
If you overlay all atomic spectra, you get a Planck distribution - hakmem
https://onlinelibrary.wiley.com/doi/10.1002/andp.202000033
======
knzhou
I've seen this blow up in several places now, but there seriously is nothing
to this paper.

Essentially all they're pointing out is that the set of atomic transition
energies (1) is positive, (2) has a smooth distribution, (3) goes to zero at
zero and infinity, (4) has a maximum somewhere in between, (5) is skewed
right. All of these things are completely mundane and well-understood, and not
at all unique to the "Planck distribution". Statisticians probably know of
tens of other distributions with these properties, which would fit their curve
about as well.

Their claim is like saying that _any_ function that goes from -1 to 1 smoothly
must be a logistic function, or _any_ function that goes to 0 at infinity but
slowly must be a power law. That's not a paper, that's a hunch. If the
researchers wanted to be serious, they could have run a statistical test to
quantify how well the data fit the Planck distribution (just like tests of
normality are routinely done in statistics). But they didn't, and the reason
probably is because the test would fail.

~~~
MooMooMilkParty
Posting this verbatim from my reddit comment, but I ran a few quick fits and
the (arbitrarily scaled) Planck distribution looks better than standard fits
of some other distributions. Of course I ran absolutely no statistics on these
or tried any sort of real analysis that should have been included in the paper
in the first place, so take it with multiple grains of salt:

I fit a few distributions to the data and actually the Planck distribution at
9000K seems to be noticeably better. I did no further statistics and haven't
even looked at the fitted parameters for this. Note: I am an earth scientist,
not a physicist. [https://imgur.com/Qg4ixF2](https://imgur.com/Qg4ixF2)

Edit: More distributions:
[https://imgur.com/IrF6lsV](https://imgur.com/IrF6lsV)

Edit: Filtering out sodium and potassium to try to account for some of the
low-wavelength counts doesn't seem to help fitting the distributions either:
[https://imgur.com/dHDUS9Z](https://imgur.com/dHDUS9Z)

You can get the data here:
[https://physics.nist.gov/PhysRefData/ASD/lines_form.html](https://physics.nist.gov/PhysRefData/ASD/lines_form.html)

And here's the (garbage) code to reproduce my plots:

    
    
        %pylab inline
        import pandas as pd
        import scipy
        import scipy.stats
        
        mpl.style.use('seaborn-muted')
        mpl.rcParams['figure.figsize'] = (18, 12)
        mpl.rcParams['font.size'] = 16
        df = pd.read_csv('nist.csv')
        
        def filter_string(x):
            x = str(x).replace('=', '').replace('"', '').replace('*', '').replace('+', '').replace('(', '').replace(')', '')
            if len(x) == 0:
                x = 'NaN'
            return x
        
        asl_comp = df['ritz_wl_vac(nm)'].apply(filter_string).astype(float)
        asl_ver  = df['obs_wl_vac(nm)'].apply(filter_string).astype(float)
        sp_num = df['sp_num'].astype(float)
        
        df_neutral = df[sp_num == 1]
        asl_comp = df_neutral['ritz_wl_vac(nm)'].apply(filter_string).astype(float)
        asl_ver  = df_neutral['obs_wl_vac(nm)'].apply(filter_string).astype(float)
        sp_num = df_neutral['sp_num'].astype(float)
        
        asl_ver = asl_ver[~asl_ver.isna()]
        
        def planck(wav, T=9000.0):
            h = 6.626e-34
            c = 3.0e+8
            k = 1.38e-23
            a = 2.0*h*c**2
            b = h*c/(wav*k*T)
            intensity = (a / ( (wav**5)) * (1 / (np.exp(b) - 1.0) ))
            return intensity
        
        
        dist_names = ['beta', 'lognorm', 'pearson3', 'gumbel_r']
        x = np.arange(0, 1500, 5)
        intensity = planck(x / 1e9)
        size = len(asl_ver)
        
        yvals, xvals = np.histogram(asl_ver, bins=300, normed=True)
        
        for dist_name in dist_names:
            dist = getattr(scipy.stats, dist_name)
            param = dist.fit(asl_ver)
            pdf_fitted = dist.pdf(x, *param[:-2], loc=param[-2], scale=param[-1])
            plt.plot(x, pdf_fitted, label=dist_name, linewidth=4,)
        
        plt.hist(asl_ver, bins=300, density=True, color='grey');
        plt.plot(x, intensity / 1.1e17, linewidth=4, color='red', linestyle='--', label='scaled planck (9000k)')
        plt.legend()
        plt.xlabel(r'$\lambda (nm)$')
        plt.ylabel('Density')

~~~
mcnamaratw
Can you link the discussion on Reddit?

~~~
banana_giraffe
[https://www.reddit.com/r/Physics/comments/gf1kbd/if_you_over...](https://www.reddit.com/r/Physics/comments/gf1kbd/if_you_overlay_all_atomic_spectra_you_get_a/)

~~~
mcnamaratw
Seemingly multiple people downvoted this. Why??

