One idea is to look at light arriving at the Earth from distant gamma-ray bursts. If momentum space is curved in a particular way that mathematicians refer to as "non-metric", then a high-energy photon in the gamma-ray burst should arrive at our telescope a little later than a lower-energy photon from the same burst, despite the two being emitted at the same time.
Just that phenomenon has already been seen, starting with some unusual observations made by a telescope in the Canary Islands in 2005 (New Scientist, 15 August 2009, p 29)Movie Camera. The effect has since been confirmed by NASA's Fermi gamma-ray space telescope, which has been collecting light from cosmic explosions since it launched in 2008. "The Fermi data show that it is an undeniable experimental fact that there is a correlation between arrival time and energy - high-energy photons arrive later than low-energy photons," says Amelino-Camelia. (emphasis mine)
I wonder if any of the following might be possible, and if they have been considered by SCIENCE:
1. Our brains are not flawless reality-perceiving machines.
2. We might someday confront questions that we are incapable of comprehending.
I have seriously considered the possibility that I am in fact a Boltzmann Brain, as have most serious cosmologists I know, so the argument that physicists are no[t] open-minded about the possibilities [. . .]
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