Thread: relativity

Perpendiculaaaaargh, bollocks, sorry. Mutually perpendicular.

I did warn you.

Originally Posted by PhilosopherStoned

bollocks. a vector isn't a line. You can think of it as a directed line segment, a translation of the plane (this is the best way to think of it at your level).

i didnt say a vector is a line. i said a line is a vector. its really not the same thing. and when i did maths we did a unit called "vectors" and it was all about 2d and 3d lines.

of course i know more about vectors than that because i do physics too. maths really did kinda leave a chunk out of it.

A line isn't a vector because a line doesn't have a direction associated with it.

Originally Posted by Xei

A line isn't a vector because a line doesn't have a direction associated with it.

what i was talking about was a vector being represented by a line. in higher maths, we didnt use speeds and forces etc. just distances (or displacement rather).

infact, doesnt that mean a line is a vector. because any time you would draw a line in maths, you could give it a displacement value, like 4 units or something.

But vectors aren't represented by lines, they're represented by arrows.

When you draw a line you aren't giving it a direction. You aren't saying if it's a displacement from point A to B or B to A.

Originally Posted by Xei

But vectors aren't represented by lines, they're represented by arrows.

When you draw a line you aren't giving it a direction. You aren't saying if it's a displacement from point A to B or B to A.

ok, good point. i basically thought a line was the same as an arrow.

soooo, does that mean you cannot integrate a line?

p.s. turns out we dont do relativity in higher physics, nor advanced physics. but you do in uni

Yeah I'd be surprised if you do, although it's not actually particularly hard. General relativity however is extremely complex, it took Einstein 10 years to work out.

Sure, you can integrate a line... for example the integral of 4x + 3 dx between 0 and 10 is [2x^2 + 3x]0,10 = 230.

Originally Posted by Xei

Sure, you can integrate a line... for example the integral of 4x + 3 dx between 0 and 10 is [2x^2 + 3x]0,10 = 230.

holy bujeezus, we went and argued all that time when i was right in the first place

Jumping in here, but I think it was Einstien who said that if you traveled at the speed of light for one year away from earth, and came back (let's say instantly) that you'd be one year younger than everyone else.

Originally Posted by slayer

Jumping in here, but I think it was Einstien who said that if you traveled at the speed of light for one year away from earth, and came back (let's say instantly) that you'd be one year younger than everyone else.

that sounds about right, because of time dillation. not that i know much about it, i guess thats why i made the thread. but to be honest, i thought it would be more extreme than that if you were travelling exactly the speed of light (hypothetically of course, since it is impossible)

So... if she weighs the same as a duck, then she's made of wood, and therefore... She's a witch!

Originally Posted by slayer

Jumping in here, but I think it was Einstien who said that if you traveled at the speed of light for one year away from earth, and came back (let's say instantly) that you'd be one year younger than everyone else.

He said that if you travel at the speed of light for one hour and come back, about 75 years will have passed on Earth.

I took calculus in college in 1991. It's all fuzzy to me now. You people are fucking with my head. I have taught algebra and geometry, but I think I need to go back and learn calculus once and for all. I don't like not understanding shit!

lul at arbitrary figure...

Nah you can't travel at the speed of light at all.

You can arbitrarily close to it however, and doing so will make time pass for everybody else an arbitrary factor faster. The factor's calculated as

1/sqrt(1-v^2/c^2)

so you can see that as your velocity v approaches c, v^2 approaches c^2, so v^2/c^2 approaches 1, so the denominator approaches sqrt(1-1) = sqrt0 = 0, and so the factor approaches infinity.

If you actually travelled at the speed of light (which you can't because it would require infinite energy), this suggests that you'd instantly find yourself at the end of the universe.

Incidentally this all has extremely solid empirical evidence.

As an aside UM, whichever artist drew your avatar clearly wasn't listening to Lennon properly. That's been bugging me for ages...

Originally Posted by slash112

holy bujeezus, we went and argued all that time when i was right in the first place

Well if you actually look at the conversation... no. :/

I explained that a line integral isn't an integral of a line, rather it involves vectors, you said a line is a vector, I said no.

I never said you can't integrate a line...

Originally Posted by Universal Mind

He said that if you travel at the speed of light for one hour and come back, about 75 years will have passed on Earth.

Holy crap

Originally Posted by slayer

Holy crap

Yeah, it's pretty damn mind blowing.

Originally Posted by Xei

As an aside UM, whichever artist drew your avatar clearly wasn't listening to Lennon properly. That's been bugging me for ages...

Why do you say that? It is an illustration of the "Lucy in the Sky with Diamonds" lyrics, "Climb in the back of your head in the clouds, and you're gone." The artist is Alan Aldridge, the author and chief artist of the book The Beatles: Illustrated Lyrics, and that painting is in it. Alan Aldridge was a good friend of all four Beatles and a design consultant for Apple Corps, which was founded by the Beatles and was the company that published a lot of their side material in the late 60's. Aldridge even illustrated the company's logo. How did he misinterpret the line?

http://www.wornfree.com/T-shirts/alan-aldridge-shirts

http://en.wikipedia.org/wiki/Apple_Corps

I explained in the post after that how that's not true... -_-

Why do you say that? It is an illustration of the "Lucy in the Sky with Diamonds" lyrics, "Climb in the back of your head in the clouds, and you're gone." The artist is Alan Aldridge, the author and chief artist of the book The Beatles: Illustrated Lyrics, and that painting is in it. Alan Aldridge was a good friend of all four Beatles and a design consultant for Apple Corps, which was founded by the Beatles and the company that published a lot of their side material in the late 60's. Aldridge even designed the company's logo. How did he misinterpret the line?

