**Note:** This is an *extremely* rough idea. It is the beginning of an attempt to deal with my longstanding discomfort with **(a)** the descriptions of black holes I've seen, and **(b)** treating the universe as if its fundamental structure is compatible with the continuum models usually used in reference to time and space.

### Continuum Models of Space

Most physical theories are based on underlying continuum models of space. Domain Theory is not.

The traditional conceptualization of a black hole is that it exists in space as an infinitessimal point body (a singularity), the gravity field (alternatively the space-time curvature) around which creates a region of space in which the escape velocity is equal to or greater than the speed of light. The surface at which the escape velocity is equal to the speed of light is called the event horizon (alternatively the Schwartzchild radius).

The Domain Theoretic perspective is that a black hole is not such a region of mostly empty space between an event horizon and a point center of divergent density. It just simply does not have an interior.

### The Planck Length and Spatial Transitivity

The Planck Length is the minimum distance at which it makes sense to talk about distance. It is on the order of 1 x 10^{-33} cm (the Planck Time is about 1 x 10^{-43} sec, and the speed of light is the constant by which they relate, 1 x 10^{10} cm/sec).

Assuming an underlying continuum as is the practice today reveals a paradoxical effect. Consider three points along a line, A, B, and C. Arrange the points so that from left to right they occur in the order just given, and so that the distance from A to B is p (the Planck Length) minus some infinitesimally small distance i (iota). Arrange C so that the distance from A to B is equal to the distance from B to C. Now, the distance from A to C is 2p - 2i, which is greater than p. So, A and B are so close as to be indistinguishable (and therefore considering only A and B there is only one point); and B and C are indistinguishable. However, A and C are far enough apart that they are distinguishable, and therefore distinct. Here we have a demonstration of the loss of transitivity in the model of space: A = B, B = C, but A != C!

### Hypotheses

**The Principle of Mutuality**: Matter affects space, and space affects matter. The presence of matter alters space, and the local characteristics of space alter the behavior of matter.

**The Principle of Homogeneity (tenuous)**:There is nothing but domains and their interactions. Empty space, photons, quarks, and black holes are all various manifestations of one thing: domains.

Suppose that as more mass/energy is concentrated into a region of space, the local Planck length increases relative to the surroundings. Consider this to be an alternative view to the Einsteinian view of curvature of space-time. In this view, the Planck length gradient is identified with the Einsteinian curvature.

**Food For Thought**: If length is relative, what does it really mean to talk about the Planck length varying? How is it measured?

Suppose that as more and more mass/energy is concentrated into a volume of space, eventually the Planck length reaches a point at which it is comparable in size to the particles, and the particles cease to exist as distinct entities, and become part of a growing energetic singular domain.

This domain has no interior since it is for all practical purposes a macroscopic point. The term "singularity" applies very well here, since it is precisely a single (large) domain. Note that in this view, the Schwartzchild radius is identified not with some boundary between reachable and unreachable continuum space, but rather the characteristic Planck length in the region, or the size of the pathological domain. The black hole behaves like a single point in space, although it has an extent relative to us. The "singularity" is not somewhere "inside". It *is* the black hole.

### Consequences of Equivalence

Through the equivalence of gravitic and accellerating frames, standing near the singularity feeling its gravity should be identical with accelerating away from the hole's position if the hole weren't there in otherwise empty space.

Imagine placing an object in the vicinity of the black hole, initially at rest with respect to the hole. There is a gradient of increasing Planck length along the line between the two bodies (from each pointing at the other), most contributed by the black hole, and a miniscule amount contributed by the object. All massive objects climb Planck gradients, and so there will be an attraction.

Creating an increase of Planck length near an object will cause it to accelerate through that increase. An object whose surroundings are isotropic will not be accellerated. Why does an object put into motion continue to move? Without a force acting on it, it has no reason to change its behavior. As an object is accellerated, the domains on its leading edge expand, and those on its trailing edge contract. When the force causing accelleration is removed, the object is "riding" a spatial wave the leading edge of which is the expanded domains.

