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Dro
Joined: 10 Jul 2006 Posts: 3897

Posted: Mon Jul 17, 2006 7:03 pm Post subject: 


There may not be an infinite number of objects of any type, but can't there be an infinity of other types? Would you say there are infinite ways for me to move from where I am to where you are? I'm not aware of any granularity in space, although maybe my mass can only 'lock in' to electron scale locations, which would make it finite. 

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Flion
Joined: 09 Jul 2006 Posts: 589 Location: Don't look up! (Damn pigeons...)

Posted: Mon Jul 17, 2006 8:39 pm Post subject: 


A good book on it for beginners is Dr. Richard Feynman's Q.E.D. He was an eccentric genius involved in the manhattan project who spent most of his career teaching and bringing science down from Olympus to us mere mortals. Also fun, but off topic, are his books about his life. Saying he was an interesting personality is like saying Hiroshima was a little explosion...
Edit  Re: the infinity question (somehow I replied after only reading the first page )  if the universe is not infinite, then there may be a continuum that is. Thought experiment: case 1  universe is infinite. case 2  universe is finite, i.e. bounded. What lies on other side of boundary? Call it metauniverse. Repeat cases 1 & 2 for metauniverse. Quandry case 3  universe is finite but unbounded, i.e. nothing exists outside boundary. Then how can there be an 'outside' or why is there a boundary?
BTW, it's not a proof, just a postulate... _________________
Halen wrote:  The reason that "people actually see the points people make" = "people agree with me" is because I. Am. Right! 


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mouse
Joined: 10 Jul 2006 Posts: 19345 Location: under the bed

Posted: Mon Jul 17, 2006 10:44 pm Post subject: 


Daugaard wrote:  I just read part of the Wikipedia article on Schrödinger's cat... Am I the only one that really don't get how observing the cat can in anyway change its state? 
it doesn't change it's state  only our knowledge of its state. in my opinion (once i worked it out) it's written oddly. the fact of the matter is, from the cat's perspective, it's immediately clear whether it is alive or dead. we, from outside the box, can't say whether it's alive or dead though, so for us, it's state is uncertain.
although as i read the wiki article  schroedinger himself set this thought experiment up not as a way to demonstrate the impossibility of determining the state of the cat, but the fact that, whether or not we know what it is, the cat has a definite state. apparently there were people arguing quantum mechanics who failed to understand our inability to determine a certain state does not mean that that particular state exists.
i expect someone to come along momentarily and demolish this argument.
....although, along schroedinger's lines, i suppose if i refuse to ever open this thread again, then my explanation both will and will not be demolished.... _________________ aka: neverscared!
a flux of vibrant matter 

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mantismag
Joined: 09 Jul 2006 Posts: 81

Posted: Mon Jul 17, 2006 11:37 pm Post subject: 


sorry that's wrong. that's a normal view of how things work. the quantum view is that both possiblities exist at the same time. the cat is both alive and dead because the particle that triggers the outcome does not exist in a definite position. it exists as a probablity wave. therefore it is in both sides of the box and neither. it is not until we observe it that the probability wave collapses that the state is determined.
of course one might argue that the cat is capable of observing whether or not the detector releases the poison gas or not and therefore itself collapses the probability wave to one side of the box.
*disclaimer* i haven't actually read the wiki article. this is just from my understanding of the schrodinger's cat thought experiment. 

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Michael
Joined: 09 Jul 2006 Posts: 10918

Posted: Tue Jul 18, 2006 12:16 am Post subject: 


even the detector can count as an 'observer'
I don't understand this myself so I really can't explain but I think mouse is right about Schroedingers intentions. Especially since Einstein was so pleased with it, who was always very against the introduction of probability in particle physics (hence the 'god doesn't play dice' (hence the beautiful reply made by Bohr: 'stop telling god what to do'))
Wiki says this:
Quote:  "The [wavefunction] for the entire system would [have] the living and the dead cat (pardon the expression) [sic] mixed or smeared out in equal parts."[1] Because we cannot get along without making classical approximations, quantum mechanics is incomplete without some rules to relate the classical and quantum descriptions. One way of looking at this connection is to say that the wavefunction collapses and the cat becomes dead or remains alive instead of a mixture of both. 
So the problem itself is not so difficult. The physics predict two cats 'smeared out in equal parts' yet we're pretty sure there's only ever one cat in the box. It's the attempt to concile these two that get fuzzy... 

