11 ms·

A number that fascinates physicists

137 points by Hooke 11y ago

glastra 11y ago
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
- deleted 11y ago
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- notthegov 11y ago
  You are probably right, that it means nothing. And I am happy people think this because nothing is meaningless. I believe there is no grand secret to this number or of life. In other words, things are the way they are because we wouldn't be able to fall in love, dance to the music and enjoy life, if things were otherwise. Thinking too much about why, distracts from the now. Mystery is what makes life worth living. And hiding ourselves from our self is what makes discovery possible. If reality is a computer simulation, then proving that is a bit redundant in my opinion. However, I think it can be proven but once it is, what will there be to know?
  - ncallaway 11y ago
    > However, I think it can be proven but once it is, what will there be to know? If reality is a computer simulation I can think of a multitude of other questions about reality: - Can we communicate "outside" of the simulation? - Is the simulation a product of intelligence that is intentionally running the simulation? Or is it a mere by-product of a higher-order universe? - By studying the simulation in great enough detail, is there anything we can learn about the "outside" universe? - Is the "outside" simulation a turing machine? Can it compute a higher class of computational problems? - Are the simulations infinite? Is the "outside" also a simulation? Is it simulations all the way down — or all the way up? Is there a "real" reality? - If its simulations all the way down, how did the first simulation get started? - If there is a "real" reality we get to start all of science over at square one studying this new reality. This is a rough initial list, but I'm sure there's an endless number of questions to be asked and answered about reality even if we prove its a simulation.
    - notthegov 11y ago
      You (and others) misinterpeted my comment and missed the point. I purposely wrote it a bit obtuse as a firewall of sorts. Consider the broader philosophical implications of what I wrote. And proving it was a simulation would explain all those questions you proposed. I have asked some of the smartest people I know about this topic, and no one seems to know. It would be awesome if someone reading this thread knew something unique about it and emailed me. That's my only motivation.
      - ncallaway 11y ago
        I'm not really sure how you come to the conclusion that others misinterpreted your comment or missed the point. There are no other replies! I may well have missed the point, though if I have done so because you purposely wrote obtusely then I have no real interest in attempting to decode your writing. I wish you luck in your ventures, and hope someone with more time and ability than I discovers your writings and sends you the e-mail you desire.
- ncallaway 11y ago
  (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.
  - jessaustin 11y ago
    ISTM the different measured values of α described in TFA constitute evidence of "other places with varying conditions"?
    - ncallaway 11y ago
      Yes, if we were able to consistently measure different values of α over space and/or time it would be significant and help to strengthen the anthropic principle as it could be applied here. There are a couple challenges to these measurements, though. Sean Carrol presents a theoretical challenge in his blog post "The Fine Structure Constant is Probably Constant"[1]. Chad Orzel has a more observational critique of the results in "Why I’m Skeptical About the Changing Fine-Structure Constant" [2]. To be fair, these critiques are from 2010 and Webb, et al. has published several papers since these critiques were made. I haven't seen updated debate or discussion over Webb, et al's findings. Still, I would think we have some potential evidence that the constant may vary, but I don't think this evidence is near conclusive yet. [1] http://www.preposterousuniverse.com/blog/2010/10/18/the-fine-structure-constant-is-probably-constant/ http://www.preposterousuniverse.com/blog/2010/10/18/the-fine... [2] http://scienceblogs.com/principles/2010/09/14/httpksjtrackermitedu20100907e/ http://scienceblogs.com/principles/2010/09/14/httpksjtracker...
- DonaldFisk 11y ago
  The component constants of α = e^2/4πεħc have dimensions, so depend on what units you use to measure them in. Their combination comprising the electromagnetic fine structure constant is, however, dimensionless, and is satisfactorily explained. The Anthropic Principle is usually invoked to explain why two very large dimensionless numbers, i.e. the inverse gravitational "fine structure constant" (which is assumed to be constant), and the age of the universe measured in atomic units (which increases with time), are both very close to 10^40. It is suggested that, for intelligent life to evolve and measure them, the two numbers must be roughly equal, and other dimensionless numbers, such as the electromagnetic fine structure constant, must similarly have values within a narrow range. And this in turn has led some people to believe it's the deliberate action of a creator, or that there are numerous other universes whose constants have different values, and almost all are devoid of life. Fine-tuned Universe: https://en.wikipedia.org/wiki/Fine-tuned_Universe https://en.wikipedia.org/wiki/Fine-tuned_Universe However, if we apply this Anthropic Principle to planetary orbits, we could conclude that planetary orbits are roughly circular because, if they were (for example) very long rectangles (or some other random shape), we wouldn't be around to