The IEEE Refutes Special Relativity

Evidence of the sad state of science education can be seen in the IEEE Transactions on Instrumentation and Measurement, which recently published papers claiming to refute special relativity. This alleged refutation first surfaced in 2003 with the publication of a paper entitled "Absence of the Relativistic Transverse Doppler Shift at Microwave Frequencies" (Vol 52, No. 5).  The paper claimed that special relativity (as described in Einstein's paper of 1905 for example, or in any freshman physics text) predicts a frequency shift for an electromagnetic signal passing between a transmitter and receiver mutually at rest in some inertial frame, if the signal is relayed by two antennas moving in opposite directions transverse to the signal. Schematically the situation is as depicted in the figure below.

 

 

Now, it's obvious by inspection that there can be no Doppler shift between transmitter and receiver in this condition, with the relay antennas moving purely transversely to the signal, because the transmitter and receiver are mutually at rest, and the path length between them is not changing. Despite this, the IEEE paper argues that the rote application of the formulas of special relativity, as given in Einstein’s 1905 for example, somehow leads to a prediction of a Doppler shift factor of (1+v2)/(1-v2). The IEEE paper then describes an experiment designed to test this alleged prediction by placing relay antennas on the rims of two counter rotating disks between a microwave transmitter and receiver. The paper reports that no shift was observed, and from this it concludes that special relativity has been falsified. Needless to say (or so one would have thought), this is absurd, since special relativity unambiguously predicts zero Doppler shift for the purely transverse situation depicted above. (We leave aside the question of whether the experimental setup was valid. Obviously when the relay antennas are in non-transverse positions, there would be some varying Doppler shift, but the IEEE paper does not consider any conditions other than the purely transverse one – nor does it report any cyclical variation in the observed frequencies, which is rather suspicious, but never mind.)

 

To show that the formulas in Einstein’s 1905 paper lead unambiguously to the prediction of zero shift for the purely transverse condition, let f0, f1, f2, and f3 denote the frequencies of the electromagnetic signal at the transmitter, the first antenna, the second antenna, and the receiver, respectively, each expressed in terms of the standard inertial coordinates momentarily co-moving with the respective objects. Also, let u = -2v/(1+v2) denote the velocity of the second antenna relative to the first, making use of the well-known relativistic velocity composition formula. Now, according to special relativity, the frequencies are related by the relativistic Doppler formula (as presented in Einstein’s 1905 paper), which gives

 

 

where f is the angle of the wave in terms of the transmitter's rest frame, f' is the angle of the wave in terms of the first antenna's rest frame, and f" is the angle of the wave in terms of the second antenna's rest frame. Notice that, as specified in Einstein’s 1905 paper (and in every introductory text on special relativity), the angle appearing in each Doppler formula is defined in terms of the rest frame coordinates of the emitting object. The angle of the wave normal is f in terms of the inertial rest frame coordinates of the transmitter and receiver, and the two relay antennas are moving with speeds +v and –v relative to that frame, so the direction cosines of the wave normal in terms of the inertial rest frame coordinates of the relay antennas are given by the relativistic aberration formula (also presented explicitly in Einstein’s 1905 paper) as

 

 

Inserting these angles into the preceding Doppler formulas, and setting f = 90 degrees, we get the frequencies

 

 

This is the unambiguous prediction of special relativity, so, contrary to the IEEE, no Doppler shift is to be expected in this situation. The error in the IEEE paper was the failure to account for aberration in the value of f'. Equations (12), (13) and (14) of the IEEE paper correspond to our equations (1), (2), and (3), except that the angle f’ in equation (13) of the IEEE paper has been mistakenly assigned the value 90 degrees, rather than the correct value given by our equation (4) with f = 90 degrees.

