Why don't ups and downs annihilate in nucleons?

[El Hombre Invisible]

Answer me that! Because they should, shouldn't they? Strong attractive forces, attractive EM forces... you'd think nothing would separate them.

 

[chroot]

Up and down quarks are not each others' anti-particles. Up and anti-up, and down and anti-down, are anti-particles.

- Warren

 

[dextercioby]

I think your question would have been much more interesting,if u had asked it referring to the \pi^{0} meson...

Daniel.

 

[El Hombre Invisible]

Hi Warren! Quark-antiquark pairs do annihilate, but what keeps an up from a down (annihilate was a bad word) in a nucleon. They have not one (strong) but TWO (EM) attractive forces between them and yet... never the twain shall meet. What's going on guys?

 

[chroot]

Dexter's suggestion of studying the pi-zero is a very good one. Perhaps I'm wrong, but isn't one of the decay modes of the pi-zero annhiliation?

- Warren

 

[dextercioby]

According to [1],there are a lotta decay modes for \pi^{0},but the most probable by far is

\pi^{0}\rightarrow 2\gamma (98.798\pm 0.032)%

,but other decay modes include

\pi^{0}\rightarrow e^{+}+e^{-}+\gamma

\pi^{0}\rightarrow \gamma+\mbox{positronium}

\pi^{0}\rightarrow e^{+}+e^{+}+e^{-}+e^{-}

and so on...So it's not an annihilation,but a decay...

Daniel.

----------------------------------------------------------
[1]PDG,"Particle Physics Booklet",July 2004,page 28.

 

[El Hombre Invisible]

Jesus. Physicists have the attention span of a- Oh, there's a girl joining the forum, look! I jest... tell me about the meson pie, but if that doesn't answer it and anyone does have any nucleon-based thoughts, chuck them my way too. Does it have anything to do with quantum states? I hate those...

 

[chroot]

\pi^{0}\rightarrow 2\gamma (98.798\pm 0.032)%

Okay, so the pi-zero does indeed annhiliate, and nearly all the time.

So, on to El Hombre's real question: what keeps quarks apart in the nucleon? The Pauli exclusion principle, I presume.

- Warren

 

[juvenal]

Hi Warren! Quark-antiquark pairs do annihilate, but what keeps an up from a down (annihilate was a bad word) in a nucleon. They have not one (strong) but TWO (EM) attractive forces between them and yet... never the twain shall meet. What's going on guys?

The strong force becomes very weak at short distances.

Charged pions can decay weakly, annihilating to a W which becomes an electron or muon + corresponding anti-neutrino.

No mechanism for a u and anti-d pair (or charge conjugate) to decay via EM.

Keep in the mind that baryon number needs to be conserved.

 

[El Hombre Invisible]

So the Pauli (wasn't he in Rocky?) exclusion principal allows a particle-antiparticle pair to occupy the same space, but not two particles? I mean... is nature really going: "Right, I need to get this up and this down in the same place, so- argh no, I can't. It's the Pauli exclusion principal!" Is there some physical reason backing this up or is just a convenient fudge?

 

[juvenal]

Burt Young (from Rocky) indeed fomulated the Pauli Exclusion Principle.

What goes on inside a hadron is pretty complex, and I don't think there is any physicist who has a real good understanding of what's going on.

But anyhow - just because you have attractive charges does not mean that things collapse into each other. Look at the hydrogen atom (proton + electron). You can have bound states due to quantum mechanics.

 

[dextercioby]

There's a related thread...https://www.physicsforums.com/showthread.php?t=68715

Daniel.

 

[El Hombre Invisible]

I'll... come back when I've learned a thing or two about Schroedinger. About 6 years I think.

 

[dextercioby]

A really key subject is group theory...Essential for particle physics.

Daniel.

