
A number that fascinates physicists - Hooke
https://cosmosmagazine.com/mathematics/number-fascinates-physicists-above-all-others
======
glastra
This so-called _fascination_ and search for meaning or reason behind constants
reminds of the anthropic principle [0], which basically goes like this:
"things are the way they are because we wouldn't be here to observe them
otherwise".

The last part of the article, however, is still quite intriguing. Nobody would
expect any of the 3 components of alpha to change, unless somehow the
measurements can be affected by the medium (as the speed of light depends on
that).

[0]:
[https://en.wikipedia.org/wiki/Anthropic_principle](https://en.wikipedia.org/wiki/Anthropic_principle)

~~~
ncallaway
(I could be wrong about this, I haven't thought about it in great detail)

I think invoking the Anthropic principle only makes sense if we can
demonstrate that there are a number of other "places" with varying
"conditions". For such a selection bias to occur there needs to be a
population to actually select from. For example, the Anthropic principle makes
sense regarding the composition of the earth because we know that there are a
large number of planets with a distribution of orbits and masses around a
distribution of stars. Of course we will be on a planet that supports life as
we know it.

To invoke the anthropic principle regarding a constant would imply — to me, at
least — that there would need to be a number of universes with different
constants. Or different regions of this universe where the constant would
vary.

If there truly is only a single universe, and the constant is _not_ changing
in time or space, then it would seem we did actually just happen to get lucky.

Edit: of course, at this point we can't say definitely either way about our
universe. We don't know if ours is one among many, or if its the solitary
universe in existence. We also, clearly, have uncertainty about how constant
this constant actually is.

~~~
baddox
I don't see why there needs to be other universes that actually exist in order
for the anthropic principle to apply. It seems to make perfect sense to apply
it to a set of _conceivable_ universes, even if such universes don't actually
exist and even if it's not physically possible for them to exist.

~~~
ncallaway
Again, I could easily be wrong about all this.

I think this entire discussion is sensitive to exactly what one means by "The
Anthropic Principle". If one's definition of the Anthropic Principle in this
context simply means that an observed universe will be consistent with a
universe that _can_ be observed, then I find it to be trivially true and
applicable to a single universe scenario.

I subscribe to a definition of the anthropic principle that invokes selection
bias as its core mechanism. I think that, in order to have a selection bias,
one needs to actually be _selecting_ from a population. Hence my assertion
that you _need_ a multi-verse (with different constants in each universe) or a
constant that is variable in space or time [2].

The difference, to me, is this:

If you are _selecting from a population_ the Anthropic Principle can actually
help explain _why_ a value is what it is. Under our understanding of planetary
bodies, we often invoke the Anthropic Principle to explain _why_ the earth
falls in the habitable-zone. Earth falls in the habitable-zone _because_ — we
think — life is most likely to arise on a planet in that zone.

However, if you are _not_ selecting from a population, I don't find that the
Anthropic Principle explains _why_ a value is what it is. In the scenario
where there is only _a single_ value, I think the Anthropic Principle simply
demonstrates that _that particular_ value must support life.

Put another way, if _all_ planets we observed were the exact same distance
from their star as Earth [1], then we couldn't _use_ the Anthropic Principle
to explain why Earth is that particular distance from the sun. We would have
to find other astronomical reasons to explain why planets form at that
specific distance from a star. In this single-distance scenario the only thing
the Anthropic Principle actually does for us is confirm that _such a distance
supports life_.

[1] Well, not distance per se, but placed such that they received the same
amount of stellar energy in their orbits.

[2] This final sentence of the introduction of the Anthropic Principle also
makes some reference to this saying: "Most often such arguments draw upon some
notion of the multiverse for there to be a statistical population of universes
to select from and from which selection bias (our observance of only this
universe, compatible with life) could occur."

~~~
baddox
> If one's definition of the Anthropic Principle in this context simply means
> that an observed universe will be consistent with a universe that can be
> observed, then I find it to be trivially true and applicable to a single
> universe scenario.

