So what is the formula?Hi Passion Flower.
neutron is slightly heavier
Mass of proton : 1,6726 x 10^(-27) kg
Mass of neutron: 1,6749 x 10^(-27) kg
Mass of electron: 0,00091x10^(-27) kg
The mass of a neutron is greater than the mass of a
proton because the neutron contains a proton, contains
an electron with some subatomic particles.
neutron = proton + electron + subatomic particles
I do not think you understand what I am asking. I am asking if we can calculate the masses or at least the difference in mass. And if so, then what is the formula.In energy units (using E = mc^2), the masses are: Proton: 938.272 MeV, neutron:
939.566 MeV, mass difference = 1.293 MeV, electron: 0.511 Mev.
I do not want to be difficult but is my question really so hard to understand?From Wikipedia
Outside the nucleus, free neutrons are unstable and have a mean lifetime of 885.7±0.8 s (about 14 minutes, 46 seconds); therefore the half-life for this process (which differs from the mean lifetime by a factor of ln(2) = 0.693) is 613.9±0.8 s (about 10 minutes, 14 seconds).[2] Free neutrons decay by emission of an electron and an electron antineutrino to become a proton, a process known as beta decay:[6]
n0 → p+ + e− + νe
I suspect you are really asking if we can predict the difference in mass from first (or at least deeper) principles.I am asking if we can calculate the masses or at least the difference in mass. And if so, then what is the formula.
This is absolutely not correct. A proton consists of two u quarks, a d quark and a set of virtual quark pairs and gluons. A neutron looks exactly like that with a d quark substituted for one of the u quarks.The mass of a neutron is greater than the mass of a
proton because the neutron contains a proton, contains
an electron with some subatomic particles.
neutron = proton + electron + subatomic particles
Well if we can predict something that implies we can calculate it right?I suspect you are really asking if we can predict the difference in mass from first (or at least deeper) principles.
This model of the neutron has been known to be inaccurate for the last 45 years, which you might have realized if you kept reading on the web page you took that from.Hi Passion Flower.
neutron is slightly heavier
Mass of proton : 1,6726 x 10^(-27) kg
Mass of neutron: 1,6749 x 10^(-27) kg
Mass of electron: 0,00091x10^(-27) kg
The mass of a neutron is greater than the mass of a
proton because the neutron contains a proton, contains
an electron with some subatomic particles.
neutron = proton + electron + subatomic particles
Ok Lattice QCD it is then.The remaining mass difference can only be explained by the strong interaction between the constituent quarks of each particle. This interaction within the proton is stronger, since the proton is stable and the neutron is not. So the proton has more binding energy, again leading to a smaller mass than the neutron. However precisely computing the mass difference is not as simple as writing down a formula, since just about all approximation schemes break down when considering the strong interaction at low energies. Lattice QCD is the most promising computational method for answering such questions, and it gives correct results for nucleon masses to within a few percent.
There is no simple formula to be written down. Lattice QCD starts with the definition of QCD observables via path integrals, discretizing on a lattice (along with techniques that took many years to develop) allows these integrals to be done numerically. The resulting spectrum can be converted to (ratios) of particle masses, but I'm not familiar (and not many people outside of the experts are either) with the details. If you want to see some general ideas about lattice methods, you could take a quick look at http://arxiv.org/abs/hep-lat/0506036 One of the more recent computations of light hadron masses appears in http://arxiv.org/abs/0906.3599 but there aren't many formulas there either.Ok Lattice QCD it is then.
Within a few percent is ok.
So what is the formula?
I can be misreading something, but it looks to me like calculated mass of hadron is still a function of something we can't calculate from the first principles - unless we assume quark mass to be the first principle...In the work presented here, a full calculation of the light hadron spectrum in QCD,
only three input parameters are required: the light and strange quark masses and the coupling g.
My understanding is that the masses of quarks would come from the Higgs mechanism, thus outside QCD. This paper is as fundamental as it gets for QCD.From the second paper:
I can be misreading something, but it looks to me like calculated mass of hadron is still a function of something we can't calculate from the first principles - unless we assume quark mass to be the first principle...
There is no need for it to be simple. We passed the time long ago where we had to calculate things by hand.There is no simple formula to be written down.
That looks helpful, in Python nevertheless. I would prefer Maple, any worksheets?If you want to see some general ideas about lattice methods, you could take a quick look at http://arxiv.org/abs/hep-lat/0506036
You are probably right that we cannot explain the absolute value of a mass but I am already satisfied if we can calculate the relative masses and according to the second paper "the Standard Model should explain the difference". However rather than asking for an explanation, which is tricky (at least to me) in QM anyway I rather see, how we can actually compute this on our desktop computers.My understanding is that the masses of quarks would come from the Higgs mechanism, thus outside QCD. This paper is as fundamental as it gets for QCD.
