## Friday, August 9, 2019

### Time and the heat death of the universe

I've been trying to wrap my brain around something for the last couple of months. I watched a video that explains what might happen as the universe dies in about 10^96 years. I can understand what a billion years or a trillion years is, but can I grasp the concept of a trillion trillion (10^24) years or a trillion trillion trillion trillion (10^48) years, or more?

In this post, I will use a relative scale to show just how loooooooooong the death of the universe might take.

Here is the video.

Because the scale is absolutely massive, I first wanted to scale down what a trillion years is. For that, let's say that a meter stick is a trillion years. Since a trillion is the same as a thousand billion, then a tiny little millimeter is a billion years. Imagine our time has been flowing at a millimeter per billion years--pretty slow, right? Imagine that we have a very slow snail that crawls a millimeter every billion years. The universe is 13.79 billion years old, and our snail hasn't yet traversed this penny which is 19.05 millimeters in diameter. The Earth is only 4.54 billion years old, so it is about a quarter of the diameter of the penny. The universe hasn't even lived long enough for that snail to traverse that penny.

Note that in the video, the creator, melodysheep (John Boswell), speeds things up as the movie progresses. This shows the various stages of the universe nicely, but one will have a hard time feeling just how long it will take for the black holes to evaporate at the end.

In the video, we hit a billion years at 3:04, and the snail has gone a millimeter in our scale. At 3:54, we hit a trillion years. He notes that most stars are starting to die off. I had read that some stars can live up to 10 trillion years or more.

Ok, imagine again our snail that goes a millimeter every billion years. That is very slow. Can you feel how long it will take this snail to go the length of a meter stick for a trillion years? Imagine that it goes on for about 11 yards or 10 meters. It would take our snail a VERY long time to go that distance, but at this scale, I can understand just how long that is compared to the current age of the Earth and the universe at the penny scale.

I can understand how long a billion years is, and I can get the gist of a trillion years (and 10 trillion years), but I had a hard time understanding what is meant by a trillion trillion years. We are still in the very early stages of the universe, and we hit that mark at 7:08 into the video.

How long is a trillion trillion (10^24) years?

I was able to guesstimate this in my head. How far is a trillion meter sticks? A km is 1,000 meters, so what is a billion km? Since a km is about 0.62 miles, how far is 620 million miles? Ahh, the Earth-Sun average distance is about 93 million miles (an Astronomical Unit), so a trillion meters is almost 7 AUs. Where does that put us?  At first, I guessed around Jupiter, and when I looked it up, the average Jupiter distance from the Sun is actually about 780 million km, so a trillion meters (a billion km) is about 220 million km farther out past Jupiter. So, imagine our snail taking a billion years to go a millimeter. Can you feel how long that snail would take to crawl out past Jupiter at that rate?

This I can sort of feel this in my gut, but it is very difficult to internalize just how long a trillion trillion years is.

What about a trillion trillion trillion (10^36) years? We hit that mark at 10:28 in the video.

What is a trillion times further out beyond the distance of Jupiter? In this case, I had to look it up; I couldn't do a quick calculation in my head. So, 10^36 meters is about 105 million light years away. This is on a galactic scale. I was able to find some galaxies that exist around 100 million light years away. For example, astronomers estimate that NGC7714 is about 100 million light years away. So, our snail going one millimeter in a billion years will take about a trillion trillion trillion (10^36) years to reach this galaxy. (Even if we found a space ship that can travel at 0.1 times the speed of light, it would take about a billion years to reach this.)

From this, I can sort of conceive just how long this would take, but it is very difficult to conceptualize.

At 12:30, it is explained that the universe has just emerged from the womb when compared to a human lifetime. At 12:47, it is shown that light as we know it only exists for an extremely short percentage of the life of the universe. Rewatch the segment between 10:28 and 13:48.

At 13:48, we hit a trillion trillion trillion trillion (10^48) years.

How far does our snail travel in this amount of time? What is a trillion times 105 million light years? This is 105 million trillion light years away. (Or a billion billion light years away.) Our current observable universe is only about 92 billion light years. So, our snail would have more than enough time to leave our current observable universe, if the universe stayed the same size, and it would go about a billion times the distance of the current observable universe. Even while travelling only a millimeter every billion years, it could leave the universe if given enough time, and do it a billion times again. This is just mind blowing to me. And, the universe is still young. Time has just started to tick. I simply cannot comprehend how long that will take. It is inconceivable to me.

How long is a trillion trillion trillion trillion trillion trillion trillion trillion (10^96) years?

Is there a better way or a different way of grasping just how long it will take for the universe to last?