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Jacopo Bertolotti

@j_bertolotti

10 Dec 21

#PhysicsFactlet (308)
There are not many problems in Physics that can be solved exactly, so we tend to rely on perturbation theory a lot. One of the problems with perturbation theory is that infinities have the bad habit of popping up everywhere when you use it.
(A thread 1/ )

If you know anything about Physics you are probably thinking about quantum field theory and all the nasty infinities that we need to "renormalize". But quantum field theory is difficult, so let's look at a MUCH simpler problem: the anharmonic oscillator.
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Disclaimer: I can't know how much you (the reader) know about this. For some of you this thread will be full of obvious stuff. For others there will be so many missing steps to be hard to follow. I will do my best, but I apologize with everyone in advance.
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Read 24 tweets

Jacopo Bertolotti

@j_bertolotti

23 Nov 21

In celebration of 10k followers, here is a new edition of "people you should follow, but that (given their follower count) probably you don't".
i.e. people I follow, with <5k followers, non-locked, active, that in my personal opinion you should follow too.
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@LCademartiriLab

In random order:
@LCademartiriLab food, chemistry, architecture, and beauty in general. Trigger warning: strong opinions.
@VKValev bit of history of Physics + chiral media
@DrBrianPatton social justice in science
@alisonmartin57 weaving and bamboo structures
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@VergaraLautaro

@VergaraLautaro history of Physics
@PKoppenburg LHCb
@OptoLia optics, entrepreneurship.
@BrunoLevy01 fluid simulations
@lisyarus physics-based graphics coding
@RobJLow mathematics and education
@bruko Photography (and overall great human being)
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Read 8 tweets

Jacopo Bertolotti

@j_bertolotti

28 Oct 21

#PhysicsFactlet (299)
Fractional derivatives: a brief tutorial/🧵. If you know some calculus you should be able to follow. If you are a Mathematician (or you like to see things done properly) I advise "Fractional Differential Equations" by I. Podlubny instead 😉
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The history of fractional derivatives begins together with the history of the much more common integer-order derivatives, and a number of big names in mathematics worked on it over the centuries.
Afaik, the first to work on the problem was Leibniz himself.
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Since differentiating twice a function yields the second derivative, the Marquis de l'Hôpital immediately wondered whether it makes sense to think about an operator which, if applied twice, gave the first derivative, i.e. some sort of derivative of order 0.5
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Read 23 tweets

Jacopo Bertolotti

@j_bertolotti

23 Jun 21

#PhysicsFactlet (283)
Lorentz transformations pre-date Special Relativity. How is that even possible?
A thread.

Trigger warning for typos (hopefully just in the text and not in the equations) and carefree manipulations of equations 😉
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The historical route is interesting but complicated, so I will leave that story for someone more qualified to write it. What I want to look at is: how do we get the Lorentz transformations without knowing anything about special relativity?
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A requirement we want all physical theories to satisfy is the "principle of relativity", i.e. the fact that the laws of Physics are the same in every frame of reference. Were this not the case, each of us would experience a different universe, making life quite complicated.
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Read 24 tweets

Jacopo Bertolotti

@j_bertolotti

26 Apr 21

#PhysicsFactlet (273)
A brief introduction to the calculus of variations.
Trigger warning: lots of formulas manipulated the way experimental physicists do 🙂
🧵 1/

The simplest introduction to the calculus of variations is to solve in a slightly roundabout way a very easy geometrical problem: what is the shortest path between 2 points on a plane?
(spoiler: it's a straight line)
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Let's pretend we have no idea, and so we are forced to take into consideration all possible functions passing through 2 given points. What we want to do is to calculate the length of each of them, and select the shortest one.
(spoiler: we are not REALLY going to do that)
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Read 20 tweets

Jacopo Bertolotti

@j_bertolotti

22 Nov 20

A few days ago I was asked by some last year students advice on how to decide whether doing a PhD is the right thing to do. I will put here a summary of what I told them, just in case it can be useful for someone else.
🧵 1/

[Disclaimer: What follows are personal opinions based on STEM disciplines in Europe. So this is a partial and (by definition) incomplete picture.
Also, I am assuming you like the subject you want to do a PhD in, and that you can find a supervisor who is not a sociopath.]
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During a PhD you will tackle one or more problems/questions that no one has a answer for. This is dramatically different from what you have ever done at Uni, where all problems had a solution somewhere.
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