A cube ten meters square doesn’t actually make sense. I assume that you mean a cube which is 10 meters on each side.
Figures from wikipedia here. I didn’t check them, but they seem to be the right order of magnitude. (Really freaking big! )
So, the observable universe has a mass of around 3x10[sup]52[/sup] kg and a volume of 9x10[sup]30[/sup] ly[sup]3[/sup].
1 ly[sup]3[/sup] = 8.5x10[sup]47[/sup]
So the volume of the observable universe is 8x10[sup]78[/sup] m[sup]3[/sup].
So we get an average density of around 4x10[sup]-27[/sup] kg/m[sup]3[/sup].
That is, in each cubic meter, there is around 0.000000000000000000000000004 kilograms of stuff. Or, about two hydrogen atoms. That’s in a cube one meter on each side. A cube 10 meters on each side consists of 1000 cubes, each one of which contains around two hydrogen atoms.
Looking up the density of the universe from other sources, we find this site which lists several figures, all of which are the same order of magnitude as the above estimate.
No, it doesn’t, unless you have a picture in your head of a little sphere zooming around. There’s nothing in electron’s wavefunction description implying some kind of underlying classical particle that we’re just not quite sure where it is.
Well, that’s always true in physics, isn’t it? All we an ever talk about is how things appear to behave. The electron’s wavefunction is the best description of the electron that we have.
Of course. And while the electron is probably not a little hard particle, either, we have no good reason for believing the space surrounding the atomic nucleus isn’t mostly empty space. Maybe it is, maybe it isn’t.
We have the wavefunction, which (by our theories) exists throughout the atom. We don’t have even that much reason for believing that the space is empty.
Exactly! It always bothers me when people talk as though a math model of some physical phenomenon is necessarily reality. The models can be extremely useful for explaining things and even make predictions, but who knows what’s really happening at the smallest atomic levels. Because we humans are used to the macroscopic world in which we live, we try to imagine things in ways that are familiar to us (particles, waves, etc.), but there could be a reality at the quantum level that’s totally foreign to us.
It’s my understanding that the wave function isn’t meant to represent a real, physical entity but rather a sort of “cloud of probability” for the position of the electrons. The resolution of the electron microscope is certainly testament to the electron being, if not a small, hard particle, then a wavelike entity with a very, very short wavelength.
No, it just implies that it’s mostly something that can be compressed a lot. You’ve got to be careful about classical notions of things like “empty”, when you’re looking at the subatomic scale.
In answer to criticisms of my OP, I’ll admit it was a little inadequately expressed, but I thought the general gist of what I was asking was fairly clear to see? All I wanted(:)) was to have the universe scaled down to a comprehensible size, and to see what the percentage of the actual physical matter was, in comparison to a 10m cube.
Please try and forgive my including a redundant ‘squared’ notion!
!.
there is a big difference between compressed and scaled. By compressed I assumed you meant taking the earth as an example and applying sufficient pressure to fit it into a box 10 m on a side along with all the other matter in the universe. Such a situation existed during the big bang, for a very brief moment, but I didn’t get anything about scaling the objects down such that the relative distances among the objects remained the same.
As for the scaling, the relative scale would remain the same and the present density would remain. As far as I can see, there would be no difference in the present situation. In fact, by simply redefining the length of a light-year, one can do what you are proposing right now. Makes me feel even more insignificant though…
I think what he’s looking for is something he can easily picture in his head. It’s one thing to say the universe is .000000000000000000001% matter (figure made up for simplicity; not an actual value; void in California) but quite another to say it would take up the space of an amoeba in a 10-m cube.
Your OP is ambiguous because in the first case, you are talking about compressing the universe down (similar to conditions shortly after the Big Bang), and in the latter case, you are talking about scaling the universe down.
These are two completely different questions. Which question are you asking?
Also, as Xema noted, you keep saying “area” when you mean “volume.” There’s a difference between these two concepts, too.
If the universe were shrunk down so that it was a cube 10m on each side, it would contain 2000 hydrogen atoms.
Such a cube is 1000 m[sup]3[/sup]. I’m not sure how easy it is to visualize such a cube, but that’s fine. It’s a smallish house.
I think that a better unit for visualization is a cube 1m on each side. In such a cube there would be two hydrogen atoms and nothing else. I believe that this is several orders of magnitude more empty than the best man-made vacuum ever produced.
For comparison’s sake, if the universe were shrunk to the size of the Earth, it would weigh around 3 milligrams, the same as three cubic centimeters of water. For the bakers out there, that’s around half a teaspoon.
Actually, it takes around 300 10m cubes with the same average density of the universe to rack up 10 attograms of mass (the mass of the smallest virus), so the amoeba is right out.
Another way of thinking of it is to say that if you had a cube 70m on each side, the same density as the universe, it would weight the same as a virus. Just one virus. And the smallest virus known to man.
If you include dark matter and the like, then multiply everything I said by 3, as it was based on 2 protons per cubic meter rather than 6. These values correspond to an average density of between 3E-30 and 10E-30 g/cm[sup]3[/sup].
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