What Happens If You Never Stop Accelerating?（原声文稿）

Imagine you are sitting in a rocket with a special engine able to generate 1G of acceleration forever.

But once you turn it on, you can never turn it off.

But since you are a curious individual without soft -presentation instinct, you press it.

Okay, 1G is not enough to escape our planet, so let's put it into orbit first and then press the button.

At this time you might think that this is going to be just a boring ride and you are going to spend rest of your life just observing the universe.

But at least you still get to enjoy Earth's gravity during your life.

But this couldn't be further from the truth and you're going to experience the oldest light in the universe, visible with your own eyes. And this happens during your lifetime.

So on this panel we depict proper time, which is time you measure directly on your watch.

This is the distance you covered, but this distance is measured by the observer Because this is what is interesting for us, because all the distances in the universe we have measured so far were relative to the Earth.

This is the gamma factor relative to the Earth, so it basically represents your speed relative to the Earth in a certain way.

This is the time an observer on Earth measures on his clock when you are at this location, so it's simply the distance you cover in Earth reference frame divided by your speed.

speed. And this is your speed in the percentage of the speed of light.

Now let's make the time moving 300 times faster.

And in roughly 2 .5 hours we reach the moon at roughly 0 .03 % of the speed of light, which is roughly 90 km per second.

At this speed we cross the entire radius of the moon in just 19 seconds.

If you look back on Earth with camera and it covers 1500 x 1500 pixels then it would be shrinking roughly 0 .4 pixels per second. So it would be kinda slow.

In one day and seven hours we are currently 200 ,000 km from Mars, moving at the speed of 0 .36 % of the speed of light, which is roughly 1100 km a second.

At this rate, if we see Mars 100 pixels large, then it grows at the rate of half a pixel a second.

We can also notice that our clock disagrees with the Earth's clock by one second, so we are starting to really feel the effects of relativity.

After roughly 9 days, 3 billion km from Earth, you reach the last planet of our solar system, Neptune.

The Earth's speed is currently sitting at 2 .5 % of the speed of light, which is roughly 7700 km per second.

At this point you register more than a minute difference with the clock on Earth.

But here I wanna pause a little, because this is not the value of the clock on Earth in your reference frame as a traveling observer, it's the value of the clock on Earth that people on Earth measure when you cross the Neptune.

And now, 26 days, you finally reach the Voyager 1, the furthest man -made object in the universe.

Your speed is 23 ,000 km a second, so there is no chance of actually seeing it, but now you are officially the furthest thing humanity has sent into space.

You can start to notice that as you go faster and faster, the stars seem to drift towards the center of the direction of your travel, creating this bright pile of stars.

This is the effect of aberration and the Doppler shift.

After roughly a month later, 51 days into the trip, you start to feel sick, and you notice that the radiation inside the ship has increased.

The space is not completely empty, there is roughly a million protons per cubic meter in the interstellar space.

At this speed, the protons are hitting the ship with the energies of 9 mega electron volts, which is highly ionizing radiation.

But you are prepared, so you deploy some magnetic shielding and continue.

And now our ship is heading into interstellar space, leaving our solar system behind.

And almost one light year away from Earth, something happens.

It's not anything you could see or experience, it's something that could affect your mental health.

This is the time you completely lose contact to your home planet Earth.

You can still receive old messages that have already been sent, but any new messages that were sent after this time won't ever reach you.

So you will never see your children getting older by more than this time.

Those events are completely disconnected to you, as long as you keep accelerating.

In special activity the accelerated motion corresponds to a hyperbolic trajectory, as you can see on this diagram.

On this diagram, light takes a straight path at a 45 degree angle, but there is a clear asymptote of your curve and beyond this time no signal can ever reach you. This is called the Rindler horizon.

So now you can still receive messages but each message is going to be much further apart from the last one.

And, surely enough, there is a last message you will ever receive in a distant future.

And now you are heading to the closest star, the Proxima Centauri, at a distance of 4 .25 light years from Earth.

You can immediately notice something strange.

The distance is more than 4 light years, yet you covered it in just 2 years and 107 days on your clock.

Yet your speed is just 98 % of the speed of light.

And maybe this is some misunderstanding in special relativity that we are somehow capped by the speed of light.

But if you have good enough engine, there is nothing stopping you to cover whatever distance you want in small amount of time.

So in your lifetime, you could traverse the entire observable universe, provided you have good enough engine.

The reason is that even though your speed never crosses the speed of light, the length Life contraction compensates this, so the distances are shorter.

And at this time we have gamma factor of over 5, meaning that for us, everything is more than 5 times closer than an observer on Earth would measure.

