A Journey to the End of the Universe

Our Universe is one of immense and inconceivable scale, punctuated by at least 70 sextillion stars - oases of light permeating the dark. There are more stars in our Universe, than there are grains of sand on every beach on Earth. It's an absurd number that defies human comprehension.

Yet despite this abundance of cosmic landmarks, there's a certain irony that we live in a Universe where the outposts of concentrated matter are few and far between. If each star were indeed shrunk down to the size of a grain of sand, then the typical separation between each grain would be about six miles. So that's sort of the distance from here at Columbia to downtown Manhattan in the Greenwich Village.

Now that distance, which is about four light years coming back to physical units, is so great that it represents an immense challenge to our modern spacecraft. For example it would take our most remote spacecraft, Voyager 2, another 80,000 years to traverse such a distance. And that's just an nearest star, the nearest galaxy is half a million times further out than this.

When faced with such epic distances, such timescales, it seems like the Universe simply forbids the dream of human astronauts ever exploring the depths of space. Like a cosmic joke teasing us with jewels of exploration which will always be out of reach. And it's at times like these that we tend to dream of other solutions based on exotic physics, such as warp drives or wormholes.

But to the best of our knowledge, these are theoretically implausible. What about using real proven physics? In our recent videos we discussed the halo drive as a possible means for interstellar travel, but even that system isn't fast enough to get you to other galaxies.

Remarkably there is a trick using proven physics that might allow a person to travel between even distant galaxies on a human lifetime. But like making a deal with the devil it comes at such a steep price that you might not be so quick to want to sign up. A cost that emerges as a natural consequence of Einstein's special theory of relativity.

Today we're going to be taking a trip onboard the constantly accelerating spacecraft. Let's imagine that we have constructed a ship capable of accelerating at 1g for as long as we like. That means that its velocity increases by 10 m/s for each and every second that ticks by.

So for example, after 10 seconds it will be traveling at 100 meters per second and have covered a distance of half a kilometer. We're just going to leave aside the issue of how a spaceship could actually conduct such a feat for the moment and just assume it is true, and that's simply for the purpose of keeping this video focused and on point. And similarly we are going to assume that a spaceship has perfect shielding capable of withstanding any kind of impact or radiation you can imagine.

One benefit of the constant acceleration would be that this would push the crew back towards the rear of the ship, with the same force that the Earth pins us to the ground, thereby creating artificial gravity - something we've 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 that undergoes constant acceleration starts out slow but gains evermore momentum over time as its voyage continues.

So this is a bit like compound interest - your gains looks more to begin with but over a long period of time those gains rapidly accumulate. After just two and a half hours we would have sailed past the Moon, after one and a half days we'd be at Mars. And after three weeks we'd have overtaken Voyager 2 and left the Solar System altogether.

By this point a ship would be traveling at 40 million miles per hour or about 6% the speed of light. That's far faster than any spaceship we've built has ever traveled before. It's fast, but it's not fast enough for Einstein's theory of special relativity to really come into play yet.

As we leave the Solar System, we head out towards our nearest star system, Alpha Centauri, and see it gradually increase in brightness as we approach, whilst the Sun rescinds into just another speck of light behind us. The next year is fairly uneventful, life on board is probably rather mundane as the days, weeks and months tick by. Yet, with each day your ship travels about two million miles per hour faster than it did the day before.

It's now impossible to have a live conversation with your friends and family back on Earth the time it takes for radio waves to travel back and forth is now many months. Yet, the loneliness is somewhat alleviated by regular letters from home, updating you about the latest family news, sports results, scientific breakthroughs and political scandals back on Earth. After 15 months into your journey, your crew celebrates crossing the first light year - you're now just under one-quarter the distance to Alpha Centauri, but over a third the way in terms of outbound journey time and that's thanks to the ship's constant acceleration.

There's another milestone that you and your crew realize you have passed as well and that's what physicists caught your Lorentz factor, given by this famous equation right here, has now passed a factor of two. That means that the time dilation between you and Earthbound observers is now a factor of 2, and thus Earthbound observers would seem to see you moving in slow motion on board the ship. From this point on Einstein's theory of special relativity will have an ever greater influence on you and your ship, that's because you are now traveling away from the Earth at 87% the cosmic speed limit - the speed of light.

Now if there were no such limit then you should expect to cross the speed of light in 45 days time. But Einstein's theory, a theory which has been rigorously tested and proven back on Earth, states that nothing can move faster than the speed of light. Moreover, all observers - no matter what their speed - will always observe the speed of light to be the same.

