Some well known and less known principles of equivalence are mass-energy, acceleration-gravity, temperature-energy, energy-frequency, spatial-temporal frequency equivalence. However, a more abstract principle of equivalence would be between probability and direction.

Probability is defined in mathematics as the extent to which an event is likely to occur, measured by the ratio of the number of occurrence of this event in question to all the total numbers of occurrence of all equally likely events. For example, a fair coin has two sides namely head and tail. Its total favorable events whenever a coin is tossed is 2 and the probability of head is ½, and of tail is also ½. The least favorable probability of the coin standing on its edge, although not completely impossible is for all likelihood zero. This is due to the existence of a center of gravity. Without the forces of gravity the coin can be oriented in zero gravity environments inside the Space Shuttle in all equally favorable direction along the line of sight. Since there are infinitely many favorable orientations the probability of a given orientation is practically zero signifying total randomness. The sum of all probabilities must always add to 1. On the other hand, the word ‘direction’ is not usually defined in physics. But it is one of two components defining a physical quantity called a vector, the other component being the magnitude. Contrary to popular belief, the direction and magnitude do change using different transformations between coordinate systems. These changes are partially dependent on the definition of a fundamental measure of length (e.g. Planck length). However, the direction component is measured in 3D by 3 angular dependences called direction cosines. By its definition, these cannot all be zero simultaneously. On the other hand, only one can take the value of 1, the rest become zeros. Furthermore, the sum of squares of these directional cosines is always 1. If there are infinitely many direction cosines of equal values as in an infinite dimension of space-time then none has the value of zero. But if one value becomes 1, then the rest become zeros by quantum entanglement. Clearly, the logical equivalence between probability and direction is shown.