------
dzdt
The correlation between global distribution of all experimentally known atomic
spectral lines to the Planckian spectral distribution associated with black
body radiation at a temperature of 𝑇≈9000K is indeed "funny". The match seems
close enough to be worth investigation.

On the other hand the observation that "This value coincides with the critical
temperature of equilibrium between the respective densities of radiation and
matter in the early universe" seems spurious and is unsupported by anything in
the paper.

I would expect rather there is some quirky statistics that happen with the
quantum mechanics of orbitals that gives a similar shaped distribution of
frequency of occurrence of spectral lines to the Boltzman distribution.

There is probably an interesting statistical story to tell, but I don't see
the connection to the early universe as a supported thing here.

~~~
SiempreViernes
Part of explaining this "funny" coincidence is going to be how one motivates
their selection cuts, like the choice to use only one database instead of
crossmatching several for better robustness [1]. The choice to ignore higher
ionisations, the choice to ignore any systematic effects from the fact that
the heavier elements, with their shorter wavelengths, are just downright
harder to work with experimentally.

Finally, what do our current best atomic models _predict_ that this
distribution should be? These authors seem to think nobody models atomic
spectra...

[1] See here for one such effort of comparing various databases:
[https://www.aanda.org/articles/aa/full_html/2018/04/aa31933-...](https://www.aanda.org/articles/aa/full_html/2018/04/aa31933-17/aa31933-17.html)

------
amluto
Thinking out loud:

When the universe was at 9000K, the vast majority of these elements did not
exist or only existed at negligible concentration. Look up “Big Bang
nucleosynthesis”. It would be interesting to see if the result is reproduced
at all when looking at only light elements.

Of course the bin width makes little difference. Bigger bins would just smooth
the curve.

There is probably a huge bias in that this looks at transitions that are
interesting to the NIST database. As the authors allude, there are huge
numbers of transitions that almost, but don’t quite, ionize at atom.
Similarly, there are huge numbers of X-ray transitions in which inner
electrons are kicked to very high levels or removed entirely. I don’t know to
what extent the latter is well represented in the database.

For that matter, there are transitions between bound states and unbound
states. Imagine that you light up Hydrogen at 13.6 eV plus a little bit. I
think you can still eject elections — the excess energy can be carried away as
kinetic energy. (There can be issues with simultaneously conserving energy and
momentum.). The unbound states are genuinely continuous.

I didn’t look for real, but the NIST data has too many entries to represent
just the spectra of cold atoms. I have a sneaking suspicion that researchers
are measuring emissions from hot gasses or plasmas, perhaps heated near 9000K.

~~~
SiempreViernes
Certainly for the ions lines (hugely important modelling stars for instance)
you are talking about trying to measure on very hot gasses, and I've been told
the problem is that it's hard to make a gas very hot while also dense enough
you get detectable radiation out of it.

~~~
amluto
That makes sense.

Part of my point is that the authors found a temperature scale in the NIST
data. One plausible source is experimental considerations: if enough of the
experiments are conducted at similar temperatures, you might expect to see
something related to those temperatures in the data.

------
hakmem
The authors have a look at the spectral line database of the NIST and make the
surprising finding, that all atomic spectral lines together approximate very
well a black body spectrum at a temperature of 9000K.

The authors not yet have an explanation for this conundrum, but also note,
that this temperature plays a role in the formation theory of the universe.

~~~
mellosouls
Don't know why you have been down-voted - thanks for the TL;DR.

------
mellosouls
From the same paper, I'm not sure this passage helps its case. It seems off-
topic, and rather breathless in it's speculation, although I respect their
positive imagination:

 _An entirely different yet equally fascinating possibility would be that, in
an abstract sense, the scientific community itself can be interpreted as a
thermodynamic ensemble. In this line of thinking, the individual members would
be subject to a Boltzmann distribution in “curiosity” associated with a
“temperature” determining how likely each researcher is to carry out research
more or less closely tethered to a specific area of interest. In turn, a type
of entropy could be associated with the amount of information contained in
this ensemble, or exchanged between sufficiently large subsets of it. If
correct, the implications would be truly profound, and could reshape the
future direction of science in ways never before imagined. Understanding the
mechanisms with which to influence the “curiosity temperature” would allow
wise policy makers to implement suitable conditions that foster scientific
progress, and usher in a new era of discovery...[goes on at length]_

------
mcnamaratw
+1 Full text of the article is available for free.

Challenge to HN community: Let's make a serious effort to understand exactly
what the paper says before either throwing rocks or talking about how awesome
it is.

~~~
exdsq
Further challenge - if someone does understand exactly what the paper says,
would you mind adding an ELI5 for those of us who don't?

