Relative Strengths of the Four Fundamental Forces Based on the Fundamental Postulate of the Final Particle

Transcription

1 Relative Strengths of the Four Fundamental Forces Based on the Fundamental Postulate of the Final Particle The fundamental postulate of the Random Final Particle posits that every natural body is composed of a definite number of final particles that are endowed with perpetual random motion all over the space. The final particles that compose such bodies interact all over the space producing the forces between these bodies in the different forms of interaction. Probabilistically there are two cases of randomness, complete random motion and biased random motion. Complete random motion arise from bodies that don't have internal structure or those that can be approximated to be so, and biased random motion arise from those that possess an internal structure. Forces that arise from the first non-biased random motion are called in current physics Gravity. However, if these forces arise between one body and the rest of the bodies of the universe we call it forces of inertia. Hence, basically, forces of Gravity and Inertia are one and the same phenomenon. From another side the forces that arise from biased random motion depend on the form of the structure of the body itself. As will be shown in the following, there are three basic cases of biased random motion: bias along one axis, bias along two axes, and bias along three axes. These three forms of biased random motion produce three types of fundamental forces other than those of the non-biased motion (i.e. Gravity and Inertia). Therefore, if we calculate the ratio between the number of interactions in one case relative to another case we will be able to calculate the relative values of those forces directly through the theory independently from experimental evidence. However, calculating these ratios necessarily subsumes a prior knowledge of the internal structure of those fundamental particles that are responsible for the emergence of the other three fundamental forces. Knowledge of these structures, in turn, requires knowledge of the way these structures emerge as well as knowledge of the processes that lead to its emergence. In other words, it requires having a model that succeeds in describing our current knowledge of the fundamental particles and its interaction, i.e. having a model for the emergence and construction of the Standard Model of Particle physics on an evolutionary basis.

2 The relative strength of fundamental forces It is not possible here to introduce a full account for the emergence and evolution of the Standard Model from the postulate of the final particle. However, we will describe the basic formation of the fundamental particles that are responsible for the appearance of the fundamental forces, leaving the details of the construction of the model to other writings. 1. The Concept of Force in accordance to the fundamental postulate of the random final particle Accordingly, matter is composed of random final particles that are endowed with two basic intrinsic features: 1) perpetual random motion all over the space, 2) the power of attraction between any two final particles upon direct probabilistic contact. The perpetual random motion all over the space makes possible for bodies that are separated in space to interact without the need of the unphysical postulate of actionat-a-distance. Interaction between two bodies takes place probabilistically in direct interaction between the final particles that compose each of the two bodies involved in interaction. In the case of bodies without structure, forces of interaction arise directly between the final particles. On the other hand, in the case of particles that possess a structure the interaction between the final particles become indirect through the direct interaction of those particles themselves. Hence, in the case of biased random motion, the particles that are responsible for a specific type of fundamental forces play the role of the final particles. As a consequence, the total forces between two bodies of a specific type will be proportional to the number of the 'composite' particles that are responsible for this force, while the unit forces of interaction between them will be proportional to the number of interactions of its constituent final particles that participate in biased random motion. In such a case we can say in an imperfect expression that those 'composite' particles 'carry' the forces, whereas in effect all forces are a result of interaction between the final particles of the two bodies involved in interaction. In addition, those particles that 'carry' this type of force is not different from any other natural body, for the nature of the specific force arise only from the way the final particles arranged in those bodies. 2

3 2. The evolutionary view of ordinary matter In this picture if a specific number of final particles bind together at random due to its 'random' motion it will constitute a structureless body that interacts through the forces of Gravity. However, the feature of 'randomness' makes other results possible probabilistically. Hence, if we have three fundamental structureless particles (call it the S particle), it becomes quite possible for these three particles to combine into a specific formation in which they become aligned along some axis (instead of having three particles without alignment) (fig.1). In this case the random motion of the aligned formation will not be of equal value in all directions. Rather, the probability of random motion of the system will be biased toward the axis of alignment with three times the probability of its random motion on the other directions. Call this type of formation type (A), or simply particle (A). P=3x Fig. 1. Type (A) particle is composed of 3 S particles with probability of biased motion along the axis of alignment of 3 times the free random motion. In comparison to the Standard Model it is called 'Zaidon'. Since particles of type (A) perform 'biased' random motion, there is a probability that two of them combine to form a new formation. In this formation we can have two of type (A) of the same alignment, which doesn't produce a new form or a new particle because it doesn't change the pattern of its random motion. However, if the two particles of type (A) combine perpendicularly it will change its pattern of random motion creating a new type of particles, call it type (B) (fig.2). P=25/6 x Fig. 2. Type (B) particle is composed of 6 S particles with probability of biased motion along any of the two axis of alignment of 25/6 times the free random motion. In comparison to the Standard Model it represents the photon. 3

