What do you think was the color of the night sky when the Universe first turned transparent?

What do you think was the wavelength of the cosmic microwave radiation at the time when the photons decoupled?

1/5 You can calculate the temperature of the Universe at that time using the measurement of the CMB temperature today: 2.725 K, the time of decoupling 380000 yrs and the fact that the Universe was matter dominated

You'll find a temperature of 3000 K

2/5

Quantum mechanics can be demystified to some degree by realising that it's probability theory with a squared norm. E.g. you'd add classical probabilities (real numbers) p1, p2, .. < 1 with

p1+p2+...+ pn = 1

In QM instead you have amplitudes and

|w1|^2+|w2|^2+...+|wn|^2=1

1/8

https://twitter.com/ns_nikhil9/status/1827945682935976236

For classical probabilities the linear norm is preserved by acting on P=(p1, ..., pn) with stochastic or Markov matrices M (non-neg matrices where all entries in a column add to 1)

M P = P' and p'1 + p'2 + ... +p2n =1

2/8

The strongest evidence for dark matter:

In hot plasma like the early Universe structure can't persist. Whenever matter is compressed by gravity it is driven apart by radiation pressure

The resulting oscillations wash out every seed of over density. Galaxies never form

1/6 Only if there's matter that does interact gravitationally but is *not* susceptible to radiation pressure, these oscillations can be suppressed

Overdensities of this 'dark' matter provide gravitational wells for visible matter (gas) to fall into

2/6

What is a proton made of?

Early scattering experiments probing the substructure of the proton found an interesting result. Instead of being made just from point-like particles (quarks), there seemed to be more going on inside the proton

A🧵1/6 Zooming into a proton corresponds to colliding it with more and more energetic beams

Similar to probing a target with light using shorter wavelength, higher energy results in a better resolution

2/6

General relativity is often called geometric, but special relativity is also a geometric theory

It explains moving at different speeds as rotations in spacetime, similar to the way we explain looking in different directions as rotations in space

Some math in this 🧵1/12

In Newtonian mechanics we can disagree about directions, but not about (relative) distances. E.g. if we stood back to back and asked about the distance to London we would agree on the distance, but not about the direction.

2/12

Did Newton know F=ma?

Newton's 'Principia' uses geometric proofs, not calculus. He didn't give differential equations for his laws, but did he know them?

Exploring whether Newton knew diff expressions for forces is a fascinating rabbit hole

NB @rmathematicus

🧵1/9 Newton published the Principia in 1687 (2nd edition 1713, 3rd 1726). In it he doesn't mention that F = ma. In fact he doesn't use calculus

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Renormalization group without any math:

For the longest time we discovered more fundamental structures in nature. The further we zoom in the more new structure we see.

The discovery of quarks is a good example

Molecules → Atoms → nuclei → protons → quarks

🧵1/13 Will this go on for ever? Will we keep uncovering layer after layer of new particles?

We don't know the answer to that, but at the most fundamental layer we have discovered Nature has a trick that sounds counterintuitive at first

If you split quarks you find more quarks. 2/13

The basic idea of renormalisation: A sketch

In Quantum field theory with interactions, there're corrections to fundamental constants

The electron mass is corrected because of the presence of the photon field

So what is measured in an experiment is the 'corrected mass' mr

1/9 You can only ever measure mr

In order to measure m0 you'd need to be able to turn off the photon field. Not the presence of any number of photons, but the existence of a photon field overall -like a Universe where photons don't exist.

We can't do that: m0 is unobservable

2/9

The Higgs can decay into a vector meson and a photon H → J/Ψ γ → μ+μ− γ

This process is so rare, it takes a quadrillion (10^15) collisions to see it once at the LHC!

It took 8+ yrs for CMS&ATLAS to see a few of these decays and now they test a never observed effect

🧵1/12 According to the standard model the Higgs boson interacts with all quarks with an interaction strength directly proportional to the quark mass.