Now this is very non-intuitive. If a horse chases down 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 that horse is running, if the train is a beam of light then it will always appear to recede away at exactly the same speed - the speed of light.

The horse can never catch up. If the speed of light is a constant to all observers then the mind-bending consequence is that space and time are not constant. They shift to accommodate this rule.

And that's exactly what happens here with our ship, time shifts such that observers back on Earth seem to see the crew moving slower than usual on board. And even space shifts such that the ship itself appears squashed in length. Both of those 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 you are now no longer accelerating at 1g, but rather your acceleration appears to be getting ever smaller as you approach the speed of light - despite the fact onboard you still feel a 1g acceleration. On board the ship, of course you and your crew would not think anything had changed. Time appears to be running just like usual.

But you would notice some strange things outside of the ship. Looking back at the Sun, you'd notice that it would have appeared to have faded into darkness, much faster than you'd expect from simple distance scaling. By the time your Lorentz factor is 2, it's now 10,000 times dimmer - only detectable with the ship's onboard telescope as a result of relativistic aberration and time dilation effects.

Not only this, but light from the Sun now appears increasingly red shifted, due to the relativistic Doppler shift - so red in fact that it now emits mostly in the infrared band where your eyes can't even see it. But ahead of you, the opposite has happened. Alpha Centauri now appears 10,000 times brighter than it would if you were not moving, yet most of its radiation is now arriving as high-energy ultraviolet light.

Not only this but the constellations ahead of you would appear distorted, warped into a kind of tunnel vision illusion. In a very real way, as you accelerate ever faster, you begin to disconnect from the rest of the Universe. But accelerating forever is not an option, because we don't have infinite fuel onboard and at some point we're going to want to slow down, step off the ship and reconnect to the rest of the Universe.

So one way of doing this is to accelerate your ship up to about the halfway mark in your journey and flip the ship over on its head and accelerate in the opposite direction, thus bringing you to a stop at some distant destination. Now let's stick with our original destination, that's Alpha Centauri, which is 4. 4 light-years away.

Remember that this means that a beam of light emitted from Earth would take 4. 4 years to reach Alpha Centauri. Yet, because of the time dilation effects on board you would land your ship on one of the Alpha Centauri planets having aged just three and a half years.

Don't worry, you didn't outrun a beam of light here, because according to clocks back on Earth, the journey took you six years. Maybe you spend a few weeks exploring this new planet then head back onboard and make the return journey home. When you get back home about seven years would have passed for you, but 12 years for everybody back on Earth.

Not a bad timescale to complete a journey to the nearest star. Recall that your ship started decelerating at the halfway mark, 2. 2 light-years from Earth.

That would be about 1. 8 years into your journey from your perspective, at which time your ship would be traveling at 95 percent the speed of light. Let's imagine that a fight broke out on board and the crew decided that they didn't want to go to Alpha Centauri anymore.

They wanted to use all of this momentum to go further, far further than anyone dreamed of. Now remember we're considering here only round-trip scenarios - we'll relax that assumption later, but for now any journey is defined by four phases. Outbound acceleration, outbound deceleration, inbound acceleration and then inbound deceleration.

With that in mind, recall that a round trip to Alpha Centauri would take seven years for the crew. But now let's go further out. Our Sun lives within a region of space of slightly higher hydrogen gas density than usual, a region about 30 light-years across and playfully known as the local fluff.

A ship which makes a trip to the edge of this local fluff would age 13. 4 years during their adventure. Upon return, they'd find that their children were now older than they were having aged those 13.

4 years, plus another 50 - giving rise to some strange reunions. Nobody believed me, but I knew you'd come back. How?

Because my Daddy promised me. Perhaps the crew are not satisfied with just leaving this local fluff though, perhaps they 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 across.

In a 1g spaceship, the crew will be able to fly to the edge of the local bubble and return back and only 22 years would have passed for them. But by the time they return to Earth they would be historical relics, as six centuries would have passed back on Earth. Perhaps the crew would be shocked and alienated by the changes which had transformed society in those six centuries gone by.

Let's go further and set a round trip to leave our Galactic spiral arm, the Orion spur, for which the round trip would take 31 years for the crew. This is where things get. .

. weird. Remember that your journey is characterized by four phases and at the end of that first phase of acceleration you're hitting your peak velocity.

