ua nt - p h / 01 06 07 9 v 2 2 9 Ju l 2 00 1 Lorentz transformations of open systems

We consider open dynamical systems, subject to external interventions by agents that are not completely described by the theory (classical or quantal). These interventions are localized in regions that are relatively spacelike. Under these circumstances, no relativistic transformation law exists that relates the descriptions of the physical system by observers in relative motion. Still, physical laws are the same in all Lorentz frames. 1. A tale of two magicians Many years ago, some time in the twentieth century, there were two itinerant magicians (probably Gypsies) who went from village to village and entertained people with sleight of hand tricks. One of them called himself a quantum magician. He claimed to have supernatural power, to use supersymmetric particles and to send quantum information with superluminal velocity. The crowds were amazed by his supernatural legerdemain. A few days later, came the second magician. That one wanted to be an educator. He showed how to mimic quantum uncertainties with a mundane deck of cards [1]. He indeed repeated every trick of the quantum magician, and he then explained how to perform it, using only the ordinary laws of classical mechanics. People were dismayed. They realized that they had been fooled: in the preceding shows they had not seen anything supernatural. No one liked the second magician, and no one thanked him for his lessons. For instance, the quantum magician produced two spin 1 2 particles in a singlet state, far away from each other. His assistant Alice measured one of the spin components, and instantaneously the wave function collapsed all over spacetime. All over spacetime? This makes no sense. A wave function does not live in spacetime, but in a Hilbert space; and in a Hilbert space, the notion of velocity does not exist.