 

[wangyi]

\pi^{0},but the most probable by far is
\pi^{0}\rightarrow 2\gamma (98.798\pm 0.032)%
\pi^{0}\rightarrow e^{+}+e^{-}+\gamma
\pi^{0}\rightarrow \gamma+\mbox{positronium}
\pi^{0}\rightarrow e^{+}+e^{+}+e^{-}+e^{-}

these can all be taken as annihilation, because imagine u and \bar{u} collide, what will be produced? we can work out the ratio, and find the
IR-safe cross section ratio is nearly the same value.

 

[El Hombre Invisible]

Well, my next question was going to be: why should the Pauli exclusion principal apply (as opposed to why do we need it to apply)? Why is it that an electron and positron, or quark and corresponding antiquark, or two photons can meet but not an up and a down, or an electron and a nucleus? In the former, the energies of each particle are equal and their charges add to zero, while in the latter either the masses or charges or both are different. If two particles of equal energy and opposite but unequal charge were combined, charge would not be conserved. Does this make a difference?

 

[masudr]

El Hombre,

the main thing is all energy eigenstates (and since *all* states are given by linear combinations of these eigenstates, we can get *all* the possible states) are given by the solution of the time-independent Schrodinger equation. The solution of this equation will show that even the lowest energy state corresponds to both particles existing without them "hitting" each other.

 

[dextercioby]

Actually the Pauli exclusion principle (more general,the symmetrization principle) cannot apply,because the particles involved in the nucleon are not identical...

Daniel.

 

[El Hombre Invisible]

Good point, Daniel. The exclusion principal cannot stop an up and a down cohabiting a point in spacetime. But it can prohibit two ups. Why? Physically, I mean. Has anyone come up with a physical theory for the exclusion principal.

Hi masudr - like I said... I need to learn a thing or two about Schroedinger. But again... why? Some guy with crazy hair cannot be the reason why matter does not collapse in on itself. I mean, if you placed a proton near to an electron with both at rest, because they are free particles they would (would they not) form a neutron. What is it about atomic electrons that overcomes the EM attraction? Where does a quantum state come from?

 

[dextercioby]

Good point, Daniel. The exclusion principal cannot stop an up and a down cohabiting a point in spacetime. But it can prohibit two ups. Why? Physically, I mean. Has anyone come up with a physical theory for the exclusion principal.

Nope,for now,there's no theory whose consequences would include the 6 axioms of nonrelativistic QM,symmetrization principle (sic!) included...

Hi masudr - like I said... I need to learn a thing or two about Schroedinger. But again... why? Some guy with crazy hair cannot be the reason why matter does not collapse in on itself. I mean, if you placed a proton near to an electron with both at rest, because they are free particles they would (would they not) form a neutron.

Nope,most certainly not.Depending on the energy of the incoming electron,the scattering of an electron off a proton can be very different;at high energies,the electron would penetrate the proton & would scatter off the 3 quarks.

What is it about atomic electrons that overcomes the EM attraction? Where does a quantum state come from?

The principles of quantum mechanics give the answer to why the hydrogen atom doesn't collapse under coulombian attraction between the electron & the proton.

Daniel.

P.S.Are u a girl?(reference to an earlier post)

 

[jtbell]

Why is it that an electron and positron, or quark and corresponding antiquark, or two photons can meet but not an up and a down, or an electron and a nucleus?

Let's consider the possibilities. If the process takes place at all, it has to take place via the electromagnetic, strong, or weak interaction.

It can't be the elctromagnetic interaction because the up and down quarks, or the electron and proton, aren't a particle-antiparticle pair.

It can't be the strong interaction, because gluon exchange changes only the color (red/green/blue) of a quark, not its flavor (up/down/charm/strange/top/bottom). So for an "annihilation" into a gluon to take place, you'd have to have (I think) a quark and antiquark of different colors.

It can't be a weak-interaction annihilation into a Z^0, because that requires a particle-antiparticle pair like with the electromagnetic interaction.

It can't be a weak "annihilation" into a W because that requires a combination like an up and an anti-down, or an electron and an anti-electron-neutrino (note the particle and antiparticle are different types, and the charge adds up to +1 or -1).

