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Register a new userA Garden of Forking Paths - the Quantum Mechanics of Histories of Events
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We present a short survey of a novel approach, called ETH approach, to the quantum theory of events happening in isolated physical systems and to the effective time evolution of states of systems featuring events. In particular, we attempt to present a clear explanation of what is meant by an event in quantum mechanics and of the significance of this notion. We then outline a theory of direct (projective) and indirect observations or recordings of physical quantities and events. Some key ideas underlying our general theory are illustrated by studying a simple quantum-mechanical model of a mesoscopic system.
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This paper studies the problem of predicting the distribution over multiple possible future paths of people as they move through various visual scenes. We make two main contributions. The first contribution is a new dataset, created in a realistic 3D simulator, which is based on real world trajectory data, and then extrapolated by human annotators to achieve different latent goals. This provides the first benchmark for quantitative evaluation of the models to predict multi-future trajectories. The second contribution is a new model to generate multiple plausible future trajectories, which contains novel designs of using multi-scale location encodings and convolutional RNNs over graphs. We refer to our model as Multiverse. We show that our model achieves the best results on our dataset, as well as on the real-world VIRAT/ActEV dataset (which just contains one possible future).
A history of Feynmans sum over histories is presented in brief. A focus is placed on the progress of path-integration techniques for exactly path-integrable problems in quantum mechanics.
Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a particle can change its energy, as it gets entangled with the barriers and the insertion points become nodes. Two seemingly innocuous assumptions representing locality and linearity are investigated. Namely, a barrier insertion at a fixed node needs no energy, and barrier insertions can be described by linear maps. It will be shown that the two assumptions are incompatible.
We present a new experimental approach using a three-path interferometer and find a tighter empirical upper bound on possible violations of Borns Rule. A deviation from Borns rule would result in multi-order interference. Among the potential systematic errors that could lead to an apparent violation we specifically study the nonlinear response of our detectors and present ways to calibrate this error in order to obtain an even better bound.
We develop a general theory of the time distribution of quantum events, applicable to a large class of problems such as arrival time, dwell time and tunneling time. A stopwatch ticks until an awaited event is detected, at which time the stopwatch stops. The awaited event is represented by a projection operator $pi$, while the ideal stopwatch is modeled as a series of projective measurements at which the quantum state gets projected with either $bar{pi}=1-pi$ (when the awaited event does not happen) or $pi$ (when the awaited event eventually happens). In the approximation in which the time $delta t$ between the subsequent measurements is sufficiently small (but not zero!), we find a fairly simple general formula for the time distribution ${cal P}(t)$, representing the probability density that the awaited event will be detected at time $t$.
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