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If the mentioned ideas are taken seriously then the nature of space-time would re-appear in a radically new light. There would be some profound consequences to be addressed and some bizarre features would emerge. First of all space and time would be comprised of fundamental `atoms', i.e. quanta of Planck length ( $ l_P \approx 1.6 \times 10^{-35}$ [m]) and time ( $ t_P \approx 5.4 \times 10^{-44}$ [s]). Space would be built up from `boxes' of the volume $ l_P^3$ [m$ ^3$] and time would be manifested as a series of strung together `time-frozen' frames separated by $ \Delta t =t_P$, exactly like a cinematic film consists of a series of pictures running at a speed of 48 images per second, creating the illusion of a continuous passage of time. Movement would be quite magical in this scenario because an idealized particle localized in such a fundamental space volume would vanish at a certain time $ t_i$ and reappear in the neighboring volume at $ t_f = t_i + \Delta t$. There exists no reality `during' $ \Delta t$. The closest picture visualizing this strange concept would be a 2-dimensional lattice of a LCD computer panel where movement is simulated by the individual pixels comprising the image switching on and off. An interesting hypothesis resting on the premise of the finite nature of reality is concerned with the transformation or evolution of the finite set of information describing the state of such a finite system (i.e. the universe) from one time frame to the next. Fredkin analyzes these processes within the context of information processing, programming and computer science; [Fre-i], [Rh00] and [Fre-ii]. These ideas propose that information is in fact the deepest layer of reality. $ ^{\text{\scriptsize\cite{apdsp5}, \cite{apdsp6}, \cite{apdsp7}, \cite{apdsp8}}}$

Further applying the ideas of discrete space time to different branches of physics:

The notion of an intrinsic energy density of space, as summarized in the first section, does in fact also induce the idea of a discrete nature of space-time. If space, i.e. the vacuum can incorporate energy then it is natural to ask why space is not a quantized entity. The idea of natural units, i.e. that energy is the only free parameter relating length and time (among other quantities) also hints at this question; see note []. Consider the two basic energy relations of special relativity and QM:

$\displaystyle E=mc^2$   and$\displaystyle \qquad E = \hbar \omega.$ (A.3)

Energy is proportional to mass and energy is proportional to the frequency of massless particles. In natural units and observing that frequency is defined as an inverted time interval one finds

$\displaystyle E=m = \omega = \frac{1}{\Delta t} = \frac{1}{L}.$ (A.4)

Hence eq. (A.5) relates energy to time intervals and length scales. This also reflects the ideas of special relativity because zero mass implies an infinite time interval (i.e. no time), whereas a finite mass implies a finite time interval. Also, Lorentz-contraction seems to be incorporated in some sense. Recall that space contains energy by virtue of $ v$ and $ \Lambda $; eqs. ([*]), ([*]), ([*]) and eqs. ([*]) (or ([*]) in natural units), ([*]). In conjunction with eq. (A.5):

$\displaystyle E=m = \omega = \frac{1}{\Delta t} = \frac{1}{L} = v = \Lambda^{1/2}.$ (A.5)

This is a very basic unifying scheme relating different fundamental phenomenas to energy. Hence the effect of linking all physical manifestations to one source which is quantized, i.e. energy, leads to the requirement that space-time should be discrete as well. Eq. (A.6) allows the introduction of at least four fundamental energy/mass scales: $ E_{space-time}$ defined by $ \Delta t$ and $ L$, $ E_{electro-weak}$ defined by $ v$, $ E_{inflation}$ defined by $ \Lambda_{inf}$ (appendix A.2) and $ E_{today}$ defined by $ \Lambda_0$ (section 3.3). A loose description of physics is also present in eq. (A.6)

$\displaystyle E= \overbrace{m = \omega}^{\text{fermions and bosons}} = \underbr...
...pace-time}} = \overbrace{v = \Lambda^{1/2}.}^{\text{Higgs mech. and inflation}}$ (A.6)

The ideas presented in this section are, of course, extremely speculative and on a hypothetical scientific level. However, the continual progression of science is slowly reaching boarder-line subjects. Especially string/M-theory, if it is to be taken seriously, will require a lot of new physical interpretations. The above ideas are tentatively proposed as a small step in such a direction, and are concerned with the most basic constituent of reality any physical theory hopes to model: space-time.

next up previous contents
Next: What Does Quantum Theory Up: The Nature of Space Previous: A.7.3   Contents
jbg 2002-05-26