These combinations come from the rules for constructing Feynman diagrams for the various interactions, which in turn come from the fundamental assumptions about how the interactions work, that is, what kind of gauge invariance produces them.

 

[El Hombre Invisible]

Nope,most certainly not.Depending on the energy of the incoming electron,the scattering of an electron off a proton can be very different;at high energies,the electron would penetrate the proton & would scatter off the 3 quarks.

So neutron decay is not a reversible process? I'm talking a direct hit here... one dimensional kinematics.

The principles of quantum mechanics give the answer to why the hydrogen atom doesn't collapse under coulombian attraction between the electron & the proton.

So what you're saying here is that Schroedinger must be correct because Schroedinger said so? I have no problem when somebody says something DOESN'T happen in ACCORDANCE with quantum theory, but I have trouble when somebody says something CAN'T happen BECAUSE of quantum theory.

P.S.Are u a girl?(reference to an earlier post)

To which earlier quote are you referring, miss?

 

[El Hombre Invisible]

It can't be the elctromagnetic interaction because the up and down quarks, or the electron and proton, aren't a particle-antiparticle pair.

Eh? Since when are EM interactions restricted to particle-antiparticle pairs?

 

[dextercioby]

So neutron decay is not a reversible process? I'm talking a direct hit here... one dimensional kinematics.

Yes,neutron decay is not reversible..."A direct hit" is called scattering (the quantum term for 'collision').Mott,Coulomb,Rutherford,inelastic,all are scatterings...

So what you're saying here is that Schroedinger must be correct because Schroedinger said so?I have no problem when somebody says something DOESN'T happen in ACCORDANCE with quantum theory, but I have trouble when somebody says something CAN'T happen BECAUSE of quantum theory.

To me the two ideas are synonimous...

To which earlier quote are you referring, miss?

I take it that you're not a girl...

Daniel.

 

[dextercioby]

Eh? Since when are EM interactions restricted to particle-antiparticle pairs?

Of course not.Incidentally,the \pi^{0} 2 photon decay mode is an electromagnetic process...Neutron decay is weak.

Daniel.

 

[jtbell]

I'm considering first-order Feynman diagrams with a single vertex here. When most people talk about an "annihilation" via the EM interaction, they're talking about a particle and antiparticle producing a (virtual) photon.

 

[dextercioby]

If you're talking about pair annihilation in QED,both the 2 incoming particles (lepton-antilepton) and the 2 outgoing photons are very real...

It may be true that the single vertex in QED can be interpreted as an incoming lepton & an incoming antilepton annihilating into a virtual photon,but i don't recall any process in which this could be really happening...

Daniel.

 

[juvenal]

So what you're saying here is that Schroedinger must be correct because Schroedinger said so? I have no problem when somebody says something DOESN'T happen in ACCORDANCE with quantum theory, but I have trouble when somebody says something CAN'T happen BECAUSE of quantum theory.

All theories that we learn in college and grad school, such as quantum mechanics, relativity, and quantum electrodynamics, are correct in the sense that they yield more accurate experimental predictions than other theories.

Have you taken ANY physics at all? Have you learned about conservation of momentum, for example? That principle is used to make theoretical predictions of experimental phenomena. Do you have a problem with me saying something is incorrect because it violates conservation of momentum?

 

[NEOclassic]

Only free positrons annihilate with real electrons

Eh? Since when are EM interactions restricted to particle-antiparticle pairs?

Hi Hombre,
The annihilation of an anti-proton impinging on a real hydride target is a multiple step process that first produces three pair of +/- pions each of which loses mass that is converted to kinetic energy and which decays to three pair of +/- muons; these also lose mass that is converted to kinetic energy and these ultimately disintegrate into a total of three positrons all of which annihilate, thus producing 6 photons. Note that the last step is the only one where annihilation takes place.
There is a fourth delayed pair of +/- pions that occur because of the kinetic energy of the impinging anti-proton coupled with the electrostatic attraction between these interacting +/- nucleons. See it all in a modern Physics textbook. Cheers, Jim

 

[El Hombre Invisible]

All theories that we learn in college and grad school, such as quantum mechanics, relativity, and quantum electrodynamics, are correct in the sense that they yield more accurate experimental predictions than other theories.

