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**Author:**

Kassir, Radwan M.

**Category:**

Research Papers

**Sub-Category:**

Relativity Theory

**Language:**

English

**Date Published:**

June 7, 2017

**Downloads:**

140

**Keywords:**

Special Relativity, Relativistic Doppler shift, Time Dilation

**Abstract:**

The period of a light wave emitted by an oscillating electron in a “stationary” reference frame was determined in a relatively moving frame using the Lorentz transformation applied on different event intervals; one being between two events on the wave propagation path, and the other between two co-local events on the oscillating source path. A critical inconsistency in the Special Relativity was revealed.

It is enough to say that blue Doppler shift is forbidden by the time dilation. But the blue Doppler shift really exists, so Einstein is wrong.

Gerd,

OK, the time interval between two consecutive co-local crests is T. But, also, the time it takes the wave to propagate spatially from one crest location to the next (i.e., Lambda) is T as well. This is the root cause of the contradiction obtained in the paper, since the LT gives different T' for the two scenarios.

Suppose we have one pulse only (produced by one oscillation). Assume the pulse crest arrives to x=x1 at t=t1, i.e. E1(x1,t1), the same crest will propagate a distance of Lambda to x=x1+cT at t=t1+T, i.e. E2(x1+cT, t+T). The two events are therefore separated by the special interval dx=Lambda=cT and the temporal interval dt=T.

Whereas, for the two consecutive co-local crests, the events are separated by zero spatial interval (dx=0) and T temporal interval (dt=T).

OK, the time interval between two consecutive co-local crests is T. But, also, the time it takes the wave to propagate spatially from one crest location to the next (i.e., Lambda) is T as well. This is the root cause of the contradiction obtained in the paper, since the LT gives different T' for the two scenarios.

Suppose we have one pulse only (produced by one oscillation). Assume the pulse crest arrives to x=x1 at t=t1, i.e. E1(x1,t1), the same crest will propagate a distance of Lambda to x=x1+cT at t=t1+T, i.e. E2(x1+cT, t+T). The two events are therefore separated by the special interval dx=Lambda=cT and the temporal interval dt=T.

Whereas, for the two consecutive co-local crests, the events are separated by zero spatial interval (dx=0) and T temporal interval (dt=T).

1 Replies

It is enough to say that blue Doppler shift is forbidden because of the time dilation.

Period is the time interval between two consecutive wave crests at the same place.

Wavelength is the distance between two consecutive wave crests at the same time.

You have:

E1=(x1,t1), E2=(x1+Δx, t1+Δt).

The two events E1 and E2 belong to the same wave crest x=(Δx/Δt)t + const = ct + const.

Regards,

Gerd

Wavelength is the distance between two consecutive wave crests at the same time.

You have:

E1=(x1,t1), E2=(x1+Δx, t1+Δt).

The two events E1 and E2 belong to the same wave crest x=(Δx/Δt)t + const = ct + const.

Regards,

Gerd

Gerd,

>>>"Actually the two events, as described, belong to the very same wave peak"<<<

No! The spatial interval between the same wave peak is zero. Whereas, the two events considered in the paper are separated by the spatial interval Lambda=cT.

>>>"(e.g. x=ct, at different times) and have nothing to do with wavelength or period."<<<

x=ct is the coordinate x of a wave front at time t. "At different times", e.g. at t1 and t2, we have x1=ct1 and x2=ct2. The expression "x=ct at different times" is not tangible.

The spatial interval Lambda=dx=cT is considered in the paper, where T is the period (interval). Lorentz transformation is applicable to intervals (spatial and temporal) as well, not only to coordinates. The whole analysis in the paper is dealing with intervals.

>>>"Actually the two events, as described, belong to the very same wave peak"<<<

No! The spatial interval between the same wave peak is zero. Whereas, the two events considered in the paper are separated by the spatial interval Lambda=cT.

>>>"(e.g. x=ct, at different times) and have nothing to do with wavelength or period."<<<

x=ct is the coordinate x of a wave front at time t. "At different times", e.g. at t1 and t2, we have x1=ct1 and x2=ct2. The expression "x=ct at different times" is not tangible.

The spatial interval Lambda=dx=cT is considered in the paper, where T is the period (interval). Lorentz transformation is applicable to intervals (spatial and temporal) as well, not only to coordinates. The whole analysis in the paper is dealing with intervals.

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