Mass
The mass, also rest mass is a property of matter and a basic physical parameter. It is given according to the international system of units in the unit kilogram. The symbol usually is. The mass is an extensive quantity.
Gravity of a body is proportional to its mass. At the same time its mass determines the inertia with which his motion state reacts to forces. This dual role of the mass content of the equivalence principle. Moreover, in the rest frame of a body its mass equivalent to its energy, that is, the two quantities mass and resting energy differ only by the constant factor.
The mass is called outside of physics as a weight. It should be noted that this word can also stand for the related but not identical meanings weight force, weight or weight piece.
- 5.1 Relativistic mass
- 5.2 rest mass
- 6.1 Invariant mass
- 6.2 mass shell
- 6.3 mass defect
Definition ( inertial and gravitational mass )
With the mass of a body three classical properties are connected:
To highlight the first property, refers to the mass as inertial mass, for the second and / or third property as a heavy mass. However, so far no difference between inertial and gravitational mass was in measurements, the accuracy could be increased to twelve significant digits, noted. The assumption that it is one and the same physical size, belongs to the equivalence principle of physics, from the Albert Einstein developed the theory of general relativity.
The SI base unit of mass, the kilogram (kg), is defined by a reference mass: A kilogram is the mass of the international prototype of the kilogram.
Measurement
Direct mass determination
The so-called direct measurement of the ( heavy ) Weight carried out on a stationary body by comparison with a reference mass. Two masses are equal if they have the same weight in the same gravitational field. You can check this with a beam balance. The strength of the gravitational field is negligible, it must be the same only different from zero and in the places of the two bodies. To define the unit of mass see prototype kilogram.
Indirect mass determination
The mass can also be determined by forces and accelerations. In the Newtonian mechanics, each change of movement is proportional to the force which has caused the change in motion (see below: ). Mass is therefore the constant of proportionality between force and acceleration:
The acceleration in this case indicates the speed change caused by a force. Such a certain mass is referred to as inertial mass.
Example 1 ( to the inert mass ): If a body by the constant force within the time interval to be faster, so its acceleration is
Its mass is then
Example 2 ( for heavy mass ): Due to the gravity of the earth be free-falling body with
Accelerated. A body which is attracted to the surface with the force of gravity, has the mass
The inertial mass can be measured for example by the force that is required to make a body through a circular path with constant velocity ( centripetal force ). The force effected by the acceleration changes the direction of the speed ( on the circular path ), but not the velocity value. When a charged particle in a magnetic field can be at a known speed and magnetic field strength from the circle radius, calculate the ratio of charge to inert mass.
Related sizes
The mass is an extensive quantity. This means that two bodies of mass in total have twice the mass. Intensive variables do not change when the system is doubling. Related to the mass following intensive quantities:
- Taking into account the mass to the volume, we obtain the density of the SI unit
- Taking into account the mass on the amount, you get the molar mass with the SI unit
Classical Mechanics
Classical mechanics does not explain the equivalence of gravitational and inertial mass. It occurs as an empirical fact, as well as the conservation of mass.
As a heavy mass is called the source of the gravitational force. The force exerted by the mass on the mass is
Wherein the compositions are point or spherical and designed according to the vector of is. is the gravitational constant, a fundamental constant.
The inertial mass in Newtonian mechanics, the proportionality between force and acceleration
From the second Newtonian axiom (action principle)
Obtained with the pulse of the body with constant mass, the equation of motion to " force equals mass times acceleration ," the " fundamental equation of mechanics":
This does not apply body with time-varying masses such as in a rocket.
Special Theory of Relativity
In the special theory of relativity, the pulse does not like Newton is the product of mass and velocity but it is
Thus, the motion of a body with light () or superluminal ( ) is excluded.
