One of the hardest things for a human to imagine is the idea of curved space. We have evolved in a three-dimensional world in which lines projected in each of the three dimensions carry on in a straight line at 90 degrees to one another and never meet, yet we are told, and Relativity supports the idea, that if we could build a powerful enough telescope and look far enough in front of us we could see the back of our own head. This is because the mass of the universe curves space in on itself. So, our three lines projected at right angles to one another all meet up eventually.
Exploring this thought a little led me to an interesting idea which I'm not sure I have grasped completely, it seems so intuitively untrue, yet, like Xeno's Paradox, logically true.
Just by looking up into the night sky, we can see objects which have turned out to be distant galaxies, often several million light years away. What this means is that we are looking back at the history of that object as it was when the light we are now seeing left it several million years ago. With light travelling at 186,000 miles per second, an object 1 million light years away will have been 186,000,000,000 (that's 186 billion) miles away 1 million years ago.
With a small home telescopes we can see even more objects, even further away and by using even more powerful telescopes we can see further still to objects possibly a billion or more light years away. We would now be seeing objects maybe 186,000,000,000,000 miles away.
Now, because the light from these objects has taken so long to reach us, and because we know the universe is expanding, we know that these objects are not now where they appear to be. They are now even further away from us. In fact, this recession is what causes the famous Red Shift, which incidentally holds true for every point in space because it's the space between objects which is increasing, which is not the same thing as everything moving away from a central point.
So, if we regard the range of our increasingly powerful telescopes as a sphere increasing in size with each increase in power we have the idea of an expanding sphere ever increasing in volume as the power increases. For the want of a better term, I will call this a 'sphere of perception'. Think of it as an expanding bubble seen from the inside.
Now, there is a limit to what any telescope could show us because we will also be looking further and further back into the universe's past and we will reach a barrier through which no light, or radio waves, etc. could pass. Until 300,000 after the Big Bang, the universe was opaque. This was because the temperature was so high it would have been impossible for electrons and protons to form any stable, electrically neutral, arrangements like hydrogen atoms or neutrons without high-energy photons smashing them apart, so there were no stable neutral particles. This meant that all particles interacted with all electromagnetic radiation and photons could not go anywhere, let alone pass through it. When, at about 300,000 years, the temperature fell far enough, protons could capture electrons to form hydrogen, and stable neutrons could form, sometimes binding with more protons to form larger atomic nuclei, and capture charged electrons to form electrically neutral atomic matter. At that point photons became free to stream through the universe and it became transparent.
So, even our most powerful telescopes our expanding sphere of perception would be physically limited to the universe as it was when it was just 300,000 years old. Our expanding sphere of perception would now be 13.73 billion light years. In other words, the radius would be the distance light has travelled in 13.73 billion years.
But supposing we could somehow see through this barrier and beyond, right back to the moment the universe came into existence 13.76 billion years ago...
How big would our expanding sphere of perception be now?
At the moment of the Big Bang, our sphere of perception would be the size of a singularity and it would occupy a 'space' inside where we now stand, albeit a 'space' that was there 13.76 billion years ago. You wouldn't really see the back of your own head because your head wasn't there in those days.
And even if we couldn't get past the 300,000 year barrier, our sphere of perception would only be as large as the expanding universe was after 300,000 years.
So, how is our sphere of perception both expanding and moving further away (intuitively) and contracting and getting closer (logically)? The thing which we thought was getting larger and moving further away was actually getting smaller and moving towards us, but just getting further away in time.
The answer to this is, I think, that light has not travelled in a straight line through space-time but has curved outwards as the universe has expanded. And so we 'see' a universe which appears to get larger as we look further back in time, whereas the reality is that it gets smaller. The problem is that we are using an intuition which was never evolved for the purpose for which we are trying to use it.
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