Could Einstein's Theory of Relativity Suggest That Interstellar Travel is Unachievable?

Could Einstein's theory of relativity suggest that interstellar travel is unachievable?

Paul Mainwood:

Quite the contrary. It makes interstellar travel feasible—or at least possible within a human lifetime.

The key issue is acceleration. Humans are relatively weak creatures, and we can only endure so much acceleration. If we subject a human to more than 1 g of acceleration for an extended period, we’ll face serious health issues. (Subjecting them to over 10 g will lead to immediate unconsciousness and quick death.)

To travel any meaningful distance, we need to accelerate to our travel speed and then decelerate at the other end. If we’re constrained to, say, 1.5 g for long durations, we hit a significant problem in a non-relativistic, Newtonian world: Everyone would die before reaching the destination. The only way to shorten the travel time is by applying stronger accelerations, so we’d have to send robots, or at least something far more durable than fragile humans.

However, relativity offers a significant advantage. Once we approach light speed, time aboard the spaceship dilates, allowing us to reach distant places in much less time (from the spaceship's perspective) than would be possible in a Newtonian universe. (Alternatively, from the viewpoint of someone aboard the spaceship: as they accelerate close to light speed, distances seem to shrink, and they will reach their destination faster—the effect is the same.)

Here’s a quick table I put together assuming we can't exceed 1.5 g acceleration. We’ll accelerate at that rate for half the journey and then decelerate at the same rate on the second half to stop near our destination.

As you can see, when aiming for destinations farther than 50 light years, relativity gives us significant advantages. And for destinations over 1000 light years away, it’s only due to relativistic effects that we can complete the journey within a human lifetime.

In fact, if we extend the table, we can see that it’s possible to traverse the entire observable universe (about 47 billion light-years) within a human lifetime (roughly 28 years) by taking advantage of relativistic effects.

So, with relativity, it appears that we could reach any destination we desire!

Well... not exactly.

There are two issues.

First, the relativistic effect only applies to the travelers. Time on Earth will pass much more slowly. (A rough estimate for the Earth time of a return journey is to double the distance in light years and add 0.25 to convert that into years.) So, if they return, they’ll find that thousands of years have passed on Earth: their families will have lived and died without them. Even if we sent explorers, we on Earth would never know what they had discovered. Although, for some explorers, this could actually be a plus: “Take a trip to Betelgeuse! With an 18-year round trip, not only do you get an interstellar adventure, but also a bonus: you travel 1300 years into Earth’s future!”

Secondly, a more immediate and practical issue: The amount of energy required to accelerate an object to the relativistic speeds we’re discussing is—quite literally—astronomical. For example, traveling to the Crab Nebula would require about 7 x 10 J of kinetic energy per kilogram of spaceship to reach the target velocity.

That is an immense amount. But it’s achievable: the Sun emits 3X10 W, so theoretically, you’d only need a few seconds of Solar output (plus a Dyson Sphere) to gather enough energy to accelerate a reasonably sized ship to that speed. This assumes, however, that you can transfer this energy to the ship without adding to its mass: for instance, via a laser anchored to a large planet or star. If the ship must carry its own chemical or matter/anti-matter fuel and accelerate that too, we’ll run into the “tyranny of the rocket equation,” and it’s game over. We would need many more orders of magnitude of fuel.

But I’m going to casually consider all of this as an engineering challenge (though one far beyond anything our current technology can tackle). Assuming we can get our ships up to these speeds, we’ll see how relativity assists in making interstellar travel possible. Counter-intuitive, yet true.

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