Relativistic mass
To be able to retain the Newtonian formula, the term relativistic mass was
Introduced so that applies. The size is in this context " rest mass " called and usually referred to as: the concept of relativistic or relativistic variable mass is still used in popular literature and partly also in the experimental physics today, but increasingly avoided because the relativistic mass instead of only leads to the equations for the momentum and the relativistic energy correct results used in the Newtonian law of gravity and the Newtonian law but incorrect produces results (except when the force is perpendicular to the direction of movement). In this and other articles, the size is no longer used, and the symbol for the mass always has the meaning of the rest mass, ie
Rest mass
Context, the rest mass is the mass of a body in its rest frame. So it is a fixed property of the body that does not accept the different, depending on the reference frame of the observer velocity different values. With the word mass ( without additives) is usually this rest mass meant. Because of the equivalence of mass and energy is
Also called the rest energy.
The force is equal to the temporal change of the pulse, in the special theory of relativity
Or, solving for the acceleration,
One can see that the acceleration does not always pointing in the direction of the force, but generally also has a share in the direction of the velocity. A force causes different accelerations at different speeds of the particle. The mass is therefore not a simple proportionality between force and acceleration as in the Newtonian mechanics. The different inertia in the direction of motion and transverse to it had initially with the terms of the longitudinal and transverse mass to capture attempted, but which are no longer used today.
The mass combines the energy and the momentum of the general energy - momentum relation
For a resting body () from Einstein's famous equation by which the equivalence of mass and energy is expressed.
For a particle without mass () Such particles follows move relative to each reference system with the postulated in the special theory of relativity upper limit speed, the speed of light. This is the case with photons. The reverse conclusion is also correct: particles that move with the speed of light, are massless.
Particle Physics
Invariant mass
From the rest mass of a particle, the invariant mass is distinguished (also center of mass energy ) of several free particles before or after a particle reaction:
Where N is the number of particles. The invariant mass is a lorentzinvariante size. They are present in the common center of mass system of the considered particle energy (as the sum of their rest masses and kinetic energies, masses and energies with c2 converted into each other ). Only this amount of energy is available for reaction, because the rest of the kinetic energy associated with the center of gravity movement of the overall system, which remains always constant. The formula for calculating the invariant mass can be applied to N = 1 on a single particle, and then votes with just its rest mass match.
In high energy physics particle collisions are considered at energies that are significantly higher than the rest masses of the colliding or possibly newly generated particles. The invariant mass of the particles before the collision is the maximum possible value for the mass of a particle, which could be formed there. For example, the Z0 boson is formed at an electron-positron collision of 45 GeV in the center of mass system of 90 GeV mass. Usually the particles formed in such collisions are short-lived ( intermediate particles ), they rapidly disintegrate into several other particles and can only be studied on these decay products. Based on the knowledge or on a presumption, in which a certain type of particles of intermediate particle decays, one identifies these decay products among all the other reaction products of the collision based on their invariant mass. It must match the mass of this particle. Is the intermediate particles still hypothetical or its mass is still unknown, searched one of the eligible combinations of decay products to determine whether a certain invariant mass with significantly greater frequency than occurs due to known other reactions would be expected. The current search for the Higgs boson follows this path.
Mass shell
Since the momentum of a particle of ( rest) mass which moves with velocity in relativistic physics
Is ( see derivation of four-momentum ), hang the energy and momentum to the ground by the energy - momentum relation
Together. According to this equation are in four-dimensional space of all possible energy and momentum values, the physically possible energies of a particle of mass on a three-dimensional surface, called the mass shell. Is a hyperboloid (describes a hyperbola in the xy plane).
The energy - momentum relation is also valid for photons. You are massless () and always move with the speed of light your energy is up to a factor of the amount of their pulse:
Mass defect
The binding energy of the atomic nucleus reduces the mass of the nucleus compared to the sum of the masses of its protons and neutrons. Is the binding energy for most nuclei 7-9 MeV per nucleon and thereby causes a ground fault between 0.7 and 0.9 percent. Very light nuclei (2H, 3H, 3He, Li, Be, B) have from 1 to 6 MeV to lower binding energies per nucleon and reduced with 0.1 and 0.6 percent mass defects.
