Sorry for such a dumb question
As you all know, in length, (as well as any other kind of measurement) there is an inifnite amount of sub-divisions, it is possible to get ever-decreasing lengths. But when you (for example) move your arm 2cm to the right, it does, but it moves in 1 flowing motion, which means that it goes through the "length markings" without a break. But isn't that impossible, since there is no end to the "smallness" of amount you can move? So, how can anything manage to move?
Sorry for such a dumb question
Sorry for such a dumb question
There may be discreet distances that particles can move. Perhaps the Planck length. This is many orders of magnitude smaller than even subatomic particles. Some people think that time isn't smooth either, but rather ticks along in Planck time intervals (the time it takes for light to travel one Planck length).
Clearly these lengths are so ridiculously tiny that everything we see - including the tiniest particles - appear to move along with perfect smoothness.
Clearly these lengths are so ridiculously tiny that everything we see - including the tiniest particles - appear to move along with perfect smoothness.
QUOTE (Justavian+Aug 20 2005, 10:53 PM)
Some people think that time isn't smooth either, but rather ticks along in Planck time intervals (the time it takes for light to travel one Planck length).
But if this is so, and there is a "tick of the universe"(reminds me of Terry Prachet's Discworld
). It still doesnt explain how anything moves, litke, does it "teleport" 
to the next Planck length? As it is 1.6 x 10-35 m, does that means that every thing is "teleporting" that distance many times over as you move? Or is it jerking, which really doesnt make sense in the common usage of the word, as when you jerk, the object still moves through that space in the middle. But I just probably dont understand either what you are talking about or the word 'jerk'.
But if this is so, and there is a "tick of the universe"(reminds me of Terry Prachet's Discworld
). It still doesnt explain how anything moves, litke, does it "teleport" to the next Planck length? As it is 1.6 x 10-35 m, does that means that every thing is "teleporting" that distance many times over as you move? Or is it jerking, which really doesnt make sense in the common usage of the word, as when you jerk, the object still moves through that space in the middle. But I just probably dont understand either what you are talking about or the word 'jerk'.
That question was asked 4000 years ago or so, from old greeks philosopher (cant remember names - sry)
do a search for calculus on google and you will find your answer.
do a search for calculus on google and you will find your answer.
Uh.. Thanks, but its no help as im absolutely unsure of what i am looking for 
... Please help! 
... Please help!
QUOTE (Draugluin+Aug 22 2005, 01:30 PM)
Uh.. Thanks, but its no help as im absolutely unsure of what i am looking for ... Please help!
he is refering to zeno's paradox...
when one wants to leave a room one starts to walk to the door..
in alf the distance half the time has past. and so on...
this division of course is infinite and therefore you never reach the door.
perhaps one way to think of this is to remember wave duality. a wave passes through zero energy and then a positive energy again. if this is what happens at the planck length, then its posible that things move by a sort of translation in their wave form by its collapse and its return....
just thinking.
... Please help! he is refering to zeno's paradox...
when one wants to leave a room one starts to walk to the door..
in alf the distance half the time has past. and so on...
this division of course is infinite and therefore you never reach the door.
perhaps one way to think of this is to remember wave duality. a wave passes through zero energy and then a positive energy again. if this is what happens at the planck length, then its posible that things move by a sort of translation in their wave form by its collapse and its return....
just thinking.
Also, the answer was also found quite a long time ago... centuries before quantum mechanics and planck...
Basicaly, you are trying to find if the following summation converges or diverges.
S[i->1;n->(infinity);i++] x/(i)^2, where 2*x is the distance seperating the two points.
The summation is equivalent to this one; x/1 + x/2 + x/4 + x/8 ...
If this sum converges, the total traveled distance is finite. If it diverges, the total traveled distance is infinite.
As expected, it does converge and we can all go back to sleep with peace of mind in knowing that the universe will still be there when we wake up... http://en.wikipedia.org/wiki/Harmonic_seri...8mathematics%29
Basicaly, you are trying to find if the following summation converges or diverges.
S[i->1;n->(infinity);i++] x/(i)^2, where 2*x is the distance seperating the two points.
