When Hannes Alfvén gave his talk at Lindau, he was well known by the general public in Sweden as the eminent scientist and Nobel Laureate who was strongly opposed to nuclear power for environmental reasons. Among his scientific colleagues world-wide, he was at the same time known to be a strong opponent of the prevailing theory of the birth of the Universe, the Big Bang theory. In Lindau he spoke to an audience of students, young researchers and Nobel Laureates, most of whom probably whole-heartedly accepted the Big Bang theory. Alfvén had been active as a political speaker in Sweden for some years and it is interesting to hear him use an old rhetorical technique to try to make his point. He several times first gives praise to the “beautiful theory” or “wonderful model” and then almost immediately brings up his criticism: “What happened before?”, “But the Universe is not homogeneous”, etc. So does Alfvén have an alternative theory? Since the 1960’s he had been working on a model of the Universe originally put forward by Oskar Klein, professor of theoretical physics at Stockholm University. In this model the Universe contains equal amounts of matter and antimatter, so that some stars that we see are made of matter and others of antimatter. When matter meets antimatter a violent annihilation tales place and energy in the form of electromagnetic radiation is emitted (radio waves, light, X-rays, gamma-rays, etc). As a plasma physicist, Alfvén had been working on mechanisms that would keep matter and antimatter mostly separated from each other. At the end of his talk, he first brings up annihilation as a possible energy source driving the very energetic stellar objects named quasars. He then describes spacecrafts actually finding a cellular structure with cell boundaries having magnetic fields in different directions. Even if a few scientists are still working on the Klein and Alfvén model of the Universe, it is today looked upon as dated. But what will never be dated is Alfvén’s strong scientific plea never to accept “final solutions” because they are beautiful, but to always look out for new empirical evidence!