Dirac Sea

This is a question on an idea I had. I've been doing work on Dirac's Equation, and the topic of the infinite sea came in, and I postulated the following:

What if to every virtual particle pair in the vacuum there is a corresponding entangled virtual particle pair?

So to every two virtual particles, there may exist two more virtual particles which are virtually-connected via entanglement?


I postulate this cocnerning the Dirac Sea. This would mean that when two particles appear from the vacuum, there remains two virtual particles in vacuum that remain closely connected to the real particles pervaiding the vacuum. To stop a degeneration in the energy levels of the electron so that it stopped from falling back into the vacuum?



As I understand the discontent among scientists concerning the issue of the Dirac Sea, is that it has an infinite amount of energy in this sea; and so to neutralize it, you require an infinite amount of positive energy as well in the form of a proton sea. This is disturbing as it requires a mathematical proceedure called renormalization which Dirac was never fully happy about, including many scientists still alive today.

If there was an extra two virtual particles always in entanglement, my question is if this can resolve the electrons from falling back in the vacuum - we would not have to deal with an infinite amount of electrons, but beleive that initially before any appeared in the universe, there where twice as many electrons in the visible universe.

 

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I'll say this as nice as possible, you haven't. In this thread you admit you've never worked with natural units before. You can't even formulate simple wave expressions and do partial derivatives for scalar expressions, so I don't for a second think you're capable of extending this to spinor expressions, as they are more complicated than vectors, which are more complicated than scalars, which you can't manage to do properly.

How precisely did you arrive at this 'postulation'? Did you actually do anything with the Dirac equation or did you just read some wordy explanations and just decide to combine two concepts you've read about?

The proton has nothing to do with it. Originally when Dirac realised there would be a particle of opposite charge he thought it was the proton, as no one else knew of any other positively charged particles but it was actually the positron, which was discovered the following year. The Dirac sea was a way of interpreting quantum field theory predictions which has seen stopped being considered the correct way to look at things. We don't view a positron as a 'gap' in the electron field, we view it as a particle in its own right, there's nothing special about normal matter.

Renormalisation is not due to the 'proton sea' or the 'dirac sea' or neutralising positive energy. Renormalisation removes the infinite vacuum energy from a calculation but it doesn't do it by 'neutralising' anything, that's a physical process. It does it by removing the irrelevant vacuum energy from the prediction.

Like I said at the beginning, I'll say this as nice as possible, stick to the simple stuff. If you're struggling to do even basic differential equations and vectors then by jumping to trying to do stuff with the Dirac equation you're only deluding yourself and you'll only harm your own learning because you'll either utterly fail to understand what you read or worse, you'll think you do and really you don't. There's a reason the Dirac equation doesn't come up in physics courses until the 4th year, it requires considerable knowledge and experience with simpler quantum mechanical concepts and mathematical methods. You'll advance a lot lot faster by not jumping ahead of where ever you are currently. This forum (and the internet in general) is littered with people who didn't want to do the simple, required 'boring' stuff like vector calculus and wanted to do black holes and quantum gravity, which they cannot actually do. I have yet to meet anyone who can actually do anything related to black holes or quantum field theory who skipped ahead of the 'boring' stuff.

 

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Emmm... Don't start twisting my words sir. I have been doing work on it. My own personal investigation into it. That is work nonetheless.

Alphanumeric, do not start to talk to me like the others here. If you do, I will do to you what I did to guest. Ignore mode, it's an excellent action in some cases.

''The proton has nothing to do with it. Originally when Dirac realised there would be a particle of opposite charge he thought it was the proton, as no one else knew of any other positively charged particles but it was actually the positron, which was discovered the following year. The Dirac sea was a way of interpreting quantum field theory predictions which has seen stopped being considered the correct way to look at things. We don't view a positron as a 'gap' in the electron field, we view it as a particle in its own right, there's nothing special about normal matter.

Renormalisation is not due to the 'proton sea' or the 'dirac sea' or neutralising positive energy. Renormalisation removes the infinite vacuum energy from a calculation but it doesn't do it by 'neutralising' anything, that's a physical process. It does it by removing the irrelevant vacuum energy from the prediction.''

That's all very nice, but is the idea consistent?

''How precisely did you arrive at this 'postulation'? Did you actually do anything with the Dirac equation or did you just read some wordy explanations and just decide to combine two concepts you've read about?''

