In the legacy system of physical theory (LST), the difference between bosons and fermions is encapsulated in the Pauli exclusion principle: Bosons can occupy the same quantum state, but fermions cannot. In the reciprocal system of physical theory (RST), on the other hand, which doesn’t employ the wave equation and the associated QM concept of state space, the difference is that bosons occupy the same space|time location, but fermions do not. In the LST, the different states in the state space are determined by quantum numbers. Thus, bosons may have the same quantum numbers and, when these numbers constitute the ground state, a set of atomic bosons in this state are then referred to as a Bose-Einstein condensate. Interestingly, atomic bosons can be configured as fermions, and fermions as bosons, in experimental apparatus (see here and here).
The same behavior in the subatomic entities of the standard model (SM) can be understood in terms of the S|T triplet version (see previous posts below) of fermions and bosons. In the boson triplets, the three constituent S|T units occupy the same S|T location, indicated by their parallel configuration, as shown in figure 1 below:
Figure 1. The Boson S|T Triplets of the Standard Model
On the other hand, the S|T units of the fermions do not occupy the same space|time location, as indicated by their non-parallel configuration, as shown in figure 2 below.
Figure 2. The Fermion S|T Triplets of the Standard Model
In the fermion triplet, the spatial coordinate position of the time-displaced (red) component, of one S|T unit, is co-located with the spatial scalar position of the space-displaced (blue) component, of an adjacent S|T unit. Conversely, we can say that the time coordinate position of the space-displaced (blue) component, of one S|T unit, is co-located with the time scalar position, of an adjacent S|T unit.
Of course, there is a major difference between these subatomic bosons and fermions, and their atomic counterparts: Unlike their atomic relatives, subatomic bosons propagate at the speed of light and subatomic fermions gravitate (this is the reason why neutrinos must have some mass, though very little, propagating almost at the speed of light).
It follows, then, that since the only difference in the boson and fermion S|T triplets is that the three constituent S|T units of the boson occupy one in the same S|T location, while the three constituent S|T units of the fermion occupy three adjacent locations, this difference must account for why one propagates and the other doesn’t (or does so at a slower speed). The next question is, therefore, what space|time changes must take place to convert a boson into a fermion, or vice versa? In the LST community’s 11D Supergravity theory, such a conversion constitutes motion, according to Lee Smolin (see his Trouble with Physics), and this is why it and string theory require Supersymmetry, which would double the current number of observed particles, by proposing a boson equivalent of every fermion and vice-versa.
However, in our RST-based theory, the difference between what makes a boson a boson, and a fermion a fermion, clearly prevents this. For instance, if a down quark were converted into a boson, its three adjacent locations merging into one location, it would become a single red S|T unit (green + green + red = red). It’s not possible to have two green and a red S|T unit in a parallel configuration, any more than it’s possible to have a scale that is both balanced and unbalanced at the same time. This is why Supersymmetry has never been observed and never will be observed. Indeed, we can say that our theory predicts that CERN’s large hadron collider (LHC) will not discover Supersymmetry. It is impossible.
Nevertheless, the question of quantum gravity remains the holy grail here, and, just as it is for the LST community, our biggest clue is this difference between bosons and fermions, because fermions gravitate, while bosons don’t. To understand the difference more clearly, we should recognize that the figures above, graphically showing the space|time relations of the theoretical entities, should be understood as schematic representations, not physical representations, of S|T units. The physical representation of the S|T unit is an expanding/contracting ball, or point, as shown in figure 3 below.
Figure 3. Physical Representation of S|T Unit
In figure 3, the two chiral versions of the S|T unit, one having the inverse space|time dimensions of the other, are shown The size of the point at the center is exaggerated. Because time has no direction in space, and space has no direction in time, the point actually has no physical extent. The red graphic of the spherical entity on the right represents the space unit expansion, which contracts to the point and then expands to the unit sphere, oscillating, at the speed of light. As was pointed out in a previous post, the expanding/contracting motion of the unit sphere entails the 720 degree angle change of spin, which is so enigmatic in terms of rotational motion, clearing up a major mystery of quantum mechanics (QM).
On this basis, the red sphere represents the physical SUDR, while the blue sphere represents the physical TUDR. The blue point, at the center of the red sphere, is the blue (time oscillation) TUDR component of the S|T unit, from the space perspective, while the red point, at the center of the blue sphere, is its red (space oscillation) SUDR component, from the time perspective. If we could view the S|T unit from both the space and time perspectives simultaneously, we would see an alternating red-blue expansion/contraction, but we can only observe one component of the displacement magnitude at a time. Larson called these inverse sectors the material (coordinate space) sector and the cosmic (coordinate time) sector. Thus, the S|T unit is represented by the graphic on the left in figure 1, in the material sector, and the graphic on the right, in the cosmic sector. In either case, the colored spheres contract and expand, or oscillate, at the speed of light, simultaneously.
Moreover, the oscillating S|T unit also necessarily propagates relative to SUDRs and TUDRs, at the unit speed of light, as shown in the world line chart, discussed in previous posts below. However, while the magnitude of the speed of oscillation and propagation are fixed at unit speed, the total speed-displacement, which is determined by the number of SUDRs and TUDRs that are joined together in a given S|T unit, determines the energy of the unit, and thus its frequency in terms of E = hv.
In our S|T triplet model of bosons, there are an even number of SUDRs and TUDRs in the three, constituent, ST units of the photon boson, which we encode as green S|T units, while in the negative W boson, the three constituent S|T units consist of more SUDRs than TUDRs, so we encode them red. Of course, the S|T units of the positive W boson consists of more TUDRs than SUDRs, so we encode them blue. The enigmatic Z boson is neutral, because it supposedly consists of a combination of the negative and positive W bosons, but we have yet to think extensively about that.
We could color the spheres to indicate the relative number of SUDRs and TUDRs in a given boson. In this way, a photon would be a green sphere, a negative W boson would be a red sphere, and the positive W boson would be a blue sphere. However, this would not buy us much in terms of clarity over the schematic representations in figure 1 above, which we are in the process of simplifying, as explained in a previous post below. Plus, it would be doubly difficult to represent the fermions as three, slightly merged, balls, or spheres, which is the form that their physical representation takes, as shown in figure 4 below.
Figure 4. Physical Representation of Three S|T Units Merging
I borrowed the graphic, in figure 4 above, from a z-merge tutorial, because I don’t have that capability in my graphics software. As already pointed out, the three colors combined together like this are impossible as a boson triplet, which must either be balanced, or unbalanced in one “direction,” or another, but it might be possible in the fermion triplet, though, if so, this configuration would be tantamount to a prediction of a new particle in our RST-based theory. Nevertheless, until I have more time to think about it, we’ll just have to shelve it for the time being.
The important thing right now is to determine, if we can, what difference this combination of adjacent positions in the fermion S|T triplet makes viz-a-viz the mass/gravity question. In order to address this question, we will have to incorporate a more advanced concept of space|time magnitudes than that discussed so far, and we will have to do so both in terms of the reciprocal system of mathematics (RSM) equations, and the graphics. Hence, it will be helpful to understand both the physical and the schematic representation of the S|T units.
We’ll start to take a look at this in the next post.