Time and Space

Dorje C. Brody, Lane P. Hughston

Space-time symmetries and internal quantum symmetries can be placed on equal footing in a hyperspin geometry. Four-dimensional classical space-time emerges as a result of a decoherence that disentangles the quantum and the space-time degrees of freedom. A map from the quantum space-time to classical space-time that preserves the causality relations of space-time events is necessarily a density matrix.

Ph. Blanchard, Arkadiusz Jadczyk

Amrit Šorli

Clocks are systems for measuring frequency, velocity, duration and numerical order ntttt.......,, 210 of physical events. Time t obtained with clocks is not a forth dimension 4X of space, time t is only a component of tciX ∗∗=4. This view of clock/time as a measuring system sees physical phenomena running exclusively in space and not in time. This view is supported with several experiments which confirm that time t of physical event can be zero. Time is not part of space; time is run of clocks in space. Past, present and future exist as a psychological time in the mind only not in the universe. We experience motion i.e. change in the space through the frame of psychological time. We “project ” linear psychological time “past-present-future ” into the space, however it is not there. Observer who distinguishes between space-time, physical time and psychological time is aware that in quantum measurement he only measures physical events in space and not in time. Clock/time is merely a measuring device. With this understanding observer’s observation, measurement and experience of quantum phenomena are closer to their real nature. Stream of numerical order of quantum phenomena ntttt.......,, 210 runs in space only and not in time. Stream of quantum phenomena has no duration on its own. Duration is result of measurement.

Paul Busch, PEKKA J. LAHTI, Juha-Pekka Pellonpää +1 more

Simon Apers, Stacey Jeffery, Galina Pass +1 more

Undirected $st$-connectivity is important both for its applications in network problems, and for its theoretical connections with logspace complexity. Classically, a long line of work led to a time-space tradeoff of $T=\tilde{O}(n^2/S)$ for any $S$ such that $S=Ω(\log (n))$ and $S=O(n^2/m)$. Surprisingly, we show that quantumly there is no nontrivial time-space tradeoff: there is a quantum algorithm that achieves both optimal time $\tilde{O}(n)$ and space $O(\log (n))$ simultaneously. This improves on previous results, which required either $O(\log (n))$ space and $\tilde{O}(n^{1.5})$ time, or $\tilde{O}(n)$ space and time. To complement this, we show that there is a nontrivial time-space tradeoff when given a lower bound on the spectral gap of a corresponding random walk.

Holger Lyre