observe their shape. Of course, no one believes that. It is accepted that Celestial Mechanics, based on Newton's Law of Gravity, (which can be derived from the more accurate General Theory of Relativity), adequately explains why planetary orbits are roughly circular. An alternative explanation is that we simply haven't worked out all the physical laws. For example, the force of gravity could become weaker as the universe gets older or less dense (or, expressed in different units, gravity remains constant but elementary particles get lighter). Dirac, and later a few others including myself, modified Einstein's equations in an attempt to explain this coincidence. Dirac large numbers hypothesis: https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis Another argument against fine tuning is the Inverse gambler's fallacy: https://en.wikipedia.org/wiki/Inverse_gambler's_fallacy https://en.wikipedia.org/wiki/Inverse_gambler's_fallacy
kazinator 11y ago
"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.
- danharaj 11y ago
  > This here desk I have here is about 1.7 times as long as it is wide. No inches or centimeters required. How did you measure your desk in order to compute its length/width ratio?
  - glastra 11y ago
    I fail to see where you're trying to get. c, e and h all have units and are measurable.
    - danharaj 11y ago
      The quote is "When scientists measure any quantity they must specify the units being used." I am not convinced they determined the ratio of his table's length and width without first measuring those quantities in some unit.
      - glastra 11y ago
        A measurement doesn't have to be direct to be a measurement. In other words, the aspect ratio of a desk is still obtained by measurement and thus is a measured quantity, subject to error and so on. Of course, both the quantity and the associated error come from previous measurements.
        danharaj 11y ago
        i'm just wondering if there's an example of a direct measurement of a ratio, rather than one computed from the measurement of dimensional quantities.
leanthonyrn 11y ago
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 11y ago
  -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.
pervycreeper 11y ago
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?
- noobermin 11y ago
  h-bar[0]: [0] https://en.wikipedia.org/wiki/Planck_constant https://en.wikipedia.org/wiki/Planck_constant
- jeffwass 11y ago
  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).
- jessriedel 11y ago
  jeffwas has explained the factor of 2pi. It's just the 2pi radians in a circle to convert from angular frequencies to regular frequencies. I don't know the detailed history, but in practice the fact that it's an inverse is essentially because it's most important role is as part of an expansion like a Taylor series. The standard method for calculating lots of observable effects gives an answer with the form X = X_0 + \alphaX_1 + \alpha^2X_2/2! + ...
noobermin 11y ago
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
tcfunk 11y ago
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 11y ago
  Here, voilá http://andreapaiola.name/magpie/?url=https%3A%2F%2Fcosmosmagazine.com%2Fmathematics%2Fnumber-fascinates-physicists-above-all-others&action=&links=on http://andreapaiola.name/magpie/?url=https%3A%2F%2Fcosmosmag...
- deleted 11y ago
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mtviewdave 11y ago
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 11y ago
  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 11y ago
    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-Rosenband-1808-12.pdf http://phys.columbia.edu/~millis/1900/readings/Science-2008-...
    - jsweojtj 11y ago
      A further layman explanation by a researcher in this field: http://astronomy.swin.edu.au/~mmurphy/research/are-natures-laws-really-universal/ http://astronomy.swin.edu.au/~mmurphy/research/are-natures-l... specifically the section titled "Aside: Is it e or c varying?"
sidcool 11y ago
Isn't π a similar pure number?
- gohrt 11y ago
  Pi is mathematically pure, independent of physics. Mathematics is full of pure numbers (obviously). The fine structure constant is physically pure.
rubidium 11y ago
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 11y ago
  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/Day5/Murphy.pdf https://www.eso.org/sci/meetings/2012/ESOat50/Presentations/... 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-structure-constant-is-probably-constant/ http://www.preposterousuniverse.com/blog/2010/10/18/the-fine... 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 11y ago
    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.
chias 11y ago
> 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 11y ago
  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 11y ago
    Thank you for this explanation. The distinction was not clear to me after reading the article, but your comment makes a lot of sense.
- spodek 11y ago
  > 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. Everyone is so fancy. One, two, three, and even zero are pretty well known, even outside physics.
mrfusion 11y ago
Why do you need 2pi for the units to cancel out?
- gradi3nt 11y ago
  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.
worik 11y ago
The formula for alpha contains pi. Another pure number being the ratio of two lengths
worik 11y ago
Omega is much more interesting. For informaticians...
poelzi 11y ago
From the BSM-SG perspective it's very clear what it is: http://www.amazon.com/Basic-Structures-Matter-Supergravitation-Unified/dp/1412083877 http://www.amazon.com/Basic-Structures-Matter-Supergravitati... 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.
zuo 11y ago
dead link

