I don't have to tell you that there are good and bad science channels on youtube. __Kurzgesagt__ is one of my favourites, always informative and stylistically wonderful. But sometimes, they don't get everything quite right. The video above is a great discussion about just how far we can explore this (seemingly) infinite universe when everything is accelerating away from us. To understand this, we have to understand the impact of various horizons at play, and, unfortunately, this is where they go a little astray.

They point out that, due to the expansion of the universe, that the further away a galaxy is, the fast it is receding from use, and eventually you get to a boundary beyond which objects are moving faster than the speed of light, relative to us. Here's their illustration:

But this is where the troubles start. They refer to this boundary as a horizon, and that once a galaxy crosses this horizon, it is irretrievably lost forever.

They also claim that we can see objects only because we are seeing them in the past (as light travels at a finite speed), at a time before they have crossed this horizon and are lost to us forever.

All of this seems quite sensible, so where is the problem?

The problem is that the boundary they refer to, the one that divides objects moving slower than light from those moving faster is not a horizon. It is the __Hubble Sphere__. This is something I know a little about:

To explain what is going on, I'm going to use what's known as a conformal representation of our universe. This is just a fancy way of staying that we have accounted for the expansion of space and time so that we can draw light rays as 45 degree lines. Here's my version:

If you want to understand this picture a little more, I suggest you check out the paper by __Tamara Davis and Charley Lineweaver__. The x-axis is (comoving) space and the y-axis is (conformal) time, with the Big Bang at the bottom. We are the solid vertical line in the middle, and the horizontal black dashed line is now. So, below that dashed line is our past, and above that line is the future. Hmmm, the future line looks a little short, but due to the way we have accounted for time, that finite line encompasses the infinite future ahead.

The other vertical dashed lines are other galaxies (and the numbers at the top refer to the redshifts of these objects as observed today. What about the other lines? Remember, light rays have been snapped to 45 degree lines. The red line is our past light cone - this is light we are receiving from the universe right now. But what of the other lines?

There are two lines called horizons. There is the __particle horizon__, denoted by the green lines. If you imagine that light had set out from us at the Big Bang, the particle horizon tells us how far that light would have reached over the life of the universe. In terms of causality, it separates the universe (in space and time) from that which we could influence from that which we could not.

There is also the __cosmological event horizon__. This is our (asymptotically) final light curve, and so denotes the universe (in space and time) that could influence us (the yellow triangle) from the universe that could not (the grey region).

Excellent. This all makes sense. Oh, but __Kurzgesagt__ is talking about the Hubble Sphere. Where is that? That's the dashed teardrop shape (cunningly labelled as Hubble Sphere), with the white region moving away from us subliminally, whilst outside of this objects are moving superluminally. And things are more complicated than the video makes out.

Firstly, the Hubble sphere depends on the expansion of the universe, which gives it its complicated shape, but clearly, it does not align with the straight lines of the horizons. It does asymptote to the cosmological event horizon in the future, but now they are separate.

Looking at our past light cone (in red), we are receiving light from objects which were moving faster than the speed of light from us when the light was emitted. Huh?? Well, it turns out that this light, whilst emitted towards us was actually moving away. To show this, here's another representation of the universe taken straight from Tamara.

This is now the usual distance and time, and in this picture, the past light cone has become a teardrop. Notice that at the bottom, the light that we are receiving today was moving away until it crosses the Hubble Sphere, and then heads towards us. So we can see objects that were moving away from us faster than light when their light was emitted. How cool is that?

In fact, objects can move in and out of the Hubble Sphere, clearly demonstrating that it is not a horizon. This is a point I've made __before__.

Perhaps the video confused the Hubble Sphere with the cosmological event horizon? Surely when things cross the event horizon, they are lost forever, just like an object falling into a black hole, a point noted in the video. But not so fast!

In my conformal figure, we can see the objects crossing the event horizon, going from the yellow region to the grey region. But how much of the future universe can we explore? If we head off now at close to the speed of light, we can get to anywhere in the red region. You'll not be surprised to hear that I've written about __this!__

Looking at the red region, there is something interesting going on. The red region overlaps the grey region and so we can get to time and places beyond the cosmological horizon! And even more exciting, this is also beyond the Hubble Sphere, so we would be able to reach objects moving from us faster than light.

Now, this might seem strange. But, of course, we could explore what's going on in a black hole by jumping in, falling through the event horizon. We can't get back, and it's the same in the expanding cosmos, but the region is not completely out of reach to us. What about catching objects moving faster than light? We are simply using the expansion of the universe to "boost" our travel, and we end up moving faster than light relative to the people who stayed behind. Anyway, I think this is all cool!

As a final point, at the start of the video they make the claim that, with even science fiction technology, we are limited to this finite patch. But this isn't correct either. With warp drives and worm holes, we can - at least in science fiction - get to wherever we want, whenever we want.

A closing point is that I think these videos are wonderful and educational, so (again) this is not to diss these approaches. I strongly encourage the effort and look forward to future videos. But in this case (which, unfortunately claims to correct the misconceptions from a previous video) doesn't get it quite right.

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