Hi All..

Hello @JohnRennie sir

1drv.ms/u/s!AozWlUoG8z4tjQSfUiCNgnSOXGxT

Pls see the link, I don't understand the calculation trick here.

@123 it's using the chain rule for differentiation.

@JohnRennie nice to see you.. if possible pls share calculation on page. Because in mobile latex not working. Thanks

It is starting by saying is that work is given by dW = Fdx. OK so far.

Ok

And from Newton's second law F = ma, and substituting for F gives dW = ma dx

Yes..

And a = dv/dt so this gives dW = m dv/dt dx

Okay..

If we integrate both sides then on the left side dW just integrates to W, so we get:

W = m ∫ dv/dt dx

Where we have taken m outside the integral because it is a constant.

Okay...

Now velocity is defined by v = dx/dt

Aye.. sir

If we treat this like a fraction (which physicists do all the time even though mathematicians disapprove) we can multiply both sides by dt to get:

v dt = dx

Then we take our equation:

W = m ∫ dv/dt dx

and use this to substitute for dx = v dt and this gives:

W = m ∫ dv/dt v dt

OK so far?

Roger that sir.. okay..

Now we can treat this like a fraction again and cancel the dts. This gives:

W = m ∫ v dv

Yes?

I have taken this picture from kleppner and kolenkow. From work and energy chapter.

Ohhhh... I see. You canceled dt

Yes :-)

And ∫ v dv is easy because it's just ¹⁄₂v²

But what knk did in this step. I confused. Look at the step

They are doing the same as me but in a slightly different way.

Suppose you take a function f and differentiate it then integrate it again Then you get back f. Yes?

If possible can you explain what method/ technique they used.

Yess..

i.e. ∫ (df/dt) dt = f

OK so far?

Okay this is what they did. It they did not cancel dt , they diff and then integerate

Yes. They took the trial function f = ¹⁄₂v²

Okay..

Thanks.. for the support @JohnRennie sir.

Then they used df/dt = df/dv dv/dt i.e. the chain rule.

They used limit of time in velocity. They are taking velocity as a function of time?

Hmmm... Okay.. thanks

If f = ¹⁄₂v² then df/dv = v

So df/dt = dv/dt v

Thank you very much @JohnRennie sir...

:-)

Knk said work and energy used in classical mechanics to predict the motion under known interaction.

@JohnRennie sir. Means this idea is primarily used to predict the future/ motion / trajectory under known forces? Is that true.

I have a thought experiment - if we consider two light clocks (Einstein style) one underwater in the ocean and the other above the water, both stationary relative to each other, if my frame of reference is the clock above water, I should see the underwater clock tick slower than mine since light travels slower in water than in air. Does that mean that time must have slowed down for the underwat...

nvm I just realised that in the underwater frame of reference, the light clock will still be ticking slower lol

damn it i thought i had the novel prize right there

"Common sense would dictate that, if the passage of time has slowed for a moving object, said object would observe the external world's time to be correspondingly sped up. Counterintuitively, special relativity predicts the opposite."

wut

if time has slowed down for me, I should see the world correspondingly sped up, how is this not the case?

@SlebLagnej They mean the symmetric time dilation paradox

@JohnRennie So in the example, the only "real" measurable time dilation difference in clocks is due to the acceleration changes of B and C?

@SlebLagnej I'm not sure what you are asking ...

In your answer in the post u sent, Albert, Bill, and Charlie, during the trip, each one of them will observe their clocks to be ticking the fastest, but if they get back together to compare clock differences, it's the acceleration of Bill and Charlie that causes Albert's clock to be some time ahead?

pls ask if something is unclear, I barely understand what im talking about

(btw I'm JingleBells, read my name backward ;-))

Is acceleration what actually causes time dilation, cuz in the twin paradox, if there was no acceleration (and instead velocity jumped from 0 to x instantaneously), then when twins get back together, there shouldn't be any clock difference?

And another question, in the twin paradox, shouldn't the rocketship deceleration undo what acceleration has done in terms of time dilation?