So if you're journeying out 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 crew would look out of the front window, and you would see something, very strange. Two-thirds of the way into your 7th year of travel, a small patch of the sky ahead looks like it's glowing red.

At first you think the eyes are simply playing tricks on you after so many years in space, but then you realize that your Lorentz factor by now is 650. And the left over radiation from the Big Bang, the Cosmic Microwave Background, has now blue shifted all the way from the microwave to visible red light. Over the coarse of your now final year of outbound acceleration, you and your crew are amazed to see this small patch of the sky ahead grow ever brighter, ever bluer, until at its peak velocity it's like staring down into the eye of a cosmic rainbow.

As if the ship has now finally caught the gaze of the Universe itself. Perhaps not satisfied with leaving the Orion spur, you instead choose to journey to the edge of the Galaxy itself - a round trip for the crew of 41 years. Having returned home from their 100,000 light-year round-trip, the crew, now in their sixties, would return to an Earth which had witnessed a hundred millennia pass by.

It's very difficult to imagine how humans would have changed after such a long timescale. Perhaps our ancestors would look different after so many generations of gradual evolution. Perhaps they would speak completely different languages to the ones we recognize today, maybe they would have even abandoned technology and gone back to a more Neolithic way of living.

Maybe even the Earth itself is abandoned at this point and there are no trace of humans on the Earth at all. Whatever happens at this point the ship's computer database very likely represents an ancient library, containing information long lost to the eons of time back on Earth. But all of this is still within our own Galaxy, what if we go truly to the beyond to another galaxy altogether.

Let's go to Andromeda. In a 56 year epic round trip you, and your crew returned in old age to Earth having borne witness to another galaxy firsthand. But back on Earth there is very likely no one even recognizable as human by this point, with five million years having passed by.

You and your crew are very likely the last humans in the Universe. Although there were no humans left, the Earth looks better than you've ever seen it before - 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 was always hers. If we wish to venture further afield than Andromeda, then we may start to need life extension technologies for the crew.

Voyaging beyond our cluster of galaxies, the Virgo cluster, would require a round trip of 67 years for the crew. The Virgo cluster lives within the Laniakea supercluster of galaxies, a region of space spanning hundreds of millions of light years and containing tens of thousands of galaxies. Your round trip now would take 76 years.

At peak velocity during that journey, your Lorentz factor would be 250 million a speed of 0. 999999998 times the speed of light. By this point, the Cosmic Microwave Background will have appeared to have increased from his ambient 2.

73 Kelvin temperature to over a billion degrees Kelvin - that's the temperature that the Universe was after just a few minutes after the Big Bang itself. Needless to say this would be an extremely hazardous radiation environment for you and your crew, not to mention the now ludicrous shielding requirements to protect against impacts. Sometimes you hear it said that as you get to relativistic speeds the momentum of the ship increases so much that that somehow protects it from impacts.

But from the perspective of the ship, it is not moving - it is the particles, the space debris out there, that has the extreme momentum, and thus collisions with these tiny particles would not be for the faint of heart. After completing your 76 year round trip to the edge of the Laniakea supercluster, your home system would be barely recognizable. Landing on Earth, continents would have shifted into unfamiliar positions.

The surface is now devoid of plants or animals and you can no longer even breathe the air around you. Over the last billion years the Sun's luminosity has now increased by almost 10%, which in turn has increased the rate of weathering on the Earth. That weathering has removed carbon dioxide from the atmosphere so much so that photosynthesis is now no longer possible, ending the rain of plant-based life, ceasing oxygen production and collapsing the food chain.

By this point even plate tectonics may have shut off 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 on to existence, for maybe a few hundred million years at best. The living Earth is gasping her last breath.

And so I think it would be a mournful return to come back to your home planet and see it not go out with a bang but be suffocated with a slow drawn-out cruel death, perhaps reminding you of the fate which likely awaits yourself as now even your own body is feeling the effects of time. One might suggest that there's no reason why Laniakea should be the limit to these types of round trips. After all the time dilation is now so extreme that we can travel exponentially further with each passing year.

Indeed you sometimes hear it claimed that we can even travel to the edge of the observable Universe using constant acceleration. Those are galaxies some 46 billion light-years away from us. But no matter how much we accelerate, no matter how extreme time dilation becomes, we will never be able to reach the edge of the observable Universe.

