Subhajit Ganguly's Blog - Posts Tagged "mathematics"
Fundemental Requirements of a Theory of Everything in Physics
Over some years now, a large part of the energies of the scientific community has been employed solely for finding a theory that will fit in all known happenings of the physical world. Various groups of scientists have tried to attack the problem from different ends. Some of these theories have been partly successful in explaining the known physical world. However none of these theories have been without shortcomings. Be it the much lauded String Theory or the Quantum Gravity postulation or any other such attempts towards arriving at a Theory of Everything, none have been proved to be foolproof. To say the least, nobody can deny that there is room for much improvement before we can even start thinking truly towards such a theory that would describe the known world satisfactorily and provide for a single basis of understanding the four forces in nature.
On top of that, we have the newly emerging problems of ‘Dark Energy’, ‘Dark Matter’ and the like. These realms are yet to be accepted by the scientific community officially, but nonetheless, they are most definitely at least a few parts of mysteries that remain unexplained. A good and effective Theory of Everything must aim towards explaining such mysteries too. Sadly, we have no theory as yet that fulfills these criteria. From the dawn of civilization, human beings have tried to find out order in the chaotic world surrounding them. It has however never been easy to find a solution to explain a given system while being a part of that system. The best bet is to find out the most fundamental components within the system and building a theory round these. In other words, a theory that is able to describe the world in totality has to keep the number of basic postulates it depends upon to zero or near zero. Deductionism hits a dead end in this regard. On the other hand, abstraction as the starting point of building up a theory may be seen to be of fitting use. It would be much more than a new way of tackling the problem. Even abstract postulates do away with the shackles that bind our theories into the system and bar them from being total descriptions of the system. The abstraction we are talking about here may be defined as,
“Postulation of non-postulation” or, in other words, “A system of postulation that gives equal weights to all possible
solutions inside the system and favours none of such solutions over others.”
Abstraction automatically gives rise to optimized solutions within the universal set of all possible solutions. It is these optimized solutions that make up and drive the non-abstract parts of the world, while the non-optimized solutions remain ‘hidden’ from the material world, inside the abstract world.
Starting from a basis of no postulation, we build our theory. As we go on piling up possibilities, we come to a similar basis for understanding the four non-contact forces of nature known till date. The difference in ranges of these forces is explained from this basis.
Zero postulation or abstraction as the basis of theory synthesis allows us to explore even imaginary and chaotic non-favoured solutions as possibilities. With no postulation as the fundamental basis, we are thus able to pile up postulated results or favoured results, but not the other way round. We keep describing such implications of abstraction in this process. We deal with the abstraction of observable parameters involved in a given system (quantum, relativistic, chaotic, non-chaotic) and formulate a similar basis of understanding them. Scaling of observable parameters in adequate ways is shown to unite the understanding of worlds of the great vastness of the universe and the minuteness of the sub-atomic realm. Finally, the mysteries involving ‘dark energy’ and ‘dark matter’ may be uncovered using such an approach.
On top of that, we have the newly emerging problems of ‘Dark Energy’, ‘Dark Matter’ and the like. These realms are yet to be accepted by the scientific community officially, but nonetheless, they are most definitely at least a few parts of mysteries that remain unexplained. A good and effective Theory of Everything must aim towards explaining such mysteries too. Sadly, we have no theory as yet that fulfills these criteria. From the dawn of civilization, human beings have tried to find out order in the chaotic world surrounding them. It has however never been easy to find a solution to explain a given system while being a part of that system. The best bet is to find out the most fundamental components within the system and building a theory round these. In other words, a theory that is able to describe the world in totality has to keep the number of basic postulates it depends upon to zero or near zero. Deductionism hits a dead end in this regard. On the other hand, abstraction as the starting point of building up a theory may be seen to be of fitting use. It would be much more than a new way of tackling the problem. Even abstract postulates do away with the shackles that bind our theories into the system and bar them from being total descriptions of the system. The abstraction we are talking about here may be defined as,
“Postulation of non-postulation” or, in other words, “A system of postulation that gives equal weights to all possible
solutions inside the system and favours none of such solutions over others.”
Abstraction automatically gives rise to optimized solutions within the universal set of all possible solutions. It is these optimized solutions that make up and drive the non-abstract parts of the world, while the non-optimized solutions remain ‘hidden’ from the material world, inside the abstract world.
Starting from a basis of no postulation, we build our theory. As we go on piling up possibilities, we come to a similar basis for understanding the four non-contact forces of nature known till date. The difference in ranges of these forces is explained from this basis.
Zero postulation or abstraction as the basis of theory synthesis allows us to explore even imaginary and chaotic non-favoured solutions as possibilities. With no postulation as the fundamental basis, we are thus able to pile up postulated results or favoured results, but not the other way round. We keep describing such implications of abstraction in this process. We deal with the abstraction of observable parameters involved in a given system (quantum, relativistic, chaotic, non-chaotic) and formulate a similar basis of understanding them. Scaling of observable parameters in adequate ways is shown to unite the understanding of worlds of the great vastness of the universe and the minuteness of the sub-atomic realm. Finally, the mysteries involving ‘dark energy’ and ‘dark matter’ may be uncovered using such an approach.