It is "trivially" true in a sense. It's a tautology. But it's still useful for
thinking about things. I think it applies just as well to a single universe or
a multiverse, because even with a single universe you can at least hypothesize
about other ways the single universe could behave.

> However, if you are not selecting from a population, I don't find that the
> Anthropic Principle explains why a value is what it is. In the scenario
> where there is only a single value, I think the Anthropic Principle simply
> demonstrates that that particular value must support life.

It might not answer the extremely broad and ill-defined question "why" to your
satisfaction, but I find it fairly satisfying. If things were another way,
then I wouldn't be observing the universe because I wouldn't exist. So it's
not strange that the universe _is_ this way, given that I exist.

------
kazinator
"When scientists measure any quantity they must specify the units being used."

No they don't. For instance, a simple aspect ratio measures how something is
wide relative to how it is long. It has no units.

This here desk I have here is about 1.7 times as long as it is wide. No inches
or centimeters required.

There isn't anything amazing or mystical about a unitless quantity.

~~~
amelius
To make things more complicated: the size of your desk isn't fixed because the
universe is expanding. So the units you are using are just a convention to
relate the size of an object to the size of other objects.

~~~
maaku
So long as the fine structure constant remains the same, your desk (and ruler)
won't change size. Rather they will heat slightly as the expanding universe
stretches the chemical bonds and those same bonds spring back to average rest
length.

/nitpick

------
mtviewdave
The most fascinating part about alpha to me is the implication that it isn't
actually constant, and varies over time and/or distance. I once read a
suggestion that perhaps the observed universe is simply the portion of the
greater universe where alpha has a value that lets things like stars, planets,
and life exist.

~~~
qubex
Being actually a derived quantity, alpha's non-constancy actually implies that
one or more of the underlying ‘constants’ vary non-homogeneously — which is
what you said, but slightly different in import... observing alpha is actually
just a convenient way of observing the others indexed together.

~~~
jsweojtj
You've got this backward. Alpha is the fundamental physical constant: c, e and
\hbar are the derived quantities. I'll quote part of another comment that I
left on this thread:

> Now for a piece that's more interesting. The fine-structure constant (alpha)
> is the coupling constant that sets the strength of electromagnetism. This
> means that its value is the thing that matters in the equation: e^2/\hbar c.
> Each of the other values is a derived quantity. Further, to speak a bit
> loosely, only changes in alpha matter -- in the sense that if the speed of
> light (c) changes, but the other constants (e and \hbar) change in a way
> that keeps alpha the same, then you wouldn't be able to tell with an
> experiment that anything has changed.

> Contrast this situation w/ a change in alpha -- a table-top experiment would
> be able to detect the change (given that it's large enough, and we have
> methods of measuring changes on year-time scales that are a few parts in
> ~10^-18 (Rosenband, 2008)), as it would mean that physics has changed in a
> fundamental way.

>
> [http://phys.columbia.edu/~millis/1900/readings/Science-2008-...](http://phys.columbia.edu/~millis/1900/readings/Science-2008-Rosenband-1808-12.pdf)

~~~
jsweojtj
A further layman explanation by a researcher in this field:
[http://astronomy.swin.edu.au/~mmurphy/research/are-
natures-l...](http://astronomy.swin.edu.au/~mmurphy/research/are-natures-laws-
really-universal/) specifically the section titled "Aside: Is it e or c
varying?"

------
leanthonyrn
I thought that -1/12 was amazing, even to Vulcan scientists.
-[https://youtu.be/w-I6XTVZXww](https://youtu.be/w-I6XTVZXww)
-[https://youtu.be/0Oazb7IWzbA](https://youtu.be/0Oazb7IWzbA)

~~~
mrob
-1/12 is the result of applying zeta function regularization or Ramanujan summation to the sum of the positive integers. It's arguably interesting, but hardly amazing to the vast majority of people who have never heard of those techniques. But the thing that really annoys me is all the people presenting it as the finite limit of a divergent series (this is the default meaning of "=" after an infinite series, if you're using a non-standard meaning you have to specify that!). The first of those videos does this! It's nonsense, and this kind of sloppy approach only encourages contempt for mathematics.

