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Negative temperature is based on the Kelvin scale and the condition dU>0 and dS<0. Conversely, there is also negative temperature for dU<0 and dS>0. When the derivation of negative temperature is examined, it necessarily requires a decrease in entropy. The concept of negative temperature contradicts the usual meaning of "temperature", as well as contradicting some basic concepts of physics and mathematics. Negative temperatures can be shown to occur only in a system which is not in thermodynamic equilibrium. It is here proposed that the decrease of entropy is possible due to magnified fluctuations and internal interactions in some isolated systems. Further, a necessary and sufficient condition for the decrease of entropy is discussed quantitatively. In addition, some possible tests for the decrease of entropy in isolated systems are proposed. They should be confirmed by many stable states in nature.

We researched the fractal-dimensional and complex dimensional mathematics and the physics that may be represented thereby. From this the fractal relativity is discussed, which connects with self-similarity of the Universe and an extended quantum theory. The space dimension has been extended from real number to super-real and complex number. Combining the quaternion, etc., the high dimensional time ict -> ic₁t₁ + ic₂t₂ + ic₃t₃ is introduced. The arrow of time and irreversibility of processes are derived. Then the fractal dimensional time is obtained, and space and time possess completely symmetry. The higher dimensional, fractal, complex and super-complex space-time theory covering all might be constructed preliminarily. We propose a generalized Noether?s theorem, and irreversibility of time should correspond to non-conservation of a certain quantity. Possible reversibility of time and possible decrease of entropy are discussed. Finally, we obtain the quantitative relations between energy-mass and space-time, which is consistent with the space-time uncertainty relation in string theory.

We introduce a principle of equivalence for the electromagnetic field: A non-inertial system with an acceleration is equivalent to a certain electromagnetic field, in which the ratio of charge to mass is the same. From this principle can be derived an electromagnetic general relativity theory (GRT) whose formulations are completely analogous to Einstein's GRT. In the electromagnetic case, the field is regarded as a type of curved space-time for charged bodies, where space-time is separated into many layers, the curvatures of which are different for different ratios of charge to mass. In a general case, electrodynamics can be obtained from this theory. But its high-order approximation will deviate from the present electromagnetic theory. Therefore, we discuss the four possible tests for this theory and some notable problems. Finally, the most universal principle of extended equivalence and the extended GRT are proposed.

Quantum mechanics implies uncertainty relations of velocity. So as a velocity, the speed of light will be uncertain. The speed of light should have statistical fluctuations within a small space-time and at high energy. This result contradicts the constancy of vacuum light speed assumed in relativity theory. Some new theoretical researches and new experimental results are discussed briefly. We believe that relativity and quantum theory will be able to be unified completely only after both are further developed.