What is the Fine-Structure Constant and its Relation to Gravity?

[yogi]

When you form a dimensionless ratio, such as alpha, you cannot let everything = 1. If you let K = 1, you have to scale q to get the correct force ratio (10^42). If G and K are both set equal to l you would have to express q in terms of mass units which is a contradiction of logic because we already know the electron mass unit is m_e.

I have always been a critic of Planck units as standing for something fundamental - nothing has ever really come out of it that makes any predictions about the real world - in that regard I liked John Baez comments re the difficulty of handling Planck units in the classical world in the paper you cited - what I don't understand is why one set of units formed from one set of so called constants is any better than any other - e.g., Stoney Constants, or Weinberg's mass constant - the physics communities thinking is that G must be a contributor to the derivation of a set of fundamental units because it has global significance - but so does q since it is a long range ... and of much greater strength. If you like G as a fundamental constant entity ( I don't) it is easy to create a set of dimensions from G, c and M_u where the latter represents the mass of the universe which most feel is constant (not I, however). But in any event, my point is that using these three so called constants of nature you arrive at GMu/c^2 as a unit of length commensurate with the Hubble scale whereas GMu/c^3 corresponds to the Hubble time and the third constant for mass is already decided upon (i.e., Mu).
If you don't like Mu as a constant, try m_e and get a length 10^-57. You may recognize that length
as significant, but my point is, its easy to generate a set of dimensional units from the many items now considered constant. IMO there may actually be only one constant c since it represent the coupling between space and time. All the rest is numerology. Modern physics tries to make sense out of the Planck scale, while at the same time tacitly dismissing the Planck mass and Planck time as having no known significance. This is inconsistent. `

 

[Dale]

When you form a dimensionless ratio, such as alpha,

You seem to be dodging the question. I agree that the fine structure constant is a dimensionless constant and it actually does tell us something meaningful about physics. That is not relevant to the question at hand which is regarding dimensionful constants such as G and K.

Again, K can be made to completely drop out of Coulomb's law simply by using Gaussian units. Thus, its value and even its existence depends entirely on the system of units. So how can it possibly tell you anything about the universe?

 

[yogi]

Back to you Dale

If you let K= 1, then you can use values for q such that the ratio of F/f is a dimensionless magnitude = 10^42. There is nothing magic about K per se. The ratio of F/f is what is significant - the magnitude of the one with respect to the other. Once you know the ratio, you can turn your attention to why the ratio has the value of 10^42.

But here is what is lost by dropping the units or using cumbersome units. Taking the example of gravity again - usually expressed as ntn-meters squared per kgm squared. To me, that doesn't translate to anything obvious - but when converted to meters cubed per second squared per kgm - something may come to mind - can you think of anything that has an accelerating volume to which the constant might be applicable?

 

[Dale]

There is nothing magic about K per se. The ratio of F/f is what is significant - the magnitude of the one with respect to the other.

Exactly my point. Same with G. There is also nothing magic about G per se, nor any other universal dimensionful constant. Only dimensionless quantities like your F/f tell us anything about physics.

Taking the example of gravity again - usually expressed as ntn-meters squared per kgm squared. To me, that doesn't translate to anything obvious - but when converted to meters cubed per second squared per kgm - something may come to mind - can you think of anything that has an accelerating volume to which the constant might be applicable?

Regardless of what you might want to apply the constant to, you can always choose units such that its value is a dimensionless 1 and it drops out of the equations entirely. Once you do that, then you look at the equations and any dimensionless constants to provide the meaning that you might erroneously want to attribute to G.

 

[yogi]

If i write a statement f = Gmm'/r^2 and let G = 1, then to get get a meaningful answer in terms of ntn, all the information must be encoded into the masses because kgm squared over meters squared does not equal force. You would have to write each mass in terms of an effective acceleration to the 1/2 power.

I recall reading some years ago, that in his original formulation, Newton treated the coefficient as a combination which incorporated the Sun - so the equation reduced to a constant and one mass divided by the distance squared. The information is retained either way - Newton's relationship between acceleration and mass is not lost.

When a constant such as alpha shows up in physics as dimensional-less - it is not always easy to unravel what meaning should be given to the factors that lead to the loss of dimension-ality We know alpha is the ratio of the velocity of an electron in the first Bohr orbit to c, but why should it have this value and not some other? No doubt there is some theory yet to be revealed that will explain this - it became an obsession for Eddington. My point is that alpha is consternation - we really don't know what has been canceled out to form the ratio. Alpha is a prime example of information lost

 

[Dale]

If i write a statement f = Gmm'/r^2 and let G = 1, then to get get a meaningful answer in terms of ntn, all the information must be encoded into the masses because kgm squared over meters squared does not equal force. You would have to write each mass in terms of an effective acceleration to the 1/2 power.

Actually, you would get dimensions of M=L³/T².

My point is that alpha is consternation - we really don't know what has been canceled out to form the ratio. Alpha is a prime example of information lost

I disagree entirely. The fine structure constant is not information lost, it is the only physical information that was ever there to begin with. The other stuff is just units, not physical information.

You still seem to think that the stuff being canceled out has some intrinsic physical information, it does not. Only the ratio has physics content. Furthermore, the fine structure constant is the coupling constant in QED, so it has meaning on its own.

 

[yogi]

Actually, you would get dimensions of M=L³/T².

I disagree entirely. The fine structure constant is not information lost, it is the only physical information that was ever there to begin with. The other stuff is just units, not physical information.

You still seem to think that the stuff being canceled out has some intrinsic physical information, it does not. Only the ratio has physics content. Furthermore, the fine structure constant is the coupling constant in QED, so it has meaning on its own.

If I told you the fine structure constant can be formed with different constants would you believe me?

 

[Dale]

Sure. I am well aware of that fact.

 

[yogi]

Sure. I am well aware of that fact.

That answer surprised me - can you tell me what constants were used that you are aware of - or give me a link to the derivation.

 

[Dale]

See the first equation in the definition section
http://en.wikipedia.org/wiki/Fine-structure_constant

 

[yogi]

See the first equation in the definition section
http://en.wikipedia.org/wiki/Fine-structure_constant

Thanks Dale - I also surfed around for some info on deriving alpha from mechanical constants ...one author came up with an interesting approach starting with the ratio of e to G - but unfortunately in the end it didn't turn out to shed any light upon the nature of q which was what I was looking for to bolster my argument re lost information.