@SlebLagnej see:

Thanks, is there are simple explanation, tl;dr? An intuitive explanation of if and why acceleration cancels deceleration in terms of time dilation.

nvm I'll just google

In the twin paradox, It'd be kinda interesting for the twin on Earth to send their clock with radio waves to the traveling twin and vice-versa. Actually, it wouldn't very well since RF will travel at c and if Lorentz factor is 2, it'd take quite a while until the RF reaches the ship

It's simple enough to work out with a diagram

just draw the diagonal lines along the trajectory

you'll see how the clock runs differently

send one light ray per second or something

I'm reading a book and it describes some weird time dilation experiment where it's imagined that if you ride 0.9c next to a light beam, you would see it travel at c, but people on Earth would see you still traveling 0.9c, but the beam traveling with you. Is that correct? I'm struggling to relate the light clocks thought experiment with this one.

I phrased that badly. Imagine ur riding next to a beam at 0.9c. Of course, you wouldn't see the light beam traveling 10% faster than you, you'd see it traveling at c, but what would people on Earth see? Will they see you traveling 0.9c and the light beam 10% faster than you?

@JingleBells Yes.

what else would "travelling at 0.9c" mean if not that the people you're travelling at 0.9c relative to see you travelling at 9/10th the speed of light?

of course lol

I'm still practicing activating the lazy/slow/analytical side of my brain rather than the fast/automatic/dumb side

(reference to Thinking Fast and Slow ^)

My intuition behind the light clock experiment is if you're traveling really fast in a spaceship and carrying a light clock with you, people on Earth would see that light in your light clock travels a bigger distance (at velocity c, which is the same regardless of the frame of reference) because you're moving, but that can't be, since you have to be seeing the light ray traveling faster than what people on Earth are seeing, so the conclusion is that time for you and the ship must have

slowed down for you to experience the light ray traveling faster.

Is there are a better way to explain this? It still feels kinda unintuitive.

of course it feels unintuitive - our intuition is tailored for the kinds of speeds where relativistic effects are neglegible

I'm struggling to put the same intuition to the experiment above, where ur traveling next to the light beam. Since I can't measure distance like with the light clock, I don't know how to explain it.

consciousness for the person on the moving spaceship slows down so he/she can perceive light at speed c. Feels like relativity plays the same consciousness/observability tricks quantum mechanics plays lol

all signs point that we're living in a sim

it's as if the universe wants to keep the speed of light constant to all observers, so if frames of reference differ in the speed that light should have (such as the people on Earth seeing the light in the light clock on the spaceship traveling a greater distance), it compensates by slowing down time (maybe so the conscious being can perceive light at the speed the universe wants it to - c)

@JingleBells Eyy long time no see

Hello!

@SirCumference Heyyy! Remember me? :-P You're the Cosmology student who had a lot of trouble going to bed at night! How've you been? It's only been ... literal years, haha.

cosmology will keep you up at night

I still haven't solved Olber's paradox by hand

You'd think for such an old famous problem, it would be easier to find a rigorous derivation of it

@KaumudiH Eyy also long time no see!

I've been pretty good, how about you?

Hi! I would say "same," but not really, lol. Been okay though, throughout.

Have you graduated?

@KaumudiH Yep, how about you?

Not yet! Couple months left.

So what are you doing these days? Going onto post-grad or..?

@KaumudiH Right now I'm doing research and waiting to hear back from PhD admissions

Getting into a program has gotten a lot harder because of covid :/

@SirCumference Oh, that's great! Good luck with that!

@KaumudiH Thanks! How about you?

@SirCumference Oh, no, yeah, I can see how that would happen. :-/ One of my friends is also in the exact same boat as you. It's just been rejection after rejection for them.

@KaumudiH Yeah, I think some schools got double their normal amount of applicants. I haven't had much good luck yet, but I'll see

Wow, double!? That's crazy.

@SirCumference I'll be working in a tech. role at a company! Not really my cup of tea though. I'm mostly just doing it to get some experience and also so I have some time to figure out which subject to choose for my Masters.

@KaumudiH Oh, that's neat! What kind of subjects are you thinking about?

Oh, dude, I am properly clueless. I have so many interests. I was thinking of going into Neuroscience for the longest time. But I don't know if, with my complete lack of Biology background, that will even work. And over the past couple of years, I've also picked up an interest in Psych/Mental Health 'cause, well, I've been totally unwell, lol. So there's that, too.

you can do neuroscience without biology if you go more for the computational aspect

Predictive coding and all that stuff

@Slereah Yeah, so I've heard!

So that's still on the radar for me.

> I've been totally unwell

Sorry to hear about that :(

General stress with covid and post graduation I'm guessing?

