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For those who feel weird about the whole "forbidden transitions being only possible with quantum tunneling" thing and want an alternative interpretation:

It's only true that the transitions are forbidden under a given simplified model of the atom. It is very much possible to calculate the transition probabilities under a more realistic model, and the previously "forbidden" transitions are now just regular transitions that occur with lower probability.

In this case, the simplified model is that of the electric dipole approximation, where the atom is taken to be an electric dipole (reasonable when the wavelength of light emitted during an atomic transition is much larger than the size of the atom).This means it interacts with electromagnetic radiation only through electric dipole interactions, which implies that energy transitions must change orbital angular momentum, hence the 21cm transition is "forbidden". However, in reality, the atom is not truly an electric dipole, and so the 21cm transition is possible by the magnetic dipole interaction, just with low probability. (This low probability is due to the relative strength of the magnetic interaction compared to the electric interaction).

I've never liked the definition of forbidden transitions as "transitions not predicted under the broader approximation", because its rare that anybody actually lays out why a given approximation is used, and therefore why that approximation is inappropriate for the "forbidden" situation.

The reality is that with e.g. 21 cm Hydrogen, or 500.7 nm Oxygen (which I knew by heart, back in the day), its hard to keep a given atom in the appropriate state long enough for it to relax by emitting the appropriate photon. Indeed, we can't create a pure enough vacuum in a large enough chamber that such things happen frequently enough to be measurable.

laser, maser, like, other excitation / energy saturation does not work here ?

No, because you need ultra-cold or ultra-low density (or both, as with 21 cm hydrogen) gas. If your mean free path divided by your mean molecular velocity is significantly less than the relaxation time, then the the atom/molecule gets knocked out of the necessary high-energy state well before the transition occurs with sufficient frequency.

With [O III] in particular, it only gets into the necessary state via collisions (that's the easy part) occurring in extremely low density plasma, but then it relaxes via photon emission (that's the hard part). So if it gets knocked around by another collision, then the photon never gets emitted in the first place.

This 21-centimeter transition was chosen by the designers of the Pioneer plaques (https://en.wikipedia.org/wiki/Pioneer_plaque) to explain to any alien readers how big we are. At top left is a cartoon of two hydrogen nuclei in opposite spin orientations, and a ruler in between them marked "1". Over on the far right you can see another ruler that measures the height of the female figure, marked with binary numeral "8" ("|---") to indicate that she is approximately 8×21 = 168 cm tall.

If only we could somehow share a physical entity of known dimensions to reference together with the drawing so that we did not need to use a physics riddle to indicate scale...

Unsure what the tone of this message is, so I don't know if you're aware, but that's included too:

> Behind the figures of the human beings, the silhouette of the Pioneer spacecraft is shown in the same scale so that the size of the human beings can be deduced by measuring the spacecraft.

It's good to have redundancy, not just so someone interpreting the plaque can confirm their hypothesis, but also in case one of the messages fail. In this case, the spacecraft could break, but we can assume quantum transitions will always be observable.

[1] https://en.wikipedia.org/wiki/Pioneer_plaque

I sarcastically referenced the plaque itself, which is a convenient disc of a known size to anyone observing the drawing, unlike the space craft or physics riddles.

Using quantum transitions is quite ridiculous in my opinion due to requiring not only the observer to have a perfectly compatible understanding of physics (even a more advanced understanding might not be compatible - maybe they don't categorize elements by electrons, or even treat elemental particles as a quantifiable entity), combined with the sheer number of deductions required to understand what was meant with two circles and a few lines.

I doubt we would ever have decoded this had we been the recipient rather than author, and that's with a perfectly compatible understanding of physics.

If we picked up that plaque from space with an illustration of some aliens and an alien solar system and someone Tweeted it, the correct hypothesis for the numbering would develop plurality consensus within one hour.

I don't know if aliens would decode it but it's not right that humans wouldn't decode it.

I highly doubt it, but it might deliver some memorable zingers about nude aliens.

Not to mention that several dozen new cults formed around the plaque.