137 points by Hooke 11y ago

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

deleted 11y ago
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notthegov 11y ago
You are probably right, that it means nothing. And I am happy people think this because nothing is meaningless. I believe there is no grand secret to this number or of life. In other words, things are the way they are because we wouldn't be able to fall in love, dance to the music and enjoy life, if things were otherwise. Thinking too much about why, distracts from the now. Mystery is what makes life worth living. And hiding ourselves from our self is what makes discovery possible. If reality is a computer simulation, then proving that is a bit redundant in my opinion. However, I think it can be proven but once it is, what will there be to know?
- ncallaway 11y ago
  > However, I think it can be proven but once it is, what will there be to know? If reality is a computer simulation I can think of a multitude of other questions about reality: - Can we communicate "outside" of the simulation? - Is the simulation a product of intelligence that is intentionally running the simulation? Or is it a mere by-product of a higher-order universe? - By studying the simulation in great enough detail, is there anything we can learn about the "outside" universe? - Is the "outside" simulation a turing machine? Can it compute a higher class of computational problems? - Are the simulations infinite? Is the "outside" also a simulation? Is it simulations all the way down — or all the way up? Is there a "real" reality? - If its simulations all the way down, how did the first simulation get started? - If there is a "real" reality we get to start all of science over at square one studying this new reality. This is a rough initial list, but I'm sure there's an endless number of questions to be asked and answered about reality even if we prove its a simulation.
  - notthegov 11y ago
    You (and others) misinterpeted my comment and missed the point. I purposely wrote it a bit obtuse as a firewall of sorts. Consider the broader philosophical implications of what I wrote. And proving it was a simulation would explain all those questions you proposed. I have asked some of the smartest people I know about this topic, and no one seems to know. It would be awesome if someone reading this thread knew something unique about it and emailed me. That's my only motivation.
    - ncallaway 11y ago
      I'm not really sure how you come to the conclusion that others misinterpreted your comment or missed the point. There are no other replies! I may well have missed the point, though if I have done so because you purposely wrote obtusely then I have no real interest in attempting to decode your writing. I wish you luck in your ventures, and hope someone with more time and ability than I discovers your writings and sends you the e-mail you desire.
ncallaway 11y ago
(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.
- jessaustin 11y ago
  ISTM the different measured values of α described in TFA constitute evidence of "other places with varying conditions"?
  - ncallaway 11y ago
    Yes, if we were able to consistently measure different values of α over space and/or time it would be significant and help to strengthen the anthropic principle as it could be applied here. There are a couple challenges to these measurements, though. Sean Carrol presents a theoretical challenge in his blog post "The Fine Structure Constant is Probably Constant"[1]. Chad Orzel has a more observational critique of the results in "Why I’m Skeptical About the Changing Fine-Structure Constant" [2]. To be fair, these critiques are from 2010 and Webb, et al. has published several papers since these critiques were made. I haven't seen updated debate or discussion over Webb, et al's findings. Still, I would think we have some potential evidence that the constant may vary, but I don't think this evidence is near conclusive yet. [1] http://www.preposterousuniverse.com/blog/2010/10/18/the-fine-structure-constant-is-probably-constant/ http://www.preposterousuniverse.com/blog/2010/10/18/the-fine... [2] http://scienceblogs.com/principles/2010/09/14/httpksjtrackermitedu20100907e/ http://scienceblogs.com/principles/2010/09/14/httpksjtracker...
DonaldFisk 11y ago
The component constants of α = e^2/4πεħc have dimensions, so depend on what units you use to measure them in. Their combination comprising the electromagnetic fine structure constant is, however, dimensionless, and is satisfactorily explained. The Anthropic Principle is usually invoked to explain why two very large dimensionless numbers, i.e. the inverse gravitational "fine structure constant" (which is assumed to be constant), and the age of the universe measured in atomic units (which increases with time), are both very close to 10^40. It is suggested that, for intelligent life to evolve and measure them, the two numbers must be roughly equal, and other dimensionless numbers, such as the electromagnetic fine structure constant, must similarly have values within a narrow range. And this in turn has led some people to believe it's the deliberate action of a creator, or that there are numerous other universes whose constants have different values, and almost all are devoid of life. Fine-tuned Universe: https://en.wikipedia.org/wiki/Fine-tuned_Universe https://en.wikipedia.org/wiki/Fine-tuned_Universe However, if we apply this Anthropic Principle to planetary orbits, we could conclude that planetary orbits are roughly circular because, if they were (for example) very long rectangles (or some other random shape), we wouldn't be around to observe their shape. Of course, no one believes that. It is accepted that Celestial Mechanics, based on Newton's Law of Gravity, (which can be derived from the more accurate General Theory of Relativity), adequately explains why planetary orbits are roughly circular. An alternative explanation is that we simply haven't worked out all the physical laws. For example, the force of gravity could become weaker as the universe gets older or less dense (or, expressed in different units, gravity remains constant but elementary particles get lighter). Dirac, and later a few others including myself, modified Einstein's equations in an attempt to explain this coincidence. Dirac large numbers hypothesis: https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis Another argument against fine tuning is the Inverse gambler's fallacy: https://en.wikipedia.org/wiki/Inverse_gambler's_fallacy https://en.wikipedia.org/wiki/Inverse_gambler's_fallacy