Now why should this be? Well when we talk about journeys of billions of light years, then the expansion of the Universe itself starts to interfere with our voyage. In 1998, two teams of astronomers used distant supernovae to independently discover that the rate of the Universe's expansion, something known since Edwin Hubble's time, was in fact increasing.

It was itself accelerating. We do not fully understand why this is happening but the cause is usually labeled dark energy. Using these measurements of the rate of the Universe's expansion, we can define various thresholds, various horizons which limit our interactions with the outside Universe.

For example, the so called "particle horizon" is the greatest distance which a particle of light could have traveled since the Big Bang itself essentially, which was 13. 8 billion years ago. Now you might naively think that that means the distance should be 13.

8 billion light years, but because of the expansion of the Universe it's actually a much greater distance, ends up being 46 billion light years across. Now coming back to our spaceship adventure, if I want to make a round trip over cosmic distances, then this expansion causes the distances between regions to gradually grow during my trip, meaning I have to travel further than I thought I did. Now this isn't important if you're traveling within a gravitationally bound region, like a galaxy say, that resists the expansion.

But, it is very important as we voyage beyond our galactic supercluster. As far as I can tell, there is no previous 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. I'll link to a paper down below where you can learn all about how to do these kinds of calculations yourself.

But to save you that pain, the resulting proper distance turns out to be 8. 3 billion light-years away. This distance represents a cosmic point of no return.

Once you cross it there's no coming back, you would never be able to get back home even traveling at the speed of light. And that's because the expansion of the universe simply 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 this point on you would never return home and see the Earth again.

Since we can't return home beyond this point let's not even, try let's 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 come to a stop and that's simply because it's very difficult to talk about how much time has passed by unless we return to the same inertial frame of reference from which we left. Now liberated from the need to come back home, you might expect that we can travel far far further into the Universe, perhaps even to the edge of the observable Universe.

But again, the answer is no. Even if we accelerate forever, we'll never catch up to the so-called event horizon, which lies at twice the point of no return. This represents the greatest distance which a beam of light emitted from Earth now could ever reach, in infinite time.

Because parts of the Universe are expanding at the speed of light then we can never catch up to such regions and thus end up being limited to distances within this so-called event horizon. But what the hell, I mean we've come this far, let's just keep going. After this point, we're not really a spaceship anymore because no matter how hard, we try we never catch up with the event horizon.

And in fact the rest of the Universe around us expands away in all directions, ever faster. Soon there are no galaxies no clusters nothing around us as the Universe expands ever faster beyond our view. We've become isolated trapped in the void.

If we're not really a spaceship anymore perhaps we've become a Timeship? Could we use a ship to travel to the end of time itself? Now certainly if you naively use the equations of special relativity things certainly do look extreme.

For example, with an acceleration and deceleration phase spanning two centuries by the ship's clock, a clock back on Earth should have recorded one hundred thousand trillion trillion trillion years. Enough time that even protons would have theoretically decayed to leave no nucleonic matter left. But here's the thing it doesn't really make much sense to even talk about time dilation anymore.

And that's because time dilation is defined as being relative, hence the name relativity, to our initial inertial frame of reference, which in our case was the Earth. But by this point after so much time, after crossing so many light-years, the Earth lies beyond our cosmic horizon. We are no longer causally connected to it.

Put another way, it is now literally impossible to compare clocks to those back on Earth. To make matters worse, not only can you not compare to Earth's clocks but you can't even compare to any other clock by this point. That's because by now the Universe has expanded by a factor of 10 to the 10 to the 55 and statistically there would very likely be no other particles within your entire observable Universe, except for you.

Even the Cosmic Microwave Background has thinned out to nothing by now. How can we even talk about measuring time, comparing clocks, when the clocks effectively exist in separate Universes by this point? The very definitions underpinning time dilation have effectively unraveled.

And so here finally your journey comes to a close. In complete isolation. A perfect void.

You and your crew have become a monument to times that once were, to a Universe that once was. And perhaps as you and your crew finally pass away into the night, you think back to that fateful day that you agreed to step on board this vessel. To be locked into a tomb that hurtled into nothingness.

The Universe right now is in its youth, we live in its flourishing years with stars sparkling across the sky, and perhaps life too proliferates across the cosmos. This is its golden era and we are a product of it. There's 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 - summer days to live grow and build by. Let us use the time that we have wisely. It's just his place to hide.

He pushed away the pain so hard, he disconnected himself from the person he loved the most. Sometimes when you win, you lose.