Lorentz invariance is such an important principle of fundamental physics that it should constantly be subjected to experimental scrutiny as well as theoretical questioning. Distant astrophysical sources of energetic photons with rapid time variations, such as active galactic nuclei (AGNs) and gamma-ray bursters (GRBs), provide ideal experimental opportunities for testing Lorentz invariance. The Cherenkov Telescope Array (CTA) is an excellent experimental tool for making such tests with sensitivities exceeding those possible using other detectors.
High-energy astrophysics and related aspects of cosmology are the breadand-butter science issues for the Čerenkov Telescope Array (CTA) [1], but some jam may be provided by measurements related to fundamental physics. One such possibility is to use transient high-energy emissions from distant astrophysical objects observed by CTA to probe the validity of Lorentz invariance.
From the quantum-mechanical point of view, the vacuum is the lowestenergy state of a physical system. It should be regarded as a medium that may have virtual structure, even if it is devoid of physical particles. As such, it may have non-trivial effects on particle propagation, even if Lorentz invariance is an underlying principle. This effect is, of course, familiar in the cases of photons propagating through plasmas at high temperatures or superconductors at low temperatures. Might high-energy photons of astrophysical origin exhibit analogous effects?
This possibility was raised in [2], where it was pointed out that distant, rapidly-varying astrophysical sources of high-energy γ rays could provide some of the most sensitive probes of some models of Lorentz invariance. This possibility was raised specifically in the context of heuristic models of ‘spacetime foam’, as inspired from string theory [3,4] in particular, according to which quantum-gravitational fluctuations in the vacuum could modify the propagation velocities of photons by amounts that increase with energy.
However, similar effects might arise in other theoretical frameworks [5,6,7,8,9,10], and the search for Lorentz violation may be pursued from a purely phenomenological point of view [11], prompted by, but not limited to, specific heuristic models. Lorentz invariance has been one of the foundations of modern physics for over a century. In the scientific spirit, it should not be regarded as a sacred principle that cannot be questioned, but rather as a theoretical dogma that should constantly be challenged by more sensitive experimental tests. As discussed in this article, CTA [1] will be uniquely well placed to carry these tests to the next level of sensitivity, potentially challenging some models of space-time foam.
The structure of this article is as follows. Section 2 surveys some physical motivations for the possibility that energetic photons might travel with speeds smaller than the classical speed of light, c. Section 3 reviews the current status of experimental probes of the propagation speeds of energetic particles, with particular attention to photons but also including other particles such as electrons and neutrinos. Section 4 then analyzes the opportunities available to CTA for extending these probes of Lorentz invariance, notably using rapidly-varying high-energy γ emissions from active galactic nuclei (AGNs) and gamma-ray bursters (GRBs). For comparison, Section 5 reviews the possible sensitivities of other future probes of Lorentz invariance, notably those using astrophysical and terrestrial neutrinos. Finally, Section 6 summarizes the prospects for probing Lorentz violation with CTA.
As already mentioned, the idea that the space-time vacuum should be regarded as a non-trivial medium that may have observable effects on particles propagating through it [2] is a very general one, much more general than the heuristic models of space-time foam [3,4] that spawned the suggestion. Nevertheless, we focus here on the motivations provided by such models, while mentioning some other suggestions.
It is a familiar aspect of quantum mechanics that in any physical system virtual fluctuations with excitation energies ∆E should arise on time scales ∆t ∼ ℏ/∆E. Wheeler extended this principle to gravity, arguing that quantum-gravitational fluctuations in the space-time continuum with ∆E ∼ M P (where M P ∼ 10 19 GeV is the Planck mass, defined by 1/ √ G N [12], where G N is the Newton constant of classical gravity) would endow it with a ‘foamy’ structure on time scales ∆t ∼ ℏ/M P (henceforth we use ’natural’ units in which ℏ, c ≡ 1). As a result of these quantum-gravitational fluctuations, Wheeler argued that space-time would no longer appear flat at distance scales ∆x ∼ 1/M P , possibly with the appearance of topological fluctuations as well as non-topological irregularities. A lattice is one example of an inhomogeneous space-time structure, but space-time foam would presumably have a more irregular, stochastic and aperiodic structure.
Heuristic models of space-time foam have been proposed, based on features present in string theory [3]. This exhibits a plethora of non-perturbative structures existing in various dimensions, notably D-branes and D-particles [13]. A common suggestion in this context is that our Universe is a three-dimensional membrane in a higher-dimensional ‘bulk’ space. If D-particles cross ‘our’ D-brane in this higher-dimensional space, they are perceived in our Universe as space-time events localized at specific locations x and specific times t.
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