Have you taken ANY physics at all? Have you learned about conservation of momentum, for example? That principle is used to make theoretical predictions of experimental phenomena. Do you have a problem with me saying something is incorrect because it violates conservation of momentum?

Easy, tiger! What I meant was that when an event occurs, its cause is not page 176 of some textbook. You said it yourself: "That principle is used to make theoretical predictions of experimental phenomena." Damn right. The principal is used to make a predication. When we make the prediction that such and such a particle will have such and such a velocity after an event, we can be so sure because it is in accordance with the conservation of momentum. But us knowing about the conservation of momentum ain't the damn reason why momentum is conserved. Likewise, the Pauli exclusion principal doesn't hold just because Pauli discovered it, and certain quantum states aren't allowable simply because Shroedinger says so.

Your counter-example suggests my point was not well made. No - I do not have a problem with you saying something is incorrect because it violates conservation of momentum. BUT nor do I have a problem with you saying something is incorrect because all of the quantum states have already been filled, or such a one isn't allowable. That falls into something working in accordance with quantum theory. But when I ask WHY momentum is conserved, the answer is not the conservation of momentum.

I am a physics undergrad. Isn't that enough for you? Now I feel so inferior.

 

[El Hombre Invisible]

Also, note I said "but I have trouble when somebody says ...", not "I have a problem with people who say...". As in: I personally can't accept that and process it and be satisfied. Not as in: I'm going to pick a fight with ANYONE who DARES say that to me! Okay? Now have another cup of coffee.

 

[juvenal]

But when I ask WHY momentum is conserved, the answer is not the conservation of momentum.

Umm - yes it is. You could talk about the laws of physics being translationally invariant in space (if you've studied Noether's theorem), but then you could ask "Why are the laws of physics translationally invariant in space?" The answer - because they are.

Why do the laws of quantum mechanics hold? Because they do. I don't think any real physicist can tell you that the world HAS to work this way. It just does.

 

[El Hombre Invisible]

The answer 'because it is' is not one I accept. Progress is made because people DON'T just settle for 'because it is'. Why does metal conduct electricity? Because it does? Or because the outer electrons form a sea of particles moving from one atom to another carrying current? Why does matter exist? Because it does? Or because photons can cause pair creation? Why is the speed of light constant in any frame of reference? Because it is? Or because time progresses differently for observers moving at different speeds? If all scientists lumped for 'because it is' then we'd still be living on a flat earth. If you have a problem with me asking 'why', seriously mate it's just tough. Get the flip over it! This is, after all, a physics forum open to anyone to ask questions. Do you go from thread to thread just saying 'because it is'?

 

[dextercioby]

If you know so many answers to difficult questions,why can't u answer the question:why is free space-time homogenous and isotrope...?

Daniel.

 

[El Hombre Invisible]

If you know so many answers to difficult questions,why can't u answer the question:why is free space-time homogenous and isotrope...?

Daniel.

Eh? Are you talking to me? Why are you beating up on me? I never said I knew jack. If I knew so much, why would I be here asking questions? My argument is to juvenile's insistence that I should just accept things the way they are and not ask questions about their meaning is that in the history of our race scientific progress has been made by people not accepting things the way they are and asking why they occur. Is this really such a controversial idea that it warrants instant hostility?

 

[vanesch]

My argument is to juvenile's insistence that I should just accept things the way they are and not ask questions about their meaning is that in the history of our race scientific progress has been made by people not accepting things the way they are and asking why they occur.

