@JohnDuffield OK, so you're saying we can't travel 10 light years in less than 10 years time?

@barrycarter : no, because you can't travel faster than light, because of the wave nature of matter. But you can travel 10 light years in less than 10 years time as measured on your shipboard clock. See the relativistic rocket for details. If you could accelerate constantly at 1g you'd get to Vega, which is 27 light years away, in 6.6 years according to your clock.

@JohnDuffield Right, that's what I'm saying. I knew that already, but was trying to understand your message.

@JohnDuffield So, if I'm traveling between Earth and a planet 8 light years away at 0.8c, I will get to Earth in 4.8/0.8 or 6 years, correct?

(8 light years away in the rest reference frame of the two planets)

@ACuriousMind I'm currently struggling through Maggiore's QFT book when I've got some time. Great intro textbook with a dense overview of many topics. Of course I can't say I have no questions, but at the moment they are not questions stemming from fundamental misunderstandings, so I'm mostly able to look up the answer. Soon going to tackle those renormalization and regularization beasts, so I'm sure there will be more questions :)

How about you? Have you settled on the topic of your master thesis?

@0celo7 eh, yeah... I remember my supervisor not giving a fuck :P

Howdy

@Bass I'm trying to settle but administrative stuff and unresponsive profs keep getting in the way :P

2 days without heating---not having a good time.

@Danu What, again?

YES

JLF:@E(+@!R*U(*#!RPUJ

how old is the building you live in?

Idk, average age here in Munich. The machine that does the heating is supposedly ~30 years old. Don't know how bad that is.

@barrycarter : it takes you 10 years. But during that 10 years, only 6 years elapsed on your shipboard clock. Your light-clocks go slower because of your macroscopic motion through space, and so do all electromagnetic processes on board, because the maximum speed of those processes is c. Time dilation is just Pythagoras's theorem at heart, see this answer. It's simpler than you think.

I lived here for the past 1.5 years without any problems---now the heating broke thrice in two weeks.

Well, did something different break, or did they just not repair it properly?

@JohnDuffield So you're saying I age 10 years but my clocks only move forward 6 years?

The former would mean it's just too old and giving up, the latter that your landlord is a cheap bastard ;)

I think it might be a mix.

Me + my "roommate" (older guy, who rents part of the apartment to me) are not the only ones living here. Upstairs there's an elderly couple, right.

@barrycarter : no, all shipboard electromagnetic processes slow down, including those within your body and your brain. Your clocks advance 6 years, and you age 6 years.

The "Neffe" of the elderly man is apparently somehow capable of fixing stuff like this so when it first broke, he fixed it by replacing some component.

@barycenter Ya'll talking about broken clocks?

Now, when it broke the second time, my "roommate" fixed it by undoing what the other guy did.

@SirCumference Special relativity...

Oh...

Oh my god

that's not your name...

@Danu lol, your landlord should fix stuff (or rather pay professsionals to fix stuff), not random people you know :D

I've been misreading it this whole time

@JohnDuffield OK, so for all practical purposes, 6 years have passed onboard ship, correct?

Now, my "roommate" is gone for a few days and it's broken again, and the elderly guy is saying he fucked it up.

@SirCumference LOL :) I didn't even catch it until just now.

@SirCumference You're not the first one to mention it.

XD

@SirCumference I had to look up and see your message, since it obviously didn't "ping" me.

@SirCumference And I am the center of the universe, so it would be a good name.

@ACuriousMind I don't even KNOW who's supposed to fix this.

Dude, you need "barrycenter"

@Danu By my understanding of German custom and law, the person who owns the apartment is responsible.

@SirCumference Or barycentre or barycenter or barrycentre or barrycenter

Well with people picking astronomy names, like @LocalFluff and @HDE226868, I don't know what to expect

Have you considered getting a fan heater if this keeps happening?

@ACuriousMind I don't know who that is.

@SirCumference Yes, in retrospect, that would've been really clever of me.

I always assumed my "roommate" owned his part of the place, but now I'm not sure.

@ACuriousMind I honestly feel like I shouldn't have to buy stuff

@barrycarter : yes, you're time dilated. You're living your life in slo-mo mode because you're moving fast through space.

@barrycarter Er...you can still change it, can't you?

