As anybody who has studied Quantum Optics knows, correlation functions play a very large role in our understanding of the behavior of light. Roughly speaking, the correlation function tells you how likely you are to detect a second photon some short time after detecting one photon from some source. This shows up in the famous Hanbury Brown and Twiss experiment, and definitive proof of the existence of photons was provided in 1977 when Kimble, Dagenais and Mandel demonstrated photon anti-bunching, where the correlation function goes to zero for short times.
Correlation functions are a powerful technique for the study of physical systems. With that in mind, let us apply the technique to the problem of a hungry baby, SteelyKid for example. Here is a histogram of the intervals between feedings, as recorded over the three weeks since SteelyKid’s birth:
(Error bars represent 1-σ statistical uncertainties.)
We can immediately see from this graph that, as in the Kimble, Dagenais, and Mandel experiment, the probability of a second feeding occurring very shortly after the first is extremely low. This is unambiguous evidence of the quantization of baby-feeding– having eaten once, SteelyKid is unable to eat again until after a digestion period has passed. There is a peak in the distribution of feeding times suggesting an average digestion period of approximately 90 minutes.
The other striking feature of this figure is the appearance of a second peak in the time distribution, between 150 and 210 minutes. This is most likely an artifact caused by medical advice: in the first two weeks after SteelyKid’s birth, we were advised to feed her at least once every three hours (180 minutes), and to wake her up for feeding if necessary. This creates a large increase in the number of feedings right around 180 minutes, and a corresponding depletion in the longer-time tail of the distribution.
We can see this more clearly in the second figure, where we separate the data into feedings from the first two weeks, and feedings from the period after the pediatrician appointment where we were told to switch to feeding on demand:
The large excess peak due to waking her up to eat is clearly visible in the early data, but much less pronounced in the later period data. Interestingly, there is still a peak in the number of feedings between 180 and 210 minutes (at the 2.2-σ level). It is not clear whether this represents a residual effect of the earlier pattern, a statistical artifact, or the existence of a new feeding-time resonance that is not predicted in the Standard Model of Baby Feeding.
More data will be required to answer these questions. Additionally, we hope that the release of these results will spur renewed interest in ab initio calculations of feeding-time distributions, to compare with the data that we anticipate in the coming months, when the Large Infant Collider begins operation.