But again. I'm not sure. These schools are so competitive these days. I don't know if, with 0 background and experience, I'll be able to make the cut.

eh, if it interests you, trying doesn't hurt, does it?

(also hello and welcome back)

@ACuriousMind I have tried many things and trying can hurt I found out

@KaumudiH I think it depends on the field. From what I heard, physics got a lot more competitive since covid limited what a lot of people could do between graduation and starting grad school, so they just decided to apply

@SirCumference Oh, yeah, that's there as well. For all of us. Which really sucks. But no. It's funny, actually. I like to think of the time I spent with y'all, here, as one of the last times I was okay, lol, mentally. Even then, it was getting kind of horrible, towards the end. But at least at the beginning. It's been a lot of different things, haha. Got diagnosed and stuff. But hey! I've been doing much better for the past 8 months or so. :-) Tysm for asking.

@SirCumference But I've heard some fields like Psych are different in that regard

@ACuriousMind ACM, hello! Tips hat. Yes, trying is good! I just don't really have much of a direction, lol, at this point. So I wouldn't know where to begin. But I agree!

@SirCumference Ahhh, yes, that's reasonable, I guess.

@Slereah knowing you it probably involved drugs and/or superglue or something ;P

@ACuriousMind I did try to smelt metal in my kitchen last month

@KaumudiH Dang, sorry about that. Good to hear you're doing better though

I do not recommend it

Molten metal stains are harsh on the counters

Oof.

that's one deposit you're not getting back, I guess? :P

I mean I own the flat

So it's all good

I'll try to sandpaper it out but it's a pretty deep burn

@KaumudiH One thing that might help is to see if you can audit a few classes for free at some unis

That way you can get a feel for what the subjects are like

@SirCumference Thanks! :-) So all your research stuff is being conducted online, or..? What's it like, the pandemic, where you are?

@Slereah dare I ask why you were melting metal?

@ACuriousMind Crom asked me to solve the riddle of steel

just general boredom? :P

@ACuriousMind It's been a long year

@KaumudiH Yeah, pretty much everything is online right now. I've been mostly doing data analysis for a telescope

My graduation was also online because of covid so that's eh

@SirCumference Oh, yeah, that's a good idea.

I will say

Props to bronze age people

@SirCumference Ooh, sounds interesting! What kinda analysis? (ELI5, I'm such a Cosmology noob, lol.)

Solving the riddle of steel isn't as easy as it seems

Even making a crucible is hard

@Slereah ah yes, I do recall this concept of "year" from the old times

@KaumudiH You could also see if a family member or friend happens to know an expert in those fields who could give you advice

@Slereah not sure, there weren't many places that made proper "steel", right?

most iron stuff was just...iron

Oh I wasn't making steel

That's just a Conan reference

@SirCumference :-( "Eh" indeed. Mine will also 100% be online. And I also missed a buuunch of other important final-year events, lol, 'cause of ... gestures broadly.

I replied to the bronze age mention, not the Conan reference! Of course I know the ol' Cimmerian

@KaumudiH Right now I'm just analyzing and modeling the spectra of galaxies/quasars

@SirCumference This is highly unlikely! But worth a try, yeah. :-)

@SirCumference I see! And to what end?

@KaumudiH Perhaps you could shoot an email to a prof from your uni in those fields and ask them questions

or ask if they could meet for a zoom meeting to give advice

I like how the villain's position is that control over people is stronger than steel, and then the moral of the movie is NO ACTUALLY BEING STRONG IS BEST

Moral for the ages

@SirCumference Oh, dude, this is the problem whenever I ask the Internet for advice about this. Someone always suggests asking professors in my uni, or maybe asking the "lab professor at the Neuroscience lab at your uni," like that is even a thing. x'D The profs. at my uni are ... not the best, sadly. I would come up with nothing at all if I had a conversation with them about this.

@KaumudiH I've only recently gotten started with it, but the first goal is to get some properties about them (e.g. their redshifts, amount of dust around them, etc.) from the model and compare it to other catalogs

True strength is being strong

and also have a sword

solid life advice

+1. Very solid.

@SirCumference Oh, I see!

I still haven't read the original Conan

I assume that it is a bit more subtle

@KaumudiH Oye, I know what you mean. Perhaps the folks at the psychology and neuroscience SE chat could help?

