[HN Gopher] Pushed Around by the Stars
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Pushed Around by the Stars
Author : thaumasiotes
Score : 19 points
Date : 2021-11-30 23:30 UTC (23 hours ago)
(HTM) web link (eighteenthelephant.com)
(TXT) w3m dump (eighteenthelephant.com)
| [deleted]
| dsizzle wrote:
| > Everything affects everything else, and the correct questions
| to ask are how much?
|
| 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.
| finite_jest wrote:
| This video by Veritasium on the unexpected effects of the
| cosmic rays is pretty interesting:
| https://odysee.com/@veritasium:f/how-distant-galaxies-
| mess-w....
| antognini wrote:
| Yeah I'm not sure about this math. Midway through the article the
| author correctly notes that their original argument was wrong.
| The relevant factor here is _not_ the gravitational force, which
| scales as 1 /d^2, but the _tidal_ force, which scales as 1 /d^3.
| But the author claims that after they make this correction, it
| only changes the result by about 30% or so. But given that they
| would have to be off by a factor of 1/d (which, in their example
| is ~4 x 10^-18). Now there's admittedly a non-linear factor here,
| but even still I have a hard time believing that a change in one
| of the inputs by 18 orders of magnitude will only result in a 30%
| change in the end result.
|
| Another hint that something is wrong with the math is that the
| author does not have a term for the width of the balloon, which
| is a relevant quantity when calculating the tidal force.
|
| Even though the math here is dodgy and the example is somewhat
| artificial, the same idea is super important when accounting for
| the effect of Galactic tides on the kinematics of stars and
| clusters in the Galaxy. Tides play a role in disrupting open
| clusters and dispersing young stars into the Galaxy.
| pfdietz wrote:
| The point he made is that because the discrepancy in angle
| grows exponentially, the change from 1/d^2 to 1/d^3 has only a
| small effect on the time until the change builds up to O(1).
| antognini wrote:
| I don't think there's the exponential dependence they claim.
| I think a more correct derivation would look like this:
|
| 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.
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