The calculations used in textbooks to determine the rotational energy associated with spin implicitly assume that elementary particles have mass even without spin. These calculations lead to contradictions with known physical facts - depending on the calculation approach, the particle would have to rotate faster than light, or the rotational energy of the spin would be greater than the energy equivalent of the particle's mass at rest.
Standard physics knows no way out of these contradictions. Instead, standard physics sees spin as an additional degree of freedom of elementary particles, which cannot be clearly interpreted within the framework of classical mechanics. Instead, we want to look for a way out by abandoning the assumption that elementary particles have mass even without spin. Instead, it could be that the mass of a particle only results from the rotation of its spin: According to Einstein's famous formula E = m · c2, energy and mass are equivalent. The formula is usually interpreted to mean that mass can be converted into energy, as happens, for example, when heavy nuclei split. However, the formula can also be read the other way round, i.e. that mass is a form of energy. In the following we will show that the mass of a particle is equal to the rotational energy of its spin.
Energy of the photon
Let's start with the photon as the first particle. In his 1905 essay ‘On a heuristic point of view concerning the generation and transformation of light’, Albert Einstein gave the formula ephoton = h · ν for the energy of a photon. Here, h = 6.626 - 10-34 Js denotes Planck's quantum of action and ν the oscillation frequency of light, which in turn is the reciprocal of the oscillation period τ. Einstein did not arrive at this formula by deriving it from first principles, but by demonstrating an analogy between the entropy of light radiation and the entropy of a diluted gas.
Einstein was not aware of the concept of spin in 1905, as it was not proposed until twenty years later by Samuel Goudsmit and George Uhlenbeck - initially as an ad hoc hypothesis relating to the electron, to explain the splitting of electron orbits in an atom when a magnetic field is applied. Today we know that all elementary particles have a spin and that the spin of the photon has a value of h / 2π. Within the period τ, the electric and magnetic field vectors of the photon rotate 360° around its direction of motion.
If you rearrange the formula for the energy of the photon a little bit, you will get an interesting correlation:
Ephoton = h · ν = h / τ = h / 2π · 2π / τ = L · ω
The energy of the photon therefore corresponds to the product of its intrinsic angular momentum L = h / 2π and its rotational speed ω = 2π / τ. If we compare the resulting formula Ephoton = L · ω with the formula for the classical angular momentum Erot = ½ L · ω, the only difference between the two formulae is the pre-factor ½. The energy of the photon can therefore be interpreted as the rotational energy of its spin, which results from Espin = L · ω.
We now want to apply this relationship to other elementary particles. To do this, we need to know L and ω.
Intrinsic angular momentum and rotation period of elementary particles
Let's start with the angular momentum: The spin of an elementary particle is a conservation parameter and is characteristic of the respective particle. Interestingly, the spin of all experimentally observed elementary particles takes on either the value h / 4π or twice the value h / 2π. The only exception is the Higgs particle, which has no spin. All elementary particles or particles composed of elementary particles whose spin is h / 4π or an odd multiple thereof are called fermions. These include, for example, the electron, proton and neutron. Particles such as the photon, whose spin is h / 2π or a multiple thereof, are called bosons. In physics, it has become common to refer to the value h / 2ππ as ℏ (read: h transverse).
Now we need to determine the period of rotation τ and the resulting speed of rotation ω. To do this, we return to the idea of Louis de Broglie (1892-1987) that a particle can also be understood as a matter wave. Depending on its energy E and momentum p, a particle has a characteristic wavelength λ = h / p and a natural oscillation time τ = h / E, where h is Planck's constant. The period τ of a particle's natural oscillation can be calculated from its rest mass m0 and momentum p from a relativistic point of view: τ = h · (p2c2 + m02c4) -½. A particle at rest therefore also has a natural period of oscillation, which in this case is calculated as τ = h / m0 c2.
The idea of matter waves leaves open which properties of the particle oscillate with the calculated natural oscillation time τ. At this point, we would like to suggest that the natural oscillation time of a particle corresponds to the rotation period of its spin.
We have thus determined the size of L and τ, which are required to calculate the rotational energy.
