Gravity and the fine-structure constant.

[The Man]

Gravity and the fine-structure constant.


Well there has never been any shortage of crazy Ideas being posted on this forum, so I figured I might give it a shot myself. The only difference is that I know this idea has no theoretical basis as far as I know and would just amount to some numerology. What I’m hoping is for some theoretical basis that I am not currently aware of or perhaps just getting someone else thinking who this might help.

Some time ago I was working on way to derive the Planck values without using G. Thus finding a way to calculate G. Generally I kept running in to the problem that although one can calculate Planck Charge (QP), Planck Force (FP) times the square of the Planck Distance (DP) or Planck Force (FP) times the square of the Planck Time (TP) without using G, but you can’t separate the force from the distance or the time without G.

I started working with the Planck Momentum (PP) as it is a value (6.525 NS) that we could encounter everyday. Also the fine structure constant (α) as it is the proportion of the charge of an electron squared to the Planck charge squared.

To make a long story short I started to notice the 1/ (αp) was very close to PP2 (only about 1.047 difference), but of course the units didn’t work out as 1/ (αp) would basically be unitless (or at least dimensionless) while PP2 has the units of N2S2.

Since α is unitless, I began thinking along the lines of radians and phase. If it were PP2 / 1N2S2 I might be able to find a phase relationship between the two (accounting for the 1.047 difference) and now both sides were dimensionless.

As cycles 1/ (αp) works out to 6.94 cycles and PP2 / 1N2S2 as 6.78 cycles. If we drop off the whole cycles and just look at the phase difference (after six cycles) as angles we get 1/ (αp) at 339.24 degrees and PP2 / 1N2S2 at 279.25 degrees, giving a phase difference (after six cycles) of 60.01 degrees.


If we consider that phase difference to be exactly 60 degrees we have (PP2 / 1N2S2)=((1/ (αp))-(p/3)) or a calculation for G of hc3/(2p((1/ (αp))-(p/3))) or 6.674317 M4N-1S-4 well within the current error of measurement for G.

So As I said I have no theoretical basis for this calculation, nor do I have any illusions that it is anything more then the result of some convoluted math. However I am certainly not well versed in the current theories on quantum gravity or tensor math. Perhaps this mathematical manipulation might have more meaning to someone more knowledgeable in those fields.

So have at it, what are your thoughts, opinions and certainly jokes, I’m looking for it all.

[ben m]

Hi The Man,

When you did "P_p^2/1N^2S^2", you may have thought you were just "fixing the units", but you were also throwing in an arbitrary not-at-all-universal constant: "one newton^2 second^2", something that's only meaningful to people who have some connection to a particular lump of iridium in Paris, France, Earth: the Standard Kilogram.

Someone reading your analysis in another unit system would ask: "OK, so we're going to divide P^p^2 by some arbitrary constant---it says here to use 0.220 pounds-seconds." After all, 0.220 pound-seconds is the same thing as a newton-second. So that really is an arbitrary constant; the fact that you get to write it as "1.000000 N-s" in this unit system sort of makes it look non-arbitrary, but it's not.

Nice bit of numerology, though. A little more salesmanship and I'd be ready to fork over $39.99 for your pyramidal Bible ion detoxifier magnet. :)

[The Man]

Hi The Man,

When you did "P_p^2/1N^2S^2", you may have thought you were just "fixing the units", but you were also throwing in an arbitrary not-at-all-universal constant: "one newton^2 second^2", something that's only meaningful to people who have some connection to a particular lump of iridium in Paris, France, Earth: the Standard Kilogram.

Someone reading your analysis in another unit system would ask: "OK, so we're going to divide P^p^2 by some arbitrary constant---it says here to use 0.220 pounds-seconds." After all, 0.220 pound-seconds is the same thing as a newton-second. So that really is an arbitrary constant; the fact that you get to write it as "1.000000 N-s" in this unit system sort of makes it look non-arbitrary, but it's not.



