2643: Cosmologist Gift

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Cosmologist Gift
These neutrinos were freshly produced by a local source just 8 minutes ago
Title text: These neutrinos were freshly produced by a local source just 8 minutes ago


This comic shows a box labeled to indicate that it contains 30,000 fresh neutrinos and four zeptograms of dark matter. The box is intended as an inexpensive gift for a cosmologist. The gift giver didn't put those things in the box—both are simply passing through it, so the "gift" consists of exactly what was in the empty space it occupies. While the caption suggests this would be a good gift for a cosmologist, what they or anyone else would do with such a box is uncertain.

There are about a billion neutrinos per cubic meter throughout space, produced during the Big Bang.[1] However, the flux of "freshly produced" solar neutrinos at Earth is around 6.5×1010/cm2/s, yielding about 2.1 million per cubic meter, and implying the box is around 12 liters, three quarters as big as a typical breadbox.

Four zeptograms is a minuscule mass, equal to four sextillionths of a gram, the mass of about 200 carbon-12 atoms or around 20 to 23 amino acids. There is an estimated 0.011 to 0.016 solar masses of dark matter per cubic parsec local to the solar system,[2] or about 900 zeptograms per cubic meter, suggesting the box is closer to 4 liters. This discrepancy could imply Randall agrees with cosmologists who believe dark matter is partially composed of primordial black holes,[3][4][5][6][7] instead of being composed entirely of ubiquitous subatomic particles. This comic coincided with the first James Webb Space Telescope science image release to the public containing gravitationally lensed very distant quasars and population III stars, the spectra of which can be used to test certain hypotheses associated with dark matter being black holes. A billion neutrinos have a mass of only about 2×10-12 zeptograms, at about 0.1 electron volts each.

The "local source" mentioned in the title text is a joke about the commercial value of fresh, locally produced items, but the comic means that the neutrinos come from the Sun. It takes solar neutrinos slightly more than 8 minutes to reach Earth once they're emitted, roughly the same time as photons take to make the trip. (While energy takes approximately 170,000 years to reach the Sun's surface from its core, where the fusion reactions occur, the neutrinos are not slowed down inside the Sun and travel at about 99.9999999999% of the speed of light. Thus, they will have aged by less than a millisecond,[8] and so are technically even fresher than indicated.)


[A picture of a box with writing on one side. The box's lid is slightly hanging off the right edge of the box so you can see inside. The inside of the box is black.]
30,000 neutrinos
Freshly produced
Plus 4 zeptograms
of dark matter
[Caption below the panel]:
Cosmologists are easy to shop for because you can just get them a box.

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- The explanation mentions “Eight zeptograms” although Randall’s box says “4 zeptograms of dark matter.”

- The 4,800 daltons in the explanation is roughly the size of a small protein; for example, insulin is about 5,800 daltons.

- Randall’s box says it contains 4 zeptograms of dark matter. Could someone explain this? My incomplete (biologist’s) understanding of dark matter is that astrophysicists do not yet know what it is. So how could Randall claim the box contains 4 zeptograms of it?


Fixed; thank you. 01:18, 9 July 2022 (UTC)
Since no one has detected ANY dark matter, you can claim any amount is in the box. SDSpivey (talk) 23:31, 11 July 2022 (UTC)

Here's a more recent PBH DM source than those already cited which could comport with Randall's 0.4% DM particles implication, but doesn't do so explicitly. 02:35, 9 July 2022 (UTC)

With the math corrected per below, the figure is 34% ubiquitous particles. 09:44, 9 July 2022 (UTC)

And this comic was the perfect birthday gift for me. 02:42, 9 July 2022 (UTC)

  • How was the 23,000 neutrinos/m³ figure obtained? A flux of 7e10/(s·cm²), or 7e14/(s·m²), at a speed of close to 3e8 m/s, gives 2.3e6/m³. That would correspond to a box size of about 0.013 m³, or a bit larger than a typical shoe box. 07:19, 9 July 2022 (UTC)
Corrected. 09:40, 9 July 2022 (UTC)

To note {and I've summarised in an edit) that photons from the Sun can have been travelling for 100,000 years from its core to space, before their 8ish minute trip to the box (assuming you let them in, e.g. leave the lid off, or filter out all but the hard X-rays/etc), whilst neutrinos hardly notice so are 8 or 9 minutes old (before being adjusted for time dilation) regardless. And you can still put as much lead-lined wrapping paper on your present as you want, to keep it a surprise! 14:45, 9 July 2022 (UTC)