------
chias
> The best known example of a pure number [...] hc/2πe2 [...] leave[s] a pure
> number, 137.03599913.

This surprises me. I would have thought pi, the ratio of any circle's
circumference to its diameter, is a much better known example of a pure
number.

~~~
duaneb
Pi is not a fundamental physical constant and has myriad uses. α is only
special when observing that it is a physical constant; you need to observe the
physical universe to arrive at the conclusion that it's a meaningful number.

~~~
chias
Thank you for this explanation. The distinction was not clear to me after
reading the article, but your comment makes a lot of sense.

------
noobermin
On non-internet[0] connected computers in my old uni's physics lab, the
passwords were often some combination of the phrase "physics" and repetitions
of the number "137". Quite the fascination.

[0] why I don't feel uncomfortable disclosing this here

------
rubidium
The article is so-so. But the physics here is really cool. Essentially,
there's growing evidence that the fundamental constants may not be perfectly
constant. See
[http://arxiv.org/abs/1510.02536](http://arxiv.org/abs/1510.02536) for the
gory details.

~~~
raattgift
Would you really characterize this Wilczynska, Webb, King et al. paper as an
argument that there is "growing evidence", rather than (say) that it's a
number-crunching argument that the small amount of observations that suggested
a dipole variation to Webb et al. (and King et al.) show a \Delta\alpha /
\alpha that's close enough to unity that one can cherry pick and say "oh yes,
there's a (small) dipole variation" or "oh no, the data is consistent with no
variation" ?

I prefer their earlier slide deck for gory details (it's mostly based on King
et al 2012).

[https://www.eso.org/sci/meetings/2012/ESOat50/Presentations/...](https://www.eso.org/sci/meetings/2012/ESOat50/Presentations/Day5/Murphy.pdf)

See especially the "Really?" slide (p 27).

(The previous "What if it's correct?" slide undersells the impact to the
standard cosmology of a violation of isotropy and the consequent erosion of
the "must be homogenous at scales > 250 Mly" part of the cosmological
principle. Also, "what if atomic physics is really obviously different only
very slightly outside the horizon?" feels like a declaration of war against
the Copernican principle with precious little evidence, and against pretty
good theory that has other lines of evidence backing it (cf. Carroll @
[http://www.preposterousuniverse.com/blog/2010/10/18/the-
fine...](http://www.preposterousuniverse.com/blog/2010/10/18/the-fine-
structure-constant-is-probably-constant/) who points to Banks, Dine & Douglas
@ [http://arxiv.org/abs/hep-ph/0112059](http://arxiv.org/abs/hep-ph/0112059)
who in turn point to other work that shows that you probably can't vary \alpha
without varying other constants like the m_e and QCD coupling).

~~~
rubidium
Missed this comment until today. Helpful slide-deck and references, thanks!

I mean "growing evidence" in the sense that it wasn't even questioned before,
and some very early-stage experiments have asked the question.

I agree with you that it's still _way_ to early to be making any conclusions,
and it all may wash away as the experiments improve.

