The proposition in this short article is that accepted science and maths supports an interpretation of quantum states which is coherent but different to any other current model, and which is more consistent with accepted data. It may also have some interesting implications for our understanding of time.

Probability amplitudes are fundamental

Probability amplitudes are well understood as the outcomes of quantum calculations. What they mean however varies wildly with interpretation. They are mathematical objects; they are the basis of superposition; they form guiding waves; they form objects; they define observers; they define particles; they are just calculations. There is no consensus, and many physicists would agree that no single interpretation stands without difficulty or qualification or is entirely satisfactory. 

In this alternative approach, probability amplitudes are treated differently. They are fundamental, rather than particles or fields conceived classically. In terms of maths and physics, this is not a contentious idea. All mathematical and experimental data remains untouched. Quantum physics is widely acknowledged to be fundamentally probabilistic. I am simply putting this upfront. Nothing to see here perhaps. It is the next step which might raise some eyebrows.

The probability amplitude is the most primitive element in the theory, from which states, particles, and temporal order are derived. 

This is the logical conclusion, given that QP is probabilistic, and it helps to establish a ‘missing link’ between science and interpretation. Why? Because if quanta are groups of probabilities, it would be these which have wavelengths, phases and frequencies. These possible objects are not objects themselves. Although this may seem strange, it would be stranger still if they were like children in a playground grown mysteriously to regularly spaced intervals in height. In other words, it is not objects that are phased in waves but the probabilities of their position or momentum. The reification implicit in the naming of things like ‘particle’, ‘observation’, ‘angular momentum’ and ‘spin’ may be highly misleading, since these names refer to quantum states, not objects. None of these apparently ‘objective’ terms are based on observed phenomena and all are in this respect metaphorical.

Phase evolution is the primitive temporal process.

‘Quanta’ are groups of probability  amplitudes and it is probability amplitude that evolves as a wave, or as multiple series of waves, over time. The calculated frequency of the probability amplitude of a particle is neither particle nor wave. We are driven to such transubstantiations by habits of arrangement of whatever we consider to exist into preconceived physical, ‘objective’ ideas.  Until we abandon these, it is may be difficult to make any conceptual and theoretical progress, and this in turn delays and obstructs the process of scientific development. 

An interesting aspect of this interpretation relates to the interpretation of time.

In the evolution of time, we cannot trace a particle in any temporal space. Instead, we treat the probability amplitudes we have calculated as the frequency trace of the probable particle, and the wavelength gives the temporal span of possibility. These traces are understood accumulatively. At quantum scale, an apparently single and instantaneous event may be a lengthy temporal process. While it appears to be a smooth process, it is  too brief to reach any secure conclusion by measurement. Calculation suggests it may be quantised.

This may offer a more useful connection between probability amplitudes, particle physics, and the macroscopic universe. Phases in probability may readily be scaled to both. A dualistic view of wave and particle does not allow this, but if probability is fundamental such dualism is not required.

There are no balls behind the goal.

There is a simple way to understand the relationship of accumulated probability and objects. During the recent world cup it was common to see penalty spot kick charts for various penalty takers. Goalkeepers use these to detect penalty placement. The charts show ball placement in distinctive patterns around the goalkeeper and generally record the outcomes of dozens of penalties. However, as the goalkeeper studies and then remembers these, a useful view is formed via accumulation and collection of data. While the events have present and future meaning they have happened in the past. It is the accumulation that is present, not the shots. We take this for granted. However many shots are represented on the charts, nobody goes looking for hundreds of balls behind the goal. In the same way, there are no actual particles in the slit experiment. The illusion of objective presence is simply the accumulation of data, and the objects that left traces are, at quantum scale, vanished to the distant past.

We may conclude that observable events are discrete records of completed quantum processes.

Macroscopic time emerges statistically from the accumulation of those records.

We do not directly observe quantum granularity. We infer it from discrete interactions and measurement outcomes. This is mainstream physics.

We do not directly observe temporal granularity either. Whether time itself is granular is an open question. Some approaches to quantum gravity suggest it may be, others do not. At present there is no experimental evidence that time is fundamentally discrete, but there is no evidence that it is not.

This proposal goes beyond both of these, by suggesting that the appearance of continuous time is an emergent consequence of a deeper amplitude structure.

The stands are empty and the spectators long gone.