Although it is always a good idea to ask questions "why", because it can lead to interesting ideas, you should also understand that, no matter what is the current level of knowledge and understanding, there will ALWAYS be things to which the question "why" has no answer of course...
The basic postulates of our most fundamental theories cannot be justified by an answer to a "why" question ; otherwise they wouldn't be the basic postulates of our most fundamental theories.
This is basic philosophy, or logic, if you like.

cheers,
Patrick.

 

[dextercioby]

There's no direct,logically accurate way to prove certain things.One has to accept some things as being the way they are.That's why he needs axioms...He has to apply the mathematical apparatus upon a model which cannot be created from 0.The model of space or space-time is crucial.

Every physical theory has its axioms,or it should have...

Daniel.

 

[juvenal]

The answer 'because it is' is not one I accept. Progress is made because people DON'T just settle for 'because it is'. Why does metal conduct electricity? Because it does? Or because the outer electrons form a sea of particles moving from one atom to another carrying current? Why does matter exist? Because it does? Or because photons can cause pair creation? Why is the speed of light constant in any frame of reference? Because it is? Or because time progresses differently for observers moving at different speeds? If all scientists lumped for 'because it is' then we'd still be living on a flat earth. If you have a problem with me asking 'why', seriously mate it's just tough. Get the flip over it! This is, after all, a physics forum open to anyone to ask questions. Do you go from thread to thread just saying 'because it is'?

Calm down, dude. There is nothing I said in my post which was meant to be inflammatory. My point is simply that there is no answer to your question of why quantum mechanics describes the universe. And honestly, I don't think that if you were in one of your physics classes and kept raising your hand and asking "Why?" and saying "I don't accept that answer", the professor would say anything much differently than I have. Go ahead - try it.

There are different kinds of "why" questions out there. Some are far, far less useful than others. As I said in my earlier post, no real physicist can tell you why quantum mechanics describes the universe. We accept it as the way the world works. So asking why is a complete waste of time for people here. Maybe there is a deeper truth out there, but if you browse through some old posts, you'll find that only the cranks bother wasting time questioning quantum mechanics.

 

[El Hombre Invisible]

Calm down, dude. There is nothing I said in my post which was meant to be inflammatory.

Uh, no you came down pretty hard just cos I said I have difficulty with something. Either that or you have a pretty loose control of your caps lock key and rhetorical questioning. ;o) No matter. We'll call that a culture clash from one end of the physics student's journey to the other.

My point is simply that there is no answer to your question of why quantum mechanics describes the universe.

No answer is a good answer. "Because it is," to me, is a kind of unscientific, kind of semi-religious answer. I like no answer, but that ain't what you said.

if you were in one of your physics classes and kept raising your hand and asking "Why?" and saying "I don't accept that answer", the professor would say anything much differently than I have. Go ahead - try it.

The moment he answers a question with "Because it is," I will. But he doesn't, so...

no real physicist can tell you why quantum mechanics describes the universe. We accept it as the way the world works. So asking why is a complete waste of time for people here. Maybe there is a deeper truth out there, but if you browse through some old posts, you'll find that only the cranks bother wasting time questioning quantum mechanics.

Well, to me a mathematical formulation of the WAY something works is just that, and it will always be worth pondering why things are as they are, as thinkers have done for millenia, so I'll join the cranks. Has your time on this thread been better spent? ;o)

 

[El Hombre Invisible]

There's no direct,logically accurate way to prove certain things.One has to accept some things as being the way they are.That's why he needs axioms...He has to apply the mathematical apparatus upon a model which cannot be created from 0.The model of space or space-time is crucial.

Every physical theory has its axioms,or it should have...

Daniel.

I asked neither for proof, nor demanded an actual answer. I just asked the question why, and said that "because it is" isn't to me a scientific answer. "No-one knows" I can understand, but when someone says X is true because X is true, my head spins and I get very dizzy, hence I said I have trouble dealing with it. Who woulda thought that sentence could have got me into so much trouble?

