There is a mysterious beam of particles emanating from the Crab Nebulae.
The crab nebula is located near the left horn of the constellation Taurus, at the end of the V-shape next to Orion. It's visible in London in the winter on a clear night, although it's easier to see if you get outside of town a bit to escape the light pollution.
In the year 1054, astronomers around the world recorded the appearance of a temporary but incredibly bright star at that location, now identified as one of the earliest supernovas on record. The debris from this explosion is now known as the crab nebula. You can just make it out with a pair of good binoculars on a dark winter night.
Here is what it looks like through the Hubble Space Telescope:
The beam of particles is one of many that are hitting us from outside the universe. These mysterious beams are known as cosmic rays. Their origin is not generally known, and their cause is not well understood. However, our best guess is that they are particles that were blasted out of various supernova.
Here is a video introducing the concept of a cosmic ray.
Whatever their origin, cosmic are particles that were once accelerated to incredibly high speeds, reaching Earth while traveling at 90% the speed of light before smashing into the Earth's atmosphere. That is, they are traveling at speeds at which the effects of Einstein's relativity theory are visible.
(This image ↑, placed here for dramatic effect, depicts Aurora Borealis and not cosmic rays, which are usually invisible to the naked eye.)
As cosmic rays smash into the Earth's atmosphere they create great showers of particles called muons that rain down on giant regions. These showers may be spread over the entire earth, or they may just hit a smaller region like Western Europe, looking something like this.
What's puzzling about this is that muons are highly unstable particles, with such a short lifetime that they disappear within 2 microseconds — that's two millionths of a second. But paradoxically, even traveling at near the speed of light, it still takes them 50 microseconds to travel from the atmosphere to our detectors on the ground. How is this possible?
The answer is time dilation. At 90% the speed of light, time slows for the muon from 2 microseconds to nearly 200 microseconds. This gives the muon plenty of time to make the 50-microsecond journey to the ground.
This means that the effects of relativity theory do not require a spaceship to observe. They are not exotic, but rather happening all the time in the Earth's atmosphere. In particular, our cosmic ray detectors are observing the natural effects of time dilation on a daily basis!