------
pervycreeper
The article fails to explain where the 2*pi comes from, and why 1/alpha is
more natural. Does this quantity arise in some context other than unit-
analysis speculation?

~~~
jeffwass
The 2pi comes from the usual method of using hbar, instead of h. Where hbar =
h/2pi, and is the Planck constant adjusted to use radians instead of cycles.

This is much more natural when working with frequencies instead of using
cycles.

Yes, this constant arises prolifically when looking at the atomic "fine
structure", which modifies the usual hydrogen energies to includes
interactions between an electron's spin and its orbit (the un-modified ones
only include the kinetic energy of the reduced electron-proton and the
electric potential energy). There are further interactions that can be added,
eg the hyperfine interaction which includes the spin-spin interaction between
the proton in the nucleus and the orbiting electron.

And if you use Planck units where hbar=c=G=1, you can do many things easily,
for example denote the potential of an electron at distance r as just alpha/r
(without all those other pesky constants embedded in Gauss's law).

------
poelzi
From the BSM-SG perspective it's very clear what it is:

[http://www.amazon.com/Basic-Structures-Matter-
Supergravitati...](http://www.amazon.com/Basic-Structures-Matter-
Supergravitation-Unified/dp/1412083877)

2.9.6.B Fine structure constant as embedded feature of the twisted prisms

12.A.5.3. Hypothesis of embedded fine structure constant in the lower level
structures of matter organization

It gets derived later to: α_c = 2 ⁄ [ ( n^2 + 2/2 )^1⁄2 + n ] = 7.29735194 ×
10–3

where n =137 results in a very accurate value of α. It is important to
understand that the fine matter constant has it's origin in a geometrical
organization of the prisms. A very low level building block of matter in the
BSM-SG model. It is 1/6th the size of a neutrino (neutral or positive flavor)
- those 2 neutrinos are composed of 6 prisms of either large or small prisms
an rectangular geometry j but the prisms is itself a very large structure
compared with the ultimate building blocks, the fundamental particles.

The prism itself is quite complex in it's internal structure but there is a
very logical explanation for its existence. On the first level of organization
or you could see it as the first crystallized structure is the Primary
Tetrahedron. You basically take a bunch of Fundamental Particles - just very,
very small balls, and create a tetrahedron with same length sides out of it.

Very simplified explanation: This tetrahedron has a very complex vibrational
mode - like every layer of our physical world. You end up basically with 2
overlaying vibrational modes, where you need n cycles of the small cycle to
result in one cycle of the larger one. Alpha is the Energy relation of those
cycles. Through alpha, you end up with 2 Energies in the prims, CP and TP.

Alpha is very fascinating feature as it is basically the driving force of most
of the complex behavior of nature, it is everywhere in the BSM-SG model.

Funny side-node: In the BSM model, the cosmological redshift is not of Doppler
kind (also no space expansion) and you can find the fine matter constant in
the periodicity of the red-shift.

[https://en.wikipedia.org/wiki/Redshift_quantization](https://en.wikipedia.org/wiki/Redshift_quantization)

Please note, that you have to do a proper Doppler correction in the BSM model
if you measure galaxies. It also explains the Lyman-Alpha-Forest phenomena
very well.

From the standard model perspective: I have no clue what it could be, like
most constants.

------
worik
The formula for alpha contains pi. Another pure number being the ratio of two
lengths

------
worik
Omega is much more interesting. For informaticians...

------
mrfusion
Why do you need 2pi for the units to cancel out?

~~~
gradi3nt
You don't, it's just that h-bar = h/2pi is the variety of planck's constant
that is more useful in quantum mechanics.

------
sidcool
Isn't π a similar pure number?

~~~
gohrt
Pi is mathematically pure, independent of physics. Mathematics is full of pure
numbers (obviously).

The fine structure constant is physically pure.

------
zuo
dead link

------
tcfunk
I really, REALLY hate this new trend of having websites swipe left and right
for different articles. Argh!

I highlight text on the internet as I read it, but this page moves all over
the place when I do! And on NYT it jumps around to different articles as I'm
reading. Makes it impossible for me to consume the text on these pages.

/rant

~~~
andreapaiola
Here, voilá

[http://andreapaiola.name/magpie/?url=https%3A%2F%2Fcosmosmag...](http://andreapaiola.name/magpie/?url=https%3A%2F%2Fcosmosmagazine.com%2Fmathematics%2Fnumber-
fascinates-physicists-above-all-others&action=&links=on)

