Dear Sir,
Quantum theory is like Pioneer Anomaly. It started with a small anomaly between the postulated and actual position of Pioneer 11 that has grown to more than 400,000 kilometers now challenging the existing theories of gravitation and giving rise to alternate theories like MOND, none of which are successful in giving a complete explanation of the phenomenon. The different interpretations of quantum theory, which are really different theories with their own sets of postulates often contradicting each other, has made the dream of a cohesive theory almost impossible. The task has been made more difficult by the blind followers of different branches. The present essay is an example of such posturing.
We fail to understand how: "the infinite connectivity of space-time implies its hyper-continuity", "introduces discreteness into particle trajectories." A "zero-distance connection with every other position in space-time" implies an all embracing spreadsheet without any intervening space. Thus the question of discreteness or dimensions for connectivity does not arise.
The Kaluza-Klein compactification and other "theories" relating to extra-dimensions are only figments of imagination. The term dimension is applied to solids that have fixed spread in a given direction based on their internal arrangement independent of external factors. For perception of the spread of the object, the electromagnetic radiation emitted by the object must interact with that of our eyes. Since electric and magnetic fields move perpendicular to each other and both are perpendicular to the direction of motion, we can perceive the spread only in these three directions. Measuring the spread is essentially measuring the space occupied by it. This measurement can be done only with reference to some external frame of reference. For the above reason, we use axes that are perpendicular to each other and term these as x-y-z coordinates (length-breadth-height). These are not absolute terms, but are related to the order of placement of the object in the coordinate system of the field in which the object is placed. Thus, they remain invariant under mutual transformation. If we rotate the object so that x-axis changes to y-axis or z-axis, there is no effect on the structure (spread) of the object. Based on the positive and negative (spreading out and contracting in) directions from the origin, these describe six unique positions (x,0,0), (-x,0,0), (0,y,0), (0,-y,0), (0,0,z), (0,0,-z), that remain invariant under mutual transformation. Besides these, there are four more unique positions, namely (x, y), (-x, y), (-x, -y) and (x, -y) where x = y for any value of x and y, which also remain invariant under mutual transformation. These are the ten dimensions and not the so-called mathematical structures. These are described elaborately in our book.
When applied to objects, one dimension implies distance, two-dimension implies area and three-dimension implies volume. Since time does not fit in this description but implies duration of each cycle of events or part thereof, it is not a dimension. Thus the description of space-time continuum or world-points is also wrong description of facts.
"Temporal orders of world points are generally different when observed from different reference frames". They do not affect temporal evolution of objects, but only describes how they are perceived by different observers. Since observation that leads to perception does not affect temporal evolution of objects, temporal orders of observation are not relevant for time evolution. We have already shown that:
Consider an example: A B → C D.
Here a force acts on A and B to produce C and D. The same force doesn't act on C and D as they don't exist at that stage. If we change the direction of the force, B interacts with A. Here only the direction of force and not the interval between the states before and after application of force (time) will change and the equation will be:
B A → C D and not B A ← C D.
Hence it does not affect causality. There can be no negative direction for time or cause and effect.
The measurement problem of Quantum Mechanics is still being debated without a solution. Different interpretations of the theory describe the concept and mechanism of collapse differently. There is no unanimity in this regard. We have described this issue at different threads. Measurement is a process of comparison between similars. We have also explained YDS and Entanglement differently.
Entanglement is related to the intrinsic relationship of particles with their fields. As we have said earlier, particles are nothing but confined fields. Confinement implies a central point (nucleus or center of mass) around which the mass concentrates due to confinement (orbitals). Thus, there is a coupling between the two mediated by a force. Entanglement is related to this mediating force. Since energy does not have a nucleus or center of mass, it does not have a fixed structure. Hence it is always dynamic unless it is contained within some container. Here also, it interacts with the container at the surface while there is no such interaction at other places. This leads to a chain reaction leading to further destabilization. Thus, energy is always mobile. All measurements are done at "here-now", which is a fixed position in some frame of reference.
Just like a fluid flows or seeps through a porous container and not through a solid one, the energy associated with the quantum particles can flow (entanglement) or seep through (quantum tunneling) macro barriers. Since all objects display a three fold structure (nucleus, orbitals or confinement and the extra-nuclear field), any release of energy in one direction will be associated with the absorption of equivalent energy in the opposite direction, which will generate chain reactions in their surrounding fields. Since particles have parallel and anti-parallel spins, the release of energy by a pair with opposite spins will induce similar reactions in opposite directions. This is known as entanglement. However, till one particle's spin is measured, there is no way to know about the spin of either. Thus, there is nothing extraordinary about entanglement. We had given its macro examples in various threads. It has unnecessarily been sensationalized. Particles move in the field automatically (in the absence of any induced force) based on the property of the field to attain uniform density. Since the density of the medium through which the energy travels is different from the density of the released energy, it gradually tapers down after a few kilo meters. Alternatively, it loses its own identity and becomes indistinguishable from the field. In both ways, the result is the same.
Truth exists independent of personalities. Hence kindly forgive us for the language used. There is nothing personal.
Regards.
basudeba