The h Bar

Why danger symbols can’t last forever

At last something good!

3B1B

Johan Liebert

8:04 AM

6 Life Changing DIY Lifehacks That Are So Amazing You Can't Live Without (OFFICIAL) FULL 1080HD

8:30 AM

Some good experimental physics here:

Korra

Sorry it's out of context but does anyone know how to use mathjax on blogger posts?

@JohanLiebert saw this in my feed yesterday. Is it good?

Slereah

Todorov

Oops

Wrong window

Johan Liebert

8:47 AM

@Korra yes indeed. 3B1B is one of the best YouTube channels to learn mathematics. Also his contents are well researched.

9:42 AM

@JohnRennie Mohammad Javanshiry has been a member of Physics.SE for 3½ years, and has almost 1000 rep, so he isn't a newbie. ;) OTOH, he is a bit of a maverick, but he doesn't seem to be on a mission to promote non-mainstream stuff...

@PM2Ring huh? I VTC'd as a homework question.

The question is just using the Rindler coordinates so it is entirely mainstream. But it is homework.

Korra

@JohanLiebert I have seen some of his videos and one which was in collaboration with minute physics and explaining a derivation of Kepler's law from Feynman's lectures. Two of my favourite things combined, I loved it. Though there is so much misinformation on the topic of coronavirus that I am bit skeptical as to what he will say.

And I successfully used mathjax on blogger

@JohnRennie Sorry, I didn't mean to imply that that question is non-mainstream. But yeah, it is definitely homework-like. OTOH, the OP may be able to transform it into a conceptual question. IMHO, I don't think it's a basic Rindler question: the acceleration abruptly commences an instant after the light is emitted.

I must admit that I'm not sure what happens the instant you start accelerating. The Rindler coordinates are stationary i.e. they assume the observer has always been accelerating. But as far as I know the Rindler horizon appears instantly i.e. light emitted from the horizon distance at the moment you start accelerating can never reach you.

Some of Mohammad J's answers have a non-mainstream feel to them though. And his book title sounds a little controversial... physics.stackexchange.com/users/127415/mohammad-javanshiry

9:55 AM

My view would be that the change to the Rindler geometry is instantaneous.

@JohnRennie I agree, but I'm not completely clear on how the transition plays out. Most of the Rindler stuff I've read assumes the coords are stationary, although they occasionally say stuff like the horizon vanishes when you stop accelerating.

FWIW, Greg Egan wrote a nice article using Rindler coords as a way of approximating the problem of dangling a rope over a BH event horizon. gregegan.net/SCIENCE/Rindler/RindlerHorizon.html

skullpatrol

sir @JohnRennie what, may I ask, is your interpretation of the quote, "Young man, in mathematics you don't understand things. You just get used to them."?

For ages now I've had an article at the back of my mind on comparing the Rindler and Schwarzschild coordinates as a way to understand the coordinate singularity in the latter. One day I will write it ...

skullpatrol

pardon the interruption :-)

@skullpatrol Only Von Neumann knows exactly what he meant. My interpretation would be that in mathematics (unlike physics) axioms are arbitrary i.e. unrelated to any fundamental assumptions about the universe.

That means you cannot understand an axiom in the sense we might understand the claim that the speed of light is invariant. The axiom is just assumed and you have to get used to it.

skullpatrol

10:10 AM

I see.

However, that is a relatively modern attitude. Before the development of non-Euclidean geometry, it was generally accepted that Euclid's axioms are fundamental universal truths. Algebra was on metaphysically shakier ground, and mathematicians tended to be suspicious of anything that couldn't be reduced to geometry. Hence every proof in Newton's Principia is given geometrically.

10:26 AM

When I was in my early teens, my maths teacher had memorized the first 40 decimal places of pi. So I decided to memorize 50 places. :) A few years later I extended that to 100 places. But then I thought "Hang on! Why get obsessed over pi? I don't really understand the much simpler irrationals, like sqrt(2) yet".

Sure, I could easily prove that root 2 is irrational, but did I really understand it? 45 or so years later, I feel very familiar with root 2 and other irrational square roots, quadratic fields, Pell's equation, etc, but I can't really claim that I fully understand that stuff. :)

Have you ever watched the Mathologer videos on Youtube?

He talks about lots of interesting aspects of number theory.

@JohnRennie No. I mostly just watch music clips on YouTube (and I don't have a large monthly data allowance, so I have to ration myself). But since yoy recommend it, I will have a look at the Mathologer stuff.

Infinite fractions and the most irrational number

For example I have just watched a video where he explains how all irrational numbers can be written as an infinitely continued fraction, which I found fascinating.