kazinator 11y ago

"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.

danharaj 11y ago
> This here desk I have here is about 1.7 times as long as it is wide. No inches or centimeters required. How did you measure your desk in order to compute its length/width ratio?
- glastra 11y ago
  I fail to see where you're trying to get. c, e and h all have units and are measurable.
  - danharaj 11y ago
    The quote is "When scientists measure any quantity they must specify the units being used." I am not convinced they determined the ratio of his table's length and width without first measuring those quantities in some unit.
    - glastra 11y ago
      A measurement doesn't have to be direct to be a measurement. In other words, the aspect ratio of a desk is still obtained by measurement and thus is a measured quantity, subject to error and so on. Of course, both the quantity and the associated error come from previous measurements.
      - danharaj 11y ago
        i'm just wondering if there's an example of a direct measurement of a ratio, rather than one computed from the measurement of dimensional quantities.

leanthonyrn 11y ago

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 11y ago
-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.

pervycreeper 11y ago

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?

noobermin 11y ago
h-bar[0]: [0] https://en.wikipedia.org/wiki/Planck_constant https://en.wikipedia.org/wiki/Planck_constant
jeffwass 11y ago
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).
jessriedel 11y ago
jeffwas has explained the factor of 2pi. It's just the 2pi radians in a circle to convert from angular frequencies to regular frequencies. I don't know the detailed history, but in practice the fact that it's an inverse is essentially because it's most important role is as part of an expansion like a Taylor series. The standard method for calculating lots of observable effects gives an answer with the form X = X_0 + \alphaX_1 + \alpha^2X_2/2! + ...

noobermin 11y ago

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

tcfunk 11y ago

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 11y ago
Here, voilá http://andreapaiola.name/magpie/?url=https%3A%2F%2Fcosmosmagazine.com%2Fmathematics%2Fnumber-fascinates-physicists-above-all-others&action=&links=on http://andreapaiola.name/magpie/?url=https%3A%2F%2Fcosmosmag...
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mtviewdave 11y ago

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 11y ago
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 11y ago
  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-Rosenband-1808-12.pdf http://phys.columbia.edu/~millis/1900/readings/Science-2008-...
  - jsweojtj 11y ago
    A further layman explanation by a researcher in this field: http://astronomy.swin.edu.au/~mmurphy/research/are-natures-laws-really-universal/ http://astronomy.swin.edu.au/~mmurphy/research/are-natures-l... specifically the section titled "Aside: Is it e or c varying?"

sidcool 11y ago

Isn't π a similar pure number?

gohrt 11y ago
Pi is mathematically pure, independent of physics. Mathematics is full of pure numbers (obviously). The fine structure constant is physically pure.

rubidium 11y ago

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 11y ago
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/Day5/Murphy.pdf https://www.eso.org/sci/meetings/2012/ESOat50/Presentations/... 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-structure-constant-is-probably-constant/ http://www.preposterousuniverse.com/blog/2010/10/18/the-fine... 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 11y ago
  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.

chias 11y ago

> 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 11y ago
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 11y ago
  Thank you for this explanation. The distinction was not clear to me after reading the article, but your comment makes a lot of sense.
spodek 11y ago
> 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. Everyone is so fancy. One, two, three, and even zero are pretty well known, even outside physics.

mrfusion 11y ago

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

gradi3nt 11y ago
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.

worik 11y ago

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

worik 11y ago

Omega is much more interesting. For informaticians...

poelzi 11y ago

From the BSM-SG perspective it's very clear what it is: http://www.amazon.com/Basic-Structures-Matter-Supergravitation-Unified/dp/1412083877 http://www.amazon.com/Basic-Structures-Matter-Supergravitati... 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.

zuo 11y ago

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