Even though there're 6 types of quarks we've only good measurements for 2 of them : top and bottom

2/12

A thread on Mermin's device used to demonstrate that Nature can't be classical

Feynman called Mermin's paper: "One of the most beautiful papers in physics that I know"

It has a switch with 3 settings and 2 lights flashing either red or green:

🧵 1/10 The full experiment has 2 such devices (A&B) and a source that spits out pairs of particles (C). Every time a particle enters a device it flashes red or green (not both)

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Physics threads 2023

Happy 2024 everyone! The product integral

https://twitter.com/martinmbauer/status/1733589338909188450

If you want to define a continuous addition you get the Riemann integral

This is what happens if you want to define a continuous *product*

One of the weirdest and most satisfying integrals you've ever seen and why it's important for physics

(a quite technical 🧵) 1/12 If you derive the Riemann integral you do so by approximating the area under a function with discrete blocks and take the limit of their sum where they become infinitesimally thin
2/12

The Aharanov-Bohm effect

Weisskopf said: The first reaction to this work is that it is wrong; the second is that it is obvious

Ehrenberg said: Ach Hiley, zis AB effect that you are discussing, is it the one that Siday and I discovered?

What is it?

1/9 🧵 The Aharonov-Bohm effect is an -at first- surprising effect on charged particles moving around a cylinder in which there is a magnetic field

Outside the cylinder the magnetic field is zero but you can see a different interference pattern if the magnetic field is turned on

2/9

The Universe expands and it expands faster and faster

There will be a time in the distant future (100s of billions of yrs from now) when all local galaxies will have merged into one single galaxy and all other galaxies have faded beyond the cosmic light horizon -forever

1/7 From this point on there will be no evidence at all that other galaxies have ever existed.

Life in our galaxy will resemble existence on an isolated island on a single planet surrounded by a vast sea where all other land has sunken in the past

2/7

To say 'for finetuning to be a problem you need to know the probability distribution of the parameters' entirely misses the point

The point is that *if* a more fundamental theory explains the value of these parameters the apparent finetuning can be a hint on its structure

1/8 Because theories that explain large hierarchies are different from theories that don't.

2/8

'Antigravity' in Newton's theory means masses repel each other. In Einsteins theory the implications are more severe.

Newton's grav force is very similar to Coulomb force. The 'charges' in Newton's law are masses. If there was a negative mass it would repel pos masses

🧵 1/6 In General Relativity the charge is energy. Mass is just one form of energy. There is a theorem by which the gravitational energy of an isolated system is always nonnegative

But some of it's assumptions could be violated, so lets assume a neg mass

2/6

en.wikipedia.org/wiki/Positive_…

Why would photons decay if the speed of light wasn't the speed limit?

Remember:
Everything wants to decay in quantum field theory. You need a symmetry to *stop it* from decaying.

Lorentz symmetry protects the photon from decaying.

You can show that in a few tweets:

1/7 One consequence of Lorentz symmetry is the conservation of the energy momentum 4-vectors of the photon and the electron and positron in this diagram:

2/7

There are 6 symmetries in Lorentz symmetry, they imply 6 conserved quantitites

rotation around 3 axes ↔ angular momentum conservation (3 components)

Boosts in 3 directions ↔ velocity of the centre of energy is conserved (3 components)

1/3

https://twitter.com/nabatiyehkfour/status/1705932709753716933

The full symmetry group of flat spacetime also includes translations (the laws of physics hold at all times and places)

time translation ↔ Energy conservation
translation in 3 directions ↔ momentum conservation (3 components)

2/3

The speed of light is constant, finite, and no massive body can ever match it

This fact is at the basis of modern physics

And we're really confident in that because it's implications have been tested to astonishing precision.

But not by measuring the speed of light... 🧵1/10 A constant speed of light implies a symmetry, Lorentz symmetry, and this symmetry dictates physical laws that we can probe. Some of those might not be intuitive and yet they affirm that the speed of light stands as the ultimate speed limit

For example : 1. antiparticles

2/10

The cleanest challenge to particle dark matter

Dark Matter explains observations across many scales: early Universe structures, grav. lensing and rot. curves

Galactic rotation curves are also well explained by modified gravity and there's a clean test: wide binary stars

🧵 1/8 Dark Matter explains galactic rotation curves by a large cloud (halo) of new, uncharged matter that therefore didn't collapse further

Modified gravity (MOND) explains them by new fields that extend Einsteins general relativity and modify newtons law at large distances

2/8

The Landau pole - when quantum field theories break down

Contrary to common lore the Standard Model is *not* consistent at arbitrarily high energies - even if you ignore gravity

🧵 1/9 The reason is that couplings -like the finestructure constant- aren't really constant. They depend on the energy of the process

This is a prediction fundamentally rooted in quantum field theory. It's not the case in classical field theories nor in quantum mechanics

2/9