Notice that the observer is shown moving away from the source in Part (a), while the source is shown moving towards the observer in Part (b) of Figure 1 and that accounts for the difference in signs of the cosθ terms of Equations (1) and (2).Īlso, notice that we do not have to specify how the observer has traveled distance (OP) in Part (a) or the source has traveled distance (SP) in Part (b) of Figure 1 whether with uniform velocity, uniform acceleration or with variable acceleration.įurthermore, if Equations (1) and (2) are not identical for (SP) = (OP), the observer will be able to measure selfįigure 1. Where is the speed of light (in vacuum), is the period of the wave emitted by the source, and is the measured period, all in a new frame of reference. From the considerations similar to those of the Part (a) with being very tiny, we obtain: Part (b) of Figure 1 then shows a stationary observer and a source S moving with velocity v along the line SP. Moreover, when the observer is moving (away from) (towards) the source we obtain (increase) (decrease) in the measured period T'. Otherwise, the two periods are different, as was Doppler’s discovery. Thus, we obtain:Ĭlearly, only when (OP) = 0 that we have T' = T, that is, the measured period T' of the light wave equals the period T as emitted by the source. The angle is tiny when the source S is distant from the observer. Let the second light-front catch the observer at P along the ray SQP at time T'. Here, c is the speed of light (in vacuum) and T is the period of the wave emitted by the source. At time t = 0, the light-front immediately following the first one is at point M, which is at distance cT from O. Let observer’s velocity be along OP making an angle θ with OS, as shown. Let a light-front reach an observer at O at t = 0. Part (a) of Figure 1 shows a stationary source S of light. In its generality, Doppler’s discovery is to be understood as follows. In what follows, we are concerned with the implications of the general explanation of Doppler’s effect, with general- ity of explanation referring here to its applicability for any state of the relative motion of the source and ob- server, whether of uniform velocity or accelerated. In 1842, Christian Doppler discovered that whenever a source of light is in motion relative to an observer, the period of the light wave as measured by that observer is different than that it is emitted by the source with. This has important implications for our ideas in cosmology. Observed frequency shifts of cosmological sources then need to be interpreted as being only due to their motions with respect to us. Furthermore, we then show that the frequency shift due to the (assumed) expansion of space, if any, is “indistinguishable” from that due to the motion of the source with respect to the observer and that the shift does not depend on the distance to the source. We first show that Doppler’s effect implies that the time runs identically in the frames of reference of the source of light and the observer. Keywords: Dopper’s Effect Implications for Theory of Gravity Cosmology Received Jrevised Jaccepted August 2, 2013 This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Central India Research Institute, Nagpur, IndiaĮmail: © 2013 Sanjay M.
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