Perhaps you should listen to the actual music...

Seriously Sgt. Pepper is in my opinion the greatest album ever recorded.

The correct line is:

Newspaper taxis appear on the shore,
waiting to take you away,
climb in the back with your head in the clouds,
and you're gone.

It's saying climb in the back of the taxi, not climb in the back of your head.

He pronounces it quite clearly... perhaps Alan Aldridge didn't actually listen to their music. Or perhaps he was just high. The latter is more likely given the period and setting.

Originally Posted by Xei

Perhaps you should listen to the actual music...

Seriously Sgt. Pepper is in my opinion the greatest album ever recorded.

The correct line is:

Newspaper taxis appear on the shore,
waiting to take you away,
climb in the back with your head in the clouds,
and you're gone.

It's saying climb in the back of the taxi, not climb in the back of your head.

He pronounces it quite clearly... perhaps Alan Aldridge didn't actually listen to their music. Or perhaps he was just high. The latter is more likely given the period and setting.

Well, the British accents might make a pronoun sound fuzzy to me sometimes, but Aldridge is British himself and knows their lyrics like he knows the alphabet. I just told you that Aldridge was a design consultant and artist for the Beatles' company and personal friend of the Beatles. Don't you think they might have caught a glimpse of that painting before it was published in the central book of Beatles art and lyrics? I'm pretty sure Alan Aldridge listened to the band's music, as I do obsessively. Have you ever checked out the book the painting is in? A lot of the art illustrates specific lines and even specific characters mentioned. The point was not always to put it all into context of the entire song. Aldridge is a creative supergenius, and he illustrated Lennon climbing in the "back" with his head in the clouds, on his way to being gone. The "back" he illustrated in the surreal craziness was Lennon's own head and not the more literal interpretation involving the context of the rest of the song. Pretty trippy, huh?

Originally Posted by Universal Mind

He said that if you travel at the speed of light for one hour and come back, about 75 years will have passed on Earth.

As xei was too polite to say, bollocks. I'll add my explanation below.

Originally Posted by Universal Mind

I took calculus in college in 1991. It's all fuzzy to me now. You people are fucking with my head. I have taught algebra and geometry, but I think I need to go back and learn calculus once and for all. I don't like not understanding shit!

I've been getting into math again recently if you haven't been able to tell. I love the stuff. I always need to keep the elementary stuff in my head so I'm always happy to answer any questions about anything. I'm pretty patient as long as you're not telling me that it's allright to torture other life forms (wrt factory farming) or evolution is a lie.

Originally Posted by Xei

You can arbitrarily close to it however, and doing so will make time pass for everybody else an arbitrary factor faster

This isn't quite right. Time is a purely local phenomenon in relativity so that what you do can't affect what other observers measure. Your time goes slower, theirs is unaffected. I'm maybe being a little pedantic but that's the way it is. Something moving at the speed of light measures zero time. so a photon from the CMBR has measured zero time since it was first emitted. pretty cool.

The reason for this is related to the whole e=mc^2 thing. essentially, the faster you go, the more energy you have and hence the more you weigh and hence the more energy it takes to further accelerate your increasing massive ass. You also get shorter and shorter as measured by a stationary observer.

xei, i've spent 15 minutes figuring out how to do the problem you gave me with just the dot product and linear equations and then 30 minutes fucking up my calculations. I redid my computer recently and so I don't have a program yet to do funky calculations for me and, unfortunately, I suck at arithmetic. I'm better than jaques hadamard though. Apparently, he couldn't (more likely refused) to count past three.

I'm not sure how 'climb in the back' could ever be translated as 'climb in the back of your head'... :l

But whatever. Just pointing out that that's not what the lyrics actually say.

This isn't quite right. Time is a purely local phenomenon in relativity so that what you do can't affect what other observers measure. Your time goes slower, theirs is unaffected. I'm maybe being a little pedantic but that's the way it is. Something moving at the speed of light measures zero time. so a photon from the CMBR has measured zero time since it was first emitted. pretty cool.

Yeah I was being sloppy, I was essentially using 'time goes faster for everybody else' synonymously with 'time goes slower for you'; is the latter correct?

I'll try and do that problem to make sure I haven't done anything idiotic. I need practice anyway before uni starts.

Originally Posted by PhilosopherStoned

This isn't quite right. Time is a purely local phenomenon in relativity so that what you do can't affect what other observers measure. Your time goes slower, theirs is unaffected. I'm maybe being a little pedantic but that's the way it is. Something moving at the speed of light measures zero time. so a photon from the CMBR has measured zero time since it was first emitted. pretty cool.

