The Universe as big as a basket ball?

[edgar23]

The Universe as big as a basket ball??

I recently came upon this quote while perusing the web: “Atoms are largely empty space, aside from spontaneous virtual particle emissions from the quantum fabric in the Universe. So, if you removed all the empty space between all the particles in the Universe, and pushed everything together as closely as you could without reaching singularity condition, it'd be no larger than a basket ball.” Now, I realize that his first statement is true. The particles that make up the mass of atoms are minuscule in scale compared to the size of the atom as a whole. (Forgive me for making another gross analogy here, but I’ve heard that if the protons and neutrons of an atom were the size of soccer balls, the electrons would be the size of grains of salt and would “orbit” the nucleus about a mile out. Please correct me if I’m wrong on this scale as well, as I seem to be relatively uncertain as to the exact dimensions of all this.) Now, what I have problems with is the gentleman’s second statement, “no larger than a basket ball.” It would seem to me, that although we are dealing with such minute particles, the sheer number of them (if the answer to the question of how many particle are there in the universe is even known) would lead me to believe that an object far greater than the size of a basket ball would be produced if one possessed the ability to remove all the empty space between all the particles in the universe without reaching a singularity condition (effectively, a Big Crunch without the crunch). So, my question is, if you were to throw all the forces out the window and just deal with the absolute material volume of the universe, would you get a basket ball? Would it be orange? Could I dunk with it?

 

[Vast]

Why would one care whether it was the size of an atom, the size of a pea, ten km across, or the size of Earth? The reason I say this is because we have no idea about how much matter there is in the universe, coming to any conclusion over the matter would be very difficult and not to mention pointless. As far as anyone knows neutron stars are the most compact objects in the universe having at least 1.4 solar masses within a diameter of about 10 km. Anything above 3 solar masses and it collapses into a black hole. So instead of asking how big an object all those particles put together would form, as is described in the quote, it would be more productive to learn how gravity pulls everything down into an infinitesimally small volume, because that's in fact what happens.

 

[Grumm]

You can probably find a rough estimate by doing the following:

-Get a rough estimate of the mass of the universe.
Assume all the mass is made up of the nuclei of hydrogen atoms. (a proton)
-Divide the mass of the universe by the mass of a proton. We now have a total # of protons in the universe.
-Using Volume of a sphere, V = 4/3*pi*r^3, take the # of protons as your total Volume, and obtain 2*r, the number of protons in the diameter of our compacted sphere.
-Now multiply 2*r, your diameter, by the diameter of a proton. (10^-15 meters is a good estimate).
-Compare with the diameter of known objects (such as a basketball)

This result will be very rough, keep in mind :)

 

[Chronos]

The basket ball thing looks bad at first glance, but I think it is probably correct [I admit being too lazy to crunch the numbers]. I recall having once calculated how big a neutron could get before it would gravitationally collapse, and the answer was shocking - it was like over a meter. Assuming a neutron is as dense as any other fundamental particle, you could cram a fantastic number of them into a pretty small space without exceeding the Swarzschild limit. Dont' forget to figure packing density - assume all particles occupy a spherical volume defined by their pauli exclusion limit.

Hi Grumm, welcome to PF! Also a good answer. We have plenty of just plain curious folks who wander through, so I have this tendency to insert blue collar answers.

 

[SpaceTiger]

So, if you removed all the empty space between all the particles in the Universe, and pushed everything together as closely as you could without reaching singularity condition, it'd be no larger than a basket ball.”

I have no idea where he's getting this number (the result of Grumm's calculation would be much larger) or how he thinks this could physically occur. This object would be described by the Schwarzschild metric, so you would form a black hole (whether you wanted to or not) long before you could shove all of the matter in the universe into such a configuration. It's also not clear what his definition of "size" is for the particles.

 

[JesseM]

What would be the size of all the matter in the observable universe if were compressed down to the Planck density? If spacetime as a whole were collapsing in a big crunch, you could get down to that size without forming a black hole, no? (see this entry from the usenet physics FAQ about why the universe did not collapse into a black hole shortly after the big bang, which I imagine would apply to the big crunch as well)

 

[SpaceTiger]

What would be the size of all the matter in the observable universe if were compressed down to the Planck density?

A number that is much too small. I get it to be of order 10^-13 cm.

If spacetime as a whole were collapsing in a big crunch, you could get down to that size without forming a black hole, no?

Of course, in a dynamic universe you can compress matter well beyond its usual gravitational radius without forming an event horizon, but it seems like a questionable interpretation of his words (or perhaps they're just questionable words).