Why does paper move erratically when falling?

[DTonesXD]

The question is in the title

Here is what i mean

What stops it from just falling in a straight(ish) line? because as you can see it moves a fair distance from where it was dropped

[J.C.MacSwell]

While the force of gravity on the paper is constant, the aerodynamic forces vary considerably with it's speed, direction, orientation, and shape. So it somewhat oscillates in movement, but in a chaotic and seemingly random way.

[DTonesXD]

While the force of gravity on the paper is constant, the aerodynamic forces vary considerably with it's speed, direction, orientation, and shape. So it somewhat oscillates in movement, but in a chaotic and seemingly random way.

why do those aerodynamic forces vary?

[michel123456]

because the paper is not "transparent" to air. When the paper displaces, the air must go round the paper.

without air, the motion is not erratic.

I suppose that when air is present, the motion of the paper that you say is erratical, is in fact deterministic, IOW not chaotic.

If you can make a device that lets fall the paper in the exactly same way in a chamber with exactly controlled null air flow and null temperature gradient, etc. the paper should fall in exactly the same "erratical" way each time.

in practice you cannot do that, I suppose. what you can do is describe a theoretical volume in which the paper will fall, and never escape from.

[J.C.MacSwell]

why do those aerodynamic forces vary?

In a nutshell (over simplified)

Speed...generally with speed to the power of 2.

Direction...drag opposing the velocity direction, lift perpendicular, by pressure distribution

Orientation determines the direction of the lift, as it determines the pressure distribution over the surface depending on the shape

Shape is affected by the pressure distribution and gravity on the flexible sheet

because the paper is not "transparent" to air. When the paper displaces, the air must go round the paper.

without air, the motion is not erratic.

I suppose that when air is present, the motion of the paper that you say is erratical, is in fact deterministic, IOW not chaotic.

If you can make a device that lets fall the paper in the exactly same way in a chamber with exactly controlled null air flow and null temperature gradient, etc. the paper should fall in exactly the same "erratical" way each time.

in practice you cannot do that, I suppose. what you can do is describe a theoretical volume in which the paper will fall, and never escape from.

It's not deterministic. The slightest imperceptible change will effect a significant change in outcome over even very short periods of time. It is deterministic macroscopically that the paper will land on the floor, but that is not the topic. With respect to the path and erratic movements it is chaotic.

 

Edit: Checked my definitions... It is in fact chaotic, but could be considered deterministic as well

 

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

 

I still don't think it is deterministic based on quantum considerations which I believe is enough on it's own to lead to non deterministic outcomes (due to significant enough subsequent divergence in the time frames involved) even at that level but I could be wrong/stand to be corrected.

Edited May 26, 2015 by J.C.MacSwell

[michel123456]

If you let the paper fall and stop its fall after 1/100 sec. you will observe that its motion is deterministic. As much you increase the duration of the fall it will become harder and harder to predict its accurate motion. But it is still deterministic.

You can even mimic with your hands the shape of the path. it is not chaotic.

Shake your hands as if you had parkinson: that is chaotic.

And I am not even sure it is chaotic enough.

Edited May 26, 2015 by michel123456

[J.C.MacSwell]

If you let the paper fall and stop its fall after 1/100 sec. you will observe that its motion is deterministic. As much you increase the duration of the fall it will become harder and harder to predict its accurate motion. But it is still deterministic.

You can even mimic with your hands the shape of the path. it is not chaotic.

Shake your hands as if you had parkinson: that is chaotic.

And I am not even sure it is chaotic enough.

You take the best physical experimental team in the World to set up the experiment under the most consistent conditions they can muster and have them run it 1,000 times and none of the trials will be duplicated. It is chaotic.

 

Chaotic does not mean it does not follow the rules of physics (not saying you are making that claim) nor does it mean that it is not deterministic. It means the outcomes diverge significantly over time with the slightest change. Someone with Parkinson's generally has control independent of a minor fluctuation that happened previously (convergence), though it can certainly lead to divergence if, say, an accident occurred that would not have otherwise.

[michel123456]

You take the best physical experimental team in the World to set up the experiment under the most consistent conditions they can muster and have them run it 1,000 times and none of the trials will be duplicated. It is chaotic.

 

Chaotic does not mean it does not follow the rules of physics (not saying you are making that claim) nor does it mean that it is not deterministic. It means the outcomes diverge significantly over time with the slightest change. Someone with Parkinson's generally has control independent of a minor fluctuation that happened previously (convergence), though it can certainly lead to divergence if, say, an accident occurred that would not have otherwise.

You take that definition from the chaos theory, that's fine.

But then how do you call a system where there is absolutely no relation between one position and the next one, although being related by cause & effect. And finally, how do you call a system that really relates to the ancient Greek ethymology of chaos, a system where there is no (apparent) law?

[swansont]

But then how do you call a system where there is absolutely no relation between one position and the next one, although being related by cause & effect.

Do you have an example of this?

 

And finally, how do you call a system that really relates to the ancient Greek ethymology of chaos, a system where there is no (apparent) law?

Again, example?

[ydoaPs]

It's not deterministic.

....in practice.