How did I arrive at it?

Entanglement as I am sure you know, involves connected particles quantum mechanically, and, it also involves particle pairs - one system is connected to another system, if the two where created from the same source. If antiparticles truely do not come in pairs, and if there is always another two virtual particles in the vacuum, then all four particles can be quantum mechanically-connected, or atleast, I would have presumed so.

 

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... scrap that.

[edited]

 

If it's anything, I also remembered another reason, or inspiration if you like, concerning the four-entanglement.

This was based on Susskinds work cosncerning that quarks do not come individually, but always by pairs or more.

In the same sense, I applied the same reasoning to the wave function. Not only does a single particle come with an antiparticle, even those particles come with virtual antiparticle-particle pairs.

My question is very simple. Is the idea consistent or flawed? One problem might be, is if there is no infinity in the equations, would this result in a constraint where electrons can show up, in their real forms? If there is atleast a small amount of spacetime where the virtual particles do not fill, will this place a crucial limit for instance, on where real particles can show up?

 

What precisely is this 'personal investigation'? If you can't do the mathematics than you are only able to 'investigate' it by reading other people's wordy explanations of their investigations. Even if you could then reach a viable qualitative conclusion you have no way of examining whether or not your conclusions are true as you're unable to examine the equation's mathematical properties.

There's nothing wrong with reading about it or finding out how its used by physicists or the formulation in terms of mathematics but if you think you're investigating it in the way someone writing research papers on it would then you're deceiving yourself. This isn't me trying to twist words or be rude, its just a bit of advice that I'm sure a great many people who do research into the Dirac equation will agree with.

This is hardly the way to behave if you're intellectually honest. I've been through the whole process of learning about the Dirac equation and I know many people who have done it too, so I know from first and second hand experiences that you're not going to do anything worthwhile if you aren't willing to put in the effort for the basics. There's a reason advanced university courses often have 'required courses', without the basic fundamentals understood then someone cannot do the more advanced material which builds on them.

If you think that this is such an insulting thing for me to say that it warrants putting me on ignore than you really need to consider what it is you want to do, do you want to learn something or just appear to learn something? Its no skin off my nose if you want to do the latter though.

Renormalisation? Yes. And its not 'all very nice', as my point was that you were mistaken about the development and meaning of the things you mentioned. Do you now accept that you were mistaken or do you wish me to explain further? I just don't want you to brush off my correction and ignore it, as its only hurting your own learning if you do that.

Why are you talking about 4 particles? The entanglement would be between the two particles created in pair production. Other pairs need not be involved, though it is possible occasionally they might interact and form entangled systems for a while.

This illustrates my point, in order to examine entanglement in quantum field theories you're going to need to know some quantum field theory, non-relativistic quantum mechanics and entanglement. Entanglement in non-relativistic quantum mechanics has particular properties which can be formulated nicely in terms of the bra-ket notation so if someone were to attempt to describe in any non-arm waving away entanglement in spinor fields of quantum field theory they'd need to demonstrate similar structures to the non-relativistic case are formed when pair production occurs.

In the case of your claim you'd need to demonstrate that not only does pair production produce entangled pairs but it produces entangled pairs of entangled pairs! Even in the simplest examples you can get different types of entanglement, depending on which particles entangle with which. The GHZ state \(\frac{1}{\sqrt{2}}\Big( |000\rangle + |111\rangle \Big)\) and the W state \(\frac{1}{\sqrt{3}}\Big( |100\rangle + |010\rangle + |001\rangle \Big)\) are both 'maximally entangled' triplets of qubits but they are not equivalent. This only gets worse as you increase from qubits to qudits and triplets to arbitrary numbers. Hence 'investigation' into entanglement in quantum field theory pair production would need to be very precise and methodical. If you lack the knowledge to be able to do the details then there's very little investigation you can do.

My advice, speaking from personal experience, is you start with non-relativistic quantum mechanics, understand formal entanglement properties in it and then move onto quantum field theory (and that's assuming you also learn all the required things for those!). Of course the only person's time you'll be wasting if you don't is your own but if you aren't just wanting to appear well read but to actually be well read then you'll heed my advice.

Pair production and colour confinement are two different things, other than if you put enough energy into a system to pull colour charges apart you 'snap' the gluonic flux tube and you get more quarks via pair production. Pair production facilitates colour confinement but it doesn't cause it. And quarks don't come in matter-antimatter pairings always, that's only for mesons. Baryons have 3 quarks, so you can't have pairings in that. The reason for the pairings and triplets of quarks is their colour, not what you're implying.