And probably complaints about "wokeness" from the Galactic Twitter owner because it used a woman as the size reference...

:sigh:

I hope I never live to see Galactic Twitter.

I submit that if the concept of quantum transitions is alien to whatever recipient of that probe (if ever), then any attempts to communicate are hopeless anyway. That is, if the recipient's physical reality is so different from our own that they can't at least get back to "oh, this distance means that transition, now the rest of the plaque makes sense", then no asynchronous communication will bridge that gap.

There is no relation between the ability to communicate and a shared understanding of our concept of quantum transitions - case in point, our invention of the technology we use to communicate with deep space far predates us learning these concepts ourselves.

I'd also hold that the only thing this plaque could ever give is clear sign of artificial creation, and by virtue the (possibly past) existence of some entity capable of creating it. Maybe they'll get a vague idea of what we look like, but if "their" culture does not commonly depict themselves in 2D as we do, or "they" have vastly different morphologies, even that would be unclear. The context needed to understand our attempt at showing our location might also be lost if the thing went far enough.

> our invention of the technology we use to communicate with deep space far predates us learning these concepts ourselves.

Maxwell published in 1873. The double slit experiment was 1803, subatomic theory developed throughout the 1800s, and Planck proposed quanta in 1900. The first radio transmission across the Atlantic came approximately 2 years after Planck's theory.

I doubt it is plausible to develop anything resembling industrial technology without stumbling across certain fundamental truths in the process because doing so requires a sufficiently accurate model of physics.

The period you're describing is that of old quantum theory, which was hugely inconsistent and predates our theories of modern quantum mechanics which is post 1925 or so.

The inventor of the arc converter was 18 at the time radio waves were discovered, 34 at the time he invented the arc converter, but 56 and with only 17 years left till his death when the era of modern quantum mechanics started with the invention of wave mechanics. It's a lifetime apart.

Some discoveries were made during that period that are of course still relevant.

(Not to mention that the hydrogen line was only discovered in 1951, as a result of years of hearing it using radio equipment invented half a century prior. Even things as basic as the proton took until 1932 to discover.)

So a period of 25 years to go all the way from "weird fringe theory that fixes some issues we've been grappling with for a long time now" to "got it all figured out". The start of that period aligns very closely with the initial invention of radio. And a variable effect due to the hydrogen line can potentially be observed by anyone operating a radio in the relevant band.

The only way this doesn't work is if the aliens who retrieve the plaque from deep space somehow stabilize in the long term at a point where they've developed rocketry and general space travel but not radio or an understanding of quantum mechanics.

However the above would seem to imply that they don't do radio astronomy, don't have a very good understanding of light (since it's all photons), and don't have high frequency electronic circuits (since designing those requires accounting for RF interference). I guess their understanding of optics is also lacking and their understanding of chemistry is rudimentary and stagnant over the long term.

In other words, aliens permanently stuck at a late 1800s technology level that have nonetheless developed the ability to travel across interstellar distances. And spotted voyager (a very small cold object in deep space). And retrieved it intact.

That's undoubtedly a very cool premise for a scifi story but as far as real life goes I think your time would be better spent worrying that voyager might be eaten by a species of space fairing wale.

Do you think that physics is somehow subjective? We absolutely would have decoded the message.

Physics is a model of reality. Reality is objective, but the model we have chosen is very much "subjective" (maybe arbitrary is a better term).

It's easy to imagine that another species might have never conceptualized electrons as little balls orbiting around a nucleus. They are neither balls nor are they flying in circles, those are simply abstractions we like because they appeal to the way we perceive reality. The way we conceptualize electrons leads to issues like the wave-particle duality, so it's likely just a local optimum we got stuck in. Another species might not even think of Electrons as being distinct entities, maybe they think of the electron field as one large ocean with some waves in it, or they subscribe to the single electron theory, or something we have never thought of and might never imagine from our perspective.