Is your thinking that "one has to accept some things as being the way they are" before they've tried to ponder the question, or after they've failed? When you get to the quantum level, do people just stop asking why once they've perfected the mathematical model? I'm genuinelly interested. Having read some Feynman, he did seem to apply physical intepretations to the phenomena the maths described, but twice now I've been quite aggressively steered away from that route.

 

[El Hombre Invisible]

Also, trying to get back to the subject in hand, isn't it a bit different to ask "Why are the laws of physics translationally invariant in space?" and "Why is it that strong and/or EM forces are rendered useless when one particle reaches a certain quantum state?" I mean, in the former you have no reason to believe otherwise, but in the latter there are forces at work that aren't doing their dang job properly so, at the risk of hitting on what appears to be a very touchy area, I still think it's a valid question - i.e. one that, for someone of my (relatively low) level of understanding, might still have expected an answer to. And as no-one of a higher level of understanding has explained to me why, when I reach their level of understanding, I shouldn't expect an answer to it (in particular), I'm still left scratching my head wondering what just happened. Just a thought.

 

[dextercioby]

Also, trying to get back to the subject in hand, isn't it a bit different to ask "Why are the laws of physics translationally invariant in space?"and "Why is it that strong and/or EM forces are rendered useless when one particle reaches a certain quantum state?" I mean, in the former you have no reason to believe otherwise, but in the latter there are forces at work that aren't doing their dang job properly so, at the risk of hitting on what appears to be a very touchy area.(...)

What do you mean by that?


Daniel.

 

[El Hombre Invisible]

Well, the above example has kind of been rendered useless. Since I last posted on this thread I read a little of Feynman's lectures vol 2 which explains precisely the phenomena I was asking about. Here's my (layman's) understanding of it: the uncertainty principal says that as the distance between the electron and proton decreases, the position of each becomes more certain and so the velocity of the electron becomes more uncertain. This uncertainty, as I understand it, makes it more likely that the electron has some velocity sideways to the direct route so when it reaches close to the proton a kind of slingshot effect is observed - scattering. Is this a reasonable layman's explanation?

I assume a similar explanation can be used for ups and downs. In essence, could it be said that the gross improbability of an actual direct route between two points known with 100% certainty is what really stops electrons combining with protons under normal conditions? Where the certainty of position can be reduced, such as if it were not known which of many protons the electron was going to combine with, the combination can still take place. I'm referring of course to neutron stars here.

I no longer have a good example to explain my last post. Sorry. Forget I said it. Twas a balls statement.

 

[masudr]

..."because it is" isn't to me a scientific answer.

Well what is a scientific answer? We look at a huge array of experimental results and strive to create a neat mathematical framework which will reproduce these results starting from some principles. While the "starting principles" (axioms, if you will) may be of a more fundamental nature (and considerably simpler) than the phenomena it describes, you can always ask, why are these principles what they are? I can only answer "because it is." If I find a reason for it, then I have only delegated the explanation of the principles to another more fundamental set of principles, which aren't explainable themselves.

You can always ask "why are Maxwell's equations of this form." I can write down an even more fundamental equation which encodes 4 of Maxwell's equations in one, using the language of differential geometry, which to me is more fundamental . But when you realize that the same people who knew Maxwell's equations also developed differential geometry, it is less a coincidence.

 

[dextercioby]

Two equations.See Felsager [1] for details.

Daniel.

--------------------------------------------------------
[1]B.Felsager,"Geometry,Particles and Fields",1983.

