Authors: Udo E. Steinemann
According to G. t’ HOOFT’s holographic principle the combination of quantum mechanics and gravity requires that a 3-dimensional space-region to be projected on the 2-dimensional bounding surface of the region. In the limit of very large regions the bounding surfaces can be taken as flat planes at infinity, thus phenomena taking place in 3-dimensional space can be projected onto distant "viewing screens" with no loss of information. The discrete lattice-sites of a screen are "pixels", each one can only store ⟨1⟩ bit of information. An analogy with a hologram can be made which stores a 3-dimensional image on a 2-dimensional film. As in the case of the hologram the flat 2-diemsional image must be rich enough to code full rotationally invariant description of a 3-dimensional object. All matter is composed of elementary structure-less constituents called partons. The presence of a parton isrepresented by projecting its location by a light-ray on screen. A space-time-event which combines all partons at a specific instant of time forms a 3-dimensional light-front. Light-front-quantization of quantum-gravitycan be formulated by taking the transverse space as a discrete lattice where the lattice is composed of binary pixels of a spacing in the order of PLANCK-length. No distribution of matter will ever require more than ⟨1⟩ bit of information per PLANCK-area on a screen. The quantization in longitudinal direction considered under the parton-concept is familiar from Quantum-Chromo-Dynamics ⟨QCD⟩ originated in works on deep inelastic scattering. The Hamiltonians are the classical ones and the eigenvectors are well-defined super-positions ofFOCK-space-states. Each parton-momentum simply acts as scale-transformations in longitudinal direction, but classical scale-invariance will usually be destroyed by divergent high frequency effects. Cutoffs in frequency-spectra, models in connection with so-called Fixed-Point-Hamiltonians and derived from string-theory will finally help to find-out that a growing amount-of-information inside a space-region may cause its extension.Given that the maximal allowable information for each part of space is finite, then it is impossible to localize a particle with infinite precision at a point of the continuum. Therefore one could assume that information is stored in points of a discretized space. In order to get information described holographically, it must exist in some duplicated form, thus it is assumed to be stored on surfaces, or screens. Screens separate points and in this way they are natural places for information about particles that move from one side to the other. Within in this environment gravity will take the form of an entropic-force. An entropic force is an effective macroscopic-force that originates in a system with many degrees-of-freedom by the statistical tendency to increase its entropy. The force-equation is expressed in terms of entropy-differences. A small piece of a holographic-screen is considered and a particle of a certain mass approaching it from the side at which space-time has already emerged. When the particle merges with the microscopic degrees- of-freedom on screen, it influences the amount of information that is already stored there. Assuming that the change-in-entropy near the screen is linear to displacement-from-screen then it is proportional to particle-mass. Force comes into play from an analogy with osmosis across a semi-permeable membrane and the membrane carries a temperature, the particle will experience an entropic-force. Based on relations from W. G. UNRUH and J. D. BEKENSTEIN temperature and acceleration can finally be brought into close connection which will let the just mentioned force to appear in the form of NEWTON’s second law.Thinking about a piece of a holographic-screen as a storage-device for information, the maximal storage-space or the total number of bits is proportional to this screen-area. Because each fundamental-bit occupies ⟨1⟩ unit-cell, the number of used bits can easily be calculated. Additionally the total energy is considered which had already been contained on screen-side when the particle was approaching (evenly distributed over the occupied bits) together with its mass-equivalence due A. EINSTEIN and temperature determined as average-energy per bit. All this combined together will let the above entropic force become NEWTON’s gravity —force. The real consequence of this finally is: A growing amount on surface of a space.region may change the surface-curvature.
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