Magnetic moment of electron

[Copernicus]

In answer to my question about the magnetic moment of the electron, Grapes had sent me to a PDF for part of the calculations.

The PDF is as follows. http://arxiv.org/PS_cache/hep-ph/pdf/9602/9602417v1.pdf

The calculations are enormous. My question is, has anyone actually really gone through these calculations? Are they real or empirical?

[kevin1981]

wow, talk about complex ! Hands up, i am lost

[Copernicus]

wow, talk about complex ! Hands up, i am lost

I admit that I am lost with that calculation as well. I just wonder if all of us on this board have to take that calculation without disbelief.

[korjik]

In answer to my question about the magnetic moment of the electron, Grapes had sent me to a PDF for part of the calculations.

The PDF is as follows. http://arxiv.org/PS_cache/hep-ph/pdf/9602/9602417v1.pdf

The calculations are enormous. My question is, has anyone actually really gone through these calculations? Are they real or empirical?

Where do you think that paper came from? They just made it all up?

[Copernicus]

I'm just asking, does anyone know anyone, that they trust, who ran through the derivations and verified them?

[Tensor]

In answer to my question about the magnetic moment of the electron, Grapes had sent me to a PDF for part of the calculations.

The PDF is as follows. http://arxiv.org/PS_cache/hep-ph/pdf/9602/9602417v1.pdf

The calculations are enormous. My question is, has anyone actually really gone through these calculations? Are they real or empirical?

Heheheheheh,they are real, but the funny part is you're not seeing the full amount of calculations by a looooooooong shot. I'll get to that below, but first, I'm quite sure they didn't do them by hand. Computers were heavily involved. Go back and read the acknowledgements. "...results presented in this note have been obtained by intensive use of the algebra manipulating programs FORM and ASHMEDAI...". And even without computers, if you notice they have broken the calculations down into manageable sections. The calculations would be extremely tedious, but not impossible. They even note on page 6 "... Fortunately, the expansion and the extremely lengthy processing of the various identities can be carried out in an almost mechanical way."

As for not seeing all the calculations, you don't see all the Feynman diagrams that they use. This presentation from 2006, shows that at the α³ level, there are a total of 75 diagrams that have to have calculations done for them(note that they list the Laporta Remiddi paper is listed). To go to the next level, which was accomplished in 2006, required the calculation of 891 Feynman diagrams. At the α⁵ level, there will be 12,672 diagrams to evaluate. As of 2007, there were still over 6,000 diagrams to evaluate, I have not found anything later to indicate the progress on this matter. Just imagine going through one of those procedures over 6,000 times, just to get the theoretical number. Page 17 is interesting for the diagrams, the plan for doing the calculations using computers starts on page 18.

[Copernicus]

Thank you!

[Tensor]

I'm just asking, does anyone know anyone, that they trust, who ran through the derivations and verified them?

Those calculations are published (the data sets for even the long, and numerous calculations are available for those who ask), and the results are checked by referees before publication. After publication, they can be checked by anyone reading the article. Obviously, calculations that take years, would also take years to check. And what is checked is that they programs they use produce they results they claim for the first few terms. But, at this point, you're looking at corrections to the magnetic moment calculations that are at the parts per billionth or trillionth and approaching the quadrillionth level. One of the calculations found an error in a previous calculation, so yes they are checked and can be relied upon. Unless you want to believe that all the scientists are somehow involved in some huge conspiracy to hide the truth. But then, why publish the answers, equations and calculations where anyone could see and check on them?

[Copernicus]

Those calculations are published (the data sets for even the long, and numerous calculations are available for those who ask), and the results are checked by referees before publication. After publication, they can be checked by anyone reading the article. Obviously, calculations that take years, would also take years to check. And what is checked is that they programs they use produce they results they claim for the first few terms. But, at this point, you're looking at corrections to the magnetic moment calculations that are at the parts per billionth or trillionth and approaching the quadrillionth level. One of the calculations found an error in a previous calculation, so yes they are checked and can be relied upon. Unless you want to believe that all the scientists are somehow involved in some huge conspiracy to hide the truth. But then, why publish the answers, equations and calculations where anyone could see and check on them?

I don't understand the calculations at all or the theory behind it, but the amount of corrective factors are just weird. Is this what they call renormalization?

[Shaula]

I don't understand the calculations at all or the theory behind it, but the amount of corrective factors are just weird. Is this what they call renormalization?

They are very similar conceptually but I think that they are different things. Renormalisation is a bulk correction which uses measured quantities to tame divergent integrals as they approach singularities (usually at r=0). I may be wrong here this is tap-dancing on the edge of my understanding. The amount of corrective factors is not weird at all - it is a natural consequence of the statistical nature of QM.

[Copernicus]

They are very similar conceptually but I think that they are different things. Renormalisation is a bulk correction which uses measured quantities to tame divergent integrals as they approach singularities (usually at r=0). I may be wrong here this is tap-dancing on the edge of my understanding. The amount of corrective factors is not weird at all - it is a natural consequence of the statistical nature of QM.