A few years ago the guys in this chat gave some very good advice to me when I was split on doing physics

I read a bunch of Conan novels from my parents' pulp fiction cellar when I was a teen, not sure whether these were the originals

Conan does have one of my favorite philosophy quote, somehow

"Let teachers and priests and philosophers brood over questions of reality and illusion. I know this: if life is illusion, then I am no less an illusion, and being thus, the illusion is real to me. I live, I burn with life, I love, I slay, and am content."

I don't remember much, but "subtle" is not among the things that come to mind :P

it's a good quote when someone asks if a physics concept is really real

@SirCumference Yes, maybe! I have considered that!

@ACuriousMind I mean, subtler than an Arnold movie, at least

now that's damning with faint praise

@KaumudiH But yeah, probably the best thing is to see if you could find some lectures or audit

Doing that helped give me a better idea of what I liked

@Slereah I love Hercules, it's so perfect

I can criticize, but really, Arnold had a remarkable acting career for a man who can't speak English

you'd think it would be a bigger hurdle

Yeah, yes. I should do that, at some point. Also, can I just say, I love how I popped in here, and we all got to talking, and immediately, more than one of you just sprung to help me figure out this stuff. Like, without me even explicitly telling you that I needed help. Even though, ofc, help is always appreciated. So tysm. <333

@KaumudiH No worries, a lot of us have probably been down that path of figuring out our careers

I'm still on that path depending on how admissions go

Yes, indeedy. :-)

@SirCumference Ah, yeah. Man, I hope things work out for you.

I don't think I have figured anything out, I just stumbled around :P

Thanks :) I'm gonna stay optimistic

@ACuriousMind Yeah I guess that might be how it always goes

But it tends to work out from what I've seen

@ACuriousMind I hear this a lot. And I think I'm just much too early in my career for me to appreciate that this is, indeed, kinda how it turns out for everyone.

Oh, btw, @SirCumference you still struggle with sleep stuff?

I'm getting the hang of it a little better haha

That is one conversation I recall having lots of times with you!

Finally

@SirCumference That's awesome. :-)

I couldn't wager a guess for how many people it works out overall, but it's definitely more common to hear "I kinda ended up here" than "This was my goal all along"

@Slereah ...is that a USB telegraph?

yes

@ACuriousMind So that's the official term for "morse code machine." I was just about to type that and embarrass myself, lol.

at least you recognized it at all ;)

they aren't exactly common these days

@Slereah This is a good quote, thanks for sharing! Very cool response to give to someone who asks what the consequences of the Universe being a simulation are, too.

it is from Queen of the Black Coast, if you want to give it a read

or cite it in your bibliography

@ACuriousMind Oh, I only recognized it because of Titanic, I think. x'D It was somewhere in my head, and I do suspect that it got lodged in there mostly 'cause I saw it in that one movie.

@Slereah Ooh, okay, thanks!

@ACuriousMind I'd say most people would?

From period pieces and cartoons

@SirCumference So are the others from that time period kinda gone, or do they still frequent the chat? I don't mean everyone, ofc, I know lots of them are still around. Like you! And John. And Daniel Sank, and ACM, and Slereah, etc. But what about the others? I remember Ocelo7, Bernardo, Barkala, Secret...

some are still around, some not, most less frequently than they used to

Ah, hm, I see.

Yeah, they pop up from time to time

@SirCumference sup

@JingleBells Ey speaking of which

How's life

good, how's urs

I've been in touch with John this whole time! But none of the others, as you can tell.

@KaumudiH Crazy to think most of us were high schoolers back then

Now we're college graduates

Oh, God, I know, right? Weren't you in your 1st year of college, or something? It's been 5 years, but I refuse to believe that it's been that long, haha.

@JingleBells Been pretty good

@KaumudiH Yeah I think I've been on this chat since I was 17

Damn.

0celo and HDE are now PhD students

I think Bernardo is working as an engineer

@KaumudiH I dunno if it's just me but it feels like time has been speeding up crazy these past 5 years

I deleted my old account. There was just too much information on here, lol, tied to my actual name. And it just felt so strange, keeping alive that part of me, when it's so far removed from the person I am, currently. But mostly for privacy reasons, lol.

time passes faster as you get older, it's a common feeling, probably because each new day progressively is a lesser fraction of the total time you've lived

@KaumudiH Yeah, I get what ya mean

@ACuriousMind Yeah but it feels like time slammed on the gas pedal when I turned 18

In fact, I had sent SO many messages here that I had to manually e-mail S.E to remove my account. 'Cause even though I did delete my account, my name was still tied to the messages here. That only got fixed after I contacted the team.

