Now, we can use the de Broglie relation (λ = h/p) to relate the uncertainty about the position to the spread in the wavelengths (and, hence, the frequencies) of the component waves: In turn, the length of that wave-train is determined by the spread in the frequencies of the component waves that make up that wave-train, as illustrated below. First, note that the uncertainty about the position (Δx) of our ‘wavicle’ (let’s say an electron) is to be related to the length of the (complex-valued) wave-train that represents the ‘particle’ (or ‘wavicle’ if you prefer that term) in space (and in time). I found one particularly appealing explanation in a small booklet that I bought–long time ago– in Berlin: the dtv-Atlas zur Atomphysik.
Δt = h equation? Indeed, we can sort of imagine what ΔE stands for, but what about Δt? It must also be some uncertainty: about time obviously–but what time are we talking about?.These pairs of variables (position and momentum, and energy and time) are so-called conjugate variables. But there is also a similar relationship between time and energy: Indeed, most (if not all) experiments illustrating the Uncertainty Principle (such as the double-slit experiment with electrons for example) focus on the position (x) and momentum (p) variables: Δx This post will focus on the Uncertainty Principle for time and energy. Let me share them with you in this and my next posts. As I’ve read some more in the meanwhile, I think I sort of ‘get’ these points somewhat better now. In all of my posts on the Uncertainty Principle, I left a few points open or rather vague, and that was usually because I didn’t have a clear understanding of them. I might review them one day, but I currently don’t have the time or energy for it.
I keep blog posts like these to see where I came from. Hence, we recommend you read our recent papers. Pre-script (dated 26 June 2020): My views on the nature of the concept of uncertainty in the context of quantum mechanics has evolved significantly as a result of my progression towards a more complete realist (classical) interpretation of quantum physics.
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