I wasn't saying the traveler has an effect on the people on Earth. I was talking about an affect on the traveler. His body does bizarre slowing down and other stuff in relation to the other objects, so when he gets back, about 75 years have passed. It's not because he sped time up for them. It is a result of slowing time down for himself. So his brain and watch's interpretation of an hour is dozens of years to those moving much more slowly. Is that right?

Originally Posted by PhilosopherStoned

I've been getting into math again recently if you haven't been able to tell. I love the stuff. I always need to keep the elementary stuff in my head so I'm always happy to answer any questions about anything. I'm pretty patient as long as you're not telling me that it's allright to torture other life forms (wrt factory farming) or evolution is a lie.

Thanks much. I think I should probably get a book, though. I might have left my old ass one at my parents' house. I should study on my own before trying to make you my personal professor. I am extremely obnoxious with a never ending onslaught of questions when I try to get people to teach me tons of material one on one. I might still have a good grip on Calculus I. I think what you guys are discussing are Calculus II. It seems like we got to derivatives at the end of Calculus I and integrals at the beginning of Calculus II.

Originally Posted by Xei

I'm not sure how 'climb in the back' could ever be translated as 'climb in the back of your head'... :l

Without a modifying prepositional phrase for "back", the meaning is open to creativity, as long as the focus is completely on the line and not the other ones.

Hmmm anyway.

I wasn't saying the traveler has an effect on the people on Earth. I was talking about an affect on the traveler. His body does bizarre slowing down and other stuff in relation to the other objects, so when he gets back, about 75 years have passed. It's not because he sped time up for them. That is what I was taught in school and by educational videos (I think Carl Sagan hosted one of them.) back in the hair band era, at least.

He'd be travelling a fraction of the speed of light, not the speed of light, as I explained.

Oh and PS I answered the vectors question... basically you put the two equations equal to s and t respectively to get them into vector form of a line, you solve simultaneously to get the intersection point, and then you cross product their direction vectors to get the direction vector of the new line. You can do it with dot products but it takes a while because you have to create a vector (a,b,c), dot it with the two perpendicular direction vectors and set it equals to cos(pi/2) = 0, then solve the simultaneous equations in terms of a, b or c, and that gets you the direction vector.

Answer in most obvious form is r = 1/4*(19, 5, 45) + q*(-7, 1, 2).

Originally Posted by Universal Mind

I wasn't saying the traveler has an effect on the people on Earth. I was talking about an affect on the traveler. His body does bizarre slowing down and other stuff in relation to the other objects, so when he gets back, about 75 years have passed.

I was talking about what xei said. I forgot to relate it to what you said, when you say that he travels at the speed of light for an hour, that only makes sense in respect to the people here on earth (or anybody that's not travelling the speed of light) because he is measuring zero time the whole way. so when he stopped, only an hour would have passed if that's what the regular observer measured. There's no way einstein said that. It could be that the traveller is travelling close to the speed of light. that would make perfect sense.

Originally Posted by Universal Mind

Thanks much. I think I should probably get a book, though. I might have left my old ass one at my parents' house. I should study on my own before trying to make you my personal professor. I am extremely obnoxious with a never ending onslaught of questions when I try to get people to teach me tons of material one on one. I might still have a good grip on Calculus I. I think what you guys are discussing are Calculus II. It seems like we got to derivatives at the end of Calculus I and integrals at the beginning of Calculus II.

I forgot to recommend essential calculus with applications

It goes straight to the point but sticks to easy functions. It also has actual proofs which are lacking in most calculus books. It's what I taught myself calculus out of when I was learning for the first time. There is a lot of stuff that it doesn't cover but it nails the stuff that it does cover. It would be a pretty good reintroduction. Plus, it's only around ten dollars (gotta love dover) so if you end up not liking it, you haven't wasted that much money.

According to mein calculator, if you wanted to go forwards 75 years in an hour, you'd have to travel at

sqrt(431648999999)/657000 * the speed of light.

Which is around 99.9999999998842% of the speed of light.

So there you go. :V

Originally Posted by Xei

He'd be travelling a fraction of the speed of light, not the speed of light, as I explained.

Yeah, I was off on that in the hypothetical. I know that traveling the speed of light is theorized to be impossible in reality.

Originally Posted by PhilosopherStoned

I was talking about what xei said. I forgot to relate it to what you said, when you say that he travels at the speed of light for an hour, that only makes sense in respect to the people here on earth (or anybody that's not travelling the speed of light) because he is measuring zero time the whole way. so when he stopped, only an hour would have passed if that's what the regular observer measured. There's no way einstein said that. It could be that the traveller is travelling close to the speed of light. that would make perfect sense.

The "close to" part is something I left out. I also talked about traveling for an hour when what I said applies to just a few minutes, according to Carl Sagan. I think a commercial for a science magazine talked about it happening after the traveler's hour. I just found that Sagan video I mentioned...

http://www.youtube.com/watch?v=lPoGVP-wZv8

I think that should clear up a whole lot.

Originally Posted by Xei

According to mein calculator

I can't find mine