Scaling The Universe
Be it the vastness of the universe or the delicate smallness of the sub-atomic world, by choosing a suitable constant scaling ratio for both, we may obtain their representations. These representations following a certain constant scaling ratio, will be self-same. In previous papers on the subject, I have mentioned the chaotic behaviour in the quantum world. Choosing suitable scaling ratios, we may turn the universe itself into such a chaotic quantum system, having its own necessary quantum states and trajectory behaviour. In that case, the study of the universe reduces to the study of some sort of a quantum chaotic system. On the other hand, choosing some other necessary scaling ratios, the atomic and the sub-atomic realm may be extended to become the universe itself, complete with its own macroscopic trajectory behaviour. Instead of formulating different ways of looking at worlds of different sizes, if we adjust the way of viewing i.e., the scaling ratio in such a fashion that the representations of the world merge, we will be looking at representative worlds of study which are practically self-same.
The Laws of Physical Transactions formulated in previous papers of the subject may then be applied in order to study such self-same representations of the worlds of various scales. Unification of the ways of studying at different ranges of scaling may thus be achieved by suitable landscaping (adjusting different scales to a suitable scaling-ratio, in order to make all the scales of study similar in size). Further, a similar approach may be applied to study the Bose-Einstein Condensation. A certain critical packing density of the constituents of each world of a certain landscape must ensure a condensation of similar sort. The quantum states (or some similar states) of each such landscape will merge and give spikes for that critical scaling ratio in their respective representations.
The quantum chaotic behaviour may be of interest to study if we are to learn about the universe as a whole. The astronomically large distances separating clusters in the universe supports a study of such sorts. Quantum chaotic behaviour, on the other hand will give rise to something similar to the Bose- Einstein condensation at some critical packing density. The study of such condensation states too will be of interest here.
Looking at a large enough part of the universe, we may draw an analogy to a system of scattered particles in motion or rest relative to each other. These particles may or may not be similar to each other, if we look at a given locality. Our idea, however, is that we can always represent even the whole of the universe on a piece of paper of our desired size. We can very well do the same with localities of sub-atomic sizes.
We may represent both the worlds, viz. the microscopic and the macroscopic, within any desired standard size. Theoretically, we are only to diminish the snaps of the universe and magnify the snaps of the microscopic world in order to put both into representations of a definite scaling-size. Looking at such a representation of the macroscopic world (due to the large number of constituents and the large distances separating them involved) we will find it to be a complex mixture of various kinds of particles. On the other hand, looking at such a representation of the microscopic world, (due to the small distances separating the constituents) it will be like the actual universe itself, with various types of constituent parts involved. Such a representation of the microscopic and the macroscopic worlds will bring out hidden properties and behaviours of both worlds, as well as providing for a similar basis of studying them both.
The Laws of Physical Transactions formulated in previous papers of the subject may then be applied in order to study such self-same representations of the worlds of various scales. Unification of the ways of studying at different ranges of scaling may thus be achieved by suitable landscaping (adjusting different scales to a suitable scaling-ratio, in order to make all the scales of study similar in size). Further, a similar approach may be applied to study the Bose-Einstein Condensation. A certain critical packing density of the constituents of each world of a certain landscape must ensure a condensation of similar sort. The quantum states (or some similar states) of each such landscape will merge and give spikes for that critical scaling ratio in their respective representations.
The quantum chaotic behaviour may be of interest to study if we are to learn about the universe as a whole. The astronomically large distances separating clusters in the universe supports a study of such sorts. Quantum chaotic behaviour, on the other hand will give rise to something similar to the Bose- Einstein condensation at some critical packing density. The study of such condensation states too will be of interest here.
Looking at a large enough part of the universe, we may draw an analogy to a system of scattered particles in motion or rest relative to each other. These particles may or may not be similar to each other, if we look at a given locality. Our idea, however, is that we can always represent even the whole of the universe on a piece of paper of our desired size. We can very well do the same with localities of sub-atomic sizes.
We may represent both the worlds, viz. the microscopic and the macroscopic, within any desired standard size. Theoretically, we are only to diminish the snaps of the universe and magnify the snaps of the microscopic world in order to put both into representations of a definite scaling-size. Looking at such a representation of the macroscopic world (due to the large number of constituents and the large distances separating them involved) we will find it to be a complex mixture of various kinds of particles. On the other hand, looking at such a representation of the microscopic world, (due to the small distances separating the constituents) it will be like the actual universe itself, with various types of constituent parts involved. Such a representation of the microscopic and the macroscopic worlds will bring out hidden properties and behaviours of both worlds, as well as providing for a similar basis of studying them both.
