General Uncertainty Relation And Its Applications

First of all, the generalized position-momentum uncertainty relation,which leads to a finite minimum uncertainty of position, is introduced.Accordingly, the density of quantum states needs to be modified. This isbelieved to have a very broad effect on our current knowledge of variousproblems. In the specific example of the blackbody radiation, we havefound that the Stephan-Boltzmann law needs to be modified at very hightemperatures compared with the Planck temperature, i.e., the energy of theradiation field as a whole will be proportional to the temperature.Second, the generalized uncertainty relation is applied to thecalculation of the entropy as well. The entropy is calculated by theimproved brick-wall method due to the generalized uncertainty relation.The entropy bound of this system not only includes the contribution of theblack hole horizon, but also includes the contribution of the cosmologicalhorizon, which is consistent with what people anticipate. It is found thatthere is an internal relation between the event horizon and the entropy; itis further revealed that the black hole entropy is an entropy which belongsto event horizon and is a kind of quantum effect. It is also apparent thatthe cut-off in brick-wall model is something related to the quantum theoryof gravity.Last but not least, we also calculate the red-shift of light frequency for gravitation by using the energy-time of the uncertainty relation ofquantum mechanical, It is shown that the result of the red-shift of lightfrequency for gravitation obtained by this method accords with the oneexpected by some people.