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In deriving that the space-time transformation between two inertial frames is linear, one commonly relies on the premises that any inertial frame has physical properties invariant under space-time translations. We present a different derivation of linearity which is based on the principle of relativity. In fact, we show that it is possible to circumvent the discussion of linearity in deriving the space-time transformation between inertial frames. Following the principle of relativity, it is inevitable that the only transformation compatible with the principle of relativity is the Generalized Lorentz Transformation (GLT which is linear). Distinct from other derivations, we prove the existence of a universal speed limit by examining the continuity and monotonicity of the velocity transformation function. In our derivation, we do not explicitly employ the translational invariance of inertial frames as the logical starting point. Neither do we invoke the constant speed of light as a fundamental postulate. The new derivation highlights the pivotal role of the principle of relativity in logically establishing the theory of special relativity.

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From the EPR prediction, the nonlocality and entangled state become the frontline in modern physics. First, we introduce briefly some researches on EPR, which include Santilli's studies. Next, based on the generalized Lorentz transformation (GLT) with superluminal in the complete special relativity, we propose that the entangled states must obey GLT because of they possess the superluminal and some characters as the spacelike vectors. Further, it changes the phase of the entangled field, whose phase particle (phason) has some characters and corresponding equations. It is tachyon, and assume that it is similar to photon and J=1 and m=0 or mass is very small as similar neutrino, and may show the action at a distance. We research that this field as wave has some characters. Third, we discuss the superluminal quantum communication by a pair of entangled states is generated on both positions, or by preparing and transmitting a pair of entangled instruments, so the superluminal quantum communication. Manipulation for one position can pass the same message or information to the other, so we may implement the superluminal communication. Finally, assume that the entangled field has a similar magnetic theory, which may be a quantum cosmic field, or be the extensive quantum theory, or God or the Buddha-fields and so on. These are all macroscopic fields, which correspond to de Broglie-Bohm nonlinear "hidden variable" theory, but it is microscopic. In a word, study and application of nonlocality and entangled field have important scientific and social significance. [ABSTRACT FROM AUTHOR]

In deriving that the space-time transformation between two inertial frames is linear, one commonly relies on the premises that any inertial frame has physical properties invariant under space-time translations. We present a different derivation of linearity which is based on the principle of relativity. In fact, we show that it is possible to circumvent the discussion of linearity in deriving the space-time transformation between inertial frames. Following the principle of relativity, it is inevitable that the only transformation compatible with the principle of relativity is the Generalized Lorentz Transformation (GLT which is linear). Distinct from other derivations, we prove the existence of a universal speed limit by examining the continuity and monotonicity of the velocity transformation function. In our derivation, we do not explicitly employ the translational invariance of inertial frames as the logical starting point. Neither do we invoke the constant speed of light as a fundamental postulate. The new derivation highlights the pivotal role of the principle of relativity in logically establishing the theory of special relativity. [ABSTRACT FROM AUTHOR]