"Arbitrary" ("existing or coming about seemingly at random or by chance or as a capricious and unreasonable act of will", "based on or determined by individual preference or convenience rather than by necessity or the intrinsic nature of something" [1]) is a very poor term. Not only is physics highly constrained by what can be observed in the universe, it is also capable of demonstrating (when it is actually the case) equivalences between apparently dissimilar modes of presentation. It is not perfect, but can you present anything that does better?

[1] https://www.merriam-webster.com/dictionary/arbitrary

> is physics highly constrained by what can be observed in the universe

It is also very highly constrained by how _we_ observe the universe. Beings with different sensory/cognitive capacities could develop very different models.

> equivalences between apparently dissimilar modes of presentation

If there was some mathematical equivalence between their models and ours, which is already a leap to assume, there is still a question about whether the specific measure used would be translated to something equivalent to our object length measure in their model, which gets much stronger than just some equivalence assumption. And it’s even stronger to assume that this equivalence could just be inferred without any other information apart from the disk.

It seems disproportionate to fuss about "a leap to assume..." when we are talking about a small plaque affixed to a probe on the highly speculative basis that something intelligent might one day retrieve it, as opposed to something that is mission-critical. Would we be better off for not making these "leaps"?

I was answering to a specific comment chain.

It would be a leap to assume another culture has something similar to (or, in some cases, anything resembling) one's ethics, sense of humor or taste in music. In comparison to these things, science has something they do not: apparently universal and impersonal 'laws', which, where we can check, appear to hold across the visible universe (putting aside some unresolved issues on the leading edge of our present knowledge.)

For some extra-solar civilization to examine the probe and its plaque intact, it will have to rendezvous with it in space. It seems to me to be the greater leap of faith to suppose this can be done without having knowledge that is isomorphic or equivalent to our formulation of orbital mechanics. Do you have any concrete ideas about how this might be so?

As a theoretical physicist, yes physics could definitely be subjective between different species. Physics is the way HUMANS describe nature to themselves. I don't doubt that it describes some greater nature outside of us that is invariant, but it is only a description - not the thing itself. Like mathematics it is an anthropocentric conceptualization that has many arbitrary and historically contingent choices in its choice of representation and its chosen objects of study.

How could we ever be certain than another intelligence (whatever that means) would be capable of understanding the intended message? Unless of course we are already starting off with the major assumption that the only things that can be intelligent are things like us. I'm not even sure that intelligent has any meaning aside from denoting behavior "similar to us".

If they could discover the probe at all and view the plaque, lots of things are already very similar.

Yeah perhaps, but its really hard to say anything concrete either way

Our understanding evolves, course corrects, spins off etc., we can use some static value as purported from the dark ages or by newtonian or later einstenian points of view. They all are measurably correct for the problems that they are trying to solve for the people who lived during those times. A million years from now would these values still be relevant or be considered as having the same value of importance or will they be replaced by even more finer and precise and contextually different values that could be more precise and more accurate etc.,

Indeed. Say, maybe a civilization didn't start out with trying to build the world of particles of progressively finer size, but started directly with a model of fields, waves and charges and therefore never had a concept of a discrete elemental particle, and in turn a system built around that to categorize elements.

Or to them, an atom is as large an arbitrary macro structure as proteins are to us, and so they would never consider two empty circles with a single line to represent something so big and chaotic. Or maybe they had the crazy idea of building everything of vibrating strings!

Who knows what the abstractions and approximations would be when the foundation of it all isn't "getting hit on the head by an apple".

The 21 cm line was chosen specifically because it’s the brightest line in the radio regime in our galaxy. Any civilization in the Milky Way capable of developing electromagnetic sensors would see that emission. There is a game theoretic component to this, as these other civilizations would also know that we could also see that line, and thus understand its importance

The prevalence of the 21 cm wavelength is something they would likely discover should they be in a part of the universe similar to ours. What I find laughable is the means of trying to communicate this wavelength and using it as a means to indicate our size.

Now if you go the other way, referenced 21 cm as a well known quantity (say, by making the plaque 21cm wide and referencing its diameter) and used that to describe the hydrogen spin flip in order to teach or communicate our level of physics understanding rather than depend on a shared understanding, then I'd say it makes more sense.

