65
Physicists Superheated Gold to Hotter Than the Sun's Surface and Disproved a 40-Year-Old Idea
(www.smithsonianmag.com)
this post was submitted on 02 Aug 2025
65 points (98.5% liked)
Science
5126 readers
105 users here now
General discussions about "science" itself
Be sure to also check out these other Fediverse science communities:
founded 3 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
Whether it's energy-time or position-momentum, the uncertainty principle is just a consequence of two variables being linked via Fourier transform. So position and wave-vector therefore position and momentum, ans time and pulse and therefore time and energy. Sure, it only has consequences when you're looking at time uncertainties and probabilistic durations, which is less common than space distributions. And sure it also happens in classical optics, that's where all of this comes from. And I agree that "quantum fluctuations" is often a weird misleading term to talk about uncertainties. But I'm not sure how you end up with "no link to the uncertainty principle"? It's literally the same relation between intervals in direct or Fourier space.
Okay, explain to me what the standard deviation of time is. I will pre-empt nonsense, just "time", not just time in reference to the duration of a finite process. It must be abstract and universal, like the position-momentum case.
You know maybe I'm starting to understand your point.
On the surface your question is easy to answer: clock uncertainties are a thing, and are very analogous to space-position uncertainty. Also time-of-arrival is a question that you can pretty much always ask, and it's precisely the "uncertain t for given x" to the usual "uncertain x for given t". Conversely you don't have the standard deviation of "just space": as universal as it is, Delta x is always incarnated as some well-defined space variable in each setting.
But it's also true that clock and time-of-arrival uncertainties are not what's usually meant in the time-energy relation: in general it's a mean duration (rather than a standard deviation) linked to a spectral width. And it does make sense, because quantum mechanics are all about probability densities in space propagating in a well-parametrized time. So Fourier on space=>uncertainties while Fourier on time=>actual duration/frequency. And if you go deeper than that, I'm used to thinking of the uncertainty principle in terms of Fourier because of the usual Delta x Delta p > 1/2 formulation, but for the full-blown Heisenberg-y formula you need operators, and you don't have a generally defined time operator of the standard QM because of Pauli's argument.
But that's a whole thing in and of itself, because now I'm wondering about time of arrival operators, quantum clocks and their observables, and is Pauli's argument as solid as that since people do be defining time operators now and it's quite fun, so thanks for that.