A Journey to the End of the Universe

Our Universe is of immense and inconceivable scale, dotted with at least 70 sextillion stars, oases of light that permeate the darkness. There are more stars in our Universe than there are grains of sand on every beach on Earth. It is an absurd figure that defies human understanding. Yet despite this abundance of cosmic landmarks, there is a certain irony that we live in a Universe where outposts of concentrated matter are few and far between. If each star were reduced to the size of a grain of sand, then the typical separation between each grain would be about ten kilometers.

That's the distance from here in Columbia to downtown Manhattan in Greenwich Village. Now that distance, which is about four light years in physical units, is so great that it represents an immense challenge for our modern spacecraft. For example, our most remote spacecraft, Voyager 2, would take another 80,000 years to travel that distance. And that's just one star closer, the nearest galaxy is half a million times farther away than this one. When we are faced with such epic distances, such time scales, it seems that the Universe simply prohibits the dream of human astronauts exploring the depths of space. Like a cosmic joke that teases us with exploration gems that will always be out of reach.

And it is at times like these that we tend to dream of other solutions based on exotic physics, such as warp drives or wormholes. But as far as we know, these are theoretically implausible. What about using real proven physics? In our recent videos we discussed halo momentum as a possible means for interstellar travel, but even that system isn't fast enough to get you to other galaxies. Surprisingly, there is a trick that uses proven physics that could allow a person to travel even between distant galaxies within a human lifetime. But, like making a deal with the devil, it comes with such a hefty price tag that you may not want to sign up so quickly.

A cost that arises as a natural consequence of Einstein's special theory of relativity. Today we will take a trip aboard the constantly accelerating spacecraft. Let's imagine that we have built a ship capable of accelerating at 1g for as long as we want. That means its speed increases by 10 m/s for every second that passes. So, for example, after 10 seconds it will be traveling at 100 meters per second and will have traveled a distance of half a kilometer. We're just going to leave aside the question of how a spacecraft could accomplish such a feat for the moment and just assume it's true, and that's simply for the purpose of keeping this video focused and on point.

And in the same way we are going to assume that a spacecraft has perfect shielding capable of withstanding any type of impact or radiation that you can imagine. A benefit of constant acceleration would be that it would push the crew towards the back of the ship, with the same force with which the Earth holds us to the ground, thus creating artificial gravity, something we have discussed in our previous video in much more. depth. And so life on board would be relatively pleasant, working and living much like we do here on Earth. A ship undergoing constant acceleration starts out slow but gains more and more momentum over time as it continues its

journey

.

This is a bit like compound interest: to begin with, your profits seem larger, but over a long period of time those profits add up quickly. After just two and a half hours we would have passed by the Moon, after a day and a half we would be on Mars. And after three weeks we would have passed Voyager 2 and left the Solar System entirely. At that point, a ship would be traveling at 40 million miles per hour or about 6% of the speed of light. That's much faster than any spacecraft we've ever built has traveled before. It's fast, but not fast enough for Einstein's theory of special relativity to really come into play yet.

As we leave the Solar System, we head towards our nearest star system, Alpha Centauri, and watch it gradually increase in brightness as we approach, while the Sun fades into another point of light behind us. The next year will be largely uneventful, life on board will likely be quite mundane as the days, weeks and months go by. However, each day his ship travels approximately two million miles per hour faster than the day before. It is now impossible to have a live conversation with your friends and family on Earth; The time it takes for radio waves to travel from one place to another is now many months.

However, the loneliness is alleviated somewhat by regular letters from home, which inform you of the latest family news, sports results, scientific advances and political scandals on Earth. After 15 months of travel, your crew celebrates crossing the first light year: you're now just under a quarter of the distance to Alpha Centauri, but more than a third of the way in terms of one-way travel time, and that's thanks to the constant navigation of the ship. acceleration. There's another milestone that you and your crew realize you've passed as well, and that's what the physicists picked up on: your Lorentz factor, given by this famous equation here, has now surpassed a factor of two.

That means that the time dilation between you and ground-based observers is now a factor of 2, and therefore ground-based observers would appear to see you moving in slow motion aboard the ship. From now on, Einstein's theory of special relativity will have an increasing influence on you and your ship, as you now move away from Earth at 87% of the cosmic speed limit: the speed of light. Now, if there were no such limit, then we should expect to cross the speed of light in 45 days. But Einstein's theory, a theory that has been rigorously tested and demonstrated on Earth, states that nothing can move faster than the speed of light.