Again, if you read up on the basics before making conclusions you will make less flawed conclusions.

I think you need to first get your head around the a 'virtual' particle is.

You've skipped ahead and now making mistake after mistake. Yes, it takes people doing this stuff full time 3~5 years to get to quantum field theory but there's a reason for that, just as there's a reason universities teach quantum field theory after quantum mechanics, special relativity, electrodynamics, linear algebra and vector calculus, QFT is very complex and requires an understanding of a great many areas of maths and physics. Without that understanding you aren't going to get far, even if you manage to convince yourself otherwise.

 

I will be back and forth a lot tonight, I will try and answer these many questions before the night is over.

 

What precisely is this 'personal investigation'? If you can't do the mathematics than you are only able to 'investigate' it by reading other people's wordy explanations of their investigations. Even if you could then reach a viable qualitative conclusion you have no way of examining whether or not your conclusions are true as you're unable to examine the equation's mathematical properties.

There's nothing wrong with reading about it or finding out how its used by physicists or the formulation in terms of mathematics but if you think you're investigating it in the way someone writing research papers on it would then you're deceiving yourself. This isn't me trying to twist words or be rude, its just a bit of advice that I'm sure a great many people who do research into the Dirac equation will agree with.

May I take you attention sir to this lecture:

http://www.youtube.com/watch?v=wUySvFEwmj8&feature=related

This has been my fourth source so far, but yet, one of the most illuminating yet so far, as the lecture take the avid listener to the derivation of the dirac equation. Many of my questions recently have came from this lecture, and it was here the dirac sea was mentioned and with some interesting conversations on the mathematics behind it.

I don't find this particular lecture one which I understand quite well, minus a few things - but, nevertheless, the derivation of the Dirac Equation uses some matrix analysis, which I didn't find too hard to understand.

This is hardly the way to behave if you're intellectually honest.

Sir to be honest, I'd rather not put you on ignore. I don't see much good from it, I just want a bit of leniency... All I want is to learn, and hopefully test my idea to a scientist like yourself. But all I ask is if it is kept civil... surely this is not too much to ask?

Renormalisation? Yes. And its not 'all very nice', as my point was that you were mistaken about the development and meaning of the things you mentioned. Do you now accept that you were mistaken or do you wish me to explain further?

I totally accept I was wrong... I can show you why I was mistaken. I read a source about there being required a positive energy which must cancel out the negative energy, but I assumed this involved a proton sea. If you look above, one of my posts was scrapped - I thought I was seeing it in the right light, but after a third time looking over it, I now realize you where unconditionally-correct.

Why are you talking about 4 particles? The entanglement would be between the two particles created in pair production.

Well, I speak of four particles, because indeed, two particles are created in pairs, and if the dirac sea is a vacuum filled with virtual particles, I assumed by a hypothesis at best that there could be a possible extra two particle entanglements in order to satisfy there entangled state to never degenerate back into the vacuum, using pauli spin matrices and entanglement, the latter here I thought might be important, as so that if the do try to degenrate, that is, either the normal or antiparticle with have corresponding virtual particles always there to ''oust out'' their attempts to fill energy states in the vacuum.

Other pairs need not be involved, though it is possible occasionally they might interact and form entangled systems for a while.

Again, I did so, because by my hypothesis/theory there will be two virtual particles in the vacuum always corresponding to the real particles that are also in entangled states.

Understand me??

Pair production and colour confinement are two different things

I was not clear enough, this is my fault. I meant this is an analogy, of my inspiration, not that I meant color charge was necessery in the hypothesis - it was just an inspiration in idea.

I think you need to first get your head around the a 'virtual' particle is.

Well, I do know that they do not follow the normal energy-mass relativistic laws. They exist in real spacetime for limited times, but they still return to vacuum - i think.

The short span in which virtual particles can appear does not follow the energy-momentum relationship, meaning that they can move faster than light in some cases.

What part of my misunderstanding, can you help me learn here?

 

Did you give up on this discussion alphanumeric?

I truely wanted the stamp of approval if it's possible.

 

Then I could worry about a mathematical side of it with entangled particles and Pauli Matrices describing their respective spins and how they related to four-entanglements.

