Moving Signals and Their Measured Frequencies

In determining the classical Doppler Effect, two assumptions are used for computing the difference in distance travelled by consecutive signals: (a) the receptor is stationary, and (b) the emitter is stationary. The calculated Doppler Effect under the two assumptions are identical, provided the velocity of propagation with respect to source and the velocity of propagation with respect to the receptor differ exactly by the velocity of relative motion. We show that, in the case of light, the ratio of the two calculated classical Doppler Effects, with propagation speed c in the source and receptor inertial frames respectively, remains constant in all geometries and orientations. Furthermore, the observed Doppler Effect, as predicted by special relativity, is the geometric mean of the two expected classical Doppler Effects in all geometries and orientations. This leads to two simultaneous conclusions: (1) by the receptor that the clock associated with the emitter runs slow, and (2) by the emitter that the clock associated with the receptor runs slow. These differences can be resolved if we theorize that light travels at speed c with respect to the emitter as it leaves the emitter and travels at speed c with respect to the receptor as it approaches the receptor.Comment: Revised in accordance with peer review process; Published August 2013 in Int. J. Engg. Res. & Sci & Tech 2(3) pp 24-3

Differing perceptions on the landing of the rod into the slot

In the usual rod and slot paradox, the rod, if it falls, was expected to fall into the slot due to gravity. Many thought experiments have been conducted where the presence of gravity is eliminated with the rod and slot approaching each other along a line joining their centers, whereby the considerations come strictly under Special Relativity. In these experiments the line of motion is not parallel to either the axis of the rod or the slot. In this paper we consider in detail the two cases when the rod does fall into the slot and when the rod does not fall into the slot, each from the perspective of the co-moving frames of the rod and the slot. We show that whether the rod falls into the slot as determined by Galilean kinematics is also valid under relativistic kinematics; this determination does not depend upon the magnitude of the velocity, but only on the proper lengths and the proper angles of the rod and slot with the line of motion. Our conclusion emphasizes the fact that the passing (or crashing) of the rod as a wholesome event is unaffected by relativistic kinematics. We also provide a simple formula to determine whether or not the rod passes through the slot.Comment: 9 pages, 6 figure

On-line control of grasping actions: object-specific motor facilitation requires sustained visual input

Dorsal stream visual processing is generally considered to underlie visually driven action, but when subjects grasp an object from memory, as visual information is not available, ventral stream characteristics emerge. In this study we use paired-pulse transcranial magnetic stimulation (TMS) to investigate the importance of the current visual input during visuomotor grasp. Previously, the amplitude of the paired-pulse motor evoked potentials (MEPs) in hand muscles before movement onset have been shown to predict the subsequent pattern of muscle activity during grasp. Specific facilitation of paired-pulse MEPs may reflect premotor–motor (PMC–M1) cortex connectivity. Here we investigate the paired-pulse MEPs evoked under memory-cued and visually driven conditions before grasping one of two possible target objects (a handle or a disc). All trials began with a delay period of 1200 ms. Then, a TMS pulse served as the cue to reach, grasp and hold the target object for 0.5 s. Total trial length was 5 s. Both objects were continually visible in both conditions, but the way in which the target object was designated differed between conditions. In the memory-cued condition, the target object was illuminated for the first 200 ms of the trial only. In the visually driven condition, the target object was illuminated throughout the 5 s trial. Thus, the conditions differed in whether or not the object to be grasped was designated at the time of movement initiation. We found that the pattern of paired-pulse MEP facilitation matched the pattern of object-specific muscle activity only for the visually driven condition. The results suggest that PMC–M1 connectivity contributes to action selection only when immediate sensory information specifies which action to make

Conformality of non-conformal correlators

We show that position space correlators of a Poincare invariant quantum field theory can be recast in terms of conformally invariant correlators, in other words, as functions of conformal cross ratios. In particular, we show that correlators of massless fields in flat spacetimes with $n-$point interactions can be expressed as position space soft limits of conformally invariant correlators with $(n+1)-$point interactions. We show that this correspondence applies at the level of every Feynman diagram that appears in the perturbative expansion of the correlators in the respective coupling constants. We apply this method to find exact answers for some Feynman diagrams including several loop examples. We also show that the analogous correlators for massive fields can be expressed as infinite sums of conformal correlators.Comment: 34+8=42 pages, 13 figure