The model of spacetime dynamics proposed here specifies how spacetime emerges, how changes of spacetime propagate, and how changes in spacetime arising from multiple sources accumulate. The overall goal of the model was to achieve maximum compatibility with general relativity and with Einstein’s equation; this goal appears to be achievable except at very small scales, where the discreteness of the units of space matters. The elementary structure of space(-time) that is assumed in this model is a derivative of causal dynamical triangulation. At the elementary level, space consists of a (discrete) number of interconnected space points, each of which is connected to a small number of neighbouring space points. The curvature of spacetime is expressed by the density of these space points and by the arrangement of the connections between them. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns “in-connections” and “out-connections” to the affected space points. Based on the model of the dynamics of curved discrete spacetime, a model of quantum field theory in curved discrete spacetime is described. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out space point connections. Compatibility with standard quantum field theory requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n ＞3 in/out connections.

Abstract:
Special relativity theory abandoned the notion of absolute space and
time. For many physicists, it also abandoned the notion of global time, i.e., a unique time coordinate that could
be assigned to the overall universe. On the other hand, with theories and
discussions on the dynamical development of the overall universe, the notion of
a global state, which is associated with global time, seems to be very useful,
if not unavoidable. This paper discusses to what extent the notions of global
states, global time and global simultaneousness can be defined such that they
are compatible with Einstein’s relativity theories. The results show that the
establishment of a global coordinate system requires, in addition to the choice
of suitable space and time coordinates the selection of a physical object with
an assumed uniform velocity.

Abstract:
The double-slit (gedanken-)
experiment is the most famous experiment in quantum theory (QT). The explanation
of the strange behavior of the electron in this experiment is used as a key example
in QT in general. The description of the experiment includes a rationalization
of when in quantum mechanics interference occurs and (most importantly) when it
“collapses”. The aforementioned rule, here called the “interference collapse
rule”, is contained in almost all textbooks of QT with only slight variations.
However, this rule makes sense only with additional assumptions which
apparently are not generally agreed upon among physicists. The paper proposes
an improved interference collapse rule that connects the interference collapse
to the QT measurement and a functional interpretation of QT measurement.

Abstract:
Models of areas of physics in terms of cellular automata have become increasingly popular. Cellular automata (CAs) support the modeling of systems with discrete state component values and enforce the comprehensive specification of the dynamic evolution of such systems. Because many areas of physics can be described by starting with a specific Lagrangian, the idea to derive a cellular automaton directly from the Lagrangian (or similar construct, such as the Hamiltonian or action) is not new. Previous work, however, indicated that the classical CA may not be a sufficient basis for the modeling of more advanced physics theories, such as quantum field theory. Specifically, the modeling of interactions in quantum field theory requires extensions and modifications of the classical CA. This paper describes a proposal for an extended cellular automaton that is suited for support of quantum field theory.

Abstract:
The enterprise to construct a local causal model of quantum theory (QT), including quantum field theory (QFT), resulted in the identification of “quantum objects” as the elementary units of causality and locality. Quantum objects are collections of particles (including single particles) whose collective dynamics and measurement results can only be described by the laws of QT/ QFT. Quantum objects run autonomously with system state update frequency based on their local proper time and with no or minimal dependency on external parameters. The autonomy of quantum objects ne-cessitates well-defined causal interrelationships between quantum objects and spacetime: 1) Quantum objects are embedded in space and move within space. 2) In the proposed causal model, the dynamics of space is triggered by the dynamics of the quantum objects. The causal model of QT/QFT assumes discretized spacetime similar to the spacetime of causal dynamical triangulation.

The non-localities in
quantum theory (QT) (the most famous example is expressed in the violation of
Bell’s inequality in experiments) impede the construction of a local causal
model of QT including quantum field theory (QFT). The laws of collective
behavior may be considered to be types of non-local laws: laws that apply to
the collection of system components as a whole. The article presents a proposal
for the treatment of the non-localities that exist in QT/QFT by the concepts of
collective behavior. The basic components of the collective behavior are the
spatial elements of the causal model of QT/QFT proposed by the author.

Abstract:
We study the asymptotic behaviour of the maximum local time L*(t) of the Brox's process, the diffusion in Brownian environment. Shi proved that the maximum speed of L*(t) is surprisingly, at least t log(log(log t)) whereas in the discrete case it is t. We show here that t log(log(log t)) is the proper rate and we prove that for the minimum speed the rate is the same as in the discrete case namely t/log(log(log t)).

Abstract:
How can we tell from a memory report whether a memory is episodic or not? Vividness is required by many definitions, whereas detailedness, memory specificity, and narrative text type are competing definitions of episodicity used in research. We explored their correlations with vividness in personally significant autobiographical memories to provide evidence to support their relative claim to define episodic memories. In addition, we explored differences between different memory types and text types as well as between memories with different valences. We asked a lifespan sample (N = 168) of 8-, 12-, 16-, 20-, 40-, and 65-year-olds of both genders (N = 27, 29, 27, 27, 28, 30) to provide brief oral life narratives. These were segmented into thematic memory units. Detailedness of person, place, and time did not correlate with each other or either vividness, memory specificity, or narrative text type. Narrative text type, in contrast, correlated both with vividness and memory specificity, suggesting narrative text type as a good criterion of episodicity. Emotionality turned out to be an even better predictor of vividness. Also, differences between narrative, chronicle, and argument text types and between specific versus more extended and atemporal memories were explored as well as differences between positive, negative, ambivalent, neutral, contamination, and redemption memory reports. It is concluded that temporal sequentiality is a central characteristic of episodic autobiographical memories. Furthermore, it is suggested that the textual quality of memory reports should be taken more seriously, and that evaluation and interpretation are inherent aspects of personally significant memories.

Abstract:
We consider Brox's model: a one-dimensional diffusion in a Brownian potential W. We show that the normalized local time process (L(t;m_(log t) + x)=t; x \in R), where m_(log t) is the bottom of the deepest valley reached by the process before time t, behaves asymptotically like a process which only depends on W. As a consequence, we get the weak convergence of the local time to a functional of two independent three-dimensional Bessel processes and thus the limit law of the supremum of the normalized local time. These results are discussed and compared to the discrete time and space case which same questions have been solved recently by N. Gantert, Y. Peres and Z. Shi.