What if you end up with a picture of the record & everything else gets lost - that riddle will still work. Say the civilisation that found it collapses & leaves behind some garbled data, including a picture of the record.

Or even future human data archeologists digging through a mix of 20 & 21 century data heavily polluted by AI slop. ;-)

I really wonder how future archaelogists are ever going to decode our timeline. Imagine a meteor strikes, civilization falls apart, and in 20,000 years they dig up a data centre. Even if they get the computers to work and the hard drives are still readable, everything will be encrypted.

Making the data fault tolerant to the discovery by another civilization, its collapse and later rediscovery by another civilization seems a bit of a stretch goal. :)

Compared to a cold object being detected and then picked up from somewhere out in deep space?

That's the "discovery by another civilization" part, so yes.

It was always a very long shot, regardless of who might be the recipients. Would we have been better off if it had not been done?

What if extraterrestrial "intelligence" didn't have a reason to "evolve" functional equivalents of a visual cortex. Even on earth where having vision gives a distinct evolutionary advantage over non-vision based living forms, species without vision far outnumber those with vision.

We did that too. There is a cartoon of Pioneer itself, drawn to the same scale.

(I was sarcastically pointing to the plaque itself, a physical entity of a well known size to anyone capable of observing the drawing on it, unlike the space craft or physics riddles.)

Yeah. It would be pretty funny if an alien reader of the plaque concluded that 1 refers to the actual length of the line between the two circle thingies and concluded, therefore, that we're only a few cm tall.

The plaque also provided a drawing of the probe itself next to the two human figured, at scale.

Banana!

They could have also used a 21cm length more directly for the male figure, but they did not.

Amazing article! It seems incredibly to weird to hear about transitions causing photons at 21cm wavelength; I guess I'm only used to seeing (no pun intended) much shorter wavelengths at hundreds of nanometers.

Yeah, it's weird to me that an atomic transition can create something with a wavelength so much longer than the atomic radius.

(Yeah, I know that it's a really low-energy transition, and I know about the relationship between energy and wavelength. But the net result I still find highly counter-intuitive.)

> Yeah, it's weird to me that an atomic transition can create something with a wavelength so much longer than the atomic radius.

Then it will be even weirder during an MRI: The protons in your body produce a wavelength that can be of order 1-10 meters.

What helps me is thinking of it in term of period instead given that the wavelength is the spatial propagation of a change in field. It’s big, but that’s because C is high.

Segmentation fault! Core dumped

It does feel a little odd that something the size of 5.29×10⁻¹¹ meter can create something 10 billion times larger.

I mean, I understand how and why, but it feels odd.

My subwoofer is approximate cubic with 30 cm to a side.

But the wavelength of sound it makes at 20Hz is approximately 17 meter.

Wavelength is merely a human conceptualization. If we reconceptialize it as peak-to-peak interval it suddenly stops being length and becomes a time instead

The sound pressure wave does take 17 meters in the air to make a full cycle, no ? It’s real, same for the photon

It's not about measuring peak to peak in distance, it's about measuring how long it takes for one spot to encounter second peak after first. The fact that the first peak traveled some distance is irrelevant, as its entirely dependent on propagation speed, which doesn't affect the frequency, only vawelenght.

Would you then say that the wavelength is meaningful for the sound example as its properties are really of a wave propagating, and meaningless for the light as the wave analogy isn’t a full description of the light phenomenon behavior ?

I have pretty strong intuition for how "sound looks". I know how to imagine a wavelength of sound, how the medium works over time etc. I don't have the same intuition about light, as the sound analogy of a wavelength (distance between 2 peaks) clash with the part of photon that behaves like a particle.

From that standpoint I can confidently say that wavelength is meaningful for the sound example, but not so much for light. Someone more knowledgeable than me would probably offer better insight.

Wavelength isn't an object though. Like if you walk around the world you haven't made something the size of the world.

Wavelength is a time thing though. To make something that low frequency (1.4GHz or 7ps), things have to happen pretty slowly.

