The Fall Arrives in Pieces

Let a slinky hang from its top until it settles. Then let go.

The expected event is almost too simple to describe: the toy falls. But slow-motion measurements divide that event into something stranger. The top moves down, the coils bunch together, and the bottom stays near its original height until the collapse reaches it. For a brief interval, the object has lost its support without every part of it beginning to descend. [1]

The bottom looks as if it has missed a message.

That is a useful beginning, provided we ask what the message actually is. Gravity has not arrived late. It was pulling on the slinky before the hand opened. What takes time is the change in the spring's internal forces.

The force that was already there

A hanging slinky is not relaxed. Its upper coils carry more weight than its lower ones, so the stretch varies along it. Before release, a small lower section is pulled upward by the section above it. That pull balances the section's weight and any downward pull from the material below. The local forces add to zero.

Letting go removes the hand's force at the top. It does not instantly remove the stretch everywhere else.

For a lower section whose local deformation has not yet changed, the old force balance can persist. The section above still pulls; the section below has not suddenly acquired a different weight. A mechanical disturbance must travel through the spring before those local conditions change. In ideal continuum models, the undisturbed lower portion remains exactly stationary until the relevant front reaches it. In a real drop, release details and measurement limits make “nearly stationary” the more careful description. [1, 2]

There is no invisible hand continuing to hold the bottom. There is a stretched material whose parts do not all change their configuration at once.

Meanwhile, the upper part has a reason to move vigorously. Before release, the hand balanced both its weight and the downward pull of the stretched material beneath it. Remove the hand and that internal pull does not disappear either. The spring is not merely a collection of beads independently beginning ordinary free fall; its stored elastic energy is also driving contraction.

The whole object is falling

The apparent contradiction sharpens if we stop looking at the bottom and ask about the center of mass.

Once the hand is gone, and neglecting air resistance, the external force on the whole slinky is its weight. All the internal pulls cancel when added over the entire object. Its center of mass therefore accelerates downward at the usual gravitational acceleration, even while a lower part waits. [1, 2]

That is not a technical escape clause. It specifies what “the slinky is falling” can truthfully mean.

The center of mass is a weighted average of the positions of all the material. It does not require every coil to move together. Upper material can move down rapidly and accumulate into a compact section while the lower material remains where it was. The average descends even though one conspicuous endpoint does not.

For scale, an object falling from rest for 0.27 seconds drops about 36 centimeters under ordinary gravity. That is a calculation of center-of-mass motion, not a claim that the waiting bottom moves 36 centimeters.

The toy makes a distinction unusually visible: free fall of an entire object's center of mass is not free fall of every piece inside it.

A spring cannot pass through itself

“The bottom hasn't heard yet” still leaves a difficult question: how does the change arrive?

In his analysis of the falling slinky, W. G. Unruh considers a deliberately impossible spring whose coils can pass through one another. This gives a clean wave calculation. Below the traveling disturbance, the solution preserves the initial position. Above it, the mathematical spring can turn through itself. [2]

The impossible part is instructive. A physical slinky cannot follow that trajectory. Its coils collide.

Unruh also considers a model in which colliding coils stick together, accumulating into a collapsed upper section that sweeps up the stationary material below. This is a shock-like collapse front, not simply the small-disturbance wave of the transparent spring. In that particular idealization, the collapse reaches the bottom earlier than the transparent wave would. [2]

So it is too glib to assign the delay by dividing the hanging length by a single “speed of sound.” The stretch is nonuniform, the wave equations distinguish material position from physical distance, and contact changes the problem. The phrase “a message traveling down the spring” earns its keep only if it leaves room for those mechanics.

The coils take time, too

Rod Cross and Michael Wheatland brought another useful complication to the problem: real turns do not finish collapsing instantaneously after the disturbance reaches them.

Their 2012 accepted manuscript reports filmed drops of two very different toys: a 215.5-gram metal slinky with 86 turns and a 48.7-gram plastic one with 39. They recorded at 300 frames per second and extracted positions at hundredth-of-a-second intervals. In their measurements of intermediate turns, the spacing took a finite interval to shrink rather than jumping immediately to its closed value. [1, Sections II and IV]

An instantaneous-collapse model can reproduce the waiting lower end while producing an impossible beginning at the top: a jump straight from rest to a finite downward speed. Cross and Wheatland instead assumed a linear decline in tension across a mass-coordinate interval behind the initiating front. The top could then start at rest and accelerate. The initiating front, the contracting region behind it and the physical top do not follow the same trajectory. This repair concerns the top: the approximate model still gives its initiating front a singular, infinite initial speed. It has not made every part of the mathematics realistic. [1, Section III]

Their fitted total collapse times were about 0.27 seconds for both toys. Yet the model's initial top-collapse interval was much shorter for the metal toy—about 0.014 seconds—than for the plastic one, about 0.12 seconds. A similar overall delay did not imply identical early motion. [1, Table II]

There is a particularly neat limit to this improvement. For fixed parameters, their finite-collapse model has the same total collapse time as the instantaneous version. Making the beginning more realistic need not change when the collapse finishes.

That does not turn the model into a complete account of contact. Its tension profile is an approximation, and its spring stiffness, collapse width and release-time offset were fitted to the top's measured positions. Separate oscillation-period measurements supplied an additional check on the inferred stiffnesses: predicted periods of 2.23 and 1.88 seconds compared with measured periods of 2.18 and 1.77 seconds. The agreement was approximate, and the plastic toy presented larger discrepancies. These were additional measurements in the same study, not replication by a second laboratory. [1, Section IV and Table III]

Even the way the toy was held mattered. Tying upper turns together to keep it hanging straight changed the inertia of the released top. Additional drops with one versus two tied turns showed different early acceleration. A supposedly trivial release fixture had become part of the experiment. [1, Figures 10–11 and accompanying discussion]

What the bottom is waiting for

I like the slinky better with the magic removed.

It is not resisting gravity, and it is not demonstrating that gravity needs a quarter of a second to travel from a hand to a toy. It is showing that a material can preserve a local balance while the conditions that sustain that balance are being dismantled elsewhere.

The hand lets go once. The slinky lets go progressively.

What remains interesting is not whether the bottom has received the news, but how the news is made physical: changing strain, contracting turns, collisions, and a front whose motion depends on what kind of spring we actually released.

The next question is almost embarrassingly practical: if changing the tied turns changes the beginning of the fall, how much of the front's later behavior can we predict from the release fixture and the coils themselves, without choosing a fitted collapse profile?

That is a better mystery than antigravity.

Sources and reading limits

[1] R. C. Cross and M. S. Wheatland, Modeling a falling slinky (2012), accepted author manuscript, arXiv:1208.4629v1. Read the complete manuscript, including methods, equations, tables and captions; the journal-final text was not separately compared. This provides the filmed measurements and finite-collapse model. It builds on earlier spring models, so its data and every theoretical ingredient should not be counted as independent replications.

[2] W. G. Unruh, The Falling Slinky, arXiv:1110.4368v2, corrected in 2021 from a 2011 preprint. Read the complete corrected theory text and captions; checked the central stationary-region and ideal-collapse relations rather than treating every printed formula as verified. This is theory, not another drop experiment.

I checked ideal equations and arithmetic using the papers' reported parameters. I did not drop a slinky, watch the source movies, analyze the figure images, or refit raw position data. Exact stationarity is a model result, not a new experimental bound on lower-end drift.