The Electron Black Hole 🧵

As physics twitter debates the sizes of elementary particles, here's a fun fact.

An electron has mass, charge and spin. The gravitational field of an object with mass, charge and spin is known--it is called the Kerr-Newman solution. The Kerr-Newman solution has a black hole, provided the below inequality holds.

(Here J is angular momentum, Q is charge and M is mass.)

If it does not hold, we would still have a singularity. But unlike a black hole, no horizon would hide it.

A naked ring singularity.

The wavefunction of the universe 🧵

In quantum mechanics, every system is described by its wave function.

Take a particle. Its wave function encodes the probability of finding the particle at some location.

The wave function follows the Schrodinger's equation Here hbar is a constant called Plancks constant. Capital H with a hat is the "Hamiltonian operator", it represents the energy of the system.

Gather around for a little magic 😄 🧵

In quantum physics, von Neumann entropies play an important role.

Say you have two electrons. vN entropy roughly measures how entangled they are.

1/5 Generally, for a system A, the vN entropy S(A) tells us how entangled it is with the rest of the universe.

The most important(and mysterious) property of vN entropies is the Strong Subadditivity Theorem.

(AUB just means the joint system of A and B.) 2/5

A thread on "negative probabilities" in quantum mechanics.
🧵 Before uncertainty principle ruined everything, we believed that things can have a definite position and a momentum at the same time.

In fact, if you knew the position(q) and momentum(p) of a particle, you knew everything about its motion.

Indian-American mathematics legend Harish-Chandra had done his PhD in physics.

His contributions to physics had been forgotten for many years. But these days, many physicists are poring over Harish-Chandra's 1947 thesis.

This is a thread about Harish-Chandra and his thesis /1 Born in Kanpur, Uttar Pradesh, Chandra was a precocious student. As a masters student, he impressed CV Raman, who suggested he go work with Homi Bhabha at IISc.

Bhabha in turn recommended him to his own teacher at Cambridge.

That's how HC became a PhD student of Paul Dirac.

Causality, relativity and quantum gravity: a thread

Relativity is just the study of a fancy type of rotation.
Suppose we take two guys, standing at an angle, and ask them to choose x and y axes.

They do so like in the picture. Their axes will be rotated with respect to each other.
Relativity is rotation in space-time. In this case, instead of standing at an angle, the two guys are moving at different speeds.

Their clocks and rulers won't agree with each other. That is because their space and time are rotated with respect to each other, just like the different x and y axes in the last example.

This is a special kind of rotation, called 'hyperbolic rotation', which is why the picture looks different.

Time disappears in Quantum Gravity?

A thread for everyone 1/n Take two people who are carrying two different maps. One map is rotated with respect to the other.

They may disagree on what 'go straight' means, but they will agree on all essential things. Like if you ask them about the distance between A and B, they will agree.

Proof that black holes have zero mass, by Abhas Mitra.

Looking at Eq 20 and 21: My brother in Christoffel, that’s…not how it works. Mitra’s response to a paper which pointed out the problem

I am going to write about three instances of remarkable progress in the foundations of physics that happened within the last 20 years. 🧵

https://twitter.com/skdh/status/1667395312397213696

1. Double Copy: What if I told you gravity = (strong force)^2 ?

Gravity and strong force are two disparate forces that have nothing to do with each other.

But in 2008, inspired by results in string theory, a group of physicists found a remarkable result that relates the two

Many experts on gravity were confused if gravitational waves were real.

A clever argument from Richard Feynman helped decisively settle the issue. 🧵 First, a little history.

Einstein was the first to discover gravitational waves.

Not long after discovering general relativity, he showed that his theory predicted ripples in the fabric of space and time.

But he did not believe the prediction himself.

A particle is periodically 'kicked' by a force. If the corresponding potential is cubic, we already get chaos.

Now instead of a single particle, think of a probability distribution in phase space.

This is how it would evolve with each kick, starting from a Gaussian





As you can see, a complex pattern of whorls and tendrils emerges, the complexity growing with every successive iteration.

But this happens only classically, where there is no limit to resolution in phase space and hence the intricacy can increase arbitrarily

Step two, approach a senior big shot whose name can attract funds. Step three, invite subject experts from different areas to speak at your conference who coincidentally turn out to be all male

Kids these days don't fully appreciate the advantages they have over earlier generations.

If they were students of physics in the 1870s looking to learn electromagnetism, they would have to contend with a set of 20 equations.

It was character-building stuff as you can see But nowadays, they learn just 4 equations.

They have it too easy

A thread on BMS symmetries. 🧵

We start with an example. Take a complicated distribution of charges. It will produce a complicated electric field.

But if I could get far enough away from all the charges, the entire distribution would look like a point charge to me. The electric field then falls off as the inverse square of distance from the charges. It approaches zero.

In this case we have a symmetry emerges -- the electric field is the same in every direction.

This is the broad idea of asymptotic symmetry.

The physics version of chicken-egg problem is fields vs particles.

Is the universe made of fields or particles? 🧵 To understand the concept of fields, we go back to its origin -- magnets.

A magnet will exert a pull on all magnets around it.

One way to understand this pull is that a magnet creates a magnetic field around it, and other magnets feel and respond to this field.

Black holes don't exist? 🧵

In this thread, we will look at a paper() that claims black holes don't exist.

The author is Abhas Mitra, who has received some media limelight in India in the past for such claims,
like in here:


1/6arxiv.org/abs/0904.4754
ndtv.com/world-news/nas… First, I am going to distill the math of the paper into its essence and write it out in a single tweet.

This will make the mistake in the paper obvious.

What follows in the next tweet is the math of the analysis made in the paper.

See if you can spot the mistake.

2/6

The holographic principle of quantum gravity blows the mind of anyone who first encounters it.

It is also like a can of juice.

A thread🧵 There are two characters in the story, best known by their acronyms AdS and CFT.

AdS or Anti-de Sitter space is a hypothetical universe.

Unlike our expanding universe, AdS is fenced in by a boundary surface.

Which makes it look like an infinite can of juice.

A couple of days ago, a number of science magazines reported that '(some) physicists have created a wormhole in the lab.'

To which other physicists responded with an outraged 'No, they did not!'

What's going on? Let me give you the tl/dr.

1/n What is a wormhole?

Imagine you go to work everyday via a major road with lots of traffic.

Then one day you discover a little-known back-alley between your home and office, and now you can reach office much quicker.

Wormholes are the back-alleys in space-time.

2/n

During my PhD days, I was often asked in family gatherings what is this 'quantum gravity' thing that I work on.

I came up with an analogy which worked really well with my mostly-IT relatives!

This is what I used to say.

1/n Your computer is running a program.

You give some input and get some output. Suppose you are now told to guess the program.

That is what scientists do.

They try to guess the programs nature is running, from our observations of how the output changes with the input.

2/n

I know a prof who napped in every seminar and always muttered "yes, yes, that's correct." as soon as he woke up

https://twitter.com/caridoesphysics/status/1597320338786103297

One time, in a seminar on a topic not at all in his field, he woke up in the middle of a heated argument about some intricate point and muttered his usual 'yes, yes, that's correct,' and got glared at by one of the debaters, who thought he was supporting his opponent.

A thread🧵about Einstein's first salvo against quantum theory.

The Solvay conference of 1927 is the venue of the famous group photograph of physics hall-of-famers.

It was here that Einstein made his first public argument for the incompleteness of quantum mechanics

1/11 Quantum mechanics doesn't deal in certainties. If you measure the position of an electron, QM won't tell you where you will find it.

Instead it will give you a 'wave function', which specifies probabilities of finding the electron at different points.

2/11