The behavior of strange matter is not well understood - least of all under the conditions we're used to on Earth! Most theoretical treatments focus on places in which strange matter is likely to be produced or remain stable, like at the centers of neutron stars. If we put our mathematician hats on, we could naïvely try to apply the known equations for strange matter conversion, but the results might be meaningless. So let's instead put our physicist hats on, and work with the limited tools we have.

There are equations for how fast matter inside a neutron star will be converted into strange matter. Originally derived in the late 1980s, they're described by Dai et al. 1995. The authors note that the condition for the conversion of the entire body to strange matter is that the conversion timescale be greater than the time required for sound to propagate through the star. This makes sense; sound speed is often used as a proxy for how quickly changes can take place inside a solid body. It's a way for information to propagate internally through objects. Astronomers refer to this as the dynamical timescale, and use it when studying the collapse of stars or gas clouds - but it's also a quantity to consider here.

(As an aside, the dynamical timescale is proportional to the inverse of the square root of the mean density: $\tau\sim(G\bar{\rho})^{-1/2}$. For Earth, this is about 28 minutes. For comparison, in a neutron star, $\tau$ is about a tenth of a millisecond, or 100 microseconds.)

Dai et al. tell us that the conversion to strange matter should propagate at a speed $$v=\left[\frac{D}{\tau_w}\frac{a_0^4}{2(1-a_0)}\right]^{1/2}$$ where $D=\mu/k_BT$, with $\mu$ the chemical potential of down quarks, $a_0$ is related to the relative density of strange quarks and down quarks in strange matter, and $\tau_w$ is a characteristic timescale that encodes the reaction rate and influences of the strong nuclear force. In a neutron star, the conversion happens on the scale of seconds - much longer than the dynamical timescale, as expected.

Some takeaways:

• $v\propto T^{-1/2}$, so in cooler bodies (and Earth is cool relative to a neutron star!), the changes should propagate quicker.
• As Earth is composed of atoms, we should consider both the electromagnetic and strong nuclear forces when computing $\tau_w$, including intermolecular interactions. I'm not aware of treatments that take this into account.
• Our computations of the chemical potential might have to change given that all of the existing quarks are bound into protons and neutrons that are themselves the constituents of atoms.
• The assumptions used to derive our expression for $v$ were based on the setting of a neutron star; the equation itself may be entirely invalid.

If we put our physicist hats on, we're forced to conclude that we don't have the right tools for the job. Sure, from a mathematical point of view, we have an equation for the speed of the changes, like you wanted! From a physical point of view, however, that equation is incomplete and invalid, with parameters we can't easily calculate. On the plus side, we do know that the changes will propagate slower than the speed of sound - that much we should feel sure about. We can see that they will occur at a much slower rate than you probably expected.

posted over 4 years ago

4y ago

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