The curves traced out by the intersection of two lines rotating at different speeds i'm not sure why i did this but i'm glad i did

Prof. Claudia de Rahm's theory of 'Massive Gravity' to explain Dark Energy is getting a lot of press as of late.

So let's dig into it. (thread: 1/n)

theguardian.com/science/2020/j… Before getting to gravity, recall that forces are transmitted by a 'mediator' which are always bosons

EM: the photon, strong force: gluon, weak force: W± & Z.

When the symmetry corresponding to the force carrier is unbroken the force carriers are massless (m=0).

(2/n)

Noether's Theorem is perhaps the most beautiful mathematical theorem in physics

•It states that: Every continuous symmetry (T) of the Lagrangian has a corresponding conservation law Caveats (1/2)

The astute reader will notice that technically Noether's theorem applies to invariance of the action, which is the spacetime integral over the Lagrangian density

Hence, you will also need to make sure that the measure is invariant under the transformation as well

Absolutely Amazing

Physicists (!) discover a new fundamental and amazing mathematical fact:

You can get the Eigenvectors of a matrix using ONLY its Eigenvalues

arxiv.org/pdf/1908.03795…
“[The proof] looked too good to be true ... Something this short and simple — it should have been in textbooks already. So my first thought was, no, this can’t be true.”

-Terrance Tao

(1) The Weak Force is extremely short ranged: its potential is *almost* Coulomb's Law (2), but exponentially suppressed due to the fact its force carriers W⁺⁻, Z⁰ are massive (i.e. m≠ 0)

(3) The second term in the last equation (kr) is what makes the strong force so "strong" How do we get the potentials of the 3-fundamental forces from first principles? Quantum Field Theory

(1) Specifically, we take the Fourier Transform of the Feynman diagram that describes each force

We can *almost* get all 3 this way. Everything except the Strong Force (2/N)

Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and will likely never exist again.

- Yannay Khaikin Suppose a new permutation of 52 cards was drawn every second starting from The Big Bang (13.8 billion years ago)

You wouldn't even be close

• To count out all 52! permutations you would need 10⁵¹ ages of the universe

A changing Magnetic flux induces an Electric field. This can create a current in a wire to power a💡!

No battery needed! This is the idea behind power generators:

• Spin a magnet with a mechanical source (e.g. water)

• The changing Magnetic field induces an AC current in nearby wires

• The current can then be sent to an "outlet" (or applied directly as shown here)

How was the Higgs Boson discovered? (1/n)

👉The main process which led to its discovery is its decay into 2 photons: ℎ → γ + γ
👉This process is occurs at "loop level" mediated by the top and bottom quarks 𝑡 & 𝑏
👉The higgs lifetime is 1.56×10⁻²² s Step (1): Smash Protons

👉The LHC smashes together protons
👉When two protons collide, it produces a "shower" of its constituent quarks 𝑞 and gluons 𝐺
👉The 𝐺 can then decay into pairs of t̅t (top, anti top)

This is not a typo. Here's a neat visualization.

👉Note that each color stacks up to make a square of dimension 1x1x1, 2x2x2, 3x3x3, ..etc.

Fractional Calculus

👉The 𝑛ᵗʰ derivative can be generalized to the 𝑞ᵗʰ derivative, where 𝑞 is a rational number

👉For polynomials 𝑥ⁿ, this is done by replacing the factorial function with its continuous generalization: the Γ-function ☝️The fractional derivative of course returns the usual derivative when the derivative "powers" add up to an integer