Furthermore, all observers, regardless of their speed, will always observe that the speed of light is the same. Now this is very unintuitive. If a horse chases a moving train, then the train appears to be moving slower than usual from the horse's perspective. But relativity says that no matter how fast the horse runs, if the train is a beam of light, it will always appear to be moving away at exactly the same speed: the speed of light. The horse will never be able to reach it. If the speed of light is constant for all observers, then the mind-blowing consequence is that space and time are not constant.

They change to adapt to this rule. And that's exactly what's happening here with our ship: the weather changes in such a way that observers on Earth appear to see the crew moving slower than usual on board. And even space shifts in such a way that the ship itself seems crushed in length. Both effects scale with this famous Lorentz factor, which at this point in our

journey

is a factor of two. This even affects your perceived acceleration from Earth's perspective: now you are no longer accelerating at 1 g, but rather your acceleration appears to become smaller and smaller as you approach the speed of light; even though on board you still feel a 1g acceleration.

On board the ship, neither you nor your crew would think that anything had changed. Time seems to pass as usual. But you would notice some strange things outside the ship. Looking back at the Sun, you'll notice that it appears to have faded into darkness, much faster than you would expect with a simple distance scale. When its Lorentz factor is 2, it is now 10,000 times dimmer - only detectable with the ship's telescope as a result of relativistic aberration and time dilation effects. Not only this, but light from the Sun now appears increasingly redshifted, due to relativistic Doppler shift; in fact, it is so red that it now emits primarily in the infrared band, where the eyes can't even see it.

But in front of you the opposite has happened. Alpha Centauri now appears 10,000 times brighter than it would if it were not moving, but most of its radiation now arrives in the form of high-energy ultraviolet light. Not only this, but the constellations in front of you would appear distorted, warped in a sort of tunnel vision illusion. In a very real way, as you accelerate faster and faster, you begin to disconnect from the rest of the Universe. But accelerating forever is not an option, because we do not have infinite fuel on board and at some point we are going to want to slow down, get off the ship and reconnect with the rest of the Universe.

So one way to do this is to accelerate your ship to about halfway into its journey and turn the ship around and accelerate in the opposite direction, thus stopping it at some distant destination. Now let's continue to our original destination, Alpha Centauri, which is 4.4 light years away. Remember that this means that a ray of light emitted from Earth would take 4.4 years to reach Alpha Centauri. However, due to the time dilation effects on board, his ship would land on one of the Alpha Centauri planets at only three and a half years old. Don't worry, you haven't escaped any ray of light here because, according to Earth's clocks, the journey took you six years.

Maybe you'll spend a few weeks exploring this new planet and then return aboard and begin the journey home. When you return home, it will have been about seven years for you, but 12 years for everyone on Earth. Not a bad timetable for completing a trip to the nearest star. Remember that your ship began to decelerate at the halfway point, 2.2 light years from Earth. From his perspective, that would be about 1.8 years of travel, at which point his ship would travel at 95 percent of the speed of light. Let's imagine that a fight broke out on board and the crew decided they didn't want to go to Alpha Centauri anymore.

They wanted to take advantage of all this momentum to go further, much further than anyone had dreamed of. Now remember that we are only considering round trip scenarios here; We'll relax that assumption later, but for now any trip is defined in four phases. Exit acceleration, exit deceleration, entry acceleration and then entry deceleration. With this in mind, let's remember that a round trip to Alpha Centauri would take the crew seven years. But now let's go further. Our Sun lives within a region of space with a slightly higher-than-usual density of hydrogen gas, a region about 30 light years across and jokingly known as the local fuzz.

A ship that made a trip to the edge of this local fluff would age 13.4 years during its adventure. Upon returning, they would discover that their children were now older than they were when they were 13.4 years old, plus another 50, which led to some strange reunions. Nobody believed me, but I knew you would come back. As? Because my dad promised me. Maybe the crew won't be satisfied with just dropping this local nonsense, maybe they'll vote to go further. The local bubble is a larger volume in which the local fluff itself resides: a collection of tens of thousands of stars spanning 300 light years in diameter.

In a 1g spacecraft, the crew will be able to fly to the edge of the local bubble and back, and for them only 22 years would have passed. But when they return to Earth they would be historical relics, since they would have spent six centuries returning to Earth. Perhaps the crew would feel shocked and alienated by the changes that had transformed society in those six centuries. Let's go further and set a round trip out of our galactic spiral arm, the Orion spur, whose round trip would take the crew 31 years. This is where things get... weird. Remember that your journey is characterized by four phases and at the end of that first acceleration phase you will reach your maximum speed.

