Image talk:Translational motion.gif

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Contents 1 Trillion times? 2 Technical details of the image 3 How long? 4 laggy 5 approximation 6 Two dimensional 7 Relevant parameters 8 Relevant parameters:Further discussion

[edit] Trillion times?

In a real environment, the atoms would be moving a trillion times faster than in the picture?

Yes, at small scales things happen incredibly fast compared with changes on the human scale. It's a whole different world down there. On the other hand, if we go up another level to something like the lifespan of a star, it happens extremely slowly relative to us. Richard001 21:38, 25 December 2006 (UTC)

This animation makes it very difficult to read when posted directly into an article. Could we have a static image of one of the frames, so that the link can invite people to click to see the animation? --Yath 15:29, 5 January 2007 (UTC)

Image:Translational motion frame.png exists now for this purpose if you want to use that. Syntax: [[Image:Translational motion.gif|thumb=Translational motion frame.png]] howcheng {chat} 18:19, 14 May 2007 (UTC)

[edit] Technical details of the image

To all: Technical details of this animation can be found in two archived forums: at the nomination to list the image for Featured Picture status, and at a nomination to delist the image as a Featured Picture. Further, a spreadsheet-like accounting of how the pressure of 1950 atmospheres was calculated is available at an archive here, which is a post I made on the talk page of a supportive user who voted for the image. A discussion of that spreadsheet and how the logical bridge is made between the 2-D animation and 3-D reality is provided in the discussion topic Relevant parameters:Further discussion, below. A brief overview describing the differences between the animation and reality is also available in Two dimensional, below.

Note that although I am the creator of this animation, I very rarely visit this page. I can be reached on my talk page. Greg L (my talk) 00:05, 16 November 2007 (UTC)

[edit] How long?

How long does this thing take to cycle round? My head starts to spin after only a few seconds . TIA HAND —Phil | Talk 12:20, 29 January 2007 (UTC)

By my watch, around fifteen seconds. It refreshes at the end of the cycle and the circles change position, but it's very easy to miss. Trebor 16:11, 29 January 2007 (UTC)

[edit] laggy

this image lags browsers. don't put it on the main page.

When it's time for its appearance on the Main Page, we'll have a still frame to put there and people will have to follow a link to see the animated version. howcheng {chat} 05:21, 11 May 2007 (UTC)

I thought I saw polka dots hehehe --Howard the Duck 03:05, 14 May 2007 (UTC)

[edit] approximation

I assume this is a classical approximation - the atoms are like billiard balls. In reality there would be extra effects due to the electron clouds, such as vibrations, and the interaction would not be a 'hard sphere' interaction, but something like the Lennard-Jones potential. Maybe this should be noted in the caption, if that is the case. BlankAxolotl 04:22, 14 May 2007 (UTC)

• Electron clouds and their interactions aren’t an effect that obscures or interferes with the collision in some way; the “collision” of helium atoms is a product only of the interaction of the electron clouds. That interaction (collision) is the reality of interaction in this animation. The attractive van der Waals force, which begins to be felt about 5 helium atom diameters away, is trivial compared to the repulsive force of the “collision.” Its effect in this animation (a slight acceleration just before a collision) would be visually undetectable. Thus, the collisions are truly and properly modeled here as “hard-sphere interactions” (fully elastic collisions) because a perfectly insulated sample of matter will retain its temperature indefinitely. If atomic collisions weren’t perfectly elastic (100% rebound), matter would cool off in short order. Greg L (my talk) 06:49, 16 December 2007 (UTC)

[edit] Two dimensional

These atoms appear to be trapped in a two-dimensional universe. If they were squeezed into a box one atom wide in our universe then I think they would behave very differently due to sticky interactions with such constraining walls. The two-dimensionality of this image removes all semblance to the reality of what would happen in a volume filled with helium at the indicated pressure of the caption. Flying Jazz 21:50, 11 August 2007 (UTC)

• One mustn’t over-analyze a scientific model. One could look at this 2-D animation as representing atoms constrained in some sort of miniature Uncle Milton’s Ant Farm but, as you point out above, “sticky interactions” (like van der Waals forces) would bring movement to a halt pronto in real life. One could also imagine that the helium atoms have an astronomically improbable alignment that allows 32 atoms to bounce off each other exactly head on for 11 nanoseconds with zero divergence out of a 2-D plane. This alignment would also require extraordinary luck with the randomizing effect of quantum uncertainty.