@Danu Oh, and if the heating is for the entire house, it's of course whoever owns the house.

@JohnDuffield OK, fantastic. But if you look at anyone else, they are in slow-mo, right?

@Danu I know, but it's better than freezing your ass off, isn't it?

@ACuriousMind Yeah, don't know who that is.

@ACuriousMind :(

@SirCumference Probably, but I've been here a while and people sort of know me as Barry Carter.

@SirCumference here = stackexchange overall, not physics.stackexchange

@Danu Surely you have property records and such in Germany?

@Danu Well, if you made your renting contract with your "roommate" and him alone, then I think from your prespective he's responsible. If he owns the flat, he has to pay to fix it, otherwise he needs to get the owner to fix it.

@ACuriousMind Yeah, I guess.

@barrycarter : generally yes, that's the twins paradox. I say the light in your light clock is moving like this /\/\/\/\/\ at a slower rate than my own, which is moving straight up and down like this ||. However you say that the light in my light clock is moving like this /\/\/\/\/\ at a slower rate than yours, which is moving straight up and down like this ||.

Thing is, he's gone till thursday.

And he is usually gone, so it's not easy, in practice, to get him to fix things in timely fashion.

...and you don't have his phone number?

@JohnDuffield Yes, but the twins paradox can be resolved because one twin accelerates and the other doesn't. And, for simplicity, let's consider regular everyday clocks, not mirror clocks.

@barrycarter : but there's no paradox. When you and I are separated by distance, you look smaller than me and I look smaller than you. We don't cry paradox at that, we just say it's perspective. There's a kind of perspective at work with our respective light clocks.

@ACuriousMind He's in Hong Kong right now.

What am I supposed to tell him? :P

@Danu Oh...well, that might make it a bit difficult for him to get someone to fix it :D

@JohnDuffield OK, but when someone accelerates, they really do age slower than the rest of the universe right?

@Danu "hey, the place burned down... do you happen to know who owns it?"

What has the couple upstairs done about the situation? Knitted warmer sweaters?

@ACuriousMind Come and ring my doorbell every morning in despair (not kidding)

...great...

They tried to have some people look at it, I think. I managed to get away last night to sleep at a friend's place so I'm not sure whether they managed to get someone this morning---but it ain't fixed.

It's like 80 degrees here, I might have to turn on the AC...

Well, I honestly don't know what to do in that situation. My landlord lives right below us, whenever something breaks, I just knock on his door and tell him what's wrong and the next day some plumber/electrician/whatever is there to fix it.

@barrycarter : acceleration doesn't resolve the Twins paradox. Who told you that? And it isn't actually acceleration per se that causes you to age slower. It's the relative motion. You need to accelerate to have that relative motion, but think about it: you could accelerate and decelerate repeatedly all the way home, but doing so reduces the time dilation factor.

@JohnDuffield I think that's the standard explanation of the twins paradox. If you accelerate to speed up and then "decelerate" (which is just accelerating in a different direction), you age less than the twin who doesn't accelerate.

@ACuriousMind Guess I'm screwed, eh?

@Danu Who pays utilities?

@barrycarter : the Twins Paradox is your clock goes slower than mine and mine goes slower than yours. Not you come back with fewer grey hairs than me.

@barrycarter I contribute a fixed amount every month, but he pays the bills.

@JohnDuffield OK, I heard the twins paradox as: one twin remains on Earth; the other travels around the galaxy accelerating and decelerating repeatedly. When he returns, he's aged less than the stay-at-home twin.

@Danu Space heater sounds like the way to go.

@Danu Yeah, for now. You should definitely try to find out who's actually responsible for fixing stuff around your place

Like I said, I think I shouldn't be spending any money on this

@ACuriousMind Yup.

@Danu Do you have a gas furnace? Or is that the thing that's broken?

@barrycarter That's what's broken.

@Danu But you have a gas stove and stuff, right? Fireplace?

No gas stove, no fireplace.

No warm water, either.

@Danu Yikes! But, somewhere, you have a gas line coming into the house, right?

In Germany most cooking is done on electric stoves btw

@Danu It's about 50/50 here.

@Danu Ah, but you do have electric stoves then?

