Sun Wukong couldn't get out of Tathagata's palm, and there's actually a physics reason behind this!

The Arctic tern is perhaps the most light-loving animal in the world. From the day it hatches, it chases the sun all the time. In the summer of the northern hemisphere, they come to the coast of the Arctic Ocean and reproduce on the tundra. In the summer of the southern hemisphere, they go to the vicinity of Antarctica and catch fish and shrimp in the Southern Ocean.

The migration route of the Arctic tern is tortuous, and on average, it travels about 71,000 kilometers per year. In its long life of more than 30 years, the total migration distance is equivalent to three round trips from the earth to the moon!

Arctic tern. Image from: pixabay.com

For a tiny bird, this achievement is enough to brag about for several geological ages. So, if humans are given 30 years to act within the known physical framework, without any restrictions on means, how far can we fly?

They literally flew for 30 years!

The first probe sent by humans to the outer solar system was Pioneer 10. By the 30th anniversary of its launch (March 2002), it had flown to a distance of 12 billion kilometers from the Earth.

However, Voyager 1, launched in 1977, overtook Pioneer 10 in its 21st year, surpassing Pioneer 10 at 10.4 billion kilometers, becoming the farthest man-made object. In its 30th year (2007), Voyager 1 had reached 15.5 billion kilometers and was passing through the heliosphere. Now Voyager 1 has flown out of the heliopause and is traveling in interstellar space 24 billion kilometers away from us.

In 2007, two travelers were traveling through the heliosphere. Image source: NASA

Although 15.5 billion kilometers is obviously much better than the three round trips of the Arctic tern, it seems too boring to simply do multiplication to compete for speed. Let's think a little wilder, is there any way to fly farther?

As long as the speed is close to that of light, a short life can run farther

The strange behavior of a microscopic particle may inspire our thinking. At an altitude of 15 kilometers above the ground, high-energy protons in cosmic rays bombard the earth's atmosphere, producing muons and neutrinos.

The lifespan of a muon is very short, decaying in about 2.2 microseconds. Logically, even if it dives at the speed of light (299,792,458 meters per second), it can only fly 660 meters and cannot reach the ground. But something interesting happened: a lot of muons can be detected at sea level and even in underground mines. This running distance is more than 23 times the original prediction.

What is going on? It turns out that the special theory of relativity is secretly helping. From the perspective of the earth, the passage of time for a muon moving at a speed close to the speed of light will be greatly slowed down. As long as the difference between its speed and the speed of light is less than 9 ten-thousandths, the passage of time will be slowed down by more than 23 times. If we and the muon each hold a stopwatch, we will find that when it flies to the ground, our stopwatch has reached 52 microseconds, but the muon's stopwatch has not reached 2.2 microseconds (it seems that "life lies in movement" is right...)

However, from the muon's point of view, it does not feel that its time has slowed down. It normally dies at 2.2 microseconds and decays into other particles. The stopwatch in our hands is the slow one. In its "eyes", it sees the following scene: the earth, which is rushing towards it at nearly the speed of light, is radially compressed by more than 23 times and becomes a "pancake" (if it knows what the earth originally looks like). The atmosphere it has to pass through is thinner than 660 meters. It can even run a little further and drill into the underground mine!

There is an optional formula for the multiples of time delay or length compression, which is purely for curious readers to verify the following data:

Here v is the speed of the object and c is the speed of light in a vacuum.

The muon reaching the ground is a classic proof of the special theory of relativity . Note that from the Earth's point of view, the muon travels 15 kilometers in 52 microseconds; from the muon's point of view, it travels 660 meters in 2.2 microseconds. In each reference frame, the muon does not exceed the speed of light. But if you mix them up, you will get a wrong (but interesting) conclusion: the muon travels 15 kilometers in 2.2 microseconds, 23 times the speed of light!

As long as you work hard and create miracles, you can cross the Milky Way?

Following this line of thought, we have a bold idea. If we accelerate ourselves to a speed extremely close to the speed of light (by whatever means), can we cross the Milky Way, which originally has a diameter of 200,000 light years, in 30 years?

This time delay or length compression is 6667 times, let's say 7000. Using the formula just now, we can calculate that as long as the difference with the speed of light is within 1 part per billion, we can radially flatten the Milky Way 7000 times, so that we can cross it in 30 years .

Of course, from the perspective of generations of descendants who remain on our home planet, we still traveled honestly at near-light speed and took 200,000 years to complete the task, but our every move was incredibly slow, even each blink of an eye took 1 hour!

How much energy is needed to reach this speed? Assuming the spacecraft is very light, including us, it only weighs 1 ton (equipped with unconventional food to avoid starvation during the 30-year journey), then the final kinetic energy is E=mc² times 7000, which is equal to 6300 trillion trillion joules. This number is actually not large, just the energy produced by the sun in 1/600 of a second, slightly more powerful than the asteroid impact that destroyed the dinosaurs, we may still be able to produce it.

So let's try harder and fly to the edge of the universe in 30 years to take a look? Since the Big Bang, the part of the universe that has time for signals to reach us (the so-called "observable universe") has expanded to a radius of 46.5 billion light years, and it is still expanding. If we can stop it and fly there in our 30 years, we have to accelerate the spacecraft to only 500 trillionths of the speed of light, and the energy required is 14 trillion trillion joules, which is equivalent to the full production capacity of the sun in 6 minutes, or 72 Three Gorges Dams in operation since the birth of the earth!

After reading the above calculations, we may have an illusion that as long as we work hard, miracles can happen. In fact, the bigger problem is that in the system we know, the expansion of the universe cannot be stopped and is still accelerating. The farther away from us, the faster the galaxy retreats, and it can even exceed the speed of light (space expansion does not violate relativity) . Even if we turn into a beam of light and set out now, we can only gradually approach the galaxy that is currently about 15 billion light years away from us (receding at the speed of light), and we will never reach it, let alone 46.5 billion light years away.

Speaking of this, I suddenly remembered the gambling match between Sun Wukong and Tathagata in Journey to the West. Sun Wukong somersaulted 108,000 miles, but he still couldn't get out of Tathagata's palm. The reason for this might be that Tathagata launched a cosmic expansion...

Sun Wukong encounters the expansion of the universe. Screenshot of the TV series "Journey to the West"

Planning and production

Author: Qu Jiong Popular Science Writer

Review丨Liu Qian, Researcher at Beijing Planetarium

Editor: Ding Zong