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〈 Berger |🎄| Dillon 〉

@InertialObservr

26 Jan

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)

What about Gravity?

The symmetry corresponding to gravity is the most respected symmetry in all physics & goes by many names

It's the one underlying Einstein's General Theory of Relativity:

General Covariance/Gauge-Lorentz Symmetry/ Diffeomorphism Invariance

(3/n)

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〈 Berger |🎄| Dillon 〉

@InertialObservr

15 Jan

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

Caveat (2)

Since surface terms do not affect the Euler Lagrange equations, the equations of motion are always trivially invariant upon adding a 4-divergence to the Lagrangian density

Read 7 tweets

〈 Berger |🎄| Dillon 〉

@InertialObservr

9 Nov 19

(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)

For the Gluons, we *do* obtain the "Coulomb" term (1/r) but we don't get the linear term (kr).

To find out what’s going on, we’ll need a couple facts.

Read 8 tweets

〈 Berger |🎄| Dillon 〉

@InertialObservr

2 Aug 19

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)

This is precisely how "induction stoves" work

• The oscillating magnetic field wirelessly induces a current in the pot

• The current flowing through the pot results in resistive heating

The coolest thing about induction stoves is that the stovetop itself doesn't get hot!

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〈 Berger |🎄| Dillon 〉

@InertialObservr

13 Jun 19

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)

Step (2): Higgs Production

👉These t̅t coming from the Gluon decay, can then interact with one another
👉These t̅t can then "annihilate" to produce a higgs particle, via the process shown below.

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〈 Berger |🎄| Dillon 〉

@InertialObservr

1 Jun 19

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.

The image is not mine, and I can't seem to find the source. If any of you can find it let me know!

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