Sorry, Chronos. I hate to shred my last bit of reliableness, but I made it up by taking the arcsec of e–which, as you can see, is pretty close to some of the recent values of the fine structure constant. But I did get the same value that Manlob claimed. I thought that one was made up too. Mea culpa.
Isn’t the fsc the ratio of the em force to the strong force? If so, it’d measure the ability of a nucleus to hold itself together. Get any where near to 137 protons in a nucleus and the em force will blow them apart. Actually, I guess the limit is 92.
Yeah, Chronos, I got the same value as Manlob, but I had to use Windows Calculator, which keeps about 32 decimal places. (I also used (Sqrt(5) + 1) / 2 for phi; I hope that’s okay.) What I want to know, Chronos, is how you raised (pi + e) to a power and got a negative number.
Anyway, to respond to what stolichnaya said, I tend to think that the reason that some of these folks like Edison get excited about the fine structure constant being around 1/137, is that to one decimal place, it’s the reciprocal of an integer. The thought that something so fundamental would be so close to an integer seems like it would have some sort of cosmic significance at first, I guess, but I say big whoop. On Earth, atmospheric pressure is within about 1% of 1 kg/cm², and nobody thinks that’s by grand design - it’s just a lucky coincidence.
I’m not going to argue whether kg/cm² is appropriate units for pressure–we all probably know what it means. But I think the value differs by more than 3%, doesn’t it?
It’s not a big deal or anything, but this site lists atmospheric pressure as 101,325 Pa, or 1.01325 kg/cm², so it’s off by 1.325%, which is about 1%, right?
By the way, I’m not going to argue either, but I didn’t mean to use kg/cm² as a unit of pressure. I was originally going to say 1000 g/cm², but because I like to use all the functionality that metric has to offer, I decided to make it 1 k(g/cm²), or 1 kg/cm².
I guess if I’m trying to convince people that this isn’t a big deal, I shouldn’t talk about it so much, so that’s enough for now.
Yes, but that’s based on a choice of arbitrary units, while the fine structure constant isn’t.
Let’s put it this way: if you can figure out a logical way in which the speed of light, the gravitational constant, Planck’s constant, etc. are all connected- such that changing the speed of light would change the strength of gravity, for example- you’re well on your way to the GUT. If the FSC were really the reciprocal of an integer, that would have been an indication that the values of the fundamental constants are non-arbitrary, and that it might be logically impossible for the universe to be different from the way it is.
Ben, I agree with you, but I’m trying to say that the FSC[sup]-1[/sup] isn’t that close to an integer. Or rather, it is, but there are just so many numbers out there that getting one close to an integer is no big deal. If the value were an integer, I’d be with everyone saying it’s something special, but the fact is, it’s not, unless everyone’s measurements are way off. They know this thing to like 6 decimals, but it diverges from a perfect integer after 2.
Also, I knew that the FSC is a special kind of constant in that it’s unitless, but the atmospheric pressure thing was the only good example I could think of. Look at it this way, though. The meter was originally based on the size of the Earth (1/10,000,000th of the distance from the North Pole to the Equator). The gram, then, was based on the mass of a certain amount of water. These units almost work out to something nice with the atmospheric pressure. So one might say that the size and atmospheric pressure of Earth are mysteriously related, so even if it’s not some Universal scheming, it’s a planetary one. [Twilight Zone music…]
My objection to kg/cm² was not to the mixing of kg with cm (hey, the World Almanac does it), but to the use of it as a unit of pressure (well, the almanac does that too). Technically, a Pa is equal to ( kg / ms^2 ), so to convert to kg/cm² you’d have to take into account the acceleration of gravity, which is 9.80665 m/s^2. If you’re going to use kg/cm², then atmospheric pressure is 101325/98066.5, or 1.03323 kg/cm². In other words, a one kilogram mass exerts a pressure on a square centimeter that is 3% less than atmospheric pressure.
Atmospheric pressure depends on the units–the meter and gram may be decimally related to the earth, but the second is not–but the fine structure constant does not. But I’m going to go out on a limb and agree that 137 doesn’t mean that much. At least not as much as 137.036