{'fraction_non_alphanumeric': 0.014394580863674851, 'fraction_numerical': 0.000846740050804403, 'mean_word_length': 5.061538461538461, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Relativistic properties for hybrid systems of particles containing photons and massive particles

The use of relativistic frame invariants is very well established, especially when it comes to the energy-momentum. Most traditional treatments use this particular invariant in order to calculate the “equivalent mass” of a system or, the “mass added to a system”. In the following paper we will take a significant departure by avoiding the notion of mass altogether and by using frame-variant quantities like total energy E and momentum p in order to characterize relativistic systems of particles. The systems under evaluations are a most general hybrid made up of both massive particles and photons. We will show the effects of adding photons to a system of massive particles. The new approach is extremely important in applications like particle accelerators where we can only work with directly measurable quantities, the energy E and the momentum p. In paragraph 4 we will demonstrate also how the new approach allows us to calculate the effect of injecting electromagnetic energy in the form of photons in a particle condensate, a very important application for plasma physics.