Quote:
Originally Posted by lyndonashmore
It clearly states that photons of longer wavelength travel faster than those of shorter ones.
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The blog does say that. However, the paper that the blog links too does not. The moral of this story is: Go Beyond the Blog (GBB).
See
Probing Quantum Gravity using Photons from a Mkn 501 Flare Observed by MAGIC; J. Albert,
et al., for the
MAGIC collaboration, which has been submitted to
Physical Review Letters.
Abstract: We use the timing of photons observed by the MAGIC gamma-ray telescope during a flare of the active galaxy Markarian 501 to probe a vacuum refractive index ~ 1-(E/MQGn)n, n = 1,2, that might be induced by quantum gravity. The peaking of the flare is found to maximize for quantum-gravity mass scales MQG1 ~ 0.4x1018 GeV or MQG2 ~ 0.6x1011 GeV, and we establish lower limits MQG1 > 0.26x1018 GeV or MQG2 > 0.39x1011 GeV at the 95% C.L. Monte Carlo studies confirm the MAGIC sensitivity to propagation effects at these levels. Thermal plasma effects in the source are negligible, but we cannot exclude the importance of some other source effect.
So, we see from the abstract that they "use the timing of photons", but we don't see how. Specfically, we see no reference here to the speed of light, or variations thereof. We do see quantum gravity mass scales. So what does it all mean? To GBB let us add GBA: Go Beyond the Abstract, and suffer the terrible indignity of actually reading the original paper.
On page 2 (upper right) we find this: "
The arrival time of each event is obtaind with high precision by signal extraction from a 300 MHz FADC, using a sliding window of fixed length (details can be found in [12]), and the absolute times are given by a rubidium clock and cross-checked with GPS." Here, [12] refers to
Signal Reconstruction for the MAGIC Telescope; J. Albert,
et al., 2006, and "
FADC" is a
flash analog-to-digital converter. So we know how the timing is done, but we don't yet know how it is used.
We find the answer to our question in the transition from page 2 to page 3. The individual event timing (that is, photon detections) are used to construct a
time-energy distribution, or in other words a pulse shape or flare shape. If the photons are travelling through a dispersive medium, then the flare shape will be smeared. So if we know the difference between the true flare shape and the real flare shape, we can derive the index of refraction of the medium, which in this case leads to constraints on quantum fluctuations that interfere with photon propagation, and smear the flare. But of course, there is a catch: What is the true flare shape? See page 3:
The true shape of the time profile at the source is not known, so we choose the following analysis strategy. In general, the fine time structure of any flare would be blurred by an energy-dependent effect on photon propagation. Conversely, one may correct for the effects of any given parametric model of photon dispersion, e.g., the linear or quadratic vacuum refractive index, by applying to each photon of energy E the appropriate time shift [7] corresponding to its propagation in a spatially flat universe: ... If the correct energy dependent QG shift is applied, the fine time structure of the emission profile is restored.
In the above I have omitted ( "...") the equations, go read the paper if you want to see the details. Now, continuing on from there ...
We implement this analysis strategy in two ways that yield similar results. In one analysis, the OG shift is varied so as to maximize the total energy in the most active part of the flare, and in the other analysis we use the shape of the flare as extracted from the original (untransformed) data. As we show below, these independent data analyses yield similar sensitivities to the possible QG scale.
So, for starters, we see that there is no attempt to derive a wavelength dependent speed of light through space. Therefore, it is just plain wrong to say that the paper demonstrates,
in any direct fashion, that the speed of light depends on the wavelength.
In fact, what the paper really does is to derive the mass scale of quantum gravity fluctuations in the space-time foam,
if the observed flare profile has been smeared by a dispersive medium. They do not know, and cannot know, if the observed profile was actually smeared, since the true source profile is always unknown.
One more point needs to be made. According to special relativity, the speed of light
in a vacuum is constant for all inertial observers. It is well known that the speed of light through anything that is not a vacuum is not constant. Chromatic abberations in refractor lenses, or rainbows from a prism, are both examples of the dispersive effects of glass. The speed of light through glass, or any other dispersive medium, depends on wavelength. The presence of quantum fluctuations means that the "vacuum" of space is not what Einstein envisioned, but is rather a dispersive medium with an index of refraction. Therefore, a wavelength dependent speed of light therein does not violate special relativity.