Information-Based Physics and the Influence Network

Abstract

I know about the universe because it influences me. Light excites the photoreceptors in my eyes, surfaces apply pressure to my touch receptors and my eardrums are buffeted by relentless waves of air molecules. My entire sensorium is excited by all that surrounds me. These experiences are all I have ever known, and for this reason, they comprise my reality. This essay considers a simple model of observers that are influenced by the world around them. Consistent quantification of information about such influences results in a great deal of familiar physics. The end result is a new perspective on relativistic quantum mechanics, which includes both a way of conceiving of spacetime as well as particle “properties” that may be amenable to a unification of quantum mechanics and gravity. Rather than thinking about the universe as a computer, perhaps it is more accurate to think about it as a network of influences where the laws of physics derive from both consistent descriptions and optimal information-based inferences made by embedded observers.

Appendix

The key idea behind employing coordinated chains is that they provide a means of delineating a specific 1 $+$ 1-dimensional subspace in the non-dimensional poset. Events are defined to lie within the subspace defined by the two coordinated chains if the projection of the event onto one chain can be found by first projecting the event onto the other chain and then back to the first. This leads to a set of algebraic relations (for example$Px=\overline{{P}}Qx$ and $Qx=Q\overline{{P}}x)$ where we consider the projections of event x onto chains P and Q. This in turn leads to several different relationships between an event x and the pair of chains (for example, x can be on the P-side of PQ, the Q-side of PQ or between PQ). For example, we say that event x is between two coordinated chains P and Q if $Px=P\overline{{Q}}x$, $\overline{{P}}x=\overline{{P}}Qx$, $\overline{{P}}x=\overline{{P}}Qx$, and $\overline{{Q}}x=\overline{{Q}}Px$ [3].

Fig. 6.6

Illustrates two consistently related chains. Chains Q and Q’ are omitted. By coordination we have $\Delta \overline{{p}}=\Delta q$ and $\Delta \overline{{p}}^{\prime }=\Delta q^{\prime }$

The derivation of the scalar measure is based on a consistency requirement that any two chains that agree on the lengths of each others intervals (coordination) must agree on the lengths of every interval that both chains can quantify. We assume that the scalar measure is a non-trivial symmetric function of the pairwise measure. That is, $s=\sigma (\Delta p,\Delta q)=\sigma (\Delta q,\Delta p)$, where $\sigma (\cdot , \cdot )$is a function to be determined. We can change our units of measure, so that we have $\alpha s=\sigma (\alpha \Delta p,\alpha \Delta q)$. This is a special case of the homogeneity equation [17]

$$\begin{aligned} F(zx,zy)=z^{k}F(x,y) \end{aligned}$$

(6.11)

where in our problem the parameter $k = 1$. The general symmetric solution is given by $F(x,y)=\sqrt{xy}\;h(x/y)$, where h is an arbitrary function symmetric with respect to interchange of x and y. We can show that the function h is unity, and that lengths of intervals are given by $\sqrt{\Delta p\Delta q}$, which leads to the interval scalar $\Delta s^{2}=\Delta p\Delta q$ [3]. We can next consider chains that are consistently related where every interval of length $\Delta p=k$ on chain P forward projects to an interval of length $\Delta p^{\prime }=m$ on $P^{\prime }$ and forward projects to an interval of length $\Delta q^{\prime }=n$ on Q’. We now want to find a function L that takes the pair quantification of the interval I in the PQ frame to the P’Q’ frame:$L_{PQ\rightarrow P^{\prime }Q^{\prime }} (\Delta p,\Delta q)_{PQ} =(\Delta p^{\prime },\Delta q^{\prime })_{P^{\prime }Q^{\prime }}$. (see Fig. 6.6). We note that we can write the projections of the interval I onto chain P in units of length k, so that the pairs can be written as $(\Delta p,\Delta q)=(\alpha k,\beta k)$and $(\Delta p^{\prime },\Delta q^{\prime })=(\alpha m,\beta n)$. Preserving the scalar measure gives $k^{2}=mn$ so that $L_{PQ\rightarrow P^{\prime }Q^{\prime }} (\alpha k,\beta k)_{PQ}=(\alpha m,\beta n)_{P^{\prime }Q^{\prime }}$. It can then be shown that the general transform is given by $L_{PQ\rightarrow P^{\prime }Q^{\prime }} (x,y)_{PQ}=(x\sqrt{m/n},y\sqrt{n/m})_{P^{\prime }Q^{\prime }}$ [3], which gives rise to the Lorentz transformation in (6.6) and (6.7).