DENSITY OF STATES IN 4-DIMENSION-
These three terms Density, States & Dimension are meant to be clear for the fellow readers before proceeding. We all know that the term Density means mass per unit volume, State refers to the form of existence & Dimension refers to the size specification of the space in which we live. There are 5 existing states and 16 existing dimensions (only 4 known). The 4th dimension of the space is known as "Time". Time is a non- physical dimension which measures the existence of the universe in a prolonged way. Mathematically it is a scalar quantity which means it has no direction. Although, Feynman Diagrams suggests that it has direction from the past to the future. Stephen Hawking mentioned that time flow is like a double conical structure consisting of two cones whose tips are joint at a single point called the "present light cone". The bases of the bottom cone is known as the "past light cone" and the top cone is "future light cone".
The term "Density of States" is the number of k-states (wavenumber) per unit volume for a 3-D structure, per unit area for a 2-D structure and per unit length for a 1-D structure. But what do we mean by Density of States in 4-D?? Most of you must be thinking that it is the number of k-states per unit second as time is the 4th dimension. But it is not that.
It is the number of k-states per unit sum of all the volume of the state and the time because mathematically time is a scalar and a non physical quantity as mentioned. The E-K relationship obtained is dependent of time which means Dirac's relativistic equation may not be required to yield the solution the density of states. This may reduce the complexity in the condensed-matter community providing a simple way to show the interaction of electrodynamics , Quantum Mechanics and Statistical Physics with time which may lead us to reveal the mystery of the universe. In other words the "Grand Unified Theory".
These three terms Density, States & Dimension are meant to be clear for the fellow readers before proceeding. We all know that the term Density means mass per unit volume, State refers to the form of existence & Dimension refers to the size specification of the space in which we live. There are 5 existing states and 16 existing dimensions (only 4 known). The 4th dimension of the space is known as "Time". Time is a non- physical dimension which measures the existence of the universe in a prolonged way. Mathematically it is a scalar quantity which means it has no direction. Although, Feynman Diagrams suggests that it has direction from the past to the future. Stephen Hawking mentioned that time flow is like a double conical structure consisting of two cones whose tips are joint at a single point called the "present light cone". The bases of the bottom cone is known as the "past light cone" and the top cone is "future light cone".
The term "Density of States" is the number of k-states (wavenumber) per unit volume for a 3-D structure, per unit area for a 2-D structure and per unit length for a 1-D structure. But what do we mean by Density of States in 4-D?? Most of you must be thinking that it is the number of k-states per unit second as time is the 4th dimension. But it is not that.
It is the number of k-states per unit sum of all the volume of the state and the time because mathematically time is a scalar and a non physical quantity as mentioned. The E-K relationship obtained is dependent of time which means Dirac's relativistic equation may not be required to yield the solution the density of states. This may reduce the complexity in the condensed-matter community providing a simple way to show the interaction of electrodynamics , Quantum Mechanics and Statistical Physics with time which may lead us to reveal the mystery of the universe. In other words the "Grand Unified Theory".
No comments:
Post a Comment