The h Bar

M.N.Raia

1:23 AM

Hello everyone!

I really need a step-by-step derivarion of the norm of 4-acceleration. I know how to write down the definition and I understand why. But I simply don't get the relation:

$(\eta_{\mu \nu} a^{\mu} a^{\nu})^{1/2} = \gamma ^{3} a$

user351417

3:20 AM

@EmilioPisanty I'm a bit busy right now; I have tests, so I can't look at the whole conversation. But no, I didn't rage-quit, and I've been toying with the idea for about a week.

user351417

I think Physics SE is awesome, and maybe I'll return after a while.

user351417

But I did consider the impact this would have on other peoples' rep, since I used to vote a lot, and I was very sure that I'd qualify for vote-preservation. I might contact the CMs. I know that after my 24 hour timer elapsed, my account was still alive and I had a message saying that a developer would be required to review my account's deletion.

user351417

I'll probably keep this account lying around: it's linked to my chem account, so if I choose to restart after a while, I might get an association bonus on physics : P

user351417

But this meta post kind of made me feel sure that quitting was the right choice.

user351417

3:36 AM

My, this is disastrous. If I'd known that I wouldn't get a vote-preserving deletion, I'd have just quietly abandoned my account : ( I'm so sorry, this looks like a whole lot of people lost rep.

user351417

Maybe it would have been a better idea for me to announce it in chat, considering the strange way OP of this question appears to have been deleted.

user351417

3:47 AM

(cc @PM2Ring @JMac @KyleKanos and everyone else in that discussion)

John Rennie

4:54 AM

@M.N.Raia you have to work out the coordinate transformation between the accelerated and unaccelerated observer. This is a somewhat messy calculation that you'll find done in any standard text on relativity. For example in Misner, Thorne and Wheeler it's done in chapter 6.

Once you have the equations relating the two frames more messy calculation allows you to calculate how the acceleration transforms. You'll finally end up with $a = a'/\gamma^3$ where $a'$ is the proper acceleration in the accelerated frame and $a$ the acceleration in the inertial frame.

The various equations, though not the working, are in Phil Gibbs' relativistic rocket article.

Emilio Pisanty

6:55 AM

@Rishi I can't speak for anyone else, but on my side the lost rep is not a concern.

But account deletion does have significant consequences beyond just the rep, both on main and on meta, particularly in what it does to the historical record - it becomes much harder to piece together the fact that it's the same person behind different posts.

We've seen users who cycle through account deletion and re-creation multiple times, and it gets extremely annoying.

But

If you had your reasons, you had your reasons.

If all you need is some enforced time away from an SE account, though, you should consider asking the mods for a voluntary suspension of the account.

DanielSank

7:20 AM

Yo, @EmilioPisanty

Suppose I have a differential equation $\dot x(t) = f(x; p)$ where $p$ is a set of constant parameters.

That's easy to solve.

Now suppose $p$ itself changes in a probabilistic way as a function of time. How do we treat that case?

Slereah

7:34 AM

Greetings, hu-mans

Emilio Pisanty

8:06 AM

@DanielSank with a whole lot of ingenuity and hard work, I should imagine, and a complete revamp of the mathematical framework

It sounds like a job for stochastic calculus

DanielSank

@EmilioPisanty blarg

Emilio Pisanty

Though maybe you're not quite deep in enough that you need to break out the Ito calculus guns

Slereah

pew pew

I had to break out the Ito calculus guns once

But I used

The physicist way

It was quite possibly the worst possible thing I've done, rigor-wise

u see, from the uncertainty relation, you have $$dx dp ~ approx \hbar$$

So that $$dx m \frac{dx}{dt} \approx \hbar$$

Or $$dx^2 \approx \frac{\hbar}{m} dt$$

Which means that in the Riemann sum, u have to keep terms of the size $dx^2$

This is 100% something that serious physicist have written down and put in very serious articles on path integration

And it actually gives the same results as Ito integrals

Emilio Pisanty

@Slereah greetings, sle-reah

Slereah

It gets even worse when you do it on a curved background

I don't remember what article used that

Let's see if I can find it again

iphc.cnrs.fr/IMG/pdf/pint.pdf

i think that one uses it

p. 17 on

user351417

11:28 AM

@EmilioPisanty Hehe no I'm sure I'm not fickle enough to do that. I'll see if I have the time and interest to re-join after a few months of college, and that starts in September. I was planning to write some answers on Physics SE over my summer break, but I decided it'd be more intelligent to spend that time taking courses and learning stuff instead: a few of the stuff I've written weren't great.

user351417

Anyways, see ya!

bolbteppa

@RyanUnger welcome back (later today)

@Slereah where's the Ito'ness

Slereah

p. 20

bolbteppa

Ah, integrating over fractal paths

Akash. B

11:52 AM

@JohnRennie you there?

Slereah

@JohnRennie is always with us in spirit

Jim

12:08 PM

^ I second that emotion

Secret

12:36 PM

This user has been automatically suspended for posting inappropriate content and cannot chat for 6 hours 24 minutes.

countdown to the GR group reassemble

Jim

1:18 PM

I went to a new dentist the other day and they made a joke that made me never want to go to any other dentist but them. They said "Both dentistry and physics have a lot in common. You see, in dentistry, like in physics, calculus is hard"

Secret

1:37 PM

26

Q: How I learned to stop worrying and start asking questions

As has been noted in the past, particularly in Question self-destruction: why don't experts ask more questions? and in Does reputation correlate with the question-to-answer ratio?, and also here, this site has the peculiarity that, in overwhelming proportion, our 'expert' users, by multiple measu...

Actually I found I tend to do the opposite, but I guess it's because I am still young in the academic ladder, being a PhD

Actually, I think I can wrote a whole essay to analyse this post, there are a lot of interesting things. Problem is it does not look like a Q and A

The part about academic folklore interested me as part of my broader personal research of the nature of the unknown

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