Just unit momentum squared, hardly arbitrary. If PP where also represented in pound seconds, unit momentum would just be 1 pound second. Certainly the pound is an arbitrary unit, but the Newton is a derived unit based on the relationship of unit mass to unit acceleration. So no, if I were using pound seconds then I would be introducing an arbitrary constant.


Nice bit of numerology, though. A little more salesmanship and I'd be ready to fork over $39.99 for your pyramidal Bible ion detoxifier magnet. :)

What $39.99? That’s a pyramidal Bible ion detoxifier quantum magnet and goes for $399.99.

[ben m]

Just unit momentum squared, hardly arbitrary. If PP where also represented in pound seconds, unit momentum would just be 1 pound second. Certainly the pound is an arbitrary unit, but the Newton is a derived unit based on the relationship of unit mass to unit acceleration. So no, if I were using pound seconds then I would be introducing an arbitrary constant.

But in pound-seconds P_p is not 6.525, it's 1.467. (1.467^2 lb^2 s^2)/(1 pound^2-second^2) has a different value than (6.525^2 N^2 s^2/1 N^2 s^2) and you won't find the same neat-looking numbers at the end of your calculation.

[The Man]

Well that was the point the value of the Planck force and thus the value of G depends on the units used. The fact is I would have to introduce some arbitrary constant as you mentioned before in order to get similar results with different values of G or the Planck force.

[The Man]

My mistake by changing the units and thus the value of for the Planck Force in the Planck momentum you also change it in the denominator as much as the numerator so the proportion remains the same. I had used the dimensionless result for the calculation of G when it should include the Newton Second or whatever units are used instead. So it should be hc3/((1Newton2Second2)2p((1/ (αp))-(p/3)). The (1Newton2Second2) is not arbitrary, certainly no more arbitrary then the system of units used, as it is dictated by the system of units used and required. Otherwise h and c would be just as arbitrary. Certainly it is not a constant again as it is dependent on the system of units used and thus not constant. Like wise h and c are only constant in some specific system of units used.

[Singularitarian]

Planck units are fascinating, at least, i think so. I've been working on them for a while now, and i can't seem to get enough of it.

[sol invictus]

My mistake by changing the units and thus the value of for the Planck Force in the Planck momentum you also change it in the denominator as much as the numerator so the proportion remains the same. I had used the dimensionless result for the calculation of G when it should include the Newton Second or whatever units are used instead. So it should be hc3/((1Newton2Second2)2p((1/ (αp))-(p/3)). The (1Newton2Second2) is not arbitrary, certainly no more arbitrary then the system of units used, as it is dictated by the system of units used and required. Otherwise h and c would be just as arbitrary. Certainly it is not a constant again as it is dependent on the system of units used and thus not constant. Like wise h and c are only constant in some specific system of units used.

The coincidence you noticed is that the ratio of two constants, in SI units, has a numerical value close to 1. The problem is that in other unit system, that ratio would not be 1.

Think of it this way: take ANY two quantities with different dimensions. Their ratio is some dimensionful quantity. Now DEFINE a system of units so that ratio is exactly 1. You can always do that (in fact it is done in SI system for some basic units).

See the problem?

[The Man]

The coincidence you noticed is that the ratio of two constants, in SI units, has a numerical value close to 1. The problem is that in other unit system, that ratio would not be 1.

Think of it this way: take ANY two quantities with different dimensions. Their ratio is some dimensionful quantity. Now DEFINE a system of units so that ratio is exactly 1. You can always do that (in fact it is done in SI system for some basic units).

See the problem?

Well yeah that is the problem, that my crude attempt to create a dimensionless proportion of momentums was not successful. Basically why I stopped working on this, but I thought I might have been missing something, guess not. The problem remains that the fine structure constant is truly dimensionless and that proportion does not change when you change the units, however the Planck momentum does.

ETA

What I needs is a momentum dependent on the units used that might actually give me a that dimensionless proportion with the Planck momentum.