  The pressure of 1950 atmospheres is that which would be achieved if the atoms had the same inter-atomic separation in 3-D as they have in this 2-D animation. If I had animated atoms at STP, on average, you’d only see an single atom scooting through the window less than 2% of the time.

  The prime purpose of the animation is to demonstrate the individual behavior of atoms whose rebound kinetics obey the Maxwell–Boltzmann distribution. The purpose of declaring the two-trillion-fold speed reduction is to give the average reader an appreciation of the true speed of atomic collisions. The purpose of declaring the pressure is to give the reader an appreciation for how rarified gases at STP truly are. Greg L (my talk) 21:07, 16 November 2007 (UTC)

[edit] Relevant parameters

Many of the parameters used to design this image may be found here with further discussion of the dimensionality issue here. Flying Jazz 08:33, 14 November 2007 (UTC) And in the below section. Greg L (my talk) 21:00, 15 November 2007 (UTC)

[edit] Relevant parameters:Further discussion

The discussions below were copied from the talk pages of Flying Jazz and Greg L for convenience of others interested in this topic.

Thanks for changing the caption on this animation to show a higher pressure. A google search led me here where I found some of the data you used. Unfortunately, I still think the caption was sufficiently misleading to be called wrong, and I've changed it. Here's why:

To most readers, a caption that says "Here, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure...atoms don’t really move in 0.062-nm-thick windows..." with no further elaboration would suggest that you are depicting an unrealistically thin 0.062 nm window and the pressure is based on that value. But a volume 0.062 X 1.66 X 1.45 nm would be 0.149 nm³. With 32 atoms in that volume, the density would be 214 atoms/nm³, not 48 atoms/nm³, so the pressure depicted would be over 4 times greater than 1950 atm value you cite (if the rest of your math is OK).

From what I could tell from your post on Froth's talk page, the starting point of your calculations was a 0.2744 nm average spacing between atoms, and the density you calculated of 48 atoms/nm³ works out for a volume of 0.2744 X 1.66 X 1.45 nm. So changing the value from 1950 atmospheres to something over 4 times greater would mean that everything else about your animation would be thrown off because your average spacing would no longer be correct.

What you seem to be doing is taking a 0.2744 nm thick layer and representing it as if it were one atom thick, and you're straight with the reader now when the caption says "in a 3-D box, they would actually pass in front of and behind each other and collide much less often," but then it becomes even more unclear that the 1950 atm value represents a 3-D situation.

Now that I think I understood what's been going on, I've tried to correct the caption. Here's my math:

0.2744 nm X (11 pixels/0.062 nm) = 48.7 pixel thickness above the computer screen. I rounded this to about 50 to be nice to the reader.

Also, as a quibble, the maxwell-boltzmann distribution for a 2-D situation is not a "perfect" representation of the 3-D case (even though it is a perfectly good distribution for a 2-D case), so I also removed the word "perfect" from your caption. I hope you like the change. Flying Jazz 08:03, 14 November 2007 (UTC)

• Flying Jazz: I got your message regarding helium atom spacing. Naw, the 0.062 nm depth of the z-axis is actually a zero depth as far as spacing goes. You can only calculate inter-atomic spacing by measuring in 2D; you can't make a “volume” calculation in a frame just thick enough for atoms to slide by. I’ll expand on that…

  The “spacing” of the atoms is the center-to-center distance between them. The 0.062 nm thickness of the pane is the space necessary to accomodate the thickness of the atoms with no space between atoms; it’s actually a “zero” dimension. In other words, we're now in the realm where the difference between the ideal gas law (assuming point particles) and reality (the particles have an actual diameter) matters 100% in the z-axis. In still other words, when examining spacing, the z-axis is zero depth. To properly examine the spacing of the atoms, we must look at only the 2-D center-to-center spacing; that gives us the equivalent pressure. We just can’t make a 2-D animation match 3-D reality. If we look at the “frame” in the animation from a 3-D point of view (1.66 x 1.45 x 0.062 nm), then it would only have “pressure” (collisions and the imparting of kinetic energy into the container walls) on four of the box’s six sides. So the jump from step 10 to step 11 in the logic shown on Froth’s archive is correct. We mustn’t over-analyze this. The animation properly conveys the appearance of helium atoms at a pressure of 1950 atomspheres. Greg L (my talk) 20:43, 14 November 2007 (UTC)

