May 24, 2012

Energy Time Uncertainty Principle

Some random thoughts...
The energy-time uncertainty principle (delta Energy multiplied by delta time equals Planck's constant) can be derived from the bandwidth theorem: frequency multiplied by delta time is about equal to one.

E = hf
f * delta t > 1
(E/h) * delta t > 1
delta E * delta t > h

The physical interpretation of the time-energy uncertainty principle is often cloudy. It's usually interpreted as allowing particle pair production to "borrow" energy from the quantum vacuum for a certain limited period of time. Here's another interpretation.

The bandwidth theorem speaks to the limitation of how fast you can transmit information given a particular bandwidth. Perhaps the time-energy uncertainty principle limits how quickly you can transmit a given photon

delta E delta t > h
delta t > h / delta E

The curious thing here is that the larger the energy of the photon, the less time it takes to transmit? But no matter, this still provides a lower limit on the amount of time it takes to transmit photons of a given energy. This could induce an interesting quantization effect: if the photon can't be emitted within this period of time, or the state necessary to emit a photon can't be maintained for this period of time, then the photon will not be emitted and the energy will not be transferred.

This could have implications for the gap between the quantum vacuum energy and the cosmological constant. (The disconnect between the magnitude of the two is something like 10^120.) Perhaps the bandwidth theorem provides a gating or screening effect on the raw vacuum energy such that only a small fraction of it can be transmitted across measurable space within a certain limited time.

Posted by todd at May 24, 2012 10:02 AM