How real is relativity?

Rotating a picture frame mixes horizontal and vertical in much the same way that relativity mixes space and time.

Special relativity is a well-established fact of nature. Although we rarely encounter relativistic effects in everyday life, they are routine in the world of subatomic particles and in the cosmos. Objects traveling close to the speed of light become spatially compressed and experience time at a slower rate. For example, lead nuclei in a stationary brick are roughly spherical, but when these same nuclei accelerate and collide in the LHC, they flatten into pancakes that collide face-on. Particles resulting from the collision, such as kaons, take a longer time to decay than stationary kaons because their internal clocks run slower. These are all measurable effects that have been observed in colliders for decades.

But how real is this stretching of time and squashing of length? Perspective makes faraway objects look small and nearby objects look large, but we do not say that they really are smaller when they’re farther away. This is because the same object can look small to a faraway person and large to a nearby person at the same time. We usually don’t call an effect real unless it is consistent among observers.

The way relativity works is similar to rotation. Suppose you hang a painting on the wall and align it well. The horizon line in the painting is parallel to the baseboard on the wall. Tilt the painting 45 degrees, however, and now the painting’s horizon is half-horizontal and half-vertical. A horizontal ruler would measure a shorter horizon than a ruler aligned with the painting (1.41 times shorter: Try it!). Special relativity is this same phenomenon in time and space, rather than in horizontal and vertical.

To understand relativity, one must first think of time as a dimension. Imagine a flip-book, a stack of cards that shows an animated cartoon when you flip through them. Time is like the depth of the stack—every moment in time is a three-dimensional picture, stacked in some unvisualizable fourth direction. It can even be measured in units of length: 1 nanosecond of time is approximately 1 foot long. A stationary object is like a tower in time, in the same spot on each page of the flip-book. A moving object is like a leaning tower, slightly offset from page to page.

Tilting an object in space-time is much like tilting a painting on the wall. Just as the painting’s horizon line occupies less horizontal space when tilted, a fast-moving nucleus occupies less space in the direction of motion—this is why it flattens like a pancake. And since part of its spatial extent has rotated into the time direction, its temporal extent lengthens—this is why its time slows down. (There is a mathematical difference between rotation and relativity, but the two are very closely related.)

So is relativity real or not? Like perspective, relativistic effects depend on your point of view: To a high-speed nucleus, we look flattened and it stays round. That’s the “relative” part of relativity. But unlike perspective, time dilation can have lasting effects. An astronaut who spends many years cruising at relativistic speeds would be physically younger than her twin when she gets back. Taking a shorter path through time has consequences that don’t depend on point of view.

Jim Pivarski

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