Space travel to the end of the universe… and back

The universe is large, and even very large. Traveling to its limits, and coming back to tell everyone what is lying there (a return ticket is always better than a single ride) is a dream that probably many of us had had.

But can a human really do that (and come back before being a dead body)?

This is the very serious question that I will try to answer in this post, using only physics arguments.

In other words, I will assess what it takes to send a human to the end of the universe, without killing him/her, and to bring him/her alive, back on Earth.

Disclaimer: this topic originates from the comments of this post, written by @sauravrungta.

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LIMITS OF THE UNIVERSE: HOW FAR SHOULD WE GO?

Before starting the journey, it is good to know how far we should go.

We know that the universe is slightly less than 14 billions years old. Therefore, as nothing can go faster than light, we may naively assumed that the end of the universe is located at a distance of 14 billions light-years. Of course, I am only considering the observable universe here.

This very naive estimation is however wrong: this ignores the fact the the universe is in expansion. Putting all things together, calculations show that the size of the universe is more or less 45 billions of light years, or exactly 425.441.472.996.960.000.000.000 kilometers, using a distance unit easier to figure out.

We must thus organize a trip to a location distant from 45 billions of light year, and come back. This means, traveling 850.882.945.993.920.000.000.000 kilometers.

Assuming we can travel at the speed of light, this consists of a trip of 90.000.000.000 years. Therefore, the naive answer to the question is: we cannot go to the end of the universe and come back with one single human.

Even worse, we are starting at rest (i.e. with a vanishing speed). We must hence accelerate from zero to the speed of light. Then, at mid-way, we need to decelerate (in short, the spaceship will rotate and accelerate in the reverse direction) so that we could stop at the end of the trip.

And finally, the same thing holds a second time for the return trip.

This trip could be way longer than expected…

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RESCUED BY SPECIAL RELATIVITY?

But wait. We forgot one important point in our calculations: special relativity. Einstein can possibly save us.

When traveling at high speed, two phenomena are predicted by special relativity: time dilation and length contraction.

This means that time is flying more slowly for someone moving at very high velocity. Similarly, distances are smaller.

Is this enough? There is one way to know: performing the actual calculations.

First, we said above that we start on Earth with a zero velocity. Then, we accelerate. But we cannot kill the human on board so that we cannot impose him/her too many G’s in his/her face.

As we may accelerate during a very long time, we impose that the acceleration cannot exceed 1G. This implies that gravity on board is the same as gravity on Earth.

Now we have everything to calculate the exact time taken for the trip.

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COMPUTATIONS FOR ALL FRIENDS WAITING ON EARTH

As said above, the one-way trip is a trip of 425.441.472.996.960.000.000.000 kilometers. We will thus accelerate until half-way, and the decelerate in order to stop at the end of the universe.

In practice, half-way means a trip of 212.720.736.498.480.000.000.000 kilometers, starting with a zero velocity and accelerating constantly with an acceleration equal to 1G.

For someone on Earth, the time (t) it will take is given by solving the equation on the right.

The l on the left-hand side of the equal sign is the distance to travel, and g = 9.81 m/s² is jsut the value of 1G.

It is not complicated to solve this equation, and the time needed for the total trip to the end of the universe (starting at rest from Earth and ending at rest at the end of the universe) is 45.000.000.000 years.

And we need to multiply this time by two, as we still need to account for the return trip. Okay, our space traveler will be dead, dead, dead and again dead…

This conclusion is however incorrect. The friends of our space traveler waiting on Earth will be dead, dead, dead and again dead. Not the traveler (we actually did not perform the right calculation for him/her).

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COMPUTATIONS FOR THE TRAVELER

In the relativistic spaceship, time is flying in a slower way. The formula above needs thus to account for this.

Using this the formula shown on the left, we can calculate the time (denoted by τ this time) needed, but for the space traveler standpoint. In other words, how he or she will feel the trip.

And here is the funny part.

We obtain that the one-way trip to the end of the universe will last slightly more than 47.5 years!

Accounting for the way back to Earth, the total trip will only last 95 years for in total. Our traveler may well be very alive after that.

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DISCUSSION AND REFERENCES

It is in principle possible to go to the end of the universe, and come back, provided that one can build a ship capable of accelerating to velocities very close to the speed of light.

In this context, it is sufficient to send a baby human, and an elder of 95 years will come back to Earth ‘slightly’ later… Okay, Earth will be 90.000.000.000 years older, but that is a small detail…

What I have also not said is that to maintain a 1G acceleration during 95 years, we need, give or take, an infinite amount of fuel. Conclusion: there is no hope to go to the end of the universe without inventing a very clever piece of technology.

There is a small flaw in the above calculations (mostly an unspoken approximation), which does not change the conclusions of course. A reward for the one who finds it! :)

More information can be found following the links below:

• About the age of the universe and its size.
• There are many textbooks about special relativity. My favorite is this one.

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