### Inertia

An object carries with it its local Planck length increase due to its mass. If it is isolated and at rest, then the total local Planck length increase is due to its mass alone. Now, if we consider the same object, but moving at a particular velocity, there will be an additional Planck length increase corresponding to the velocity. As long as the object is riding the peak of the wave, it will continue along at the same velocity. This is inertia. However, if we want to accellerate it some more, we have to create an increased Planck length on the leading edge. But, the current peak is greater than the peak at rest, so it will require more input energy to achieve the same net gain in velocity for the inertial system. This is why as you approach the speed of light, it takes increasingly more energy to achieve a unit gain in velocity.

**Food For Thought**: As the object goes faster, the local Planck length increases, too. A massive enough object travelling fast enough could (perhaps) become a black hole by increasing its planck level sufficiently that it becomes macroscopic.

The larger the Planck length, the larger the Planck time has to be to keep the local speed of light constant.

An inertial frame is the shape of the domain size gradient surrounding an object. A moving object has an inertial frame with a leading edge and a trailing edge. The directions orthogonal to the direction of motion don't have this distinction.

### Photons

Consider the possibility that a photon might be a single energetic domain that moves about, or alternatively an affect that transfers from domain to domain. Given the relationship between the Planck length, the Planck time, and the speed of light, a photon then moves at one domain per Planck time. Assuming that no skipping of domains is possible, this would be the fastest speed available.

Since it has no extent, a photon doesn't interact in the same way as particles that do have extents.

When a photon is created, it has a particular energy (which determines its wavelength). As it travels, it may encounter regions of different Planck length. It may also climb up or down a gradient in its path (for instance if it is emitted by an object that is in motion. Travelling up the trailing edge or down the leading edge of an inertial frame causes a blue shift, and traveling down the trailing edge or up the leading edge causes a red shift. So, if two bodies are moving at the same speed in the same direction, and their masses are the same, there won't be any shift in photons traveling between them because the effects will cancel. If, however, the objects are of different masses, then the effects won't cancel precisely, since the gradients will be asymmetric. This may be testable.

When a photon encounters a black hole, it is absorbed.

### The Domain Field

Think of space like a multidimensional field of domains of varying relative sizes. Somewhat like a mass of soap bubbles.

Some dimensions (such as the the three traditional dimensions of space) are simply connected in an approximation to a lattice. Other dimensions might be curled in upon themselves and be the source of varying qualities. For example, a single closed "curled-up" dimension could account for electromagnetic waves. There would be a periodicity produced by cycling around the dimension. As a photon moved through the spacial dimensions, encountering new territory, it would be simultaneously cycling around the other dimension one direction or the other (which would account for polarity). Photons move one domain per unit time, and time is dependant upon domain size. In this way, time relative to the curled-up dimension might in some way be partially disconnected from time relative to the "normal" dimensions, so that the energy of the photon is encoded in the size of the domain, part of which extends into this other dimension.

### Dimensional Analysis

*[NOTE: This section is just some very rough notes that eventually need to be sorted out.]*

Thanks to Denny Dahl for enlightening discussions.

Three fundamental constants (all calculations here use cgs units):

- Speed of light:
**c**cm / s - Gravitic constant:
**G**cm^{3}/ g s^{2} - Planck's constant:
**h**g cm^{2}/ s

The Planck length can be expressed in terms of these as: L_{p} = sqrt(h G / c^{3})

Energy has units of g*cm^{2} / s^{2}.

Energy density (epsilon) is g / cm*s^{2}. In terms of the constants above, its is: K_{d} * c^{7} / G * h^{2}.

l_{p}(e) = L_{p}(1 + K_{d} * (e h G^{2} / c^{7} ).

L_{p}^{4} = h^{2} G^{2} / c^{6}.

L_{p}^{4} / h c = h G^{2} / c^{7}.

so, l_{p}(e) = L_{p} (1 + K_{d} ( e L_{p}^{4} / h c ) ).

## No comments:

Post a Comment