4 The relative strength of fundamental forces New values for the probability of random motion (i.e. its probability function) for this new particle will appear, and hence a different number of interactions will arise. Similarly, Type (B) particles can combine together, however, it will not produce new formations because it is symmetric in two directions. But if three particles of type (A) combine it can produce a new formation with three symmetric directions (on 60 degrees angles). This new formation will create yet another new particle with different number of interactions, call it Particle (C) (fig.3). P = 5 x Fig. 3. Type (C) particle is composed of 9 S particles with probability of biased motion along any of the three axis of alignment of 5 times the free random motion. In comparison to the Standard Model it represents the gluon. This produces an evolutionary view to three fundamental forms of construction that leads in turn to three fundamental forces due to the different values of its probability function. Since we have now three different types of elementary particles that are responsible for three different fundamental forces, we can still expect appearance of new formations. These formations will be constructed out of these three basic particles that produce the new forces, and will constitute a second level of construction. However, as mentioned above, it is not our task here to present a full account of the evolutionary view of the subatomic realm, hence, we leave discussing the second level of particles for other writings. 4

5 3. The Zaidon Model In the Standard Model (SM), we have three types of fundamental forces (the weak, the electromagnetic and the strong). Four elementary particles 'carry' these forces ( and for the weak, photons for the electromagnetic and gluons for the strong). These are called the elementary Bosons. On the other hand there are fermions that are divided into leptons and quarks, each comes in three generations, and each is composed of two types. Added to this picture, is the newly discovered particle the Higgs Boson. Here we concentrate on the emergence of the fundamental forces due to biased random motion. In comparison to SM, the three forms of construction discerned above, i.e. particles A, B and C, represent the Bosons, while fermions constitute the second level of construction. We concentrate on the emergence of the 'Bosons' that are responsible for the three fundamental forces. As will be shown in the following, Particle (B) represents the photon, and Particle (C) represents the gluon. Deviation from the Standard Model is in the particle that is responsible for the emergence of type (A) forces which represent the weak forces in SM. In our model presented here, the forces of type (A) arise from Particle (A) which we call 'zaidon', and the model will be called the 'Zaidon' model. Deeper analysis (which is not presented here) shows that the Z particle is composed of four zaidons (hence the name is derived from the 'Z' particle plus the 'on', like the phot-on and the glu-on). This is inferred from the fact that the Z current results from interaction of an electron and a positron. Electrons and positrons (particles of level two) are composed of photons. Interaction between the two results in interaction between two photons with opposite spin that leads to its disintegration. Each photon is disintegrated into two zaidons. Since we have two photons in each interaction this leads to a total of 4 zaidons. On the other hand, the particle is composed of one photon plus one zaidon because it results from disintegration of one gluon, which is constructed out of three zaidons. Having this picture in mind, in the following we present the biased probability function of each of the three elementary 'Bosons' that lead to the emergence of the three fundamental forces. 5

6 The relative strength of fundamental forces a) Probability functions of the three basic elementary particles The three 'elementary' particles are constructed out of a specific number with specific construction of one structureless particle, called the S particle. Each S particle performs random motion with equal probability in every direction. Modeling the random motion into a random walk on a 3D grid, the particle performs random walk with 1/6 probability in every direction. The first 'elementary' particle is the zaidon, which is constructed out of three S particles aligned along one axis. The zaidon as a collection of the 3 random S particles performs biased random walk with probability along the axis of alignment of 3 times the probability of the single particle (fig.1). The second elementary particle is the photon which is constructed out of two zaidons in a symmetrical configuration, i.e. perpendicular to each other. Along any of its four directions in a random walk we have a probability of motion of 4 times the probability of one particle, in addition to contribution from the other two particles which is 1/6. Hence, the total value is 25/6 times the probability of one S particle (fig.2). The third type of elementary particles is the gluon, which is constructed out of three zaidons in a symmetric form, i.e. in three directions with equal angles. The probability along any of the three directions is 5 times the probability of one S particle with no contribution from the other four particles. The reason is that the other four particles, due to the gluon's configuration, lie outside the 3D grid and hence it will not contribute to the matched random motion which generate the forces of attraction (fig.3). 4. Probabilities of matched random motion according to the Zaidon model Calculation of the relative values of the fundamental three forces with respect to the force of gravity is based on calculation of the relative values of what we call 'matched' random motion, as opposed to the free non-biased random motion. Matched random motion means that the S particles of each 'composite' particle perform 'matched' biased random motion, i.e., the biased random motion of each body is constrained by being in complete harmony with each other. This means that the two 6