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mantismag
Joined: 09 Jul 2006 Posts: 81

Posted: Tue Jul 18, 2006 1:58 am Post subject: 


not two cats. one cat. it's probably easiest to understand in scifi terms. two alternate realities. they exist together in the same space and there actually is some interaction between them. when we observe it, one of the realities is chosen and it becomes almost as if it was that way all along.
except on the very small level. when you deal with things like photons you can get some weird interactions between the two alternate realities. for example when you shine two light beams on top of each other the waves interfere with each other. think ripples of water. where two peaks intersect you get a peak twice as high. if you want an easy to see example of how this works grab a slinky and a friend. you wave your arm and send a wave down the slinky and your friend does the same. when they cross the wave will double. now, you can split a light beam in two and shine both beams on photographic paper and capture an interference pattern. here's where it gets interesting. if you slow down the light beam so that only one photon leaves at a time with a 50% chance of being on either side of the split, over time you'll still get that interference pattern. it's as if the photon is going both ways at the same time and interfering with itself. if you put detectors just after the split to figure out which side each photon went to the interference pattern goes away because we know where the photon is and so it exists as a photon and not as a probability wave of where the photon is so it can't interfere with itself. 

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Jinx
Joined: 09 Jul 2006 Posts: 3654 Location: America, fuck yeah!

Posted: Tue Jul 18, 2006 4:16 am Post subject: 


Flion wrote: 
if the universe is not infinite, then there may be a continuum that is. Thought experiment: case 1  universe is infinite. case 2  universe is finite, i.e. bounded. What lies on other side of boundary? Call it metauniverse. Repeat cases 1 & 2 for metauniverse. Quandry case 3  universe is finite but unbounded, i.e. nothing exists outside boundary. Then how can there be an 'outside' or why is there a boundary?
BTW, it's not a proof, just a postulate... 
You're mixing up "infinite" and "unbounded". In fact, in your quandrous case 3, you actually postulate the universe being unbounded, then refer to "outside [the] boundary".
The surface of the Earth is finite, but it is not bounded.
Likewise, a finite, 3dimensional universe can be finite, but by curving through a 4th dimension, no have a boundary. IOW, given sufficient time, one could travel in a straight line and return to his/her starting point from the opposite direction, just as one can travel in a straight line on the surface of a sphere and return to the same point.
The universe, or the number of stars at least, is definitely finite. _________________ The universe we observe has precisely the properties we should expect if there is, at bottom, no design, no purpose, no evil, no good, nothing but blind, pitiless indifference.
 Charles Darwin 

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mantismag
Joined: 09 Jul 2006 Posts: 81

Posted: Tue Jul 18, 2006 4:43 am Post subject: 


not having endpoints doesn't make it unbounded. bounded simply means it's contained. it has limits. i can define a sphere of a certain radius and say that the entire earth is contained within that sphere. it is bounded.
conversely something that is unbounded would have no limits. for example, when you define an unbounded number set that means you continue to count unto infinity. 

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Jinx
Joined: 09 Jul 2006 Posts: 3654 Location: America, fuck yeah!

Posted: Tue Jul 18, 2006 5:51 am Post subject: 


mantismag wrote:  not having endpoints doesn't make it unbounded. bounded simply means it's contained. it has limits. i can define a sphere of a certain radius and say that the entire earth is contained within that sphere. it is bounded.
conversely something that is unbounded would have no limits. for example, when you define an unbounded number set that means you continue to count unto infinity. 
Perhaps I am inappropriately applying a layman's semantics here. When I say "not bounded" I mean "without a boundary", not "unlimited". I believe that defining something as finite implicitly puts a limit on it.
While a sphere has a boundary, it is it's surface. Within the 2dimensional "universe" of the sphere's surface though, there exists no boundary, no edge. You can travel indefinitely along a straight line as defined in obtuse geometry following the great circle of a sphere. You will never encounter an edge. However, the surface of that sphere is most definitely finite, and it can be measured.
The thought experiment previously described implies the universe cannot be finite because it would then have a boundary at "the end of the universe", followed by the question "What exists beyond the edge?"
My point is that something finite does not have to have an "edge" or "boundary", not that it is "limitless". _________________ The universe we observe has precisely the properties we should expect if there is, at bottom, no design, no purpose, no evil, no good, nothing but blind, pitiless indifference.
 Charles Darwin 

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bun bun Guest

Posted: Tue Jul 18, 2006 9:03 am Post subject: 


