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According to the Big Bang theory our universe used to be a lot smaller in size.

It actually used to be so small that in the beginning it used to be a singularity.

And the universe started to expand and it keeps on expanding ever since.

But you already know all that.

So what I'm wondering is, if the universe used to be a "singularity" at some point, if it used to be infinitely small or even just extremely small, does that even make any sense?

I mean if at some point in time all there was was that singularity, then wouldn't that singularity be infinite in size and therefore not be a "singularity" after all?

If space does not exist independently of all that is, then if all that was, was that singularity, isn't it true that this singularity wouldn't exist like a tiny dot floating inside a vast empty space but that it would enclose and include space itself and therefore be infinite itself in size?

In a more simple analogy, what I mean is that if all there is a single grain of sand, then wouldn't that grain of sand be everywhere? Up, down, left and right, anywhere you'd look there would only be that one thing, that single grain of sand, and if that grain of sand existed everywhere, since it would be the only thing that existed, wouldn't its size then be infinite, without an end to it? Without an end to its size? Because for a size of something to be finite and specific and measurable it should end where something else starts, but if all there is that something, then isn't the idea of that something having a size a naive and meaningless one?

And if someone was trapped inside that singularity wouldn't that singularity, from inside, look and be infinite to the person inside it, much like our universe looks and is infinite to us existing inside it?

I understand that the conditions during that so called "initial singularity" are extremely different from what we have now and that we are indeed talking about 2 completely distinct states of the universe in time so I'm not denying this fact or that "initial" state.

The point I'm trying to make is mostly about the concept of size regarding the universe.

I am wondering how distinguishable or not our current universe is from a so called "singularity". Wouldn't our current state of the universe look like a similar "initial singularity" to a future observer 13.8 billion years from today?

I'm not sure whether this post belongs here or to https://physics.stackexchange.com/ or whether it's complete nonsense. Feel free to close it if it is.

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    $\begingroup$ Your question is ok here, but see physics.stackexchange.com/q/136860/123208 which covers a lot of your points. $\endgroup$ – PM 2Ring May 27 at 23:46
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    $\begingroup$ Your initial premise is questionable. While a singularity is one possible “origin” of the universe, there are other models that don’t involve a singularity. And unless the universe is closed (current evidence suggests not), the universe is infinite in size and has always been so. $\endgroup$ – Chappo Hasn't Forgotten Monica May 28 at 7:55
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A singularity isn't an object. It is a property of a differential equation. For example:

$$t \frac{dx}{dt} + 2x= 0$$

This can be "solved" to give $x = \frac{C}{t^2}$, and given a value of $t$ and the corresponding value of $x$ the constant of integration can be found unless $t=0$.

If you are given this equation and the value of x at time t=0, you can't get a solution. Now the equations of the gravity of the universe are similar, except they have four dimensions and the solution is a lot harder. They also have a singularity and that singularity is at time=0.

So you can't say "the universe was a singularity". But you can say "there was a singularity at the start of the universe.

We can't use our models to describe the state of the universe at time zero. It isn't certain how this singularity should be interpreted: It may represent some kind of physical reality, or it may represent the insufficiency of our model of the early universe. Sometimes singularities appear in solutions that aren't physically real: The solutions to the black hole equation have a singuarlity in a sphere called the event horizon. But if you change your perspective from an observer at rest to an observer in free fall you find that the singularity disappears (but there is still a singularity at the centre of the black hole)

Many of your questions therefore are meaningless or at least unanswerable: You can't be "trapped in a singularity". The universe was never a singularity at any time t>0. Certainly the universe in 13.8 billion years will be a lot similar to how it is now than how it was 13.8 billion years ago.

The question of "size" is interesting but at the moment unanswerable: If the universe is "open" (as it seems to be) then the universe may be infinite in dimension, and always (for t>0) has been. Infinite universies create philosophical problems, but so do universes with an "edge". And there isn't a scientific way test if the universe is infinite.

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