Pushed Around by the Stars

Pushed Around by the Stars
eighteenthelephant.com

I don't think this is true. It's true that interstellar mass movements affect atomic motions on earth (the theory is well understood!), but it's not true that the movements affect, say, whether a particular computer program correctly meets a given spec: they're simply at different levels of explanation. One can't even imagine a theory that connects them. Maybe the interstellar motion could cause a bug in a particular computer, but we can consider a computer program's properties independent of a particular execution on a particular hardware. Furthermore, we can even test this using an ensemble of physical computers in the presence of error-producing radiation or whatever.

Let's suppose that we place a 1 g mass at 4 ly. How does this affect the internal dynamics of a helium balloon? The relevant change is the tidal acceleration induced by the 1 g mass:

a_tide ~ GMl/r^3

where l is the mean free path in the balloon (l ~ 1 / n sigma), where n is the number density and sigma is the cross section of a helium atom. At room temperature, we have l ~ 4 x 10^-5 m.

Now, we want to calculate the change in angle induced by the tidal force across a single mean free path. This is (ignoring factors of order unity)

delta phi ~ delta x / l ~ al / v^2

Noting that the mean velocity is v ~ sqrt(kT / m_He), and substituting in the tidal acceleration, we have

delta phi ~ GMml^2 / kTr^3

Given these numbers this gives us

delta phi ~ 10^-78

At this point it should be pretty clear that this is not going to be a big effect. But let's see how long we would need to follow these interactions until the delta phi had built up to be large enough that a collision that would have happened doesn't. This is:

phi_crit ~ r_He / l ~ 10^-6

Now, I think a critical error that the author made is in assuming that the delta phi's build up exponentially. There is a non-linear dependence here, but I don't think it's as fast as described. Consider, for example, an atom bouncing head-on between two stationary atoms. Classically, the atom would continue indefinitely. How long would it be before an atom perturbed by delta phi would miss one of the stationary atoms entirely? There will be a linear increase in delta phi over time, along with a non-linear increase of order ~y / r_He where y is the vertical displacement. But this non-linearity is essentially a cosine, which is very close to zero initially. So the non-linear term will be essentially irrelevant until the linear term has grown to be large enough (i.e., of order unity) that the non-linear cosine term can take over. So it will require of order 10^78 collisions, which given the velocity of the atom of ~1000 m/s, means that it will take ~10^68 years for the atom to miss.

Now, due to other non-linearities in the system it would probably in practice be much less than this. But it would certainly be nowhere close to the few microseconds claimed by the author.

You are saying that atomic motions on earth cannot affect computer programs?

Or are you saying that some atomic motions on earth cannot affect computer programs?

If the latter, then how, theoretically, would you divide them into those that can and those that can't?