The Laws of Physics in an Animation Universe: Alice in Wonderland

One of the beautiful things about the medium of animation is you can do things that would be quite impossible and unrealistic in live action, and in fact some stories almost beg to be animated. Disney’s “Alice in Wonderland” from 1951 is one of those stories. Alice is a young girl who falls down a rabbit hole into an unpredictable world of nonsense known as Wonderland. Alice soon realizes this world is obviously not part of our reality and she is unsure what to expect around each corner. The physics of Wonderland differ from the real world in several ways, often in unpredictable and exaggerated manners.

Wonderland’s Action-Reaction principle is very different from the real world and also very unbalanced. In the real world, Newton’s Action-Reaction Principle says that “For every action force there is an equal reaction force in the opposite direction”, but Wonderland’s Action-Reaction Principle would go something like, “For every action force there is an exponentially larger reaction force, related to the character’s emotions, in whatever direction it feels like”. For example, the White Rabbit jumps around quite a bit, and when he does this his glasses will rise off his nose a small amount from the force of his jump propelling his body upward. However, the more excited or agitated he his, the higher his glasses fly, even when he is physically not jumping any higher than before (figure 1). Tweedle Dee and Tweedle Dumb’s hats also illustrate this principle; in certain scenes they appear to be jumping 12 inches off the ground, yet their hats fly up several feet above their heads a do a full loop-de-loop before settling back down! The hat could not have gained that much momentum from their jump, so it almost appears as if they are alive and moving on their own (figure 2). This principle also applies to forces exerted on characters as well as inanimate objects. When Alice is stuck inside the White Rabbit’s house while she is 20 feet tall she violently sneezes, launching another character more than 50 feet into the air (figure 3). However the unbalanced force only acts upon the one character, because the force of her sneeze does not blow open the shutters of the house, break the windows or force Alice through the wall at all. Then there are cases where something should be exerting a large force on a character, but it appears to have to have no effect. At one point several characters of varying sizes are running in a circle as large waves periodically wash over them. The waves are 4-5 feet high (which is well above all of their heads) but there is no change in the speed or direction of their run (figure 4). We would expect the animals to either be pushed over by the waves or see them push back against the force of the water to maintain their position in some way, but they simply keep running without acknowledging the force of the water at all. It is hard to predict exactly what will happen with an Action Force in Wonderland, but the only thing you can say for sure is that the reaction will be different than our own world.

Figure 1

Figure 2

Figure 3

Figure 4

Gravity works in strange, unpredictable ways in Wonderland, and sometimes seems to be entirely optional. Falling people and objects often seem to hang at the top of their arcs for an impossibly extended period of time. Many characters seem to go into slow motion at the top of their arcs, and I would almost call it the “8th down at half-time rule.” When small Alice is falling into the pool of tears, she slows into the top of the arc for almost 20 frames, then appears to fall several feet in only 8 frames (figure 5). This is the most extreme case, but many times different characters seem to stick at the top of a jump for longer than physically   possible in our world. Then there are some characters, like the Chesire Cat, seem very floaty in their movements despite their larger mass. Several times his hindquarters rise up above his head, without him pushing off from the tree branch he is sitting on (figure 6). His movements do not slow in or out, but happen at a very slow and even pace. This gives the viewer a slightly unsettling feeling, because he is the only character who consistently moves in this way. It appears that the gravity of Wonderland and how it acts upon a character is directly related to that character’s emotions and mental state. The White Rabbit does not have very much hang time, because he is often in a rush and moving very quickly. The Cheshire Cat is a very relaxed and carefree character, so much so that gravity seems to forget about him all together.

