should also be extended to chemical and electromagnetic processes, which assumption has so far been successfully carried out in all areas: There is one in a physical system that is isolated from the outside world Sum of energieswhich remains constant for all changes that occur.

Now to the sentence of the Conservation of mass. The mass is defined by the resistance that a body opposes to its acceleration (inert mass). It is also measured by the weight of the body (heavy mass). That these two very different definitions lead to the same measure for the mass of a body is a very surprising fact, the deeper meaning of which was only clarified by the general theory of relativity. The principle (for the conservation of mass) reads: The masses remain unchanged during any physical (and chemical) change. The mass seemed to be the actually essential (because invariant) quality of matter. The mass (or the total mass) does not change when it is heated, melted, evaporated, dissolved or when chemical compounds form.

This Conservation law of mass, to which physics ascribed exact validity until a few decades ago, was recognized as inadequate by the special theory of relativity. It was fused into a unit by this theory with the energy principle in a similar way as the law of conservation of mechanical energy and that of the conservation of heat were fused together about 60 years earlier. It could be better said: the principle of the conservation of energy has previously swallowed that of the conservation of heat and more recently that of the conservation of mass, and so it alone has maintained the field.

The Theorem of the equivalence of mass and energy is maintained (somewhat imprecisely) by the formula E = m · c2 express, where c is the speed of light (3 x 1010 cm / s). E is the energy that is in a (resting) body, m its mass. The energy that belongs to the mass m is equal to this mass, multiplied by the square of the tremendously high speed of light, that is, an enormous amount per unit of mass.

Now one may ask in astonishment: How is it that one has so far not noticed this enormous energy that is in every gram of matter? The answer is simple: as long as nothing of this energy is given away to the outside, one cannot notice its energy nature. It's like a rich man who doesn't spend money; how can one show his wealth?

Now one can also reverse the relationship and say that with an increase in energy E, an increase in mass E / c2 must be connected. But I can easily add energy to the masses, e.g. B. by heating them by 10 degrees. So why not the one associated with it Mass gain (or weight gain) measure? The bad thing about this business is that the enormous factor c2 occurs in the denominator. This means that the increase in mass in such a case is far too small to be measured directly, e.g. with the help of a sensitive balance.

So for an increase in mass to show itself in measurable quantity, the change in energy per unit of mass must be enormous. We know only one area in which enormous changes in energy per unit of mass are released, namely during radioactive decay. Such a process is of the following kind schematically. An atom of mass M splits into two atoms of mass M 'or M' ', which move apart with tremendous energy. If one imagines these two masses to be brought to rest, i.e. if one withdraws this kinetic energy from them, then taken together they are considerably less energetic than the original atom was. This causes after Equivalence theoremthat the mass sum M ’+ M’ ’of the decay products must also be slightly smaller than the original mass M of the radioactively decaying atom (a contradiction with the old conservation law of mass). The relative difference between the two is one tenth of a percent.

Now it is true that the atoms cannot be weighed individually. But there are sensitive indirect methods for the exact measurement of the atomic weight which we do not need to go into here. You can also use indirect methods to determine the kinetic energies that are transferred to the decay products M ’and M’ ’during disintegration. It has thus been possible to test and consolidate the equivalence formula. The law also makes it possible to calculate in advance from precisely determined atomic weights how much energy will be released when an atomic decay is contemplated. Of course, the law says nothing about whether and how an envisaged decay reaction can be brought about.

What happens to the mass or energy of the atom M during radioactive decay can be illustrated by the rich man mentioned above. M is a rich curmudgeon who didn't spend any money (energy) at all during his lifetime. In the event of his death, he leaves everything to his sons M ′ and M ′ ′ with the obligation to give a very small amount, namely less than one per thousand of the huge inheritance (energy or mass) to the community. The sons then together have a little less than their father had (the sum of masses M ′ + M ′ ′ is slightly smaller than the mass M of the radioactive atom). The percentage that is so small that is delivered to the community is, however, so immensely large (in its form of expression as kinetic energy) that it brings with it all the disaster that has become the most urgent problem of our time to avert.