Please forgive me for over-analyzing this, but the statements "The animation properly conveys the appearance of helium atoms at a pressure of 1950 atmospheres" and "the z-axis is zero depth" cannot both be correct because zero depth means zero volume, and that would mean infinite atmospheres. Have you seen the new caption here? I'm pretty sure that I understand that you determined the pressure that would give the same inter-particle spacing in 3-D as is shown in the 2-D model. A statistical mechanics person or a physicist or another kind of "particle person" might understand the old version of the caption and have no issues with it. However, readers (like me) with more of an engineering background than a particle physics background or kids who are just learning about the gas laws for the first time really do need to relate to a 3-D volume if a 3-D pressure is given. Of course you're right that we can't just make a 2-D animation match 3-D reality, but maybe we can give the volume that makes PV=nRT hold if we were to try to make a 2-D animation match a 3-D reality. Flying Jazz 00:20, 15 November 2007 (UTC)

• Flying Jazz, regarding your recent post on my talk page (difference here), I understand what you’re trying to convey with the “50 pixel depth” language. I can see that you accurately understand the math because, as you pointed out, the actual value would be 48.7 pixels (50 is close enough), and where you’re going with this is that the average separation of the helium atoms (48.7 pixels) should apply to the z-axis. But doing so has the effect of mixing an isolated 3-D phenomenon into a purely 2-D model (it’s not even a 2-D projection of a shallow, 3-D window) while ignoring other, very important, 3-D effects that are also absent from the model. You’re reasoning basically is that if you have that pitch in 2-D, then you should be able to tessellate the pitch into the Z-axis. Your mental model is basically that of imagining the average atomic spacing as if it was a 2-D slice of a giant block of cubes on a 0.274 nm pitch. But it doesn’t work. And this is because we don’t have 0.274 nm-width cubes on a 0.274 nm pitch; we have 1) much smaller 0.062 nm diameter balls on the 0.274 nm pitch, 2) their moving, and 3) they have zero movement in the third dimension.

  The animation is purely a 2-D phenomenon—exactly like a pinball machine and can not be looked at as having volume. Here’s why: If you want the viewer to imagine that the helium atoms in the animation are moving in a 49-pixel-deep box, then the atoms would pass in front of and behind each other. So the animation isn’t even a 2-D projection of a 0.274 nm-deep 3-D field. As you can see in the animation, the atoms are constrained to move only in the X and Y axis; they have zero movement in the Z axis. Your mental model of tessellating into the third dimension is the same as saying that the Z-axis depth of the pinball machine is four inches (the distance between the surface the balls roll on and the bottom of the glass). That would be great if it weren’t for the fact that the steel pinballs still collide rather than take advantage of any of that depth.

  Because of this enormous difference between a purely 2-D (pinball-like) world and the 3-D world, captioning the animation as you have done has the effect of selectively—and improperly—dragging 3-D concepts into something that is simply not 3-D in any sense. What the animation does do, is accurately convey visually (by flattening 3-D separations to a 2-D plane), the apparent separation between atoms at 1950 atmospheres. Discussing it in volumetric terms is improper because it drags in spurious and excessive specificity; there’s just too much of a chasm between a purely 2-D model and 3-D reality.

  The most important thing the animation shows is how random rebound kinetics follows the Maxwell-Boltzmann distribution curve over time; that is a concept that translates perfectly well from the 2-D world to the 3-D world (other than the frequency of collisions). Beyond that, the animation illustrates the average inter-atomic separation and what the equivalent pressure would be if atoms were free to move in three dimensions with that separation. Greg L (my talk) 00:52, 16 November 2007 (UTC)

• I’ve taken a stab (image summary here) at explaining the important distinction between the animation and reality in terms that non-technical readers can understand and yet doesn’t sacrifice scientific rigor in the explanation. Given the huge gulf between apparent physics separating the animation and reality, I think the new treatment gets the point across without belaboring the details too much. Greg L (my talk) 21:57, 15 November 2007 (UTC)