13 research outputs found
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
Uncertainties inherent in the decomposition of a Transformation
This contribution adds to the points on the <indeterminacy of special
relativity> made by De Abreu and Guerra. We show that the Lorentz
Transformation can be composed by the physical observations made in a frame K
of events in a frame K-prime viz i) objects in K-prime are moving at a speed v
relative to K, ii) distances and time intervals measured by K-prime are at
variance with those measured by K and iii) the concept of simultaneity is
different in K-prime compared to K. The order in which the composition is
executed determines the nature of the middle aspect (ii). This essential
uncertainty of the theory can be resolved only by a universal synchronicity as
discussed in [1] based on the unique frame in which the one way speed of light
is constant in all directions.Comment: 10 pages including an appendix. Published in the European Journal of
Physics as a Comment. Eur. J. Phys. 29 (2008) L13-L1
Differing observations on the landing of the rod into the slot
In the usual rod and slot paradox a rod falls into a 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. In these experiments the line of motion is not parallel to the axis of the rod or the slot. We consider the cases for which the rod falls into the slot and 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 if the rod falls into the slot as determined by Galilean kinematics, the same conclusion is valid for relativistic kinematics. Our conclusion emphasizes that the passing Í‘or crashingÍ’ of the rod is unaffected by relativistic kinematics. This determination does not depend on 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
Reversal in time order of interactive events: Collision of inclined rods
In the rod and hole paradox as described by Rindler (1961 Am. J. Phys. 29
365-6), a rigid rod moves at high speed over a table towards a hole of the same
size. Observations from the inertial frames of the rod and slot are widely
different. Rindler explains these differences by the concept of differing
perceptions in rigidity. Gron and Johannesen (1993 Eur. J. Phys. 14 97-100)
confirmed this aspect by computer simulation where the shapes of the rods are
different as observed from the co-moving frames of the rod and slot. Lintel and
Gruber (2005 Eur. J. Phys. 26 19-23) presented an approach based on retardation
due to speed of stress propagation. In this paper we consider the situation
when two parallel rods collide while approaching each other along a line at an
inclination with their axis. The collisions of the top and bottom ends are
reversed in time order as observed from the two co-moving frames. This result
is explained by the concept of extended present derived from the principle of
relativity of simultaneity