How would I find the mass of "pure" matter, that is, non-quantized matter, for a given volume?Let's say I have a volume equal to 1 meter squared, and I completely filled it up with matter - that is, no space in between. What would be it's mass?
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1$\begingroup$ I'm sorry but I have no idea what you mean. And I'm pretty sure 1 meter squared is a surface. ;-) $\endgroup$– WouterCommented Aug 9, 2014 at 13:05
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$\begingroup$ 1 meter cubed, ach. I mean, matter that isn't made up of particles, there is no space inbetween. "PURE" matter $\endgroup$– Trace FleemanCommented Aug 9, 2014 at 13:08
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3$\begingroup$ What do you mean "not made up of particles"? Let's start here: what is matter to you? $\endgroup$– WouterCommented Aug 9, 2014 at 13:11
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$\begingroup$ Anything that takes up space and has mass. I mean, something theoretically not made up of particles. A volume of 1 meter cubed that is completely filled with pure matter - no particles, just matter - would have a mass of what? $\endgroup$– Trace FleemanCommented Aug 9, 2014 at 13:13
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5$\begingroup$ Everything with mass is made up of atomic particles. Your "pure" matter does not exist. $\endgroup$– David HammenCommented Aug 9, 2014 at 13:24
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3 Answers
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Are you thinking of something like neutronium? This is the (hypothetical) matter formed when you compress the electrons into the protons to make neutrons, then pack the neutrons tightly together. If so, then the density is $4 \times 10^{17}$ kg/m$^3$.
However you should note that even neutronium isn't pure matter, because neutrons are made up from quarks and there is free space inside the neutron between the quarks. There have been suggestions that if you compress neutronium you could collapse if further to make strange matter with a density that is about 100 times higher still. However this is currently only speculative.
By coincidence a paper on this subject has just appeared on the Arxiv: Properties of High-Density Matter in Neutron Stars
answered Aug 9, 2014 at 13:29
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Suppose classical "pure matter" as you describe it existed and suppose a spherical volume $V$ of $1\,\text{m}^3$ of this stuff has mass $M$. Since it exists of pure matter only, one expects a uniform mass density $\rho$ and $M$ is just $\rho V$. So you'd have to define the mass density of "pure matter" to answer your question.
Say you make it 1 Planck mass per Planck length cubed, a natural density to assume for your hypothetical pure matter:
$$\rho_P = \frac{m_P}{{l_P}^3} = 5.15500\times10^{96}\,\text{kg}\,\text{m}^{-3}.$$
Now, that's heavy stuff.
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$\begingroup$ @celtschk and the people who voted earlier: I've edited my answer. I can't comment more on the implications of having a Planck density right now, but sufficit to say this is quantum gravity territory. $\endgroup$– WouterCommented Aug 9, 2014 at 14:49
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$\begingroup$ I've deleted my comment, since it no longer applies to the current version of the answer. $\endgroup$– celtschkCommented Aug 9, 2014 at 17:41
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Not a cosmologist but there some interstellar objects known as neutron stars that are extremely dense. Some neutron stars can have masses of 500,000 times that of earth with a diameter of about 25km. In the core of these stars, it is hypothesized that "quark liquid" exist which is when quarks get pushed into each other with no spacing between them. In such a way as a traditional nucleus has protons and neutrons conjoined. This result in extremely dense matter. A teaspoon of this type of matter could be equivalent to the weight of mountains here on earth
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$\begingroup$ Interesting, but would be improved with links and references. $\endgroup$ Commented Aug 9, 2014 at 14:37