I saw your very interesting source was from 1997 and mostly about neutrino cycles -- which surprisingly match the menstrual cycle better than the orbit of the moon does -- but not mostly about energy migration out of the sun. It looks like the sun actually has multiple layers that engage in different forms of energy transformation. I added a link to the radiative zone (where gamma rays spend 171 thousand years colliding with matter, getting longer wavelength at each collision, until they leave) but somebody should probably learn about all the different zones at some point and make sure the text is correct. I never knew the sun was so complex! I partly imagine high-energy ancient civilizations somewhere deep inside, having their own forms of night and day and seasons. 14:44, 10 July 2022 (UTC)
I took the 28 day neutrino cycles link out, because it really doesn't help explain anything in the comic, and was out of place and confusing where it appeared. 17:20, 11 July 2022 (UTC)

I don't see how the box containing dark matter is at all consistent with the premise of dark matter being primordial black holes. PBHs wouldn't be ubiquitously distributed through space such that any given volume contains a constant tiny number of them, would they? Black holes that are that tiny would have evaporated long ago by Hawking radiation, by my understanding. BunsenH (talk) 17:26, 11 July 2022 (UTC)

If dark matter was 100% particles, then a volume on Earth containing 30,000 solar neutrinos would have 12 zeptograms of dark matter, not 4. Since the box is labeled with only a third as much dark matter, the implication is that Randall might think some is clustered in MACHOs. (I'm going to ignore modified gravity, which gets more attention than non-PBH MACHOs but way less than PBHs, and has some foundational issues along with zero successful simulations compared to very successful large-scale simulations using generalized DM.) In the past decade the only MACHO DM theory with more than a handful of papers per year is PBHs, which skyrocketed in popularity after LIGO/Virgo, but are still less popular among mainstream cosmologists than 100% WIMPs. The elephant in the room is that there's lots of evidence for intermediate mass black holes (LIGO/Virgo being the most compelling, but recent indirect observations exist too) but only one out of about thirty WIMP detector experiments have painfully meager positive results, which nobody else has been able to replicate. It's been a similar situation for almost four decades now. Back in the mid-1970s dark matter was assumed to be mostly 100,000 solar mass black holes. A couple generations of constraints assuming monochromatic mass suggested it was a particle instead. But all the constraints, including microlensing, which assume all black holes have even approximately similar masses had to be rejected after the LIGO/Virgo results.
To answer your question about the sizes, assuming LIGO/Virgo's 3-160 solar mass range is representative of typical black holes and likely contains their median is kind of unavoidable at this point. If the median is 50 solar masses and all dark matter is black holes, that would work out to around one per star.
The group to watch as JWST's first light comes in is Yale's, who propose specific testable hypotheses for its deep IR source count distribution, and use a non-monochromatic (platycurtic) mass distribution for black holes, which is the only correct choice for merging bodies. Specifically, NASA is releasing a SMACS 0723 field from JWST tomorrow, which should be able to test these predictions. Another author to keep an eye on as JWST results roll in is Bernard Carr (paywall-free preprint) known for his DM literature reviews over the years, and who has become an ardent PBH DM proponent post-LIGO/Virgo. 20:38, 11 July 2022 (UTC)
W00T! They decided to do SMACS 0723 first today! https://www.nasa.gov/image-feature/goddard/2022/nasa-s-webb-delivers-deepest-infrared-image-of-universe-yet A gift to cosmologists indeed! 22:23, 11 July 2022 (UTC)

"what they or anyone else would do with such a box is uncertain." - Put things in it, obviously. 06:32, 12 July 2022 (UTC)

Why would any self-respecting cosmologist want to mess up the box with more than the minimum extraneous contents? 10:16, 14 July 2022 (UTC)

How much more mass do neutrinos have when they're going 1-10-n times the speed of light? I swear this is not a homework question. 10:05, 27 July 2022 (UTC)

(The attempt to fix the question assumes that was not intending values of n<0, already... What if you've negated their negative! :P I agree it was messy, though. Just think it's rude to alter someone else's comment, hence why I didn't make it "1-(1/10ⁿ)", which was my own first (and equivalent) thought. Shortly before "but I bet it is a homework question...") 09:48, 29 July 2022 (UTC)