In one of the letters written to the Infeld group in Warsaw Einstein wrote:
"A new manner of thinking is essential if humankind is to survive."

First, let us shortly review the difference between Phenomenon #space (PS) and Model #space (MS). (See STRUCTURE OF SCIENTIFIC THEORIES or GLOSSARY for more details.) PS is a set of contingent observable events or observations MS is an abstract structure. PS may be considered as a unique territory and MS - a perticular map. A common error consists in confusing PS with MS by saying, for instance, that Special Relativity postulates events to happen in Minkowski's 4 dimensional #space (space-lighttime). Events happen in PS which is theory independent and are mapped to Minkowski's #space MS. A theory, a model such as SR associates PS with a particular MS (for instance Minkowski's #space), this association meaning that events of PS are expected to map into MS complying with its abstract patterns (for instance Lorentz contraction).

MASS AND ENERGY.

Mass never appears in PS which encompasses only observable events and entities such as force, displacement, speed, acceleration, etc. Having observed and measured force F acting on body B and acceleration A of B, we insert their values into the MS of postulating their proportionality and satisfy this postulate by associating with B an abstract coefficient m(B) = F/A. Consequently, mass has no autonomous phenomenal existence (is not an element of PS), but is a pure abstract mind's construct, a coefficient allowing to correlate events of PS coherently and in a way supporting reliable predictions. Now, within the theory we refer to mass FOR SIMPLICITY's SAKE as if it were a phenomenal quality and say that B has the mass m(B). It is indeed much simpler to say that for an external observer m(B) increases with v(B) (speed of B) rather than to say that the ratio of force acting on B to the acceleration of B increases with v(B). It's ok and even necessary to consider mass ALWAYS WITHIN THE THEORY as a physical quality as long as we do not forget that it is an ABSTRACT ARTIFICE destined, as all mathematics, to simplify theory's language and expressions. If we forget it, we will lose all intuitive creativity with respect to modifying the theory, or complementing it with new types of observations. The same holds for energy. Consequently: MASS and ENERGY have no autonomous phenomenal existence (they do not appear anywhere in PS). They are pure abstract constructs of mind appearing only in MS and destined to correlate physical events (elements of PS) in simplest possible way, respecting the postulates of the involved theory.

MATTER.

Let's now talk about matter remembering that we are concerned exclusively with field theory, not with quantum theory. We shall talk about matter with respect to the gravity field, which is a singularity field. A singularity field is described by equations which lose validity at the singularity. That's theoretical. In physical practice they lose validity in the whole 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 gravity field. It does not appear anywhere in PS, nor in MS, i.e. it has no phenomenal, nor abstract meaning. Scientifically speaking it does not mean anything at all. When we throw a stone which flies along a parabola, we may, of course, forget all above considerations and follow the "common sense" to which the stone is a lump of matter weighing so much and flying along a corresponding trajectory. It's certainly simpler than to imagine a high density singularity area moving across the field's #space like a rabbit within a boa. But "common sense" may be a bad guide in science. Forgetting that we do not know nor can possibly know anything about singularities makes a lot of amateurs and not only amateurs lose time and effort to prattle about them. Indeed, the temptation is strong: to do something in the defined area takes years of hard work and produces usually not very spectacular results. My daughter, after 10 years of studies spent four years at the observatory in Chilian Andes to clarify the nature of two or three stars at the far end of our galaxy known only by radio-telescopes. Peanuts compared with people juggling with matters, antimatters, insides of black holes, bangs, cyclic or pendular universes, etc. Indeed, the beauty of chatting about singularities is that you may say absolutely anything about them without ever being wrong. Nor right, of course, but who cares ? Let's hold it for a moment. When a sincere scientist having spent 40 years on trying to get a millimeter closer to the singularity gets tempted to cross the frontier, to take it easy for a while and to do some science-fiction at the other side, he may be respected. And if he considers the singularity of singularities such as the Big Bang he may produce lovely and impressing science-fiction. But it will stay science-fiction, we will never know anything about the singularity itself. All we can do is to come another bit closer to it.

TO RESUME:

Mass and Energy are pure constructs of mind having no autonomous phenomenal meaning. They appear in MS as coefficients coordinating events of PS. Matter as such does not mean anything at all and is used as metalanguage term to denote singularity areas of field.