The summation is equivalent to this one; x/1 + x/2 + x/4 + x/8 ...
If this sum converges, the total traveled distance is finite. If it diverges, the total traveled distance is infinite.
As expected, it does converge and we can all go back to sleep with peace of mind in knowing that the universe will still be there when we wake up... http://en.wikipedia.org/wiki/Harmonic_seri...8mathematics%29
Cool Stuff! Anyway, thanks to all. 
Just a thought. Quantized movement can be seen on a macro scale with super-fluid helium. A thimble sized bucket of super-cooled helium (cooled til it's friction is 0) spun will show the helium going from one level to another on the sides of the 'bucket', never being in between.
Mispoke a little. Check out this web site:)
http://london.ucdavis.edu/~zieve/Research/super1.html
http://london.ucdavis.edu/~zieve/Research/super1.html
Though I belive that what they are saying is that the super fluid helium would just seperate itself into sections according to its speed. It seems to move through the spaces between to get to where it should be though....right?
Drauglin -
right - in the He(l) case, yes. It prefers to quantize as stated, but the liquid does have to go through the "non-quantized" states. They're really not "non-quantized states, however. This doesn't violate QM at all, since the preferred states or eigenvalues (b/z of the temperature) are offset by the fact that the system is rotating. The rotation is another axis and induces a different set of eigenvalues for the atoms to take, since now there is a competing system w/ a different axis orientation.
We encounter this w/ different nuclei, like iodine-125 or bromine-79 whose eigenvalues in the magnetic field compete w/ the nuclei's own massive electric field gradient (EFG) which is almost as strong. You end up w/ a different set of eigenvalues from either the magnetic field or the EFG - what a pain! But still supercool!
-ss
right - in the He(l) case, yes. It prefers to quantize as stated, but the liquid does have to go through the "non-quantized" states. They're really not "non-quantized states, however. This doesn't violate QM at all, since the preferred states or eigenvalues (b/z of the temperature) are offset by the fact that the system is rotating. The rotation is another axis and induces a different set of eigenvalues for the atoms to take, since now there is a competing system w/ a different axis orientation.
We encounter this w/ different nuclei, like iodine-125 or bromine-79 whose eigenvalues in the magnetic field compete w/ the nuclei's own massive electric field gradient (EFG) which is almost as strong. You end up w/ a different set of eigenvalues from either the magnetic field or the EFG - what a pain! But still supercool!
-ss
All these answers are crap, it has nothing to do with anything, Its just your perception, how you pervceive movement. Its just as reasonable to say for every 1 inch that my arm moves, there will be 100 elephants created instantaionsly on the underside of a table.
The rules by which you consider measurement of movement are your own!
How does it happen? You tell me!
The rules by which you consider measurement of movement are your own!
How does it happen? You tell me!
oh, great -
Another armchair philosopher. Aaron - you are incorrect. Come under my magnet and I will prove that QM is very real and I would give it up in a second for a less abstract discipline, but I can't.
ss
Another armchair philosopher. Aaron - you are incorrect. Come under my magnet and I will prove that QM is very real and I would give it up in a second for a less abstract discipline, but I can't.
ss
Hey, there is nothing wrong with an ArmChair!
Seriously tho, I really have my doubts as to what people know verses reality. I think that if, when and if we get there, we will laugh at all the certainties we knew then and how they turned out to be incomplete.
I guess I walk through life freely admitting that I dont have anything really figured out. I cannot shrink myslef down to the size of a vibrating string and get out my trusty slanley 24' measure and report back what I find. 99.99? of everything we think we know came from someone other than ourself, who if you really knew the truth, had his own doubts about it all!
Seriously tho, I really have my doubts as to what people know verses reality. I think that if, when and if we get there, we will laugh at all the certainties we knew then and how they turned out to be incomplete.
I guess I walk through life freely admitting that I dont have anything really figured out. I cannot shrink myslef down to the size of a vibrating string and get out my trusty slanley 24' measure and report back what I find. 99.99? of everything we think we know came from someone other than ourself, who if you really knew the truth, had his own doubts about it all!
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