 

[masudr]

I don't have quick access to Felsager at the moment, but you are (as usual) correct. Am I correct in saying these are the correct equations:

Defintions:
A^\mu=(\phi/c,A_x,A_y,A_z)
j^\mu=(\rho c,j_x,j_y,j_z)
F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu

Equations:
F^{\mu\nu} {}_{,\nu}=\mu_0 j
F_{\mu\nu,\lambda}+F_{\lambda\mu,\nu}+F_{\nu\lambda,\mu}=0 (\mu\ne\nu\ne\lambda)

 

[El Hombre Invisible]

Masudr: we have, I guess, a difference in philosophy, and only time will tell me exactly how uninformed mine is. For instance, why is the amount of energy in the universe what it is? That's a fairly fundamental question, and I predict your answer is "because it is", whereas I would say "no-one knows" (unless someone does, in which case this is a really bad example). There is no doubt no end to the list of such questions, I agree. The amount of energy in the universe may be a consequence of its starting conditions. Answering it would lead to more questions which in turn may or may not be answerable. But, to me, this is still a matter of the limits of knowledge. There is surely a difference between not knowing the answer and there not being an answer. I so far have no reason to believe that the phenomena discussed in this thread will never be physically explained, and if you do then please explain because it's this ignorance that's causing me grief.

"why are these principles what they are? I can only answer "because it is." If I find a reason for it, then I have only delegated the explanation of the principles to another more fundamental set of principles"

And is this not indeed the history of scientific endeavour? We accept laws before we can explain them, but still strive for the explanation, be it Newton's laws of gravity, the constancy of the speed of light, the nature of the periodic table... I guess I see an unexplained phenomenon as pending the indefinite discovery of a physical explanation. If you answer a question with "because it is" due to no other available answer, and then some discovery is made to explain the phenomenon, then the answer "because it is" prooves misleading with hindsight. I would have thought that this was just cause enough not to give the answer in the first place.

I feel I'm coming across as unfairly demanding answers to unanswerable questions - believe me, I'm not. But "because it is" seems to lead to an investigative dead-end. In your quote above, you hint yourself that what is currently deemed a fundamental property of the universe may well turn out not to be so fundemental. If questions are not asked about why such properties are as they are, or if they are discouraged as they have been here, I would have thought we'd never know. Hence it seems unscientific to me.

It does seem the raison d'etre of quantum mechanics is to explain more how things happen than why, in which case forgive me if my questioning falls outside its scope. Whether you call the questioning physics or philosophy, I still don't understand why so many people see no worth in asking the questions. I keep no secret of my ignorance of quantum theory, but the practise of not seeking answers to why things are as they are is one that I fail to understand the justification of.

Daniel: thanks for the link but, being a mere undergrad, I fear that will go waaaay over my head (description says it's a post-grad level volume), hence my hope for an answer nearer layman's terms. To which part of my post does your reply refer? What is explained by two equations?

 

[dextercioby]

I don't have quick access to Felsager at the moment, but you are (as usual) correct. Am I correct in saying these are the correct equations:

Defintions:
A^\mu=(\phi/c,A_x,A_y,A_z)
j^\mu=(\rho c,j_x,j_y,j_z)
F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu

Equations:
F^{\mu\nu} {}_{,\nu}=\mu_0 j
F_{\mu\nu,\lambda}+F_{\lambda\mu,\nu}+F_{\nu\lambda,\mu}=0 (\mu\ne\nu\ne\lambda)

Masud,i think you may have meant (using your column notation,though in that case u should have defined the 2-form "F" using the same column notation) (in c=1 from SI-mKgs units)

F^{\mu\nu}{}_{,\nu}=j^{\mu}

F_{\left[\mu\nu,\lambda\right]}=0

and again,i infer you to Felsager for their geometrical form.Or you prefer the first chapter from Carrol's notes on GR posted online ?

Daniel.

 

[El Hombre Invisible]

Oh. That wasn't meant for me. I will leave you to Maxwell. Sorry. [sniff] One day I'll know what that meant.

 

[masudr]

Daniel,

Yes, the notes I had were slightly sloppy in that they didn't maintain the column (or "up") notation throughout etc. And the antisymmtrization bracket is much neater than the 3 separate terms. My knowledge of differential geometry isn't good, but I'm slowly getting there.

On that note, El Hombre, I am too only an undergraduate, and my lack of knowledge is what makes me want to learn more! So give the text a go, there's nothing like giving it a good try.

Masud.