@barrycarter Eh, not obviously so

@barrycarter Sure

@Danu So you could crank the electrical stoves and use them to heat up other things and so on?

Things like what?

@Danu Candles... well, ok, I can't think of anything else, but keeping the stove going should generate some heat.

@barrycarter : that's just SR time dilation. When you move fast through space you "local motion" within the ship is of necessity reduced by virtue of your macroscopic motion through space, because the maximum rate of motion is c.

@barrycarter It's on the opposite end of the house from my room, though.

@Danu Do you have a regular fan?

@barrycarter No

@Danu hmmm.... so no way to redirect the air flow... fans are pretty cheap though

Lol

@JohnDuffield I'm not sure I followed that. Assume shipless travel for the moment then.

That's one inefficient way of heating a hosue :P

@Danu Yeah, but you're not paying for it :)

lol

Already told you to play graphics-intensive games ;)

@ACuriousMind Ah yes, CPU heat.

Frayed extension cords might help too...

electric blanket?

Bah, just set your blanket on fire, that'll help.

@barrycarter : make sure you read the simple inference of time dilation due to relative velocity. You are affected to the same degree as the light because you're made of molecules which are made out of atoms which are made out of electrons and things, which have an electromagnetic nature and a wave nature. They can be diffracted.

@ACuriousMind I did, in fact, start playing Transistor (a year after you recommended it)

@JohnDuffield OK, let's drop the twins paradox momentarily and go back to my original question. Suppose I start 8 light years away from Earth at rest with respect to the Earth. Good so far?

Another enlightening discussion, I see? :D

@Danu Ha, nice :)

Did someone explain the facts of life to @barrycarter

@ACuriousMind Beat "the spine" yesterday---the game is a bit weird IMO.

I'm struggling to find really "nice" flow in the fights. They're mostly kinda clumsy

Maybe they're supposed to be...

@barrycarter : yep, no problem.

@Slereah ??

I cannot say it

It is

FORBIDDEN

@JohnDuffield OK, I then accelerate to 0.8c (with respect to Earth, in the direction of Earth) in one second. A bit fast, but still OK in theory?

@Slereah I honestly have no idea what you mean? :) SR?

@barrycarter Oh, he just means that most regular users here think JohnDuffield is mostly wrong in what he says.

And that's all I will say to that.

@ACuriousMind Yes, I did notice 3 downvotes.

@Danu Hmm...I think mine felt flowing nicely after the first few where you haven't that much choice yet

@ACuriousMind But hey, I'm dealing with @WillO so why not add one to the mix

Maybe you should experiment with other program combinations

@ACuriousMind I spent some time trying to get a "get" + "bomb" idea working

But it didn't really work out nicely. I mostly struggle a lot against those dogs, so far.

Also, I think the "limiters" are super OP: How am I only getting +4% for taking double damage?!

Hmmm, it's been a while, I don't remember all the combos

Well there's this "pulling" thing (Get)

and then there's this thing that just makes a bomb appear

which, if you hit it, deals a lot of damage.

Welp

Sandwich is made

So I tried to use attacks that hit a lot of people + the Get upgrade to make them suck guys to me, and then bombing them.

Time to go to bed

@Danu The limiter things are like the idols in bastion - more there for your own challenge than for their bonuses

Doesn't really work because most fights are a few strong units + a lot of support lame-o's

@ACuriousMind Hm...

@JohnDuffield Should we continue or have the others disheartened you?

G'night

@Danu Good night, and may you dream of warmth ;)

@barrycarter : no problem. Sadly some of the people who hang around here who don't want to help take a sadistic delight in downvoting the people who do. They won't explain why I'm wrong, because I'm not.

@JohnDuffield OK... so, I accelerate 0.8c in 1 second, are we still good with that?

@barrycarter : Yep, no problem.

@JohnDuffield and after I accelerate, the Earth is now 4.8 light years away (in my reference frame), correct?

IT LOADED

@Danu lol

@JohnDuffield I take delight in downvoting all wrong answers.

@barrycarter : no. When you change your speed, the distance between those two planets doesn't change one iota. The Earth is still 8 light years away, and whilst you're moving through space towards it, it goes round the Sun ten times.

@JohnDuffield So you're saying the Lorentz contraction doesn't apply?