 

In view of the obvious lack of understanding of aberration in the IEEE paper, it is perhaps not surprising that the paper also expresses uncertainty about the appropriate value of the angle represented by f" in our equation (3). Indeed the paper says

 

...an uncertainty exists, as one could argue that the blue shift the wave experiences during propagation from the stationary [transmitter] to the rotating antennas mounted at the rim of disk 1 could possibly be compensated by an equal red shift occurring during transfer of the signal from ... disk 2 into the stationary [receiver]... In these equations, the "worst" case has been assumed that the first blue shift f1/f0 is compensated by a red shift f3/f2 of equal amount.

 

Thus the IEEE paper acknowledges that it has not arrived at its equation (14) in any well-defined way, it simply says vaguely that "one could argue" that equation (14) is the appropriate shift for the transition from disk 2 to the receiver. Contrary to these remarks, there is actually no ambiguity in special relativity about this. One simply applies the relativistic Doppler formula (our equation (3)) with the appropriate values for the velocity and angle, taking aberration into account.

 

The IEEE paper then goes on to make the following curious remark:

 

On the other hand, the principle of relativity would call for another blue shift at the pickup or, if a red shift would occur for f1/f0, then a red shift should also occur for f3/f2.

 

Thus the IEEE paper is claiming uncertainty even as to the first transition, from the transmitter to the first antenna, arguing that the principle of relativity somehow renders the predictions ambiguous (obviously insinuating that special relativity is logically inconsistent). As we’ve seen, this is not the case. None of the transitions are ambiguous. (Ironically, the only one of the three equations (12), (13) and (14) that the IEEE paper treats as unambiguous is (13), which is actually the only equation that is wrong.)

 

The analysis presented in the IEEE paper of 2003 was criticized in a subsequent issue of the same journal. A comment in the Feb 2010 issue (vol 59, No. 2) correctly identified the fact that equation (13) of the original IEEE paper was erroneous. However, the explanation given in the Comment was frankly absurd, since it claimed that there is never any Doppler shift for light reflected off a moving mirror in any direction. This is obviously not true. Like the original IEEE paper, the 2010 Comment failed to correctly account for the aberration of angles relative to the frames of the transmitter, relays, and receiver, and the Comment erred even further by conflating the angle of incidence and the angle of reflection. To compound the confusion still more, the IEEE published along with the Comment a “Rebuttal”, which essentially just repeated the egregious errors and misunderstandings of the 2003 paper. All this over a question that would make an easy homework exercise for a freshman physics class!

 

The readers of the IEEE Transactions are left with the claim that special relativity has been falsified, along with the distinct impression that special relativity is logically incoherent (since the paper argues that special relativity can equally well predict a red shift and a blue shift for each transition, and since the “defense” of special relativity in the Comment was incoherent gibberish). As explained above, these assertions are nonsense, based on nothing but ignorance and misunderstanding of one of the most fundamental and elementary cornerstones of modern science. For this nonsense to appear in an IEEE journal is deplorable.

 

Incidentally, I sent an email to the editor of the IEEE Transactions on Instrumentation and Measurement (who is described as a specialist in electromagnetics), pointing out the errors in both the 2003 paper and the 2010 Comment and Rebuttal, and suggesting that it would be useful to print a correction. Naively imagining that he would welcome the clarification, I outlined for him the simple and straightforward derivation presented above. He responded immediately and with admirable succinctness:

 

Thanks for the e-mail.  This issue was looked into in detail after external independent review of the paper and the comment.  I appreciate your interest in this matter.

 

Evidently, rather than recognizing the 2010 Comment and Rebuttal as incoherent gibberish, both the editor and an “external independent reviewer” actually consider them to be a suitable resolution of the issue raised in the 2003 paper. Also the editor apparently finds the simple derivation (above) to be either incomprehensible or wrong. It’s sad that the editor and some “external independent reviewer” were both incapable of discerning the utter nonsense that they approved for publication. One can only hope the IEEE will improve its standards, and stop publishing obvious falsehoods and promoting ignorance and misunderstanding of basic physical principles.

 

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