Not what I was expecting, and indeed interesting.
I can address this in a few ways, I’ll start with this one:
You’re conflating mass and volume (or “space”). In other words, the amount of “stuff” that something has is only one function of the amount of space the “stuff” takes up.
For example, if you fill a balloon with air at 78 degrees, it fills up to a certain size. If you put the balloon in a freezer for 10 minutes, the air inside the balloon cools to 60 degrees, and it is less full. In practice, we can cool air to the point that it becomes liquid, and in theory we could compress air to the point that it becomes solid. In each physical transition, the mass remains the same but the volume decreases. Thus there is an inverse relationship between volume and temperature.
There is also direct relationship between pressure and volume, given by Boyle’s Law. As pressure increases, volume decreases. This is why your blood doesn’t boil at body temperature on earth - there is sufficient pressure (exerted partially by air, at about 14 psi, and partially by your skin) to keep it liquid. If, however, you place someone in a vacuum, the capillaries on their skin will break as their blood boils. A less gruesome, but more exotic demonstration, is on Jupiter. The planet is gaseous, but the pressure is so intense that its core is thought be made of hydrogen metal - a gas condensed to the point that it is solid.
Returning to your argument:
- It is said that the universe began to exist from an infinitely dense point, and thus the universe is finite in size.
“An infinitely dense point” describes the combination of pressure and volume such that pressure is exceedingly large while volume is exceedingly small (indeed, they must be, given Boyle’s Law). At this point, the universe was “finite in size”
relative to the universe at any other point in time, because:
- Thus you cannot determine the true objective size of the universe as a whole, as this would involve a comparison between the universe and another object - which must have an absolute size - existing outside of space.
However, because at the time of the Big Bang we could not measure the size of the universe, at the time of the Big Bang the universe was also infinite in size. But this is relativistic and entirely theoretical because as you point out:
- Width, length, or size, is something that can only exist in space. There is absolutely nothing (no space or physics) outside space.
But you only show three of the four measurable dimensions. The other is time. If two objects do not exist at the same time, you cannot compare them. For lack of a better term, the boundaries of the universe at two different points in time cannot be compared.
I would make one further adjustment to your argument:
- The universe contains all space.
The universe comprises all mass and volume with respect to time.