How to build a shrink ray

Take three black holes and...

Shrink rays have been a feature of science fiction since the early 20th century. From Fantastic Voyage to Honey I Shrunk the Kids!, shrinking is a concept we can all wonder about. But is it physically possible?

The 20th and 21st centuries have seen advancements in miniaturization, particularly for electronics, but shrinking an object in the sense of reducing its size is well within the realm of science fiction.

Nevertheless, we have known how objects shrink in size since 1905, and the person who proposed it was none other than the young Albert Einstein.

In his 1905 paper introducing special relativity, Einstein deduced from first principles a length contraction proposal that had been circulating since the 1890s. In it, he showed how, when an object approaches the speed of light, time, appears to slow down from the perspective of a “stationary” observer. This is called time dilation. He also showed its length contracts in the direction of motion.

While time dilation is pretty easy to demonstrate using arguments about light beams and mirrors, length contraction is trickier:

Imagine a car driving through a garage with two doors, one on each end. The car is slightly longer than the garage so there is no way to close both doors with the car inside.

Suppose, however, I drive the car at a significant fraction of the speed of light such that its length contracts sufficiently that it will fit inside the garage from your perspective. The garage doors are nearly instantaneous (perhaps they are futuristic forcefields that can open and close at the speed of light). As the car passes through the garage, we close both doors for a fraction of a second and then open both at the same time.

But, length contraction is a relative phenomenon. Those in the car do not experience any length contraction. In fact, from their perspective, the garage is rushing to meet them at a significant fraction of the speed of light, and its length is contracted. The car is even longer than the garage than if they were both stationary. How can both doors close at once?

My high school physics teacher posed this to our class one day. I admit that 17 year old me had no idea how to answer the question.

The answer is that they don’t both close at once from my perspective in the car. The exit closes first, then opens, and the entrance closes second, then opens, allowing the car to pass through. Only in the reference frame of the garage do both appear to open and close at once.

This is intimately connected to why length contraction occurs. Events that are simultaneous in one frame are not simultaneous in another. Likewise, when we try to measure a car or rocket traveling close to the speed of light, our ability to measure it depends on making measurements in time as well as space. If, on the other hand, we try to measure the length by measuring the front and back simultaneously with lasers, in another frame those measurements will occur at different times. If we try to measure length by having it interact with a measurement device over time, the length of time during which it interacts with that device is different in different frames, so we get different lengths.

Length contraction is a fascinating phenomenon. It is observed but never seen, at least not the way Einstein conceived of it. Einstein for example suggested that a sphere traveling close to the speed of light would appear as an ellipsoid, but that is wrong. Three-dimensional objects don’t appear shorter when traveling close to the speed of light, they appear rotated. This doesn’t mean that the length contraction isn’t real. Rather, the rotation and lack of contraction is a trick of the light, literally. As this article explains, when we use light to observe a length-contracted object, because light takes different amounts of time to travel from the front and back of the object, it gives it a rotated rather than contracted look, canceling out the effect of the rotation.

This means that, although fast-moving objects appear to shrink, in one direction, they don’t look like they’ve shrunk.

That doesn’t matter that much however because although they don’t look like they have shrunk, they have, and we can compensate for the travel time of light to observe length contraction, even if we can’t “see” it.

The bigger problem here is that length contraction only happens in the direction of motion. To shrink something properly, we want to shrink it in all three dimensions, and special relativity is just not up to the task.

All is not lost, however, because we have not considered the more powerful framework of General Relativity, the theory of gravity that explains black holes and the universe as a whole.

A 2-meters-tall astronaut hovering above the event horizon of a supermassive black hole with negligible tidal forces would have a much shorter height from the perspective of distant observers.

Since this can occur in one direction, why not more than one?

Suppose I have 3 supermassive black holes orbiting one another. I now have my astronaut placed such that their feet are towards one black hole, the other is to their left, and the last one is in front of them. In this situation, the astronaut should experience length contraction in all three directions (to first order at least). Provided the distances and masses of the black holes are correctly balanced, this length contraction can be made equal.

To a distant observer, this astronaut will appear to have “shrunk”.

This isn’t much practical use, but it demonstrates the principle that it is possible to warp space such that an object can appear to have shrunk. If such a warping of space could be contained to a small area just around the person, a kind of shrinking bubble, then, for all practical purposes that person would have shrunk even though, from their own perspective, they have not.

This is what a shrinking ray would have to do in order to come close to shrinking a person, atoms and all.