What's the Matter?

A Series of Ruminations

S.Roof, Mar 2003

This paper will take a look at the philosophy behind a Grand Unification of theories of physics. How do we unify Quantum Theory with Relativity? A clue is that there is a feature common to both theories. This feature is mass. Unfortunately neither theory gives an exaplanation for the observed values of masses in the physical world. Mass always seems to always be an empirical fact or a given in some equation. We will demonstrate here a striking way in which mass might the link for tying these two theories together. In the process we will demonstatre a way to evoke a fundamental mass value from a relational equation alone.

The ontological properties of matter seem to be the ideas of impenetrability, weight or inertia, resistance to change, and potential for acting as a positional repository for other properties i.e. color, form, heat, smell, etc. As such it seems to function as a malleable but resistant substrate or medium for events in the physical world. This may be an illusion, though, that results from an incomplete semiotic process. We shall introduce the idea in this paper that mass can be described and explicated purely by the space-time in which it is embedded.

To unify profoundly different theories it is necessary to grapple with the fundamental elements of these theories and discover the connecting threads of concept. Physics and all science in general is pre-immanently concerned with making measurements. The aim of this process is to assign numbers to physical observables or theoretical variables. Now, numbers are by definition cyclic, regardless of whether they are integer, real, complex etc. The number base of any given number system equates to the cyclic period of the digits that define the symbols of that system. All measurements of observed values or theoretical variables thus has a discrete cyclic system of representation.

These measurements are also always relative to some arbitrary reference point. Any measurement thus resides within a framework or coordinate system that relates it to a position or location within a reference system. This means that behind every measurement there is a viewpoint which establishes the center of the frame of reference. Every measurement taken therefore is a semiotic process that involves at the very minimum a virtual observer, a result of some comparison, and a framework of observation. The triple relation of form-function-content is applicable. The vitual observer functions as the function/functor and can be machine or living. The content is the measured value observed by comparing the thing being measured against the form of the framework. The content of any measurement is thus always a finite sum of digit units which nest as a series of whole number pieces of varying period into one abstract form. One can easily verify this as he uses a ruler to make a measurement. First you count the number of large divisions (inches) that will fit into the distance being measured. Then you add in the next smaller number of pieces (1/2 inch) etc. on down to the degree of precision afforded by the reference system (ruler). Measurements thus can be seen as a superposition of discrete values each with a certain symbolic periodicity. This process can be theoretically carried out to the precision of the coordinate system. Each piece of the summary measurement is a whole number of cycles of a certain periodicity.

The number 314 has three digits whose periods under decimal positional notation are ... 100 ... 10 ...and 1 .... This number equates to a sum of 4 units of period 1, 1 unit of period 10 and 3 units of period 100.

The point of this mental exercise is to establish that making a measurement is an exercise of counting whole number cycles of representation. The semiotics can be replicated physically by adding up or superposing integral waves of those frequencies. The resulting waveform would represent that particular number. Making measurements is an exercise in quantization. In other words, quantification implies quantization. Now we could obviously take pieces of a waveform less than it's wavelength, but to do so adds uncertainty of representation, so the next level of quantization (shorter period, higher frequency) that has an integral number of wavelengths is used. The count at each level specifies the representational digit or number of quanta of that frequency.

This business of quantization is easy to visualize. Imagine looking at the blinking tail light of a car on the road ahead of you. It appears either on or off as it blinks but actually the light filament in the bulb heats up and cools down in a more or less sinusoidal fashion and the light intensity does likewise. We instinctively count only the periodic returns to a similar state i.e. the 'on' state. The bits in a computer likewise flip in a continuous fashion, but it is the on or off position that is stabilized and noted. We can also quantize waves by filtering thresholding so that only a certain intensity or above is allowed through. Quantization can also be seen as constructive interference of waves.

The above quantization refers to abstract semiosis of representation and not the quantization of quantum physics but I think one can see that, from this viewpoint, even classical physics from the very beginning had an epistemology that encouraged ideas of quantization and also ideas of relativity. Now let's look at the measuring frameworks of physics i.e. coordinate systems.

Quantum Physics and Relativity both use real numbered continuous orthogonal coordinate systems in {x,y,z,t}. The idea of continuity is that the metric space is infinite and measurements can in principle be applied to any degree of precision. Also the dimensions are considered infinite in that the axes extend out to inifinity. These axes have to be orthogonal to make sure that measurements along one dimension are independant of measurements along another dimension. Any relateness of measurements then is independent of the coordinate system and dependant only on the causal features of the system being measured. The laws of physics have to be invariant under coordinate transformations.

Relativity establishes that measurements by different observers differ if they are moving with respect to each other and that the maximum velocity difference is the speed of light in a vacuum. At the very heart of relativity theory, mass is related to motion and so is space. Mass curves space and curved space induces motion in mass. The law of gravity models this relationship. Gravity bends light in a direction at right angles to the radius of curvature. If gravity is strong enough, light will go in a circle and cant escape from the potential well created by the curvature of space. This circle has a specific radius and is called the Schwarzchild Radius. It is the defining size of the event horizon of a black hole. This relation of light to gravity gives some interesting clues as to the origin of mass and how quantum theory can be related to the theory of relativity.

