TL;DR – Scientific investigation is not simply finding patterns and generalizing from them. Sometime ago I met someone who had high standards for what truth is. “Science cannot give any real truth!” “Science uses induction, which is not logically sound.” “All that scientists do is find patterns and generalize them to a rule.” I guess …
TL;DR – The uncertainty relationship in quantum mechanics exists before and independently of measurements. Some books still perpetuate the idea that the uncertainty introduced by quantum mechanics is caused by measurements. Either as an observer effect (i.e. the measurement causes the uncertainty) or as an observed relationship (i.e. our measurements are limited by that relationships). …
TL;DR – The Schrodinger equation can be seen as the deterministic and reversible limit of the projection (i.e. collapse) associated with a measurement. Quantum mechanics comes with two ways to go from an initial to a final state. The first is the Schrodinger equation that represents time evolution and the second is the projection (or …
TL;DR – There may be infinitely many parallel worlds but there is nothing to be detected. A friend of mine is really into science fiction. “Did you know that there are infinite parallel worlds?” “And that there are infinitely many you and me, each a little bit different?” “And one day we will be able …
TL;DR – No quantum state is more uncertain than the other. All states can be identified by a set of perfectly prepared quantities. When studying quantum mechanics, you may get the (wrong) impression that some states are better defined than others. Some are eigenstates while others are just a superposition. Or that the gaussian packets, …
TL;DR – Commutators, like Poisson bracket, tell us how a quantity changes under a transformation generated by another. Commutators play a fundamental role in quantum mechanics. Mathematically, they tell us how multiplication between operators behaves but this does not provide any physical insight. What is more interesting physically is that they are intimately related to …