28-11-2012, 05:27 PM
Scalar Science
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Larsonian Science
New science
Based on unification of all things
New ideas call for new approach
Includes some of Newtonian science
Changes some foundational mathematics and physical concepts, but not all
“Whole New Science”
Smolin
“Great unifications become the founding ideas on which whole new sciences are erected.”
What are the RST’s “founding ideas?”
Redefinition of space, time, energy and matter
What is conserved?
Motion is conserved
Calculus
Defines velocity in context of infinitely divisible continuum.
Velocity can vary in arbitrary distances
Thus, must take delta to the limit
Applies to M2, change of position motion
Does not apply directly to M3 and M4 motion
The Newtonian Concept of Force
Ultimately a quantity of change of motion
A quantity of acceleration
F = ma, or a scalar times a component vector
Has evolved to fundamental, autonomous, status
Electromagnetic “charge”
Weak nuclear “charge”
Strong nuclear “charge”
Gravitational “charge”
Newtonian Principles of Analysis
Based on concepts of M2 motion
Vectors
Vector spaces
Functions in vector spaces
Focuses on Analysis of vectors in vector spaces
Spaces of vectors are linear spaces
Thus, in a given vector space
Vectors can be added together
Vectors can be multiplied by scalars
Need not be limited to geometric spaces (visualizable in three dimensions), but may also be abstract spaces
Represents vectors with complex numbers
Opens whole new world of possibilities
Transforms vectors into scalars!
The Vector Space of Transformations
Linear operators
Operator = transform of functions
Example: differential operator (f(x) -> f’(x))
An operator is a symbol that tells you to do something with whatever follows the symbol
Linear operator
Satisfies two conditions: An operator O is said to be linear if, for every pair of functions f and g and scalar s ,
O(f+g) = Of +Og and
O(sf) = sOf
In other words, distributive (ordered) functions (functions compatible with the addition and scalar multiplication)
Learning from Newtonian Science
Examine history of mechanical analysis
Vector analysis
Examine history of quantum mechanical analysis
Functional analysis
Examine history of mathematical development
Differential calculus
Linear analysis
Operator and group theory
Translate into lessons learned
Quantum Mechanical Analysis
Examine changes in mechanical concepts
Rotation and angular momentum
Discrete energy viz-a-viz potential/kinetic concept
Role of potential energy in wave equation
Look for mathematical meaning of rotation
Complex numbers and vector spaces
Quantum phase and renormalization
Meaning of non-commutative mathematics
Master key concepts of standard model
Gauge principle
Lie groups and Lie algebra
Higgs potential and Higgs Boson
Conclusions from Lessons Learned
The concept of M2, (change of position) motion, has been utilized to
attempt the description of magnitudes of M3 (change of interval) and M4 (change of scale) motion
The attempt has been only partially successful
As far as it goes, it’s extremely accurate, but it’s incomplete without the Higgs potential and Higgs boson
There are many flags to alert us that chart of motion will shed light on these problems
Natural explanation of spin
Insight into rotation – change of interval correspondence
Clarification of point particles and charges (distribution of charge on electron)