[hammock]

Traditional calculus is not well-suited to describing the behavior of particles at extremely small scales because it leads to infinite values in calculations: Traditional calculus is based on real numbers, which are continuous and can take on any value. However, at the subatomic level, particles behave more like waves than like particles with a definite position, and the value of some physical quantities, like energy, can become infinite at certain points, which makes the equations used in traditional calculus break down.

To overcome the issues with traditional calculus, alien calculus involves replacing the standard real numbers used in calculus with "fuzzy numbers" that represent probabilities instead of definite values. These fuzzy numbers allow the equations to describe the behavior of particles more accurately because they capture the uncertainty inherent in subatomic systems.

Alien calculus calculates the probability that particles will be in certain positions or states, rather than trying to determine their exact positions or states. This is because particles at the subatomic level are constantly in motion and their position or state cannot be precisely determined at any given moment. By using probabilities, alien calculus can provide a more accurate description of the behavior of particles at this level.

[rolenthedeep]

Wait, is this new? This is exactly how I'd assumed quantum calculations worked already

[l33tman]

Yeah the above comment and it's reply is exactly what I'd assume GPT-4 would reply if asked what "alien calculus" is ;) (the linked article isn't about this at all, it's about technical details of perturbation series in mathematics as they relate to non-perturbative treatments)

[hammock]

You are correct that the probabilistic nature of quantum mechanics has been known for many years. However, what is new in the approach of "alien calculus" is the use of a mathematical framework that replaces traditional calculus with a more probabilistic approach to avoid infinities and better describe the behavior of particles at the subatomic level. Alien calculus is a novel approach that aims to improve upon traditional methods and has shown promise in resolving some of the issues that arise in particle physics calculations

[mathattack]

Thanks! Would you be aware of any kid-friendly sources that could be used to inspire students? Of the “We love calculus because it explains how a ball moves. Now let me show you something really cool!”

[hammock]

There is a nice discussion of quantum mechanics here - note you have to click to "reveal all steps" at the very bottom - https://mathigon.org/course/probability/randomness

Also check out https://ed.ted.com/search?qs=quantum+mechanics

[mathattack]

Awesome - thanks!