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In his recent article [arXiv:1604.04950], Adler questions the usefulness ofthe bound found in our experimental search for genuine effects of hyper-complexquantum mechanics [arXiv:1602.01624]. Our experiment was performed using ablack-box (instrumentalist) approach to generalized probabilistic theories;therefore, it does not assume a priori any particular underlying mechanism.From that point of view our experimental results do indeed place meaningfulbounds on possible effects of "post-quantum theories", including quaternionicquantum mechanics. In his article, Adler compares our experiment tonon-relativistic and M\"oller formal scattering theory within quaternionicquantum mechanics. With a particular set of assumptions, he finds thatquaternionic effects would likely not manifest themselves in general. Althoughthese assumptions are justified in the non-relativistic case, a propercalculation for relativistic particles is still missing. Here, we provide aconcrete relativistic example of Klein-Gordon scattering wherein thequaternionic effects persist. We note that when the Klein-Gordon equation isformulated using a Hamiltonian formalism it displays a so-called "indefinitemetric", a characteristic feature of relativistic quantum wave equations. InAdler's example this is directly forbidden by his assumptions, and thereforeour present example is not in contradiction to his work. In complex quantummechanics this problem of an indefinite metric is solved in secondquantization. Unfortunately, there is no known algorithm for canonical fieldquantization in quaternionic quantum mechanics.

Comment on Adler's "Does the Peres experiment using photons test for hyper-complex (quaternionic) quantum theories?"