Superluminal Velocity To Time Machines ?

Various experiments have shown superluminal group and signal velocities recently. Experiments were essentials carried out with microwave tunnelling [1], with frustrated total internal reflection [2], and with gain-assisted anomalous dispersion [3]. According to text books a superluminal signal velocity violates Einstein causality implying that cause and effect can be changed and time machines known from science fiction could be constructed. This naive analysis, however, assumes a signal to be a point in the time dimension neglecting its finite duration. A signal is not presented by a point nor by its front, but by its total length. On the other hand a signal energy is finite thus its frequency band is limited, the latter is a fundamental physical property in consequence of field quantiza-tion with quantum hν. All superluminal experiments have been carried out with rather narrow frequency bands. The narrow band width is a condition sine qua non to avoid pulse reshaping of the signal due to the dispersion relation of the tunnelling barrier or of the excited gas, respectively [4]. In consequence of the narrow frequency band width the time duration of the signal is long so that causality is preserved. However, superluminal signal velocity shortens the otherwise luminal time span between cause and effect. Can a signal travel faster than light? If this happens, would it really violate the principle of causality stating that cause precedes effect [5, 6]? The latter statement has been widely assumed as a matter of fact. It has been shown according to the theory of special relativity that a signal velocity faster than light allows to change the past. The line of arguments how to manipulate the past in this case is illustrated in Fig. 1 [6, 7]. There are two frames of reference displayed. In the first one at the time t = 0 lottery numbers are presented, whereas at t =-10 ps the counters were closed. Mary (A) sends the lottery numbers to her friend Susan (B) with a signal velocity twice the velocity of light. Susan