Over the last century, the quest to formulate physics to account for Reality has attracted a large number of theoreticians to propose various models that have tended toward a growing level of abstractness. While space and time have been largely recognized as the four fundamental dimensions that make our perceived reality, their completeness has been challenged either by positing hidden dimensions, or by exploring the possibility that spacetime itself is an emergent property of a more fundamental physical structure.
One quantity that has not entered this exploration is frequency---a measure of how often something repeats. Although it is featured in numerous physical contexts, it is normally implied that it is a mere parameter that is determined by the boundary conditions, or that it contains the same information as the time, period, wavelength, or energyâall supporting the notion that frequency is fully dependent on the other dimensions. In contrast, in psychophysics of vision, hearing, and touch, frequency is a quantity that appears independent, so that both its input and output are not directly dependent on the perception of space and time. Additionally, many important engineering applications treat frequency as a variable rather than as a parameter that is constrained alongside time.
This work explores the various conventions with respect to frequency in the physical, mathematical, and engineering literatures. It further scrutinizes frequency against the standard dimensions of space and time along nine properties that may be deemed universal. While a case for frequency being its own dimension can be made in different situations, a more general theorem is proven that states that only one of these three propositions can be simultaneously true:
1. Time is not a fundamental, obligatory dimension of Reality.
2. The universe is fully deterministic with total knowledge of past and future.
3. Frequency is a fundamental dimension of Reality.
The validity of this counterintuitive theorem is demonstrated using examples of epistemological nature with growing complexity and diminishing generality, which deal with problems of traffic flow, acoustic measurements, radio transmission, and psycholinguistics. It is proposed that if the incompatibility of the three propositions (or modes) is encountered within the analysis of any one system, there may be a discontinuity associated with the transition between modes. This is explored within the measurement problem and nonlocality of quantum mechanics, where it is suggested that these strange quantum effects may both be corollaries of the discontinuity between the modes of Reality. It is further proposed that the frequency dimension, should it exist, is nonlocal in some conditions and may have an ontological role within Reality, being neither in space nor in time. Dwelling on the interrelationship between determinism, time, and frequency, further metaphysical corollaries are explored in the appendices, including an emergent solution for the problem of foreknowledge, and by association, of the paradox of free will.