@barrycarter : not the way that you think. When you accelerate you change. The Earth doesn't flatten into some ellipsoid shape just because you stepped on the gas. It doesn't actually length-contract. In similar vein the space between planet x and Earth doesn't change either.

@JohnDuffield OK, I agree that the planet and Earth still see each other as 8 ly apart. But, from my reference frame, the distance now appears to be 4.6 light years, right?

@barrycarter : right. The distance appears to be 4.8 light years. The time by your clock to travel that distance is 6 years. Speed is distance over time, and 4.8 divided by 6 is 0.8c. There's less to it than meets the eye.

@ACuriousMind Is there a function which is differentiable at one point, but nowhere else?

Before you tell me to google it, google doesn't work, internet is kaput

@JohnDuffield OK, so now let's ask the main question. Before I (the ship) start accelerating, I see Earth's clock as reading zero, correct?

@0celo7 Google doesn't work, but you can chat here? Color me skeptical.

@0celo7 I'm tempted to say that can't be true, since there must be an open interval around that one point where it is also differentiable.

@0celo7 I think you can prove that using the epsilon-delta definition of limit and derivative.

@ACuriousMind It's a DNS thing, Skype, texting and other things work, but I can't do physics homework or get my lit reading

Main site PSE won't load

@0celo7 Use a different DNS server, eg 4.4.4.4 or something

Wolfram is down

I only have a limited amount of time here!

@0celo7 How long does it take to change your DNS server?

I don't know what that means

@barrycarter : you can't actually see it, but there's no real issue is setting clocks. You and I could use some distant orthogonal GRB signal which reaches us at virtually the same time. We use that as t=0.

Okay, since the answer is straightforward, I'll write it here: Such a function exists: $$f(x) = \begin{cases} x^2 & x\in\mathbb{Q} \\ -x^2 & x\notin\mathbb{Q}\end{cases}$$

@JohnDuffield Right, because the Earth is still 8 light years away at this point. However, we can agree that, for practical purposes I can say "Earth's clock is at time 0 just before I accelerate", right?

@barrycarter : yes, no problem.

@ACuriousMind o.o

@JohnDuffield After I take 1 second to accelerate to 0.8c, what does the Earth clock now read?

@barrycarter : it's something like 0.8 seconds.

@JohnDuffield OK, but a negligible amount of time, right? So, I'm now traveling at 0.8c, and the Earth appears to be 4.8 light years from me, correct?

@ACuriousMind Ah, the difference quotient is $x$ if $x\in \mathbb{Q}$ and $-x$ if $x\notin\mathbb{Q}$

@barrycarter : correct.

but that goes to $0$ at $0$

@ACuriousMind Danke

@JohnDuffield Since I'm traveling at 0.8c relative to Earth, Earth's clock is moving slower than mine, correct? (as I view it)

@0celo7 Well, not "the derivative" since it's not differentiable at $x\neq 0$, but you got the right idea.

@ACuriousMind I should never combine math and intuition.

@ACuriousMind I edited it to difference quotient.

Did the edit not show up? My messages are lagging

@barrycarter You just need to train your intuition to be more mathy ;P

I did that once, got a man killed

@ACuriousMind No, I'm going to abandon my intuition by the roadside.

Calculating derivatives of my driving path did not work out for the guy riding the bike!

@barrycarter It'll get up and follow you whereever you went, that's human nature.

@ACuriousMind Intuitively, I realize that my intuition will follow me. Theoretically, however, I can get rid of it.

@barrycarter : not correct. You can't see it. And this is not the Twins Paradox. You're the one who accelerated and is now moving at 0.8c with respect to the universe. You can detect his via the CMBR dipole anisotropy. Your clock is moving slower than the Earth clock. You're the one who's time- dilated. Which is why yor clock ends up reading t=6 and the the Earth clock ends up reading t=10.

Wait a moment, there is a cauchy surface through every point!

@JohnDuffield wow the closed causal curves go around the wormhole into the parallel antiverse through the brane compacified flux moduli superspace

@JohnDuffield So you're saying there is a fundamental rest reference frame? That I am moving at 0.8c and the Earth is not?

