The only method for in vivo dose delivery verification in proton beam radiotherapy in clinical use today is positron emission tomography (PET) of the positron emitters produced in the patient during irradiation. PET imaging while the beam is on (so called beam-on PET) is an attractive option, providing the largest number of counts, the least biological washout and the fastest feedback. In this implementation, all nuclides, independent of their half-life, will contribute. As a first step towards assessing the relevance of short-lived nuclides (half-life shorter than that of (10)C, T1/2  =  19 s) for in vivo dose delivery verification using beam-on PET, we measured their production in the stopping of 55 MeV protons in water, carbon, phosphorus and calcium The most copiously produced short-lived nuclides and their production rates relative to the relevant long-lived nuclides are: (12)N (T1/2  =  11 ms) on carbon (9% of (11)C), (29)P (T1/2  =  4.1 s) on phosphorus (20% of (30)P) and (38m)K (T1/2  =  0.92 s) on calcium (113% of (38g)K). No short-lived nuclides are produced on oxygen. The number of decays integrated from the start of an irradiation as a function of time during the irradiation of PMMA and 4 tissue materials has been determined. For (carbon-rich) adipose tissue, (12)N dominates up to 70 s. On bone tissue, (12)N dominates over (15)O during the first 8-15 s (depending on carbon-to-oxygen ratio). The short-lived nuclides created on phosphorus and calcium provide 2.5 times more beam-on PET counts than the long-lived ones produced on these elements during a 70 s irradiation. From the estimated number of (12)N PET counts, we conclude that, for any tissue, (12)N PET imaging potentially provides equal to superior proton range information compared to prompt gamma imaging with an optimized knife-edge slit camera. The practical implementation of (12)N PET imaging is discussed.