با تشکر - حسین جوادی

javadi_hossein@hotmail.com

The Origin of Mass

The inertial mass of matter is caused by the fact that every extended object has necessarily an inertial behavior

In today's physics – the Standard Model – it is assumed that the fundamental particles which build up our matter do originally have no mass. So since quite a long time the physicists are looking for a reason why matter has an inertial behavior. - The search for the Higgs boson which was intensified in recent times is an example of it. However, there is an easy and very fundamental way to explain the inertial mass.

If two particles are bound to each other in a way that the binding field forces a specific distance then, at every change of the position of one of them, it needs a finite time caused by the finite speed of light to make the other particle moving. This delay is sufficient to explain the inertial behavior.

It turns out that the inertial mass of an elementary particle is given by the universal equation

Also the relativistic increase of mass at motion and as a consequence the mass energy equivalence (Einstein) is perfectly explained by this mechanism.

In the Basic Particle Model every elementary particle is built by 2 mass-less constituents which orbit each other with the speed of light c. The frequency of the circulation is the de Broglie frequency (Figure1).

The Mass to Size Relation of a Particle

The circular motion of the basic particles within an elementary particle has the orbital frequency

where c is the speed of light and R the radius of the elementary particle.

According to the Basic Particle Model this frequency n is the de Broglie frequency.

Eq. (2.1) can be written also as

where c is the speed of light and R the radius of the elementary particle.

According to the Basic Particle Model this frequency n is the de Broglie frequency.

Eq. (2) can be written also as

using the circular frequency .

If we take the empirical result

and the well known relation

  (4)

and insert both into (2) we get;

  (5)

for the relation between the radius R of a particle and its mass m.

Remark: This is only a short formal deduction for equation (5). The detailed deduction which justifies the use of eq. (2) and eq. (3) is given in the context of the 'Origin of Mass'.

Equation (5) can be reordered to

   (6)

The left side is the formal definition of the angular momentum for v = c.

The right side fulfils the expectation into the spin of an elementary particle in so far, as it is independent of any particular particle properties; so it has a universal value.

The factor 1 on the right side is not satisfying at the first glance as the measured spin corresponds to a factor of ½. It can, however, not be a surprise. Eq. (6) would be the angular momentum of the configuration of two objects which orbit each other and carry half of the classical mass of an electron each. The configuration of the basic particle model is, however, different in the way that both objects (basic particles) do not have any classical mass.

In spite of this the lack of a conventional mass the orbiting basic particles do have an inertial behaviour. The path they can move is destined by the field of the other partner. There are directions a basic particle can follow without the effect of any force, and there are other directions where a force, corresponding to the inertial mass of the entire configuration, is effective.

So the average angular momentum will be a bit less than

.  (7)

A factor of ½ as an average is possible, but it has still be proven quantitatively.

In the Stern-Gerlach experiment an atomic beam of spin 1/2 was split into 2 beams by an inhomogeneous magnetic field. From this observation it was concluded that the magnetic moment can only have 2 orientations in space and that therefore only 2 orientations of the particle's spin are possible.

If a particle flies towards the magnet it can have arbitrary orientations is space. The magnetic force depends on the co-sine of the angle between it's rotational axis and the direction of the magnetic field. Therefore it is classically to be expected that the distribution of the deflection angles has some kind of a flat shape. However, it was found that the distribution was peaked at two angles which caused the assumption of 2 possible spin orientations.

An elementary particle built by two basic particles does not behave in this way. The magnetic force will depend on the co-sine as classically expected. However, from the Basic Particle Model it follows that also the inertial mass depends on the direction of the attacking force. The dependency of the magnetic force and the inertial force from the angle are correlated to each other. As a consequence the deflection distribution of the particles is suppressed in forward direction.

On the other hand every force acting on the constituents of the electron with an axial component will cause the electron to perform a precession motion, as it behaves as a gyro.

The simultaneous action of both effects can at least qualitatively explain the deviation of the Stern-Gerlach result from the classical expectation.

It has to be mentioned that in the Stern-Gerlach experiment the deflection distribution did not build 2 sharp peaks but a somewhat washed-out distribution. This was explained by the thermal velocity spread of the atoms; it can as well be taken as an indication of the process explained above.