* 714 ps

At the same time any one individual walking around the world is a highly improbable event.

From the article:

Of course, there’s another possibility that takes us far beyond astronomy when it comes to making use of this important length: creating and measuring enough spin-aligned hydrogen atoms in the lab to detect this spin-flip transition directly, in a controlled fashion. The transition takes about ~10 million years to “flip” on average, which means we’d need around a quadrillion (1015) prepared atoms, kept still and cooled to cryogenic temperatures, to measure not only the emission line, but the width of it. If there are phenomena that cause an intrinsic line-broadening, such as a primordial gravitational wave signal, such an experiment would, quite remarkably, be able to uncover its existence and magnitude.

Isn't that basically an H-maser? Not something found every day on eBay, but not really all that exotic either. Every VLBI site has one or more.

Given a suitable state selection mechanism, which is what masers rely on, I don't see why it would be necessary to flip the states "manually" through ionization or any other mechanism. Keeping the state-selected atoms away from the container walls is the real trick.

I’m reading that an H-maser emits 1.4GHz. Maybe you mean something besides it’s emission frequency?

1.4 GHz = 21 cm. Masers use the same transition AFAIK.

In fact, natural H-masers have been found: https://www.cfa.harvard.edu/news/hydrogen-masers-space

Loved this article! I initially was confused by how this transition would work with the conservation of angular momentum (since the electron would be flipping from spin ±½ to the opposite one). But then remembered that photons are spin 1 particles, so the math works out. Neat.

that's not right. if photons were truly spin 1, there would be 3 spin eigenstates available, but in fact there are only 2 (Sz=0 is unavailable). the pithy argument invokes the absence of a stationary frame of reference. for all practical purposes, photons are behave like spin 1/2 particles (despite being bosons). see, for example, the jones algebra / calculus.

The 21cm wavelength is also the wavelength that was proposed for potential SETI radio communication, I guess because of its distinctiveness. Of course modern SETI searches look at a wide range of frequencies.

if that frequency can be generated by natural phenomena then why it is so good for seti ? should not signal distinctive from natural fenomena be used instead ?

SETI uses the gap between the H line and the OH line (the "water hole"). The whole region of the spectrum is kind of quiet for reasons, and the H/OH area is (perhaps parochially) thought to be a natural place for other water-chemistry life forms to look.

In Contact the alien beacon arrives at 4.4623 GHz. Pi times the Hydrogen line...

Yup. And interestingly enough, that detail wasn't in the original novel by Carl Sagan. It was added for the movie, based on (AFAIK) a 1993 paper by David Blair and Marjan Zadnik: https://articles.adsabs.harvard.edu/pdf/1993A%26A...278..669...

Intelligent aliens would use Tau, not Pi :)

But do they know what is a second?

Don't need to. It's the hydrogen wavelength / pi.

Wouldn’t be required. Take any frequency, Hydrogen in this case, and multiply it by pi which is unitless. The resulting frequency is pi times whatever you started with no matter how you count the passage of time.

Out of the question, it has no definition which is only related to physics. Well, there's the "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" definition, but this was chosen to match the celestial-based unit related to the Earth's rotation (which does not tell anything to extraterrestrials).

"ringworld" had a nicely poetic passage about how the 21cm band had been swept clean by all the hydrogen in the universe and was therefore a natural frequency for aliens to try establishing communication over

That could be some freaky case of Doppler effect. To rule that out, the aliens could send both 21 cm * pi and 21 cm * e.

It's ruled out by the signal being modulated.

The question the choice is answering is where do you put a signal where other intelligent minds might look for it, yet which isn't at a frequency where the universe is particularly loud in ways that will make detecting your signal harder.

The signal is always going to be modulated, unless the source is maintaining a position with zero relative velocity to the Earth, or deliberately compensating for same - both of which would be far more impressive as a "hello" than a random-ish number which will always be distorted by orbital and proper motion.

Otherwise it's going to have a varying frequency - maybe not by much, and maybe not quickly, but certainly not static.