~~~
whatshisface
A spectral line is a special key frequency that can unlock and electron in an
atom and cause it to move to a higher energy level. Several thousands of these
lines are known. The authors made a bar chart that showed how many spectral
lines were known for each frequency. They found that the shape of the bar
chart looked like the shape of the spectrum of the light that would be emitted
by a glowing stove element at 9000K (admittedly this would vaporize the stove
element but just imagine the red-orange-yellow-white thing extended a bit
further). The "spectrum" of the light means a chart of how bright each color
of the rainbow would be if you made a rainbow out of the light by diffracting
it through a prism. (For example, if I made a rainbow out of an Edison
lightbulb's light, the blue and purple part of that rainbow would be much
dimmer than if I made a rainbow out of sunlight.)

There is no particular relationship known between these two things. The
authors are curious about why the charts look the same. The authors forgot to
pull the old trick where you publish your speculation separately from your
experimental results[0], so HN is complaining about their speculation.

[0] The trick works because physicists are mainly interested in remembering
right answers, so if your speculations are wrong they will remember only the
experiment, and if your speculations are right they will remember both.

~~~
ianai
Could this be used to hypothesize about the existence or characteristics of
new elements?

~~~
whatshisface
Whether or not an element is stable is determined by what goes on in the
nucleus - the electrons are like little flies that show up and hang around
something thousands of times heavier. Now, there are such things as nuclear
spectral lines, which tell us important things about what goes on in the
nucleus. One idea the authors might want to pursue would be checking whether
or not their chart similarity also happened for nuclear lines.

------
twic
Years ago, i read a paper that looked at a database of all known organic
molecules, and found that a disproportionate number of them had an even number
of carbon atoms. I can't find it now, of course.

The paper was a similar "that's funny, i wonder why" sort of piece. The
tentative explanation i remember is that a lot of those organic molecules are
natural products, and the nature of biosynthetic pathways is that they tend to
add carbons two by two. Which i don't think is even true - terpenoids are
built five carbons at a time.

------
posix_me_less
The authors describe an observation of similarity between two plots of
completely different things. That could be an interesting paper, if they
investigated this similarity with some skepticism and the similarity was shown
to be robust, independent of the particular choices they made (bin width,
choice of the subset of all spectral lines).

But they apparently did not do their job. Instead, they indulge in
speculations about even crazier connections with a past state of the universe
or with behaviour and biases of scientific community.

This kind of half-baked observation and speculation is an interesting
discussion topic for a lunchtime that can potentially lead to something
substantial, but really should not be published as scientific paper.

Also this paper is a good example of what is wrong with physics academia (and
perhaps other academic workers as well). 4 authors, 18 references to other
people work, and a statement of conflict of interest.

Sad state of physics, year 2020.

~~~
kaffeemitsahne
Do you think there should be more, or less authors? And more, or less
references? I don't get your objection.

~~~
foobarbecue
Also, is it bad that the conflict of interest was disclosed?

~~~
posix_me_less
It's a meaningless section.

~~~
foobarbecue
Are you saying that conflict of interest disclosures in general are
meaningless? Or this one is just poorly implemented? I'm having a hard time
interpreting your meaning here.

~~~
posix_me_less
I do not know in general, but in case of paper on theoretical physics, I have
trouble seeing how such a statement provides anything to the reader.

------
centimeter
Worth keeping in mind that the blackbody emission curve is generated by some
pretty simple equations, multiplying the higher density of states at higher
energies with the lower probability of states being occupied at higher
energies. Not surprising that something similar (exponential suppression of X
via the pontryagin dual of X) would show up in other contexts, so I think
“coincidence” is actually pretty likely.

------
hakmem
A couple of days ago, there also has been a disussion on reddit on this topic.

[https://www.reddit.com/r/Physics/comments/gf1kbd/if_you_over...](https://www.reddit.com/r/Physics/comments/gf1kbd/if_you_overlay_all_atomic_spectra_you_get_a/?sort=new)

------
kortex
Very cool finding that IMHO goes beyond coincidence. Some are saying the
authors compared "two completely different plots" \- this is a strange thing
to say. Both plots have an X axis of wavelength, that's obviously the same.
There's some ambiguity of the units on the Y axis, since the BB is in W/m^3
while histogram is unitless.

However it's really not a stretch to consider the BB as some relative
intensity. So it's totally reasonable to overlay these plots.

A possible way to reconcile this would be to model some gas mixture
composition and determine the aggregate spectra of that, and that would be in
W/m^3.

E: downvote(s), do you have a rebuttal, or just think I'm wrong?

------
scottlocklin
Jesus, physics has gotten REALLY BAD indeed. This is clown car tier.

If you overlay all atomic spectra, you expect the result to be something like
Gaussian Unitary Ensemble (aka eigenvalues of a random matrix), which looks
much like the Planck distribution. Nothing to do with matter in the early
universe; most atoms didn't exist in the early universe. TLDR; contemporary
physicists fail at elementary statistical distributions, and, like, common
sense.

~~~
andi999
Thanks, I remembered GUE and was wondering if it is related.

------
steerablesafe
It's hard to come up with a thought-experiment where this radiation would
manifest.