7 (or more, if we have more than two bodies) S particles move together in all their biased steps and separate only in their free steps of random motion. This condition requires pre-specification of the pattern of motion independent of the biased random walk of the two (or more) S particles. Hence, for a specific step of the random walk we have a predefined direction of motion which is to be followed by the two (or more) S particles. This is reflected on our calculations of the 'matched' biased random motion of the S particles of the bodies involved in interaction in a specific way. For interaction between two bodies with non-biased random walk we get the probability of 'matched' motion between any two S particles by multiplying the probability of each step of the random walk of each one by the other, i.e. by taking the square of the probability of each step, which is 1/6. Hence, the probability of matched motion in this case is 1/36. On the other hand, for the case of biased random motion, if we apply the condition above, we multiply the probability of one step of the random walk in the biased direction by the probability of the predefined direction which is equal to 1. Applying these rules, if we calculate the probability of the matched biased random motion for the case of the zaidon, Dividing this value by the probability of matched motion for the case of free non-biased random motion (i.e., the case of Gravity) which is 1/36 we find that the number of the matched motion in the case of the zaidon is 18 times that of Gravity. For the case of the photon the probability of matched motion is given by, Dividing this value by the probability of matched motion for the case of free non-biased random motion, which is 1/36 we find that the number of the matched motion in the case of the photon is 25 times that of Gravity. by, Similarly, for the case of the gluon the probability of matched motion is given 7

8 The relative strength of fundamental forces Dividing this value by the probability of matched motion for the case of free non-biased random motion, which is 1/36, we find that the number of the matched motion in the case of the gluon is 30 times that of Gravity. 5. Classification and calculation of the fundamental forces of nature The above calculations of the relative probabilities of the matched biased random motion for the three cases pointed out above reflect in a direct manner the relative values of the forces of these three types of forces with respect to the case of Gravity, for each step of the random walk on a 3D grid. This is because the matched motion for one step for each final particle generates unit of attraction force, which we call here. Hence, for a complete random motion of the two bodies, the probability of generating a unit force for each step of walk is 1/36. For the case of the zaidon, the probability for generating such a force is 18/36, i.e., 0.5. For the case of the photon the probability is 25/36, i.e For the case of the gluon, the probability is 30/36, i.e., The relative values of the forces can't be calculated on the basis of one step of random walk, because the forces in reality appear as a result of interaction in 3D space. Hence, if we want to compare the relative forces we have to compare the probabilities of the forces for equal volumes of space. The simplest volume is the unit volume of a grid that is composed of one step in each direction. This unit volume of a grid is then composed of points, i.e. 27 points. In order to calculate the total value of the probability of generating the force of interaction laws of probability state that we multiply the value of the probability 27 times, i.e. to raise the probability value to the power of 27. Hence, in order to derive the relative values of the forces between the above three types of forces that are based on biased matched random motion to the forces of Gravity we have to raise the values above of the four cases to the power of 27. Hence, the relative value of the forces of type (A) that results from matched random motion of the zaidons with respect of Gravity is given by, 8

9 And the relative forces of type (B) that results from matched motion of the photon with respect to Gravity is given by, And the relative forces of type (C) that results from matched motion of the gluon with respect to Gravity is given by, This leads to the well known classification of the three fundamental forces calculated through experimental procedures and mathematical formulations of the Standard Model. The force due to the zaidon is the weakest followed by the force due to the photon and the strongest is the force due to the gluon. According to the calculations above, the weakest force due to the zaidon is by of the strong force by the gluons. On the other hand, the strong force by the gluon is only times the force by the photon if we take the total forces described above. However, if we use the net force, i.e., with subtracting the overlap between the two forces (i.e., subtracting 24/6 out of the 25/6 probabilities), the ratio between the two becomes Using the total force or the net force is a matter of convention. Finally, the force of Gravity is only by of the strong force by the gluon. These results are generally consistent with the current classification of basic forces: the Gravitational, the weak, the electromagnetic and the strong. In addition, the relative values of such calculations match to a high degree the findings of the Standard Model (in the static case), and in low energies (i.e. before taking the effects of high speed into consideration). Therefore, these results represent an experimental evidence for the Zaidon model as a means to represent the subatomic realm at the most fundamental level. 9