or, how to find the uncertainties on parameters in a fit — The likelihood of a data distribution can be seen as a function of the parameters of the function that describe data. For example, consider the following data One can write the logarithm of the likelihood function as

and their uncertainties — A convenient way to determine the parameters of a data distribution is to minimise their χ² using the least squares method. …

Stemming from the Bayes Theorem, the principle of Maximum Likelihood (ML) is a powerful tool to estimate the value of unknown parameters — The Bayes Theorem states that where P(g|x) represents the probability of an event g, given the observation of one or more events x. P(g) is the probability of an event to occur, irrespective of any other event. As physicists, we can read the theorem as follows: we don’t know, with…

If the sun suddenly became a black hole, would the earth be sucked in? — According to a widespread belief, black holes suck, inexorably, any object within the range of their gravitational force, regardless of the kinematic state of the poor prey. In fact, this is misconception. A black hole’s gravitational field is no different from the one of any other body. …

Using Arduino, it is straightforward to investigate the Faraday-Neumann-Lenz Law — The pandemic has severely restricted the possibilities to attend practicals at schools and university. Arduino can be exploited, not only to mitigate the effects of the lockdowns, but to introduce a new way of engaging students in laboratory activities. …

Teaching energy before forces is not only possible but desirable. — This post was motivated by a tweet by Frank Noschese, reproduced below, to which I responded that I am a big fan of the “energy first” approach. I must say that the approach I am advocating is not an idea of myself. I started thinking about it after reading…

Using Arduino we can measure temperature and pressure of a gas and study its equation of state — In my last post, I show how to obtain experimental data from Arduino via BLE. As promised, I now come to the collection and the interpretation of these data, in the case of an experiment in which a gas is subject to an isovolumetric process, i.e., …

How to collect and publish data using Bluetooth Low Energy with Arduino — In this post, I illustrate operation of an Arduino with BLE (Bluetooth Low Energy). As usual, physics being my field, I do not discuss a generic example (the equivalent of “Hello, World!”), but a concrete physics application. Sometimes, for brevity or clarity, I will not be rigorous, and purists may…