A Little Glitch on Reality

The laws of physics are not to be democratic. They are not to satisfy opinions of majorities, but to rule imperially, regardless of our ignorance about their true forms. Intuitively enough, the laws of physics should be the same for everybody, regardless of where we are, when we are, or how we are. This was stated by Einstein in 1905 in his paper “On the Electrodynamics of Moving Bodies“, together with  the claim that there is a maximum speed allowed in the universe, that of light.

Continue reading


A Little Technical Interlude

What I’m about to tell you is not something new. These ideas have been around for many years already (since classical mechanics was still a thing). Moreover, I have been bothering my friends, students, teachers and some angry chemists with this for the last four or five years, ever since a student in San Luis Potosi made the mistake of saying the word “Hamiltonian” in front of me. This let another professor to reveal me one of the most guarded treasures for the physicist: the all-mighty  Lagrangian.

Continue reading

I dreamed a little dream

Do I have any reader left?

After abandoning my blog for around a year and a half I felt the need to share something, but I was not sure what. In the last year and a half I discover such beautiful physics and math, but I was not sure what I wanted to share. Some months ago I finished my bachelor in Physics, so I decided to share one of the main reasons that convinced me to study this or, better said, one of the main problems: Here I present you:

Laser cooling of atoms

Continue reading

A Little Spring…

This one I wanted to do for a while. I like very much the math that can be derived from the Quantum Harmonic Oscillator, but there’s also a lot of stuff that I personally don’t like about the approach that is taken in some quantum physics books. I prefer a rather algebraic analysis of this system since I think that it is pretty much cleaner and easier to justify; then again I’m not pretending to be absolutely formal, just enough for it not to look like some kind of magic trick in the middle of the thing.

Continue reading

A Little Pulse…

This past semester I was working as T.A in a Mathematical Physics course. One of the main topics studied was Fourier analysis which I consider a really beautiful subject, but also rather cryptic. This area is fulled with mysterious and magical-looking identities, one of them in particular calls my attention every time I use it and I would like to discuss it here. Also, I think it may be useful to show a more complete (but not formal at all) proof of this fact, because once you “believe” it, the derivation of the Fourier transform identities comes as pretty straight forward. I’m assuming here a certain knowledge or intuition about the Dirac delta function and its sampling property Forgetting about suspense, here is the thing I would like to prove:

\delta(x)=\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i\omega x}\mathrm{d}\omega

Continue reading

A Little Charge

Hello everyone! First of all, I would like to apologize because I have really forgotten about this blog for a really long time, mainly because of academic reasons and maybe a lack of inspiration. I know it is a bit unusual for me to be writing this in English, but recently I’ve got some new friends that were interested in my blog but don’t actually speak Spanish.

Well, this time I wanted to analyse a beautiful and simple problem in physics. So… Let’s get to work!

Continue reading

Una pequeña suma

Una disculpa por no haber escrito en los días pasados, pero fueron vacaciones y había que ponerse al corriente con las amistades y las clases, pero ya estamos de regreso.

Muchos ya deben conocer la famosa fórmula por Gauss que mencionan desde secundaria, que nos dice que:

\displaystyle 1+2+3+\mathop{...}+n=\frac{n\mathop{.}(n+1)}{2}

y la mayoría debe de haber escuchado la demostración en que copiamos esta suma, la escribimos al revés, sumamos por pares y formamos términos repetidos para luego simplificar.

Continue reading

Hagamos una pequeña fila

Contar cosas puede ser muy entretenido, y muchas veces es necesario. En las competencias de matemáticas se dedica un tiempo de entrenamiento en ocuparnos de como contar bien y en algunos cursos de probabilidad y estadística lo estudiamos también, pero estos últimos no siempre me agradan porque se vuelven en cursos de fórmulas solamente, como si las deducciones de estas estuvieran fuera del alcance de los alumnos. En honor a esas personas que me han preguntando sobre el origen de algunas fórmulas, escribo este pequeño post sobre conteo.

Continue reading

Pequeña observación sobre fracciones

¡ Hola !

Para empezar quería contarles de una relación muy evidente y muy fácil de probar, que puede ser usada al momento de resolver problemas con fracciones para simplificar expresiones, pero por alguna razón no he visto que la utilicen mucho cuando puede ser conveniente para reducir mucho el trabajo y la talacha y evitar dar rodeos inútiles. Para algunos quizás les parezca un poco obvio, pero me gusta mucho y quería contarselas, además que no quiero espantar gente apenas abriendo el blog.

La relación es la siguiente:

Continue reading

Let the game begin


Para quien no me conozca, mi nombre José Alberto de la Paz Espinosa, estudio Ing. Física Industrial en el Tecnológico de Monterrey y mis dos principales gustos son la física y las matemáticas. este es el primer post de del blog que pretendo crear, aquí estaré publicando un poco de mis intereses sobre matemáticas y física, algo de noticias que me parezcan interesantes, desarrollos de algunos problemas y temas de mi interés, quizás algo de las olimpiadas de física o matemáticas o algún asunto que me sugieran.

Continue reading