 

In theory, however, it's perfectly deterministic. We'd just have to make our description a LOT more complicated. You have to factor in the initial shape and orientation of the paper. You have to factor in the pressure change caused by the air displacement (roughly--low pressure on top and high pressure below, but is it even? ). You need to factor in all of these quantities that are normally ignored because this problem is generally irrelevant.

 

Edit: Checked my definitions... It is in fact chaotic, but could be considered deterministic as well

Indeed. Don't think I'm correcting you, just clarifying.

[overtone]

A system in which quantum level behavior, or Heisenberg uncertainties, or influences from beyond the "light cone" (such as the position and mass of an electron at the exact edge of the known universe when the action is begun), or the like, can be amplified sufficiently to be measured by an observer, is not from that observer's point of view determined in fact or in theory.

 

Whether a system can be "deterministic" without being determined in fact or in theory I leave to the philosophers.

 

Most technically "chaotic" systems fall into this category.

 

Example: a system consisting of billiard ball set into motion on a perfectly flat, perfectly uniform, perfectly elastic, completely frictionless, vacuum housed, evenly accelerated (perfectly smooth gravity ), billiard table, is not a determined system from the point of view of any human being. If it rebounds from a cushion once per second on average, it's path will exhibit enough variance, from any path initially determined by any calculation however (even impossibly) precise, to be observed by the naked human eye, within about ten minutes.

 

How long it would take to smear the possible positions evenly over the table (again, within the best resolution of the human eye, so no hole bigger than than about a micrometer) I never figured out - but the answer is not "never".

Edited May 28, 2015 by overtone

[michel123456]

 

But then how do you call a system where there is absolutely no relation between one position and the next one, although being related by cause & effect.

Do you have an example of this?

 

The shaking hands of a human with parkinson disease

 

 

And finally, how do you call a system that really relates to the ancient Greek ethymology of chaos, a system where there is no (apparent) law?

Again, example?

 

Hum. That is mythologic χάος. It is a "soup" of unrelated things. Not sure is anything like that really exists, but anyway there was a name for this concept.

Maybe something like the blinking of stars in the night, where each blinking is totally unrelated to the other one, apparently.

 

 

 

[swansont]

The shaking hands of a human with parkinson disease

 

And how do you establish that there is no relationship? I doubt the shaking is instantaneous, so that for short intervals, s = vt applies.

[michel123456]

 

And how do you establish that there is no relationship? I doubt the shaking is instantaneous, so that for short intervals, s = vt applies.

Laws of physics apply to the shaking hands. But one position and velocity does not tell you anything about where will be te hands the next instant. It is not like a double pendulum.

http://en.wikipedia.org/wiki/Chaos_theory#/media/File:Double-compound-pendulum.gif

[MigL]

Any classical motion, even chaotic, is deterministic, by definition.

Chaotic motion is just a rapidly diverging effect, which requires vast computational power to model.

But, theoretically, it can be done.

 

But I suppose, even at the macroscopic level, quantum effects will become apparent, and non-trivial, after a large number of iterations ( Mr. Heisenberg will have his 'pound of flesh' ) and so, one could say that there is no such thing as a completely deterministic system.

[ydoaPs]

Any classical motion, even chaotic, is deterministic, by definition.

What about, say, Norton's Dome?

 

 

 

(try this http://en.wikipedia.org/wiki/Norton's_dome )

Edited June 3, 2015 by swansont
add link

[michel123456]

What about, say,

Interesting. Never heard of Newton's dome before. is there gravity in this thought experiment? Edited June 2, 2015 by michel123456

[ydoaPs]

Interesting. Never heard of Newton's dome before. is there gravity in this thought experiment?

Norton gives a simple rundown of his dome here.

[swansont]

Norton gives a simple rundown of his dome here.

 

Further discussion on this here

http://www.scienceforums.net/topic/89432-nortons-dome/

[overtone]

Any classical motion, even chaotic, is deterministic, by definition.

Chaotic motion is just a rapidly diverging effect, which requires vast computational power to model.

But, theoretically, it can be done.

It's a strange determinism, when nothing is determined.

Chaotic motion cannot be determined, even in theory - the bigger the computer and the better the initial conditions have been measured, the longer it may take you to notice the divergence, but the the end result is the same: your computer modeling will diverge from your observation. It won't take that long, either - consider roundoff error.

An incomplete list:

 

quantum level behavior, or Heisenberg uncertainties, or influences from beyond the "light cone" (such as the position and mass of an electron at the exact edge of the known universe when the action is begun),

Edited June 4, 2015 by overtone

[swansont]

It's a strange determinism, when nothing is determined.

Chaotic motion cannot be determined, even in theory - the bigger the computer and the better the initial conditions have been measured, the longer it may take you to notice the divergence, but the the end result is the same: your computer modeling will diverge from your observation. It won't take that long, either - consider roundoff error.

 

Roundoff error is a practical limitation, not a theoretical one. Same with "bigger computer"

[imatfaal]

!

Moderator Note

MitchBass - do not introduce speculative / nonsensical suggestions into mainstream threads; I have hidden your post as any discussion should take place in your new thread in Speculations. Do not respond to this moderation within the thread.