This thread is intended to provide a space for 'crazy' ideas. Ideas that spontaneously come to mind (and feel great), ideas you long wanted to tell but never found the place and time for and also for ideas you think should be obvious and simple - but nobody ever mentions them.
This thread itself is such an idea. Or rather the tangent of such an idea which I post below as a seed for this thread.
Rules for this thread:
- Each crazy idea goes into its own top level comment and may be commented there.
- Voting should be based primarily on how original the idea is.
- Meta discussion of the thread should go to the top level comment intended for that purpose.
If this should become a regular thread I suggest the following :
- Use "Crazy Ideas Thread" in the title.
- Copy the rules.
- Add the tag "crazy_idea".
- Create a top-level comment saying 'Discussion of this thread goes here; all other top-level comments should be ideas or similar'
- Add a second top-level comment with an initial crazy idea to start participation.
Noise is certainly a problem, but the biggest problem for any sort of atomic modelling is that you quickly run into an n-body problem. Each one of of n electrons in an atom interacts with every other electron in that atom and so to describe the behavior of each electron you end up with a set of 70 something coupled differential equations. As a consequence, even if you just want a good approximation of the wavefunction, you have to search through a 3n dimensional Hilbert space and even with a preponderance of good experimental data there's not really a good way to get around the curse of dimensionality.
Am I understanding the relevance of the curse of dimensionality to this correctly: Generally, our goal is to find a simple pattern in some high-dimensional data. However, due to the high dimensionality there are exponentially many possible data points and, practically, we can only observe a very small fraction of that, so curse is that we are often left with an immense list of candidates for the true pattern. All we can do is to limit this list of candidates with certain heuristic priors, for example that the true pattern is a smooth, compact manifold (that worked well e.g. for relativity and machine learning, but for example quantum mechanics looks more like that the true pattern is not smooth but consists of individual particles).