@ACuriousMind time dilation from getting fatter, perhaps

@SirCumference It's both, for me. Sometimes, it just goes SO unbearably slowly. And then, all at once, years have passed, somehow.

@SirCumference I'm 18 now, turning 19 in a month. I saw Veritasium had a video on this (why time seems to pass faster as you age), gonna watch it

It's crazy to think we're living in "the 20s"

or at least people will call it that eventually

I have read that part of the reason is that you just have less exceptional events and your mind uses them a lot to mark the passage of time

Just do something bold

Rob a bank

@Slereah I was literally just about to type this.

@KaumudiH Hopefully not all of it lol

How you cease to have novel experiences after a certain point.

well, the more you've experienced, there more likely you don't go "oh this is new and exciting" but "oh, this is new but kinda similar to the time when..."

When is GR gonna give a way to do reverse time dilation

that'd be nice

slow down everything a bit

still not going to college, I'm a man of my word, wish me luck :P

@SirCumference Hahaha, no, I most certainly do not condone that kinda crime. Or any kinda crime, for that matter.

@JingleBells for sure

eh, some crimes are fun

uh

mostly those relating to illegal substances :P

@SirCumference Ewww. Damn. That is very weird to think about.

I suspect that at this rate, it'll mostly just be remembered as the decade of the 'rona.

ACuriousMind with that profile picture and talking about drugs be a new level tho :D

The actual years in which shit hit the fan and all the repercussions.

2010s were better than 1910s, and 2020s were worse than 1920s

so maybe 2030s will be better than 1930s

well then again that's not a high bar to clear

@KaumudiH not so sure about that - look how little the Spanish flu features in our cultural memory compared to the "Roaring 20s" after it

then again, there kinda was a world war at the same time :P

imagine someone coming from the future and saying - which pandemic is this, the first or second covid?

@ACuriousMind Ahhh, yes.

just like ppl were calling ww1 the great world war

people also called ww1 "the war to end all wars"

that didn't exactly pan out as planned but hey

wars in 2021 be like Putin coming and nuking half the globe

@SirCumference F.

things are hopefully getting better with covid tho now that the vaccine is out

@SirCumference Yeah. But where I am, they've already run out of vaccines.

i wonder if it'll be a year or two when masks won't be necessary any more

we can use them as sleep masks

@KaumudiH dang, that's rough :/

@SirCumference Man, I sure hope it won't be 2 years and all.

@KaumudiH I guess that's a conservative estimate

though I don't want to be like the last us president who said it would've passed last april

I hope shaking hands never comes back :P

the age of fist bumps?

@SirCumference :-/ Yes. But they're also saying that all 18+ adults will be able to get vaccines starting next month. As for whether or not they will actually be available, who knows.

@SirCumference :'-)

I remember being a dumbass, talking to one of my friends, thinking it'd pass by the time his birthday rolled around. In May. Yeah. Dumbass.

Of last year, to be clear.

@KaumudiH Hindsight's 20/20 but I don't think any of us expected it'd last this long

I guess not, yeah.

more than anything it's kind of impressive that a vaccine was created so quickly

Certainly didn't expect this to happen, that's for sure:

woah, what happened?

(out of the loop on a lot of news lately)

The 2nd wave. :-) Is roughhh. And mostly, I think people stopped giving an eff.

oye, that's crazy

just when it seemed "flattening the curve" was relatively successful

but based on what you said, it might get better next month

There's loads of mismanagement in certain parts of the country. Wayyy more people dying than actually would have, if only the resources were being managed efficiently. Hospitals running out of beds, oxygen.

I know this is kinda cheesy but on a serious note, I wanna thank everyone who has helped me thru the years with all my weird questions and has stuck with me even when they had every reason to not. I learned a lot and I appreciate every help that I've gotten. Thank you ACuriousMind, JohnRennie, SirCumference, Semiclassical, Slereah, and more. Just letting you know, you made a difference in my life, and certainly helped me understand a lot of things.

@JingleBells 'Course dude

@SirCumference Hopefully!

Welp. I'm off, then! Getting pretty late 'round here. I'll talk to you all later. Thanks! And take care! It's a nightmare out there.

@KaumudiH Take care, also feel free to pop in when you want :-)

Yes! I shall. :-)

@DanielUnderwood Eyy also long time no see!

A classic tale