So does it have to do with the radiative affects of the electron and the unpredictability of its location?

[Shaula]

Renomalisation is basically because integrals treat everything (space, energy etc) as continuous. They become increasingly badly behaved when you get down to the points where the quantities integrated over become quantised. What we actually want when we integrate is a sum-over-everything - but the continuous nature of an integral is a poor fit to what we are trying to do because our theories don't actually do down to the smallest length scales/highest energies.

[Copernicus]

Renomalisation is basically because integrals treat everything (space, energy etc) as continuous. They become increasingly badly behaved when you get down to the points where the quantities integrated over become quantised. What we actually want when we integrate is a sum-over-everything - but the continuous nature of an integral is a poor fit to what we are trying to do because our theories don't actually do down to the smallest length scales/highest energies.

So in QEM are we saying that calculus doesn't work well at the smallest scales because an infinitesimal is not accurate because there actually is a smallest increment?

[Shaula]

Pretty sure that is the basic problem - certain functions are divergent in the limit of the continuum. That is basically because the models and methods we use begin to have issues at that limit. Renormalisation is essentially a way of saying "We know that things go wrong but we also know that we can correct for this by using this technique".

Note that this is only a problem for SOME of the integrals we are interested in. Others don't have this problem due to cancelling terms or the integral being convergent.

[Copernicus]

Tusenfem had helped me find a reference to the corrective factors for the magnetic dipole moment of the electron. In the reference the term "radiative correction to the magnetic moment of the electrons". I was wondering what this exactly means for a single electron that is not orbiting a proton.

[PraedSt]

I may be wrong, but I presume you wouldn't have to apply the correction.

[publius]

"Radiative corrections" are a Quantum Field Theory thing that are part of renormalization and has to do with the "bare" vs physical constants and all that mess. We'd need an expert to really explain it, but it has nothing to do with radiation in the classical sense at all. It may be "radiative" in QFT terms of virtual photons and all that.

[Copernicus]

The g factor, for the electron magnetic moment, has different components at alpha, alpha squared, and alpha cubed. What is the significance of the 3 levels?

Thanks in advance!

[Shaula]

Because it is using three-loop QED? ISTR each loop is suppressed by a factor of alpha, hence alpha, alpha squared, alpha cubed. They represent the basic probabilities for a first, second or thirds order effect in QED.

[tusenfem]

Because it is using three-loop QED? ISTR each loop is suppressed by a factor of alpha, hence alpha, alpha squared, alpha cubed. They represent the basic probabilities for a first, second or thirds order effect in QED.

Basically, the theory is turned into a Taylor series in α, and then you can chose how far down you want to go, keeping in mind that in this kind of calculations each higher power in α will lead to more complicated calculations.

[grapes]

In answer to my question about the magnetic moment of the electron, Grapes had sent me to a PDF for part of the calculations.

The other thread: http://www.bautforum.com/showthread....f-the-electron

As all can see, I dug up that paper from the wiki references, not from my personal store of knowledge, so I haven't even looked over that paper. Sounds impressive.

But I would like to discuss the idea of renormalization more, perhaps in another thread, which I'll link to here, once the thread exists.

[Grey]

What's really cool is that you do this phenomenally complicated calculation and get a value. Then you do experiments to actually measure the magnetic moment of the electron, and you find that it matches the calculation to something like eight decimal places. It's really remarkable.

[Copernicus]

What's really cool is that you do this phenomenally complicated calculation and get a value. Then you do experiments to actually measure the magnetic moment of the electron, and you find that it matches the calculation to something like eight decimal places. It's really remarkable.

It's insanely cool, but isn't it more decimals than 8, I thought 10 or 11 for the electron. I was wondering if the alpha squared and alpha cubed had physical or theoetical significance?

[Copernicus]

It's insanely cool, but isn't it more decimals than 8, I thought 10 or 11 for the electron. I was wondering if the alpha squared and alpha cubed had physical or theoetical significance?

I checked out Taylor series, the alpha squared, cubed, etc are part of a mathematical tool and the g factor is actually 12 digits. Thanks for all the help.

[Copernicus]

I was wondering if someone could direct me to the g factor numbers for the magnetic moment of the proton neutron and muon.

thanks

Copernicus

[Copernicus]

The first g factor correction for electron magnetic moment is the fine structure constant over 2*pi. In simple terms, what is the basis for this first correction factor? Is this the same first factor for neutron, proton, and muon as well?

[tusenfem]

All merged into one, as this is basically the same question in four different threads.

[Copernicus]

I would appreciate if anyone could answer the last few questions. Thanks!

[PraedSt]

Have you checked out arXiv Copernicus? You'll probably get a ton of papers from a search, and of those I'm sure a few would be review papers.