Jinx wrote:  mantismag wrote:  not having endpoints doesn't make it unbounded. bounded simply means it's contained. it has limits. i can define a sphere of a certain radius and say that the entire earth is contained within that sphere. it is bounded.
conversely something that is unbounded would have no limits. for example, when you define an unbounded number set that means you continue to count unto infinity. 
Perhaps I am inappropriately applying a layman's semantics here. When I say "not bounded" I mean "without a boundary", not "unlimited". I believe that defining something as finite implicitly puts a limit on it.
While a sphere has a boundary, it is it's surface. Within the 2dimensional "universe" of the sphere's surface though, there exists no boundary, no edge. You can travel indefinitely along a straight line as defined in obtuse geometry following the great circle of a sphere. You will never encounter an edge. However, the surface of that sphere is most definitely finite, and it can be measured.
The thought experiment previously described implies the universe cannot be finite because it would then have a boundary at "the end of the universe", followed by the question "What exists beyond the edge?"
My point is that something finite does not have to have an "edge" or "boundary", not that it is "limitless". 
The universe is shaped like a taurus, according to most astrophysicists (shaped like a doughnut) FYI, anyone who was wondering. Um, also, <3 to Jinx for explaining it better than I could.
What really helped me, though, was to realise that it's not that the universe is floating in some ether of space and is bent, because then you could leave it, rather, that it is spacetime that is bent. this is why, when physicists say that the universe is expanding, they don't mean, expanding into something else, they mean that the space that exists, period, is increasing. The big bang was not an explosion like you see in the movies, but rather, a sudden expansion of the existing space in the universe. 

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Usagi Miyamoto
Joined: 09 Jul 2006 Posts: 2249 Location: wish you were here

Posted: Tue Jul 18, 2006 10:50 am Post subject: 


heard _________________ The reward for a good life is a good life.
Last edited by Usagi Miyamoto on Fri Jun 29, 2007 9:55 pm; edited 1 time in total 

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WheelsOfConfusion
Joined: 09 Jul 2006 Posts: 13148 Location: Unknown Kaddath

Posted: Tue Jul 18, 2006 10:50 am Post subject: 


bun bun wrote:  The universe is shaped like a taurus, according to most astrophysicists (shaped like a doughnut) 
Torus?
Last I heard the exact sort of geometry was still up for debate, though I have heard some "open" or "closed" tidbits in the news which would help a lot in determining the best model to use as a representation. It could still be saddleshaped, or even sfeerikal. Anyway, a torus is another example of an unbounded but finite shape. 

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bun bun Guest

Posted: Tue Jul 18, 2006 12:19 pm Post subject: 


yeah. because a taurus is a star sign. or a car. duhhhhhhhhhhhhhhhhh...
I am Dumb. Nice to meetcha. 

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Fhqwhgads
Joined: 11 Jul 2006 Posts: 1337 Location: sfcaus

Posted: Tue Jul 18, 2006 12:35 pm Post subject: 


Jinx wrote:  Within the 2dimensional "universe" of the sphere's surface though, there exists no boundary, no edge. You can travel indefinitely along a straight line as defined in obtuse geometry following the great circle of a sphere. You will never encounter an edge. However, the surface of that sphere is most definitely finite, and it can be measured. 
OK. I think I'm starting to see what people are meaning by "unbounded" vs "limitless". My only nitpick with the above is: in order for Mr Flatlander to get back to where he started, he has to (albeit unknowingly) curl through the 3rd dimension to get there. Which is fine, just not 2D. Website pimping time...
...so does the torus shape then indicate that the entire universe is curling through higher dimensions in order to be unbounded? _________________ There are 4 boxes to use in the defense of liberty: soap, ballot, jury, ammo. Use in that order. Starting now. 

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Flion
Joined: 09 Jul 2006 Posts: 589 Location: Don't look up! (Damn pigeons...)

Posted: Tue Jul 18, 2006 1:20 pm Post subject: 


Jinx wrote:  mantismag wrote:  not having endpoints doesn't make it unbounded. bounded simply means it's contained. it has limits. i can define a sphere of a certain radius and say that the entire earth is contained within that sphere. it is bounded.
conversely something that is unbounded would have no limits. for example, when you define an unbounded number set that means you continue to count unto infinity. 
Perhaps I am inappropriately applying a layman's semantics here. When I say "not bounded" I mean "without a boundary", not "unlimited". I believe that defining something as finite implicitly puts a limit on it.
While a sphere has a boundary, it is it's surface. Within the 2dimensional "universe" of the sphere's surface though, there exists no boundary, no edge. You can travel indefinitely along a straight line as defined in obtuse geometry following the great circle of a sphere. You will never encounter an edge. However, the surface of that sphere is most definitely finite, and it can be measured.
The thought experiment previously described implies the universe cannot be finite because it would then have a boundary at "the end of the universe", followed by the question "What exists beyond the edge?"
My point is that something finite does not have to have an "edge" or "boundary", not that it is "limitless". 
Fhqwhgads beat me to it. You are actually adding a complication to the thought experiment by arbitrarily discarding dimensions and turning it into a perceptual question. You should be using the entire set of dimensions rather than a subset; if you assume three spacial dimensions total then the problem is easy to visualize but it should hold true no matter how many dimensions there are. _________________
Halen wrote:  The reason that "people actually see the points people make" = "people agree with me" is because I. Am. Right! 


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