Fair, I should have said "modulated by something other than obvious physical processes".

Oh wow. That’s wild.

It’s neat to see theory that allows us to practically see further into the past.

Precisely 21cm or a precise amount that is approximately 21cm?

It's a badly worded subtitle, probably by an editor. From later in the article: "By measuring light of precisely the needed wavelength — peaking at precisely 21.106114053 centimeters".

it is not 21 in binary number system nor in mayan, so does not matter, it is just number. same importance for physics as horoscopes, numerology ...

but i was pretty annoyed after i read in article - "exactly 21 cm" and then inside of first diagram - "v=1.4GHz" ...

I find it disturbing/puzzling that there is this fundamental physical behaviour like emission of light with wavelength of _exactly_ 21cm -- assuming one centimeter wasn't based on any such property but was just a "random" unit measure that stayed with us historically and through sheer volume of use (in U.S. inches filled the same niche; still do). I mean what are the odds that the wavelength is _exactly_ (the word used in the article) 21cm?

The article does say "precisely 21cm" in the subtitle, repeats it in the "key takeaways" section, and then close to the end of the article these's this:

>By measuring light of precisely the needed wavelength — peaking at precisely 21.106114053 centimeters

Which I assume is the actual measurement every time "21cm" is brought up in this article.

The author uses "precisely" incorrectly, which is quite surprising for an article on physics.

No more probable than any other value, whole or otherwise. In particular, its (per wikipedia) 21.106cm.

Its funny how our brains find nice whole numbers unsettling in the natural world. I was always sort of weirded out by the distance light travels in a nanosecond: just shy of 1 foot. How weird it is that it flops between systems!

isn't a cm now defined based on the distance light travels in a vacuum in a very small period of time?

so it's not arbitrary really, or rather it probably goes the other way around. a cm used to be based on an arbitrary physical distance but was I think redefined to avoid needing to keep a standard meter cube in Paris.

It started with the grandfather clock. Everyone's clock pendulum needed to be the same length to have the same length of a second. So a meter also happens to (approximately, this was before we could easily be precise to several decimal places) be the length of pendulum that cycles at 0.5 hz (each swing back and fourth is a second) in 9.8 m/s^2 gravity.

It started with the French.

https://en.m.wikipedia.org/wiki/History_of_the_metric_system

The meter was originally based on the measured dimensions of the Earth.

I think there were multiple competing suggestions at the time, the grandfather clock was one while the standard ended up being the French proposed one that you mention

Ah yes, you're right. Another nice coincidence that a seconds pendulum is less than 1% away from 1/10 millionth the distance between the equator and poles.

tanach still does not acknowledges science. so does 1/10 millionth error even matter in grand scheme of things ?

The standard metre was a rod 1 metre long, you might be thinking of the standard kilo which is a compact cylinder?

Was, they made the smoothest silicon sphere, Avogadro project. And now apparently they define it via physics as mentioned in ops article, "namely a specific transition frequency of the caesium-133 atom, the speed of light, and the Planck constant"

> precisely 21 cm

Imprecise use of "precise" in the strapline. According to https://en.wikipedia.org/wiki/Hydrogen_line the best measurement of it so far is 21.106114054160 +/- 0.000000000030 cm

That not just imprecise usage of that term; it’s completely incorrect. The correct term would be its exact opposite, “approximately”.

Indiscreet discrete mathematician checking in. If they said "exactly" we'd have a real problem. Instead, "precisely" in this context means "human eye cannot distinguish from exact value at a stone's throw."

Yes, physicists and engineers hate me, why do you ask?

"It's precisely 21 cm."

"Is it 21 cm?"

"No."

I expect the non-technical author/editor was playing the telephone game and originally wanted to emphasize that the frequency is always the same value, not that the hydrogen emissions frequency is related by arbitrary factors of 9192631770.000 Hz, 1/299792458.000 seconds, and then exactly 21.000/100.000 to the caesium-133 frequency.

so the claim is inaccurate by 1mm and missing precision data. I'd call it inaccurate and imprecise XD

The exact opposite would be ”imprecise” or ”inaccurate”

Accuracy and precision are orthogonal concepts. “Approximately 0 light years” is accurate but not precise.