The classical derivation of the Schwarzchild Radius is easy:

Force of Gravity F = GMm/r^2

Now the centripetal force on an object going in a circle must by pure geometry be F = ma = mv^2/r

Equating these two gives mv^2/r = GMm/r^2

the little m cancels and we are left with:

the Schwarzchild Radius r = GM/v^2

Now since we are talking about light, its velocity v is equal to c so:

r = GM/c^2

A mass M great enough to pull light in a circle will establish a radius of curvature given by the equation above.

But mass equates to energy by the equation E = mc^2, so an equivalent amount of energy in the same spot will curve space to the same Schwarzchild radius. We now ask the question: If energy curves space and light has energy, then might not a photon trapped in a sufficiently tight circle curve space enough that it cannot escape its own curvature? Could it generate an apparent mass equal to 'M' above. If so what would the frequency of the photon have to be and what would the apparent mass be?

Quantum physics provides the answer. The energy of a photon is given by E = hf where h is Planck's constant and f is the frequency.

therefore E = Mc^2 = hf and M = hf/c^2

Substituting for M in r = GM/c^2 gives:

r = G(hf/c^2)/c^2 = Ghf/c^4

Now we know that the velocity of light is equal to the frequency times the wavelength. Therefore f = c/wavelength.

We can thus establish the wavelength of the light in a circle. At this point one has to imagine that if only a single wavelength was thus encapsulated in a circle it would rejoin its tail in the correct phase and no destructive interference would occur. This would establish a fundamental minimal limit to the above equation.

The distance traveled around a circle is 2pi r so this distance has to equal the wavelength c/f.

f = c/wavelength = c/(2pi r)

Substituting for f in the Schwarzchild equation yields:

r = Ghf/c^4 = Gh(c/2pi r)/c^4

this reduces to r^2 = Gh/2pi c^3

h/2pi is conventionally called hbar so:

r = sqrt( G *hbar / C^3)

We now have r defined by the fundamental constants of physics. This is a unique value for the radius of curvature for the minimal frequency of light which can eat its own tail.

Black Holes and Fragmentation

Hey guys, I was thinking about black holes the other day and had some unusual ideas. I have been reading about encryption, secrets etc. and somehow the idea of a black hole popped into mind as the ultimate secret compartment for physical information. I have been used to thinking about a black hole as a bunch of matter smushed together with it's event horizon defining the boundary. Further thought led me down a strange path though.     I recalled the idea of 'sphagettification' wherein the gravity tidal forces are so great that matter inside the horizon gets stretched into thin time lines. Then it occurred to me that the ends of a body so stretched actually are on the opposite sides of their own event horizon as they close in on the singularity i.e. light from the inner side or piece cannot get to the outer end or piece. Relatively speaking the event horizon occurs as a shell recursively defined for each point along a time line going inward. This means that matter must fragment as it goes inward ultimately fragmenting down to the smallest possible components (quarks?) each fragment being forever (remember that 'forever' is the time dilation looking outward from the singularity) separated from it's closest neighbor by this relativistic horizon which must occur all the way from the outer horizon inward to the singularity. This discontinuity is so profound that each point inside the absolute outer horizon must necessarily be mathematically discontinuously separate from it's closest neighbors. Matter must thus be some sort of disconnected fractal dust inside the horizon driven by an immense attractor. The question is what happens to the energy when even the final fundamentals disassociate? If they go into pure energy, then doesn't that amount of gravitational field dissipate? Seems to me it can only go into pure curvature of space-time itself.     Along the same lines of reasoning, I thought originally that photons must circle in orbits inside the horizon at right angles to the time lines for masses. Since masses cant achieve velocites which aren't even enough for light to escape, their trajectories must go straight inward at right angles to photons. But then it occured to me that if I buy into my own view that photons are really only metaphysical abstractions for electron-electron correlations, then light cannot exist inside the shell distance at which 'spaghettification' of electron orbits would occur. At that point the extra energy associated as photons must go where?     The whole affair looking outward from the singularity must be an infinite series of starry shells, frozen snapshots of time all supposed on each other. Looking inward it would be a star burst into light speed travel and over before you even get a chance to see it.     Is a black hole fragmented and deep structured? What happens at the distance from the singularity equal to the radius of say the first stable shell of an electron around a hydrogen atom? Any ideas come to mind?     Black holes are being found at the center of almost all galaxies now and the velocity of rotaion of the outer stars is directly proportional to the size of the black hole even though they are too far away to be thus affected. The relation is born in the birthing process of the galaxy.     I'm convinced that there some really heavy illuminations will be coming down the pike soon. Anyhow I was startled to discover in my own thought experiment that fragmentation is at the very heart of the most integrative allpowerful force in nature and at the same time, unification occurs at the most fragmented cosmic distances.        

There was a recent Scientific American article that came out after I wrote the above piece. It considers the above idea in terms of maximum information or entropy. Turns out that one can measure the maximum information content or entropy of a spatial volume as being that of the the black hole which it would collapse into - it turns out to be the number of planck volumes divided by 4.