The binding energy of chemical bonds is typical 2-7 eV per bond (per nucleon it would be according to the molecular weight again significantly smaller) to 7-9 orders of magnitude lower. Therefore, a chemical mass defect could not yet be detected by weighing.
Although the values are some of the reactions in the detection limit of current mass comparators ( percent): The largest chemical mass defect per cent in the binding. To include a mass defect of percent. However, these reactions are highly exothermic and should therefore be carried out in thick-walled and absolutely dense reaction vessels, so that the relative mass change that would be observed after cooling, is with percentage in a non -detectable range.
The fact that in the field of chemistry of the mass defect is beyond the measurement, in turn, is the basis of the discovered by Antoine Lavoisier mass conservation law. This realization was the end of the 18th century significantly to the shift away from alchemy and phlogiston theory and in that way was an important basis based on the chemical elements chemistry.
General Theory of Relativity
In the general theory of relativity the free fall of particles is understood in the gravitational field as a force-free. Cause forces that the trajectories differ from the free fall. On the size of the force will be held by free fall with the particles to show their inertial mass.
The world lines of freely falling particles are straight lines (more precisely, geodesics ) of spacetime. They are established in full compliance with all observations by the initial location and the initial velocity and not depend on other Eigenschafte such as size or mass of the free-falling particle from ( principle of equivalence). Since the spacetime is curved, usually results in the projection of the geodesics in the three-dimensional position space is no straight line, but for example trajectories.
Source of gravity is in the fundamental equation of general relativity, the energy -momentum tensor, ie: energy density, momentum density, energy flows and pulse flows. Since the energy of resting particles is determined by its mass, the mass of resting particles causes gravity. Is it possible to neglect the movement of the gravity -generating body and the velocity of the freely falling particles small compared to the speed of light, so the mass of the gravitational generating body acts like in Newton's theory of gravitation. For light as test particles, this restriction is not true: it is diverted twice in the sun, as would be expected according to Newton.
At its gravitational effect can be read off the ADM mass at large distances from the gravity- generating energy and momentum densities. It does not change over time, because radiation does not pass through infinite spatial distances in finite time. The Bondi mass is read in general relativity theory for large times and the speed of light increasing distances. You decreases due to radiation and is non-negative, that is, in the general theory of relativity is the energy that can be radiated, bounded from below.
Origin of the masses of the elementary
In the Standard Model of elementary particle physics, the origin of the masses of elementary particles is explained by the Higgs mechanism. Through interaction with the Higgs boson, a scalar elementary particle that may have been observed experimentally, they get a mass if the associated Higgs field does not disappear even in a vacuum. Only the mass of the Higgs boson itself is not thereby explained.
The masses of the baryons, which include proton and neutron include, but are about 100 times larger than the masses of the three quarks of which they consist. The Baryonenmassen be explained dynamically. Approaches to calculating provide lattice calculations in QCD. Half vividly one can argue with the small size of the baryons of about 10-15 m: If the quarks in the baryon focus on such a small space, they have such a short de Broglie wavelength that their kinetic energy according to Einstein's formula substantial mass means. Three such constituent quarks arise then actually about the mass of the proton or neutron.
The baryons make up the majority of the mass of visible matter. It is believed that " WIMPs " ( weakly interacting massive particles engl. ), such as the hypothetical LSP ( lightest supersymmetric particle engl. ) could build invisible dark matter.
Usage: Mass and Weight
In common parlance, the mass of an object is known as its weight. Examples are the excess weight, tare weight, drained weight or weight indicated in recipes. This also applies to many laws and regulations. Examples are the German Maternity Protection Act and the Swiss Road Traffic Act.
When equating mass and weight might get the impression that mass depended on the locally dominant gravity. For example, the following statement is misleading: " On the Moon, a 60 kg man weighs only about 10 kg. " Is clearer: "A man with a mass of 60 kg weighs on the moon about as much as a man with a mass of 10 kg on Earth weighs ".