Would have been odd if it had magically matched the arbitrary distances we use in the metric system. It's not that 1m is in any way a "natural" distance that was chosen for anything but practical reasons.

I was expecting some spectacular revelation that the definition of the second, the period of a Cesium atom, and the speed of light were somehow related to the definition of a meter by a factor of 0.21.

If our system was based on Planck units then it would be interesting. It would also cause tons of other fundamental constants to be greatly simplified to either integers or integer multiples of known transcendental constants.

Nope.

The so called Planck units are the worst system of units conceivable and they could never be used in practice. This has nothing to do with the values of the Planck units, but with their uncertainties.

When Planck has suggested that system of units, as a possible improvement over the system of natural units proposed by Maxwell a quarter of century before him, by removing 2 somewhat arbitrary choices required by the Maxwell system of units (of 2 kinds of atoms, one for providing a frequency unit and one for providing a mass unit), that was before the development of quantum mechanics and before of the discovery of several quantum effects that are useful in metrology.

The reason why the Planck system of units is bad is because it defines the Newtonian constant of gravitation as an exact constant.

However, the Newtonian constant of gravitation can be measured only with an extreme uncertainty, many, many orders of magnitude greater than the uncertainty for measuring any other fundamental physical quantity.

By forcing the Newtonian constant of gravitation to be exact, its uncertainty does not disappear. That uncertainty just moves into the values of all other physical quantities that include mass in their dimensional formulae.

This means that in Planck's system of units most absolute values of physical quantities have uncertainties far too great to be usable. In Planck's system of units, for most quantities only the ratio between 2 quantities can be accurate, not also their absolute values.

Nevertheless, not all is bad in Planck's system of units. Only using the Newtonian constant of gravity is bad. Using the Planck constant to provide a unit of mass instead of using the mass of some arbitrary atom is good.

By combining Maxwell's system of units with the good part of Planck's system of units, you can obtain a system of natural units where there is only one arbitrary choice, of an atomic transition that can provide a unit of frequency. All the other "fundamental constants" can be defined as 1, with the exception of 2 constants that must be measured experimentally, and which provide the intensity of the gravitational interaction, i.e. the Newtonian constant of gravitation, and the intensity of the electromagnetic interaction, i.e. the so-called constant of the fine structure, a.k.a. Sommerfeld constant.

After its last revision, the International System of Units has actually become equivalent with such a Maxwell-Planck system of natural units, except that this is masked for historical reasons by the use of a large number of "fundamental constants" that are inserted into the relationships between physical quantities, and which are exact, but instead of being equal to 1 they have various weird values.

For theoretical work, or inside some simulation programs, it can be more convenient to use a system of units where all "fundamental constants" are 1, and where the unit of time is taken to be the period of the electromagnetic wave corresponding to the cesium 133 transition on which the SI is based (i.e. about 0.109 nanoseconds), so that any value in such a system of units can be converted by an exact factor into a value in SI, e.g. for displaying the results. (Actually that is what I always do.)

Yes that bugged me too. If you replace 'precisely' with 'approximately' everywhere in the article it becomes much improved ;)

On the other hand, since it's a property of the universe maybe now's the time to define 21 cm as this value.

then cm will become a bit longer and it'll break many things

Like the width of an A4 sheet of paper.

But everyone's hand is precisely 21cm long, of course

Ok, we've made the title not be precise now.

I had a CS professor that used to hold up a length of string roughly that length and talk about how that is how far a bit of data can travel at the speed of light during a clock cycle or something. Honestly don't remember the point he was trying to make.

Probably trying to recreate this lecture by Grace Hopper [1]

[1] https://www.youtube.com/watch?v=9eyFDBPk4Yw

I still have my nanowire, received directly from Grace herself during one of her last lectures I attended in the 80’s.

Of course, it’s in among about a thousand other wires and cables and nonsense.