So if you travel to the edge of the Orion spur, that first phase would take you about eight years. But, after about six and a half years, you and your team looked out the front window and saw something very strange. Two-thirds of the way into the seventh year of the journey, a small portion of the sky appears to glow red. At first you think your eyes are just playing tricks on you after so many years in space, but then you realize that your Lorentz factor is now 650. And the radiation left over from the Big Bang, the Cosmic Microwave Background, now it has a blue color. completely switched from microwave to visible red light.

Over the course of your final year of launch acceleration, you and your crew are amazed to see this little patch of sky getting brighter, getting bluer, until at full speed it's like staring into the eye of a bow. cosmic iris . As if the ship had finally caught the gaze of the Universe itself. Perhaps he is not satisfied with abandoning the Orion spur and opts to travel to the edge of the galaxy, a round trip for the 41-year-old crew. After returning to hisA round trip of 100,000 light years, the crew, now in their sixties, would return to an Earth that had witnessed the passage of a hundred millennia.

It is very difficult to imagine how humans would have changed after such a long period of time. Perhaps our ancestors would look different after so many generations of gradual evolution. Perhaps they would speak completely different languages ​​than we know today, perhaps they would even have abandoned technology and returned to a more Neolithic way of life. Maybe even Earth itself is abandoned at this point and there is no trace of humans on Earth. Whatever happens at this point, the ship's computer database likely represents an ancient library containing information lost eons of time on Earth. But all this is still within our own galaxy, what if we really go to the afterlife, to another galaxy?

Let's go to Andromeda. On an epic 56-year round trip, you and your crew returned to Earth as old men after witnessing another galaxy firsthand. But on Earth it is very likely that at this point there is no one even recognizable as human, after five million years have passed. You and your team are very likely the last humans in the Universe. Although there were no humans left, the Earth looks better than ever: biodiversity has almost recovered to pre-human levels, coral reefs have recovered across the planet, and cities and concrete have disappeared as Nature has now reclaimed what always before her.

If we want to venture beyond Andromeda, we may begin to need technologies to extend crew life. Traveling beyond our galaxy cluster, the Virgo cluster, would require the crew to travel 67 years round trip. The Virgo cluster lives within the Laniakea galaxy supercluster, a region of space spanning hundreds of millions of light years and containing tens of thousands of galaxies. Their round trip would now take 76 years. At the maximum speed during that trip, its Lorentz factor would be 250 million, a speed of 0.999999998 times the speed of light. At this point, the Cosmic Microwave Background will have appeared to have risen from its ambient temperature of 2.73 Kelvin to more than a billion degrees Kelvin: that's the temperature the Universe was just minutes after the Big Bang.

Needless to say, this would be an extremely dangerous radiation environment for you and your crew, not to mention the now ridiculous shielding requirements to protect against impacts. You sometimes hear it said that as relativistic speeds are reached, the ship's momentum increases so much that it somehow protects it from impacts. But from the perspective of the ship, it is not moving: it is the particles, the space debris that is out there, that have the extreme momentum and therefore collisions with these small particles would not be suitable for weak people. heart. After completing its 76-year journey to the edge of the Laniakea supercluster, its home system would be barely recognizable.

Upon landing on Earth, the continents would have moved to unknown positions. The surface is now devoid of plants or animals and you can no longer even breathe the air around you. Over the past billion years, the Sun's luminosity has increased by almost 10%, which in turn has increased the rate of Earth's erosion. That erosion has removed so much carbon dioxide from the atmosphere that photosynthesis is no longer possible, ending the rain of plant life, ceasing oxygen production and collapsing the food chain. At this point, even the tectonic plates may have shut down as water evaporates from the Earth's surface.

These would be the last days of multicellular life on Earth; Beyond this point, only simple microbial life will be able to cling to existence, perhaps for a few hundred million years at best. The living Earth is breathing its last breath. And so I think it would be a sad return to return to your home planet and see it not go out with a crash but be suffocated with a cruel, slow and prolonged death, perhaps reminding you of the fate that probably awaits you as now. Even your own body is feeling the effects of time. One might suggest that there is no reason why Laniakea should be the limit for this type of round trip.

After all, time dilation is now so extreme that we can travel exponentially further with each passing year. In fact, you sometimes hear it said that we can even travel to the edge of the observable Universe using constant acceleration. These are galaxies about 46 billion light years from us. But no matter how much we accelerate, no matter how extreme the time dilation, we will never be able to reach the edge of the observable Universe. Now why should this be? Well, when we talk about trips of billions of light years, then the expansion of the Universe itself begins to interfere with our trip.

