What Size Would the Universe Be if Compressed to Neutron Star Density?

[AndrzejBania]

TL;DR Summary

How big is all the matter in the observable universe?

Specifically, if you took all the regular matter that we believe to be in the universe and condensed it down to ‘neutron star’ levels of compression (Rather than ‘black hole’ levels)...

How big a sphere would it make?

I’ve always wondered, but never seen an answer posted anywhere

Hopefully someone on here knows!

 

[berkeman]

Have you tried using Google to figure this out? Seems pretty straightforward...

Please click into Google and come up with some initial numbers, and show them here and ask if they seem correct. Thanks.

 

[AndrzejBania]

I’ve seen some answers - but they don’t account for the kind of compression you would get by bringing it all together.
For example, you will get an answer like, “If we convert it all to hydrogen/helium, then the sphere would be >200 light years”.
Most science programmes etc will discuss the early universe, expansion etc - but none of them touch on the size (in modern universe terms) of the matter that was present.

 

[Nugatory]

You want to start with the total mass (which is a more sensible definition of “how much?” than the volume in any case). Given that mass, you can calculate the size of the sphere at neutron star density, or any other density you please.

 

[AndrzejBania]

If it was around 10^53 Kg... How does it help to make a calculation?

 

[lomidrevo]

There is a very simple relationship between mass, density and volume. I am pretty sure you know it.
Hint: for your estimate you can consider constant density.

 

[AndrzejBania]

I genuinely have no idea... I stopped physics at GCSE level... M C Theta

 

[lomidrevo]

I think this stuff is taught in the elementary school (at least in my country)
Do you remember something like,
$$\rho = \frac{m}{V}$$?

 

[jbriggs444]

but they don’t account for the kind of compression you would get by bringing it all together.

There is no possibility for a stable assembly containing the mass of the observable universe at neutron star density. The assembly would collapse into a black hole -- which you do not want to consider.

So there is no way to calculate the density it would have if it did not collapse into a black hole because there is no way that it would not collapse into a black hole.

 

[AndrzejBania]

Sorry if I have not understood this correctly... But neutron star density is pretty much the 'last point at which physics still makes sense' - but a black hole introduces lots of issues... That's why I was looking at the neutron star density.
I'm not that good with maths - but will see if I can get some values for (a) the known matter in the universe, (b) the packing density of neutron stars and (c) see if I can make this P=M/V thing work.
Swapping P for V and introducing the large numbers should work... right?

 

[jbriggs444]

Swapping P for V and introducing the large numbers should work... right?

Yes. Starting with $\rho=\frac{m}{V}$, you can multiply through both sides by $V$ yielding $\rho V = m$. You can then divide both sides by rho ($\rho$ is the Greek letter rho) yielding $V=\frac{m}{\rho}$.

Then, as you say, plug in the big numbers for m and rho, making sure that they are expressed in appropriate units first (e.g. kilograms and kilograms per liter).

 

[Buzz Bloom]

Summary: How big is all the matter in the observable universe?

Hi Andrzej:

Let us start with the total mass M in the Observable Universe (OU). One needs to know two values:

1. V = the size and shape of the OU.
2. ρ = the density of matter which is assumed to be statistically uniform throughout the entire whole universe at a sufficiently large scale.

What do you know about these variables? Can you find the values on the internet, or related values from which you can calculate these values? For V you can assume a sphere of a specific radius which you an find in light-year units. For ρ you can find it directly in kg/m³. Can you calculate M from V and ρ?

When you have M you can then find the typical density of a neutron star. If you assume a single spherical neutron star of mass M you can then calculate its size. However, this result will not be realistic since it would be unstable. I am not sure what changes it's instability would cause, but I am guessing it woud be a combination of explosions and the formation of a black hole.

Regards,
Buzz