Short answer to both questions is: we don’t.
1. We don’t know how big the Universe is. It can be infinite. It could also have a curvature and be of limited size. We are unable to measure that curvature yet, so we can give some _lower_ boundaries on how big the Universe is (if it was smaller we would be able to measure the curvature).
2. This is an even bigger “we don’t know”. Best we can do is to provide some models, that can explain some of our observations. But these models are sometimes contradictory and sometimes we make observations that they can’t explain.
Thats a big broad and vague as a question.
We dont know how big space is, we know how big the observable universe is if thats what you mean, we dont know how long space goes on after that, because the observable universe is all we can ever see.
We dont think its looping back around behind that because we have measured the curvature and it seems flat.
You have to elaborate what you mean with the second question you ask. Most things you mean “we know” is probably a theory based on multiple observations. Like for example we know the universe is expanding by observing that all galaxies move away from each other.
We don’t know how big space is.
We have been able to accurately measure the speed of light. And we can also accurately measure the shift of light over large distances. This gives us tools to work with when judging objects that are far away.
What we do see when we look out into space is there is a boundary called the ‘observable universe’. This boundary is where objects further than it are so far away that their light cannot possibly reach us, either because there hasn’t been enough time since the big bang or the universe is expanding too quickly for the light to get to us. Past this boundary we cant see anything, so we have no idea how much bigger space is.
We are never sure that we are “right” when we look at things in space. Everything is observational and quite often we make new discoveries. An example of this is that there exists a thing called dark matter that we literally know nothing about.
However based on what we do know, we are able to make predictions, and if those predictions come true, then generally we consider that we must know what we are talking about. An example of this is that the planet Neptune was predicted before it was actually observed.
We don’t.
What we have are models and observations.
As long as observations match with models (to the accuracy of the observation), we can assume the model is correct. Until there’s a contradiction with new observations.
And right now the model that best matches observations is one that says the observable universe is 96 billion lightyears across.
Imagine someone blind folds you and drops you off in a body of water. You’re floating in a small raft and there is nothing but water as far as you can see. That is us trying to observe space. We can measure the areas within sight, and a bit further with tech, but that’s about it. Space kind of has to be infinite, so there is no way to measure it anyway, as the size is infinite
We are in our infancy when it comes to understanding all of space and the universe. We are literally like kids in grade 3 confidentially discussing how something like an oil refinery works. We understand some broad concepts. But when you read things about expanding/contracting/dark matter/black holes/gravity/exotic particles/etc take it all with a huge grain of salt, it’s all very likely right in a broad sense but wrong in many of the details.
We don’t. We have no idea if the universe is finite or infinite. We can’t see beyond the horizon. As for how we know we’re right about things, we don’t. You can never know with 100% certainty that your explanation is perfect. We do know the distance across the visible universe because we can observe the light from distant objects and see how redshifted it is.
What we do know is that the scientific method will always get us closer to the truth. We form a hypothesis about how something works, do an experiment to test it, and record our observations. If the results of the experiment match our predictions, we think the hypothesis is correct. That doesn’t mean we won’t run into a situation where the hypothesis doesn’t work. It does mean we then have to adjust the hypothesis and do more experiments, until all the results match our predictions.
For example: quantum mechanics has never had an experiment done that disagrees with it. As far as we can tell, it accurately explains the universe at very small scales. It may be that some day we’ll run into a situation where it doesn’t work, but until then, all the evidence points to it being correct.
We know how big the observable universe is because we can measure those distances. If you look at a star and measure it’s angle, then wait six months and check again, you can use the differences in the angles to calculate how far away it is. (Yes, it’s more complex than that, but ELI5.)
Anyway, we actually have no idea about anything outside the observable universe, including whether there even is anything there.
Finally, we don’t know that we’re right about anything, including space. All science can do is come up with theories that seem to match what we see. We have some pretty good theories, but so did Galileo, and Copernicus, and lots of other people. As we get better telescopes and other instruments, we find out that our theories weren’t exactly right, and we change them to match what we can see now. So we’re closer to “exactly right” than people were before, but we’ll still be changing our theories a little bit as we discover new things, probably forever.
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