In 1998, two teams of astronomers used distant supernovae to independently discover that the expansion rate of the Universe, something known since the time of Edwin Hubble, was in fact increasing. She was speeding up herself. We don't fully understand why this happens, but the cause is usually labeled as dark energy. Using these measurements of the expansion rate of the Universe, we can define several thresholds, several horizons that limit our interactions with the outside Universe. For example, the so-called "particle horizon" is the greatest distance that a particle of light could have traveled from the Big Bang itself, which occurred 13.8 billion years ago.

Now, you might naively think that means the distance should be 13.8 billion light years, but due to the expansion of the Universe, it's actually a much greater distance, it ends up being 46 billion light years away. diameter. Now, returning to our adventure with the spaceship, if I want to make a round trip across cosmic distances, then this expansion causes the distances between regions to gradually grow during my journey, which means I have to travel further. About what I thought. Now, this is not important if you are traveling within a gravitationally bound region, such as a galaxy, which resists expansion.

But it is very important as we travel beyond our galactic supercluster. As far as I can tell, there is no prior mention or calculation of a round trip horizon in the literature, but we should be able to calculate it by solving the following set of equations. Below I will link you to an article where you can learn all about how to do these types of calculations yourself. But to avoid that pain, the resulting appropriate distance turns out to be 8.3 billion light years. This distance represents a cosmic point of no return. Once you cross it there is no turning back, you can never go back home even traveling at the speed of light.

And that's because the expansion of the

universe

just outpaces you, and yes, space can and does expand faster than the speed of light. So it would be a strange feeling on board the ship as you cross that threshold, knowing that no matter what happens, from that moment on you will never return home or see Earth again. Since we can't return home beyond this point, let's not even try to change the rules of our trip and make it a one-way ticket. Now I'm still going to assume that the second half of our journey is a deceleration phase, where we stop and that's simply because it's very difficult to talk about how much time has passed unless we return to the same inertial frame. reference from which we start.

Now, freed from the need to return home, we might be expected to travel much further into the Universe, perhaps even to the edge of the observable Universe. But again, the answer is no. Even if we constantly accelerate, we will never reach the so-called event horizon, which is twice the point of no return. This represents the greatest distance that a ray of light emitted now from Earth could reach, in infinite time. Because parts of the Universe are expanding at the speed of light, we will never be able to reach those regions and therefore end up limited to distances within the so-called event horizon.

But what the heck, I mean we've come this far, let's move on. After this point, we are no longer really a spaceship because no matter how hard we try, we never reach the event horizon. And, in fact, the rest of the Universe around us is expanding in all directions, faster and faster. Soon there will be no galaxies or clusters around us as the Universe expands ever faster beyond our sight. We have been left isolated, trapped in the void. If we're not really a spaceship anymore, maybe we've become a Time Ship? Could we use a ship to travel to the end of time?

Now, if the equations of special relativity are used naively, things certainly seem extreme. For example, with an acceleration and deceleration phase spanning two centuries according to the ship's clock, a clock on Earth should have registered one hundred quadrillion trillion trillion years. Enough time so that, in theory, even the protons had decayed and there was no nucleonic matter left. But here's the thing: it doesn't make much sense to even talk about time dilation anymore. And that is because time dilation is defined as relative, hence the name relativity, with our initial inertial reference frame, which in our case was the Earth.

But at this point, after so much time, after crossing so many light years, the Earth is beyond our cosmic horizon. We are no longer causally connected to it. Put another way, it is now literally impossible to compare clocks with those on Earth. To make matters worse, not only can it not be compared to clocks on Earth, but at this point it can't even be compared to any other clock. This is because by now the Universe has expanded by a factor of 10 to 10 to 55 and statistically there would most likely be no other particles within the entire observable Universe except you.

Even the Cosmic Microwave Background has already been reduced to nothing. How can we even talk about measuring time, comparing clocks, when right now the clocks effectively exist in separate

universe

s? The very definitions that support time dilation have fallen apart. And here your journey finally comes to an end. In complete isolation. A perfect vacuum. You and your crew have become a monument to times that once were, to a Universe that once was. And maybe when you and your crew finally pass away in the night, you will remember that fateful day when you agreed to come aboard this ship.

Being locked in a tomb that plummeted into nothingness. The Universe at this moment is in its youth, we live in its blooming years with stars shining in the sky and perhaps life will also proliferate throughout the cosmos. This is their golden age and we are a product of it. There has never been a better time to be alive and there probably never will be again. Like all things, the Universe must eventually end, but for now we have a moment in the Sun: the days of summer to live, grow and build. Let's use the time we have wisely.

It's just their place to hide. He pushed away the pain so hard that he disconnected from the person he loved most. Sometimes when you win, you lose.