Applications of interval computations usually assume that while we only know an interval containing the actual (unknown) value of a physical quantity, there is the exact value of this quantity, and that in principle, we can get more and more accurate estimates of this value. Physicists know, however, that, due to uncertainty principle, there are limitations on how accurately we can measure the values of physical quantities. One of the important principles of modern physics is operationalism -- that a physical theory should only use observable properties. This principle is behind most successes of the 20th century physics, starting with relativity theory (vs. un-observable aether) and quantum mechanics. From this viewpoint, it is desirable to avoid using un-measurable exact values and to modify the mathematical formalisms behind physical theories so that they explicitly only take objective uncertainty into account. In this paper, we describe how this can be done for objective interval uncertainty.