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BACK TO SITE PLAN Site Plan :
DAA.MATTER, MASS, ENERGY Phenomenon #Space (PS) and Abstract #Space (AS)
NOTE: neologies defined in GLOSSARY are marked "[G]". Let us shortly review the concepts of Phenomenon #Space (PS) and Abstract #Space (AS)[G]. PS encompasses Events[G] or Aspects[G] of Phenomena[G]. AS is an abstract structure. PS may be considered as a unique territory and AS - as a particular map. A common error consists in confusing PS with AS by saying, for instance, that Special Relativity postulates Events to happen in Minkowski's 4 dimensional LightTime-Space #Space. Events happen in PS which is Model independent and are mapped to Minkowski's #Space AS. A Model such as SR associates PS with a particular AS, meaning that Events of PS are expected to map into pertinent (consistent, predictable and falsifiable) structures of AS.
Mass and Energy
Mass never appears in PS which encompasses only observable Events such as force, displacement, temperature, speed, acceleration etc. Having observed and measured force F acting on body[G] B and acceleration A of B, we insert their values into AS postulating their proportionality and express this postulate by associating with B an abstract coefficient m (Mass): m(B) = F/A. Consequently, Mass has no phenomenal sense (it does not appear anywhere in PS), but is an abstract mind's construct, a coefficient allowing to order Events of PS in pertinent structures of AS. Now, within the Model we refer to Mass FOR SIMPLICITY's SAKE as if it were a phenomenal Aspect of B and say that B has the Mass m(B). It is indeed much simpler to say (in SR) that for an external observer m(B) increases with v(B) (relative speed of B) rather than, that the ratio of force acting on B to the acceleration of B increases with v(B). It's ok and advisable to talk about Mass ALWAYS WITHIN THE MODEL as if it were a phenomenal Aspect of bodies, as long as we do not forget that it is an ABSTRACT ARTIFICE destined, as all mathematics, to simplify Model's language and expressions. If we forget it, we will lose understanding of the Model and intuitive creativity with respect to modifying, or complementing it with new types of Events. The same holds for Energy, which has been also stated by Feynman in a 1961 lecture: “There is a fact, or if you wish, a law, governing natural phenomena that are known to date. There is no known exception to this law — it is exact so far we know. The law is called conservation of energy; it states that there is a certain quantity, which we call energy that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity, which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number, and when we finish watching nature go through her tricks and calculate the number again, it is the same." Consequently: MASS and ENERGY have no phenomenal sense (they do not appear anywhere in PS). They are pure abstract constructs appearing only in AS and destined to correlate Events (elements of PS) in pertinent and simple way.
MATTER. Singular Field
A singular field is described by equations which lose validity at its singularity points. That's mathematical. In physical practice they lose validity in the neighborhood of singularity where field density exceeds some value and which we shall call "Singularity Area". Now, "Matter" is a metalanguage term denoting for simplicity's sake SINGULARITY AREAS of the four known fundamental Fields (and eventual other ones not yet known). It appears neither in PS nor in any known AS, i.e. it has no phenomenal, nor abstract sense. Scientifically speaking it does not mean anything at all. In metalanguage of the General Relativity "Ponderable Matter" designates a macroscopically lumped together Poisson-like Field Singularity Area (see Appendix). In the metalanguage of the Quantum Field Theory "Material" Particle designates a microscopically considered Quantum Singularity "packet" of Field. "Mass" and "Energy" are abstract constructs having no phenomenal sense. They appear in AS as coefficients helping to map Events of PS in pertinently ordered structures. Matter has no scientific meaning at all and is used as metalanguage term to denote Singularity Areas of Fields.
Appendix
Quotation from DERIVATION OF GENERAL RELATIVITY, Steps 1, 2 For readers familiar with Tensor Calculus we recall Einstein's Field Equation, which may be considered as GR's equivalent of Poisson's equation: R(/m,/n)-0.5g(/m,/n)R=-µT(/m,/n) EFE(Einstein's Field Equ.) where R(/m,/n): contracted Riemann Tensor g(/m,/n): Metric Tensor R: scalar R=g(m/,n/)R(/m,/n) T(/m,/n): energy tensor of the "matter" µ: constant related to Newton's gravity constant. Left side of EFE represents the Field OR #Space in terms of metric and curvature. This common representation shows the homomorphism of both constructs which defines them as P-Equivalent aspects of some basic Phenomenon (which we called "Universe" in 1A INTRODUCTION TO RELATIVISTIC PHENOMENOLOGY). In spite of being abstract constructs of Mind, Field and #Space have full phenomenal sense secured by their observable manifestations: force, speed; etc. for Field, geometry for #Space. Right side of EFE represents the "singularity term" replacing Poisson's "matter" with its relativistic equivalent, viz. energy, encompassing that of gravity and of electro-magnetism.