Physics Help Forum Proca Equations and nonzero mass of photon

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Dec 4th 2015, 06:19 PM   #21

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I'll have to get back to you sometime tomorrow. I'm not doing well at the moment. But a few quick comments:

 You appear to keep thinking of this as a problem in quantum mechanics when you keep referring to spin. This is a problem in classical electrodynamics.
The Proca equation is the wave equation for a spin 1 particle. Of course I'm talking about it in terms of QM! The solutions are wavefunctions, which are not Classical Physics. Would you talk Classically about the Dirac equation? There is nothing Classical about it.

 Actually there is a name for the Proca Lagrangian with m = 0. It's called the Lagrangian for the EM field. When the Proca Lagrangian is plugged into Lagrange's equation its called the Proca equation
Yes.

 The Proca Lagrangian only applies to the electromagnetic field and nothing else. And it only applies to the EM field if its found that the proper mass of the photon is not zero. It can't be used for the W's and Z of the weak nuclear force because its not defined for them.
The Proca equation is the wave equation for a spin 1 particle. Any spin 1 particle be it massive or massless. Yes, when we set m = 0 you get Maxwell's equations. I'm not arguing against that. But if m is not 0 then we don't have the Maxwell equations.

I really don't understand where the confusion is. If there is no mass in the Proca equation then the particle behaves like a spin 1 massless particle, in this case the only known elementary example that I'm aware of is the photon. If it has a mass then we have a new term in the Proca equation and the particle behaves as a spin 1 massive particle. The only (again elementary) examples I know of these are the W and Z bosons. If you want to introduce a mass for a photon then the photon wavefunction is given by the massive Proca equation as well.

I don't want to get into a war about who has the better sets of reference material but I have three texts that say exactly what I just said above. And I had two more references when I was working on my Masters in Electroweak theory.

I'll try to reply in more detail tomorrow. Maybe then we can see why we disagree.

-Dan

Addendum: This might interest you. Section 2 is a quick rundown of the the main Relativistic wave equations. Specifically refer to section 2.4 and a comment at the end of section 3.
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Dec 5th 2015, 01:19 AM   #22
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 Originally Posted by topsquark Of course I'm talking about it in terms of QM! The solutions are wavefunctions, which are not Classical Physics.
That is totally incorrect my dear friend. The solutions are not wave functions. In the event that the result is a wave then it's a classical wave, not a wave function. E.g. if you set m = 0 then the solution is Maxwell's equations. It need not even be a wave. It could be a static EM field in fact.

 Originally Posted by topsquark The Proca equation is the wave equation for a spin 1 particle. Any spin 1 particle be it massive or massless.
That is absolutely wrong. The solution is MAXWELL'S EQUATIONS (ME). You can't claim that ME use any other particle to carry the EM field other than photons. Where are you getting this ideas from Dan? Please read Jackson on this to learn what it's actually all about.

In the mean time see: https://en.wikipedia.org/wiki/Proca_action
 Originally Posted by Wikipedia The field involved is the 4-potential Aμ = (φ/c, A), where φ is the electric potential and A is the magnetic potential. The Lagrangian density is given by:... The field transforms like a four-vector, but consists in contrary to electromagnetism generally of four complex valued functions.[3] When m = 0, the equations reduce to Maxwell's equations without charge or current.
In contrary to this you hold that the equations will reduce to something else if m = 0. What is it that it reduces to in your mind?

 Originally Posted by topsquark Yes, when we set m = 0 you get Maxwell's equations. I'm not arguing against that. But if m is not 0 then we don't have the Maxwell equations.
But what you're failing to grasp is that the solutions are still the electromagnetic equations. The only difference is that it applies to electrodynamics when the photon has non-zero proper mass.

 Originally Posted by topsquark I really don't understand where the confusion is.
The problem is that you appear to think that the solution yields something other than the equations for electrodynamics with non-zero photon mass.