Proxima centuries are relatively cold star, the temperature of roughly 3000 Kelvin, which puts it into red dwarf category. But this is not what you would see.

At your speed the Doppler shift factor is roughly 10, so you would basically see effective temperature of 30 ,000 Kelvin, which puts it into a blue star category.

Moreover, the intensity of the star changes even more drastically, as it scales with the fourth power of the Doppler factor.

This would make the star roughly 10 ,000 times brighter per unit of solid angle, but since the aberration makes the apparent size of the star smaller, the total received flux of radiation is just roughly 100 times larger.

When we talk about radiation it can sometimes be a little messy, we use terms like radiation intensity and radiation flux.

What I mean by flux is how much energy per second is passing through a square meter and take just the perpendicular component of that.

This is a forward -facing flux.

Intensity on the other hand is how much a unit of solid angle contributes to this flux.

So flux is an integral of this intensity through the spherical angle.

When you look at the star, the velocity, the intensity grows as gamma to the power of 4, which is very fast.

But the radius shrinks as r over gamma due to aberration, and therefore there is less solid angle that radiates.

Therefore the total flux scales just as gamma squared.

Moreover, for such a large gamma, the Doppler shift moves the peak of radiation out of the visible range for a star.

And therefore, even though the star is 113 times brighter, it's only 54 times brighter in the visible range.

But Proxima has the peak well behind the visible range at zero velocity.

So with the velocity, the brightness in the visible range grows much faster than the total brightness, as you can see here.

And then it slows as the peak moves away from the visible range into ultraviolet.

As you pass by, you see the start to dim and move towards the red part of the spectrum, as the Doppler effect reverses.

Interesting observation is also that you will still see it spherical and not contracted according to Lorentz contraction phenomena.

This is due to Terral -Penerose effect, where a combination of length contraction and finite speed of light compensate and makes spherical object women's spherical but rotated.

As you pass the star it would appear larger at the same distance than when you were moving towards it due to aberration, but the star would be very dim.

At this point all the stars in the universe are concentrated into a small region of space and around them warm red glow starts to appear.

This is the cosmic microwave background radiation, but heavily blue shifted to effective temperature of 1500 Kelvin.

You are now looking at the oldest light in the universe.

The light emitted in less than 400 ,000 years after the Big Bang.

If the universe was empty, DCMB would be visible even sooner, but it was outshined by the star pile.

But at this gamma, the radiation peak of these stars is well beyond the visible range, So the visible flux of stars doesn't grow as much.

On the other hand, the radiation peak of CMB is slowly moving towards the visible range.

And there is also a lot larger energy density of the CMB photons in the universe compared to the photons emitted by the stars.

So now the CMB visible flux starts to grow a lot as the radiation peak approaches the visible range.

At this time, the radiation flux of the CMB reached 1350 watts per meter squared, which is the same flux as we experienced from the Sun on Earth.

So now the whole universe is illuminated as if it was a daylight on Earth.

But this star would be kinda different.

It wouldn't be a white star, but it would be a very hot blue star with effective temperature of 50 ,000 Kelvin.

The flux in the visible range would therefore be just 0 .4 watts per meter squared, which is roughly 400 times brighter than a full moon, and it would appear kinda blueish. And all this happened in less than 10 years.

And you're already 9000 light years from home, so you didn't left your galaxy yet.

But do you remember our initial problem with proton radiation?

It got significantly worse.

Now we are basically inside L8C with each proton having more than 8 teraelectron volts.

That's even more than L8C actually.

This creates 3 .5 terawatts per meter squared, there is nothing that could survive this. So this is where this video could end.

But it took less than 10 years to travel 9000 light years.

But how far could we go in our lifetime?

And actually, from now on, things start to go quite quickly.

Right now you are 9000 light years from home and in less than 12 years you traverse the entire Milky Way galaxy.

In 15 years you reach the Andromeda galaxy and in less than 25 years you reach the end of the observable universe, which is currently 46 billion light years away.

So as you see, simple 1g of acceleration can get you anywhere, but the universe won't allow you to do this even if you had enough fuel, as this is not an empty space.

So now let's enjoy the whole trip from start to finish again.

I already uploaded a short video of the trip in the HDR for my members.

HDR is kinda important when you wanna display brightness, as the pixels contain not only information about the color but also about the brightness. This gives you wider range of intensities you can display.

But even with HDR, properly displaying what you would see is still kinda difficult, as you have to think of saturation threshold of your own eyes.

But this changes depending on how wide your pupil is.

And I think that the video I posted is kinda overly bright.

So I will probably post another video with corrected intensities for my members.

And if you are my Patreon member, I will share the link with you.

Just send me a message there and I will send it to you when it's finished. See you next time.