There's a computational obstacle that I don't completely understand related to doing computations with light quark masses. Obtaining physical results is done by some sort of scaling procedure (in masses, this is separate from the lattice spacing) and they must require some extra data to complete the definitions of physical results.From the second paper:
I can be misreading something, but it looks to me like calculated mass of hadron is still a function of something we can't calculate from the first principles - unless we assume quark mass to be the first principle...
Almost, but due to renormalization, the quark masses at the electroweak scale are very different from those at GeV scales. There are other papers that compute light quark masses and coupling renormalization at GeV scales, but they also use light pion masses as inputs.My understanding is that the masses of quarks would come from the Higgs mechanism, thus outside QCD. This paper is as fundamental as it gets for QCD.
I'd expect many of the lattice codes are still written in Fortran and run on parallel supercomputers. I don't think that Maple or Mathematica are well-suited yet to doing these things. While you could probably put all of the formulas into a notebook, neither program would do the computations in a particularly optimal manner. It's still better to explicitly code hard computations.That looks helpful, in Python nevertheless. I would prefer Maple, any worksheets?
Can we do the full calculation in Maple or mathematica (I prefer Maple).
If the answer is no then what software is used to calculate it?
Quenched means that corrections from fermion loops are being neglected. This is because dealing with Grassmann variables on a lattice is a very hard problem in the first place and the approximation schemes that must be used are computationally intensive.We certainly can do path integrals, Wick rotations and Monte Carlo stuff in Maple. Discretizing on a lattice I am not sure. What is quenched approximation?
From the paper on computation of neutron/proton masses (light hadron masses):A side question then would be how computationally intensive is the full calculation. So do I understand correctly that there are two main approaches, e.g. perturbation and QCD lattice and that quenched optimization is a shortcut for the second approach which is a shortcut to the perturbation method?
So how computationally intensive is it? Wasn't this done decades ago? As far as I understand the computing power decades ago can now easily be reproduced on even a laptop.
From the paper on computation of neutron/proton masses (light hadron masses):A side question then would be how computationally intensive is the full calculation. So do I understand correctly that there are two main approaches, e.g. perturbation and QCD lattice and that quenched optimization is a shortcut for the second approach which is a shortcut to the perturbation method?
So how computationally intensive is it? Wasn't this done decades ago? As far as I understand the computing power decades ago can now easily be reproduced on even a laptop.
Computing the nucleon mass is one of the most expensive calculation done from lattice supercomputers. Not maple on a desktop. Besides, calculating the nucleon mass means that the calculation is not accurate enough to distinguish proton and neutron. There are other calculations dedicated to this differencedesktop computers.
Am I wrong in thinking we can already have similar speeds with NVIDIA's CUDA technology?Blue Gene supercomputers at FZ J¨ulich and IDRIS
and on clusters at Wuppertal and CPT.
Interesting article. Do we know what kind of hardware this was computed with?Computing the nucleon mass is one of the most expensive calculation done from lattice supercomputers. Not maple on a desktop. Besides, calculating the nucleon mass means that the calculation is not accurate enough to distinguish proton and neutron. There are other calculations dedicated to this difference
http://arxiv.org/abs/hep-lat/0608023
Where did you see such claims? I thought the early successes of QCD were all about predicting high energy reactions accurately. Surprisingly, this is much simpler than computing masses. I have a friend who worked on lattice QCD years ago - he likened it to computing weather, only harder.Am I wrong in thinking we can already have similar speeds with NVIDIA GPU's?
Interesting article. Do we know what kind of hardware this was computed with?
The apparent lack of computing power makes me wonder, how were those claims that the Standard Model can accurately calculate the relative masses ever verified say 30 years ago? I guess they were not right?
Calculating the relative masses is a huge part of verifying QCD, but there are many other tests. At energies large compared to the mass of the proton, the QCD coupling is much smaller (what's called asymptotic freedom) and perturbation theory is valid. So a huge body of evidence for the correctness of QCD was the agreement between perturbation theory and experiment at those scales.The apparent lack of computing power makes me wonder, how were those claims that the Standard Model can accurately calculate the relative masses ever verified say 30 years ago? I guess they were not right?
Got ya.Calculating the relative masses is a huge part of verifying QCD, but there are many other tests. At energies large compared to the mass of the proton, the QCD coupling is much smaller (what's called asymptotic freedom) and perturbation theory is valid. So a huge body of evidence for the correctness of QCD was the agreement between perturbation theory and experiment at those scales.