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A new way to get Hubble-like redshifts

  1. Jul 21, 2008 #1
    Some time ago, in a couple of Usenix newsgroups, I had discussed early indications of a hitherto unnoticed interaction between any nonzero drift in spectrometers and the phase spectrum of received light. The intuition, shared by at least one referee, was that the total path delay from the source, necessary for causality, itself represents different phase offsets k.r in proportion to the wave number k. At large r, the k.r offset would dominate over any starting phase differences at the source, hence the gradient of phase carries the absolute source distance information, even though no individual tone in the received spectrum bears that information.

    The connection to drift is that if the spectrometer scale happens to be drifting, i.e. if either the grating intervals are changing or the photodetector array is moving relative to the diffraction pattern, then the successive E (or B) field values arriving at any given detector element cannot all come from any one component tone, since as the tone's fringe move past the element, the next tone's fringe takes its place at the element. Therefore, the detector response must be driven by a succession of E (or B) field values from successive component tones, producing a chirp. But recall that the successive tones not just differ in frequency, but arrive with different phase offsets from the source, hence each successive frequency in the chirp has an additional phase offset, and the offsets themselves change at the rate dk/dt x d/dk(kr) = r dk/dt. But a changing phase offset is a frequency shift. Hence each instantaneous tone in the observed chirp would have been shifted by r.dk/dt.

    Why is this be more than just signal processing and of general physics interest? Two reasons.

    First, the shifts are proportional to source distances r , times the drift rate dk/dt. Hence, even a "geologically" slow drift, say due to creep which is so slow we don't currently worry about it in any ground or space spectrometer design, will lead to large shifts for sufficiently far sources. For cosmological sources say 10+ Gyr away, the normalized dk/dt to worry about would be 1/(10 Gyr) = 3.18 x 10-18 per second. This is small enough to well within range of a systematic residual creep in all past and current instruments, but is also the same order of magnitude as the Hubble constant! (This aspect has been explored in great depth, as summarized in the paper.)

    Second, the mechanism would allow any receiver to selectively listen to any specific (narrow band) source regardless of any number of other non-colocated sources transmitting on the same frequencies. This means we wouldn't need modulation and code division methods to separate received signals, and would no longer need to care about FCC spectrum allocations and spectrum auctions around the world... So this discovery is about a new form of physical information that fundamentally improves over signal processing and communication theory (as discussed in two leading communication conferences in 2005).

    In a poster at the SPIE Optics+Photonics/Nature of Light II conference in San Diego, I will be graphically demonstrating a complementary result that we can achieve exactly the same result by applying an exponential chirp transform, instead of varying a front-end diffractive frequency selection. Chirp transforms have been used in radar and image processing for years, but almost always in chirp-dechirp pairs, which cancel out the effect when applied to received waves.

    The peer-reviewed Proceedings paper, giving a rigorous treatment of this result for the first time, is available for private viewing at http://www.inspiredresearch.com/conf/spie2008.pdf , and the poster is http://www.inspiredresearch.com/conf/spie2008-poster.pdf . A journal paper is now being planned and would likely benefit from viewers' comments.

    thanks in advance,
  2. jcsd
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