Mass at rest of bosons with spin ℏ
In addition to the photon, the Z boson and the two W bosons are elementary particles with a spin ℏ. Like the photon, they can be assigned a rotational speed of spin ω = 2π / τ. Unlike the photon, they can be at rest and therefore have a mass at rest.
We now set Espin = L - ω, as for the photon, where L = ℏ and ω = 2π / τ. For a particle at rest, the de Broglie relation τ = h * (p2c2 + m02c4) -½ is simplified to τ = h / m0 c2.
For a boson at rest with a mass, the rotational energy of its spin is calculated as
Espin = L · ω = h / 2π · 2π / τ = h / τ = h / h · m0 c2 = m0 c2
We have thus obtained the astonishing result that the rotational energy of the spin corresponds exactly to the rest energy m0 c2. Does this correlation also apply to fermions?
Ruhemasse von Fermionen mit Spin ½ ℏ
In contrast to bosons, all known fermions are ascribed a spin L = ½ - ℏ = h / 4π. Fermions have the somewhat strange property of only being identical to themselves again when they rotate by 720° = 4π. Consequently, their rotational speed ω is not 2π / τ as usual, but ω = 4π / τ. With this knowledge, the rotational energy associated with the spin of a fermion at rest can be calculated as
Espin = L · ω = h / 4π · 4π / τ = h / τ = h / h · m0 c2 = m0 c2
Consequently, the energy at rest of fermions can also be equated with the rotational energy of their spin.
Consequences
We were able to show that the rotational energy associated with the spin of a fermion or boson corresponds to the energy at rest m0 c2. Einstein's famous formula E = mc2 is usually interpreted in such a way that mass can be converted into energy, whereas our derivation suggests the opposite interpretation: Mass is nothing other than a special kind of energy - namely the rotational energy of spin.
The mass at rest of the elementary particles could therefore be explained without resorting to an interaction with the Higgs field. However, if the Higgs field is not required to explain the mass of particles, the question arises as to whether the Higgs particle actually exists or what alternative interpretation can be found for the CERN discovery, which is generally regarded as the Higgs particle.
Assessment of the explanatory approach
Strengths:The interpretation of the mass at rest as the rotational energy of the spin eliminates a well-known contradiction in the theories of physics. Einstein's formula for the energy of the photon E = h - ν is thus given a new foundation. It also opens up new horizons for understanding the physical world: for example, the remarkable fact that all elementary fermions have the same intrinsic angular momentum L = h / 4π, but different mass at rest, leads to the idea that the particles have different moments of inertia J = L / ω.
Weaknesses:
It is not discussed why the pre-factor ½, which appears in the formula for the classical angular momentum Erot = ½ L - ω, is missing in the formula for the rotational energy of the spin Espin = L - ω. According to the authors, there are several possible explanations for this: First, classical mechanics describes the motion of point masses or bodies with mass, whereas elementary particles cannot be understood in this way. Second, elementary particles require a relativistic consideration, as is done in the determination of τ via the relativistic energy-momentum relation, whereas relativistic mechanics does not recognise a simple formula for rotational energy. Thirdly, the prefactor ½ could be introduced into the energy equation of the photon (and thus into the formula for the rotational energy of the spin) by setting the value of h twice as high and adapting this redefinition in all physical formulae in which h occurs by inserting a prefactor ½. Which of these possible explanatory approaches is the best can only be revealed by further testing of the considerations presented here for consistency and coherence with accepted physical knowledge.
Another point of criticism is that the mass at rest of the Higgs boson cannot be explained as the rotational energy of the spin, as the Higgs boson has a spin of 0 and should therefore have no mass. However, the mass at rest of the Higgs boson cannot be described without contradiction using the Higgs mechanism, which is usually used to explain the mass at rest. According to the authors, this fact is a (further) indication that the cause of the mass at rest is not to be found in the Higgs mechanism and that possibly neither the Higgs mechanism nor the Higgs particle exist. In this case, however, the alleged observation of the Higgs boson at CERN requires a different interpretation.
Comments powered by CComment