 Originally Posted by topsquark I don't want to get into a war about who has the better sets of reference material but I have three texts that say exactly what I just said above.
All that I'm doing is asking you to read the section on the Proca Lagrangian in Jackson's text so we can discuss it. I don't believe any other text will say that will differ.

Dan - This isn't a war. All we have here is a disagreement. I might just be wrong but I don't change my beliefs because you or someone else tells me to. I only change my belief when I'm convinced that I'm wrong. And if I'm wrong then it's extremely important to me to find out. That's what I'm asking you to do, i.e. have the patience to do what I'm doing and remaining polite and discussing it. I will not make this into a war and I can't believe that you'd make it into one either.

I've been using terms like "I can't believe that you think that way etc." I beg you to have patience with me. I'm not trying to diss you. I just don't want to take a lot more time writing responses because I spend a great deal of time trying to phrase it better. Okay buddy?

Best wishes my friend,
Pete

ps - If you're ill then I hope you feel better. Get well soon.

Dec 7th 2015, 07:28 AM   #23
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 Originally Posted by topsquark I Googled this and only found an argument for an imaginary mass. Is this what you are talking about? Or are you solving the Proca equation with a photon mass to a first approximation? -Dan
Dan - You stated below that you studied this in grad school. As such you shouldn't have been so confused about what a non-zero proper mass is and how it applies to the Proca Lagrangian. Also from the opening post it's 100% clear that he's referring to classical physics whereas all the arguments you presented are from field theory. This appears to be the cause of our disagreement. I.e. it appears that you never knew or studied the Proca Lagrangian in classical electrodynamics.

Dec 8th 2015, 03:32 PM   #24

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 Originally Posted by Pmb Dan - You stated below that you studied this in grad school. As such you shouldn't have been so confused about what a non-zero proper mass is and how it applies to the Proca Lagrangian. Also from the opening post it's 100% clear that he's referring to classical physics whereas all the arguments you presented are from field theory. This appears to be the cause of our disagreement. I.e. it appears that you never knew or studied the Proca Lagrangian in classical electrodynamics.
I haven't read through all the posts yet, but this last one seems to cover it for me. No, I never covered the Proca equation in Classical EM. I've never encountered the concept of a Classical "matter wave" before. But hey, the equations can be derived so who am I to say?

The key point here for me is that you were referring to massive "photons." I don't think about photons Classically and I had thought that ended with Young's double slit experiment. So the only discussion I had thought of was naturally QM.

By the way, I never had any ill thoughts. If I had then I would have PMed you about it. No worries.

And yes, I'm doing a bit better now. I had a rude shock on Friday that I'm still trying to get over. Thanks for asking!

-Dan
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Dec 11th 2015, 10:15 PM   #25
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 Originally Posted by topsquark I haven't read through all the posts yet, but this last one seems to cover it for me. No, I never covered the Proca equation in Classical EM. I've never encountered the concept of a Classical "matter wave" before.
There's no such thing. The Lagrangian density is just like the Lagrangian density for the EM field in classical electrodynamics. That's why I raised an objection. Before you mentioned it I never knew that this Lagrangian was used in field theory. Thank you for that.

 Originally Posted by topsquark But hey, the equations can be derived so who am I to say?
No worries my dear friend. Nobody's perfect and nobody has read all books and papers in physics, so your allowed.

 Originally Posted by topsquark The key point here for me is that you were referring to massive "photons."
That's right. The purpose of the Proca Lagrangian in classical EM is to take into account the proper mass of a photon if it was ever discovered that it was different from zero. That's what's discussed on page 7 of Jackson's EM text (3rd Ed.).

 Originally Posted by topsquark By the way, I never had any ill thoughts. If I had then I would have PMed you about it. No worries.
Excellent my friend, excellent!

 Originally Posted by topsquark And yes, I'm doing a bit better now. I had a rude shock on Friday that I'm still trying to get over. Thanks for asking!
I'm so glad to hear that. And you're welcome.

- Pete

 Tags equations, mass, nonzero, photon, proca