@frank-dimeglio I summon thee to this place.

doesn't work like that, you're not a mod-wizard

@0celo7 Yes, but he doesn't know that ;)

What?

You're not going to ping him if you're not a mod!

@barrycarter He doesn't have 20 rep; even if that ping worked, there wouldn't be any point in doing so.

@0celo7 By mentioning his name, it should show up in his inbox, no?

@barrycarter Nae.

@0celo7 Well that sucks. Guess I'll have to become a mod.

@HDE226868 He seems so amusing.

@barrycarter Oh man, if I were a mod

Things would be mighty different around here

I could tell you why... the ocean's near the shore...

huh?

@0celo7 Wizard of Oz reference

@barrycarter Don't feed the trolls unless you've got backup.

@barrycarter : yes. The CMBR reference frame is the rest frame of the universe. See this answer which refers to Professor Douglas Scott: "There clearly is a frame where the CMB is at rest, and so this is, in some sense, the rest frame of the Universe". Note that it isn't an absolute frame. If you can't look outside your spaceship, you can't tell whether you're moving.

@JohnDuffield "But for doing any physics experiment, any other frame is as good as this one". So, I don't think there is a fundamental rest frame, that would violate the whole concept of relativity.

@HDE226868 Oh well, I've invited him to contact me directly.

@barrycarter Well, what you invite into your own mail account is your business, but please don't summon even more trolls here.

@ACuriousMind Apparently, I haven't the power.

Troll summoning must be a 4th level spell.

@ACuriousMind Dang, Black Hawk be slamming whites for shaming sluts in the 19th century

@barrycarter lol, you're not even 7th level?

Wimp.

huh?

@barrycarter : it doesn't violate the whole concept of relativity. Not at all. Relativity is really the theory of invariance, which says all your experiments inside your spaceship give the same results regardless of your motion, provided you aren't accelerating. It doesn't say you can't look out the window and measure your motion with respect to the universe.

@ACuriousMind I'm a cleric/fighter :P

@bar

Wow, that was weird

@JohnDuffield OK, but you're saying there IS a rest frame, and if I'm moving at 0.8*c with respect to the Earth, and the Earth is moving at 0.8*c with respect to me, Earth sees my clock as slow, but not vice versa?

@barrycarter Oh, so you might be 7th level, but you suck at efficient gaming :P

@ACuriousMind I meant a ranger/paladin or something.

@ACuriousMind I havent' played D&D in over 30 years.

@ACuriousMind Has it changed any?

@barrycarter Ohhhh...when someone writes cleric/fighter, that usually means they're multi-class, i.e. with levels in both cleric and fighter

@barrycarter Oh, yes, although I don't know the recent editions well.

@ACuriousMind Yes, that's what I meant. I was just trying to cover. We only had 6 levels back in my day!

@barrycarter : I didn't say that. I said you can't see that clock on Earth. I said this is not the Twins Paradox. I can't see the clock in your spaceship either.

@JohnDuffield I can look at Earth's clock, can't I? I mean I'd need a really good telescope, but at least in theory I could look at it?

@barrycarter I think you might feel at home up to the 2nd edition, recognize the game up to 3.5, but the 4th and 5th edition will look completely alien to you

@ACuriousMind Actually, I have seen some of the newer editions... I literally played the basic edition.

wtf are you people talking about

I rarely play D&D though, mostly know it from the computer games. My pen and paper games are usually FATE these days.

@ACuriousMind Back in my day, D&D was the only gaming system we had.

@JohnDuffield Bah, the chat is filled with video games

@0

@0celo7 VIDEO games?

@ACuriousMind Even more?

@barrycarter I know, and I don't know whether to pity you or the envy your lack of option paralysis ;)

???

@ACuriousMind It took two minutes to roll a character and about 5 minutes to kill one off.

@barrycarter : OK, if you had a "gedanken" telescope, yes you could look at it. You could watch that clock every moment of your trip home. Let's make it a big clock so you can see it more easily. Let's make this clock the Earth's orbit round the Sun. You would see it tick ten times whilst you were travelling home.

@JohnDuffield Actually, let's make it a regular clock since I don't want to deal with the Earth's acceleration around the Sun. My question: after I'd finished accelerating, that clock would read about 1.8 seconds or something, right?