One of these days I should sort it out and try to identify it by length.

She had a very firm handshake, and a very definite glint in her eye as she handed those out to her star struck fans ..

I'm sure that's what it was. I probably should have remembered that, but it was such a small part of one of his lectures it didn't resonate as deeply as it should have.

That's a different thing, the signal travel length in a nanosecond, roughly. This is about the 21 cm RF wave that glows from the sky - https://en.wikipedia.org/wiki/Hydrogen_line. One of the (hyper) finest names of things in nerddrom - "hyperfine transition".

Admiral Hopper[1] used to use string to demonstrate how long pieces of time are:

https://www.youtube.com/watch?v=9eyFDBPk4Yw

[1] https://en.wikipedia.org/wiki/Grace_Hopper

She didn't use string, she used wires, and would sometimes hand them out after lectures.

Woah. Imagine extrapolating that for life. What does it mean to throw away a day?

Or to be given one more

I suppose it's interesting to think about. At today's clock rates, the distance between the CPU and RAM actually adds a small, but still significant delay.

It's ultimately what killed having a memory controller on the northbridge of a motherboard. Having the CPU talk to a separate chip to ultimately talk to the RAM simply added too much latency into the entire process.

And it may end up causing CAMM2 to end up being the next standard. The physical layout of the chips on the board means the traces can be shorter - leading to lower latency and higher stability.

I really hope CAMM2 takes off. It'd be a rare standard that could be used for both laptops and desktops. Having upgradable memory in a laptop again would be great. Using the same standard a desktop would make it easy to find sticks as time goes on.

And capacitance, etc too.

Well everyone knows if you want your network to be twice as fast, just cut all of the cables in half.

The point of how fast computers are, and why you need to make them smaller to make them faster. Think about the bus between the CPU and GPU, not much shorter than that. Information cannot travel faster than the speed of light, so there is a hard constraint on how quickly the GPU can respond to commands. The same is true for RAM and even within the CPU, signals take time to propagate across it. The total length of your circuitry for a single instruction can't be longer than 21cm if that's how far light travels.

https://youtu.be/9eyFDBPk4Yw: Admiral Grace Hopper Explains the Nanosecond

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Its clearly only half of the answer.

The complete answer of the universe would of course be 42cm.

But do you know where your towel is?

The article gives the answer to the question in the title in the first paragraph. This is really commendable. (Suspense is—wait for it!—overrated.)

We've replaced the magic title with the more informative subtitle now. Standard mod trick.

42/2

When I replied, the article had been posted 42 minutes ago and had 42 upvotes.

That can’t be a coincidence.

The people running our simulation are just fucking with us at this point.

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Though 13 is totally the average!

Ah, so the answer to life, the universe, and everything was actually 42/2 …

Is this going to be τ vs π all over again?

I recently did a bit of programming exploration using tau exclusively instead of pi (and `sintau` instead of the new `sinpi` function etc.)

In almost every aspect this was far simpler, but there was the curious case of the constant `M_2_SQRTPI = 2 / sqrt(π)`. Even after looking up what weird formula that constant is used in, it wasn't at all clear to me where would be the most sensible place to put the constant.

Chickens take 21 days to hatch and give us the most protein rich food you can eat. Does this mean that chickens are the magic creature of the universe?

Pretty sure newly hatched chicks are not the most protein rich food you can eat. But the crunch must be amazing.

Is this why cows and horses eat them?

Damn that's 42 / 2!

... so the question is "What is twice the magic quantum light length?"

Doesn't seem all that great, but I'm probably missing something.

How many inches is that

It is 21.1061… cm worth of them.

Fun fact, your computer is really good at answering this question for you. So is (say) Google Search.

Or an LLM, or even just using MacOS spotlight search autocompletes "21cm how many inches " to the right answer.

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Apt

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Please don't do this here.

Reddit gave me bad habits. My apologies

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I posted this thread to o3 and found the results interesting. https://chatgpt.com/share/680aad8d-ce54-800c-8973-df4258bbe1...