Figure 5 

Figure 6 

The liquids of Wonderland are ones that should be familiar to you, like tea and water, but they behave in very unfamiliar ways. The Mad Hatter and the March Hare are rather violent with their tea cups, so it is understandable that there is some splashing and spilling, however these splashes have very unusual and unpredictable arcs. When the cup is abruptly lowered, the tea will splash up 3-4 times the height of the drop and hang at the top of the arc for a few frames.Another example can be seen when the cup is moved to the side very quickly. You would expect the spilling drops of liquid to appear to trail behind the cup, because they are still at rest from the previous position, but the splashes jump straight up into the air. The tea also defies gravity in more extreme ways, like when the March Hair cuts a cup in half down the middle then pours tea into that half (figure 7). Another liquid that has its own unique physical rules is the red paint the cards use to paint the roses red. The paint is obviously very runny, because it drips off the rose bushes very steadily after they have been painted, but while it is still on the brush it behaves in a very different manner. As the card wave the brushes around, the paint trails behind like hair, but always “snaps” back into the brush like elastic. This does not seem so strange at first, but the trailing paint does not follow the brush, it takes its own path and appears to move of its own accord before coming back to the brush (figure 8). Before we examined how a character’s emotions can affect inanimate objects, so perhaps the frantic behavior of the cards simply infected the paint.

Figure 7

Figure 8

There are a few examples of Wonderland physics behaving like real world physics, the most notable being the effect of a parachute on a falling object’s terminal velocity. When Alice first falls down the rabbit hole she is falling rather quickly. She would continued to accelerate for a few seconds because it would take that long for the force of air resistance to balance out her weight, but her skirt opens up and acts as a parachute (figure 9). The open skirt gives her more surface area, which gives her a lower terminal velocity and that means she falls slower and will survive the fall. The same thing happens to the Doormouse, who is launched into the air by a firework at the tea party. As he falls he opens up an umbrella, which allows him to slowly float to the table (figure 10). However, the Doormouse probably did not need the umbrella in the first place, because he is so small and light the drop of 8 feet would not have killed him. However, in both cases these “parachutes” slowed the fall by an extreme amount, more than was proportional to the increases surface area.

Figure 9

Figure 10

Wonderland is nothing like our world with regards to physical laws. In the real world, these things are constant and predictable but that is not the case with Wonderland. Most of the differences from our world happen when the characters are experiencing extreme emotions, and these emotions amplify the already exaggerated physics of the universe. There are many more examples than the ones I have mentioned here, and I chose to avoid some of the more obviously “magic” examples, like Alice growing or shrinking throughout the story. However, it is difficult to come up with rules, because nothing is really constant throughout the film. In one scene a character’s hat my fly up 5 feet when they jump, in the next it might stay firmly stuck on his head. I believe these inconsistencies make the work feel more believable though, after all it is a world of nonsense.

Curiouser and Curiouser: The Physics of Wonderland Outline (Paper 1)

The Laws of Physics in Alice in Wonderland

I. Introduction
a. Introduce “Alice in Wonderland” (Disney, 1951)
b. Hypothesis: The physics of Wonderland differ from the real world in several ways, often in unpredictable and exaggerated ways.

II. Unbalanced Actions and Reactions
a. Characters hats or glasses seem to jump off their heads at times. Their movement is often un-proportional to the character's movement.
b. Alice's sneezes propel her back several feet, and even launch a character between 50-70 feet into the air
c. At one point the characters are running through the surf. Even though the waves are above their heads, they are completely unaffected by the push of the waves.

III. Gravity and Hang Time
a. Characters falling/jumping seem to pause at the top of their arcs for an extended amount of time
b. lighter objects fall faster than heavy ones
c. Cheshire cat and some of his body parts tent to float through the air, without slowing in or out

IV. Behavior of liquids
a. the splashes from cups/bowls often have impossible arcs
b. liquids can defy gravity, like the "half cup" of tea
c. the red paint on the rosebushes doesn't act like a liquid. Instead of dripping from a moving paintbrush it trails far behind then recoils like elastic

V. Competing Hypothesis: Accurate depiction of "parachutes" on falling objects
a. at certain times the film accurately portrays the effects of changing the surface area of an object to change the terminal velocity and slow a fall
b. when Alice falls down the rabbit hole her skirt poofs out like a parachute and slows her fall
c. when the Doormouse is launched into the air by a firework, his fall is slowed when he opens his umbrella

VI. Conclusion
a. Most of the differences from our world happen when the characters are experiencing extreme emotions
b. it is difficult to come up with rules, because nothing is really constant throughout the film
c. these inconsistencies make the work feel more believable, after all it is a world of nonsense

Video Analysis of Path of Action

Tracker Video Analysis of Falling Ball

Shooting Video Reference