Time dispersion in bound states

Abstract

In quantum mechanics time is generally treated as a parameter rather than an observable. For instance wave functions are treated as extending in space, but not in time. But from relativity we expect time and space should be treated on the same basis. What are the effects if time is an observable? Are these effects observable with current technology? In earlier work we showed we should see effects in various high energy scattering processes. We here extend that work to include bound states. The critical advantage of working with bound states is that the predictions are significantly more definite, taking the predictions from testable to falsifiable. We estimate the time dispersion for hydrogen as $.177$ attoseconds, possibly below the current threshold for detection. But the time dispersion should scale as the $3/2$ power of the principle quantum number $n$. Rydberg atoms can have $n$ of order $100$, implying a boost by a factor of $1000$. This takes the the time dispersion to $177$ attoseconds, well within reach of current technology. There are a wide variety of experimental targets: any time-dependent processes should show effects. Falsification will be technically challenging (due to the short time scales) but immediate and unambiguous. Confirmation would have significant implications for attosecond physics, quantum computing and communications, quantum gravity, and the measurement problem. And would suggest practical uses in these areas as well as circuit design, high speed biochemistry, cryptography, fusion research, and any area involving change at attosecond time scales.

arXiv comment77 pages, 13 figures, earlier version presented as talk at International Assocation for Relativistic Dynamics 2024 conference at Aalto University, Finland. This version submitted to the associated conference proceedings

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