 

So first you don't want to hear what I have to say because you think I'm such an arrogant arse you'd put me on ignore and decided to leave and now you want my comments? No doubt if I don't say what you want to hear you'll not what to listen.

Yes, you want someone to strengthen your self delusion, as if you're seen to be using technical words then maybe someone will think you actually understand them.

Sure you did.... The fact you don't know any calculus, you can't do basic algebra, you don't understand tensors and you have repeatedly mixed up vector and scalar expressions demonstrates you didn't understand 'some matrix analysis'.

Two particles is a pair. They are paired with one another, not two other particles.

Let's see your working/thoughts involving the Pauli matrices. Don't arm wave, I previously asked you to provide the details of your 'thoughts' and explained why superficial work is not going to get very far or lead to anything concrete. Demonstrate, quantitatively, clearly and explicitly using the things you've mentioned, why four particles are needed. What precisely needs to be 'satisfied'?

Let me make that clear, I don't want you to answer with a paragraph of arm waving, I want you to show, using algebra, how you arrived as your conclusion. You mentioned Pauli spin matrices so I want to see precisely what you've done in terms of them. You brought them up and now I want you to put your maths where your mouth is.

You appear not to know what 'virtual' means as you've just used it in an incorrect manner.

Justify that claim. And like I just said, don't just spout some wordy bullshit, I'm not going to facilitate you deluding yourself into thinking you're doing science by allowing you to just spout buzzwords, I want you to back up your claims and justify your 'hypotheses'. Clearly you want to be involved in discussions which use lots of technical words and I firmly think its because you want to be seen to be talking about high level stuff in order to appear like you know and understand high level stuff. If you actually know high level stuff you shouldn't be needing to just do arm waving, you should be able to provide copious amounts of quantitative workings and if you can't do that and you just spout arm waving nonsense then don't whine when you get bitch slapped for spouting crap.

Understand me??

And how in any way does that link to your 'hypothesis' about four particles being entangled?

I don't for a nanosecond think you can do anything quantitative relating to those things, as your other threads on attempting to do mathematics have demonstrated repeatedly. If you think I'm wrong demonstrate as much, show that you aren't just desperately trying to convince people (yourself most of all) that you can do these things by dropping buzzwords left, right and centre. You do that and I'll play nice. If you come back with absolutely nothing to justify your claims and nothing that demonstrates your supposed understanding of Pauli matrices, matrix algebra and the Dirac equation then don't be surprised when people think you're just blow smoke out your backside.

 

I will listen, if you have anything other to say, than making out the other person to be a liar. I said I understood the matrix computations. I have done some matrix work in the past, I understand how to multiply matrices, even by row or column vectors. But when you sit there and say ''no you didn't'' - I can't help but feel you are quite accusationally calling me a liar.

 

Besides, I've taken some classes in physics. You'd be pretty surprised if some had, but was not able to do matrix-calculations. Afterall, it's practically part-and-parcel of QM.

 

Bingo.

When you can actually demonstrate you can do anything other than flail your arms and spout buzzwords let me know.

 

I don't feel threatened one bit. I know I can do matrix computations.

 

Then lets see you respond to my requests you actually show you can do anything related to the Pauli matrices. You brought them up and I've asked you demonstrate your claim you can do them and that you've been 'investigating' the Dirac equation in a way which is more than just reading wordy explanations.

Can you do anything more than just arm waving and desperate attempts to convince people you can do mathematics while not doing any mathematics?

 

Well no, I don't know much about Pauli Matrices, only that they are matrices. I've read up on them a few times, but I forget their details. No, I wan't talking about that, and you know fine well.

You called me a liar when I said I understood the matrix calculations. I did not lie, I know how to multiply matrices together, get their time-advanced forms, multiply matrices with row and column vectors. I've even been taught a little on subspaces in matrix algebra. I have a problem when you call me a liar when I know fine well I am not.

 

And you know fine well the lecture I took you to was more than a wordy explanation. You're also a liar for saying I could do the pauli matrices - I asked you if it was possible so I could only then need to worry about the mathematics - my exact words.

If you are going to start making erreneous claims, I will put you back on ignore. That's a promise.

 

That contradicts your claim you've been 'investigating' the Dirac equation but obviously you don't realise that because you don't understand how the Pauli matrices relate to the Dirac equation.

The Pauli matrices form a set of operators which act on 2 dimensional Weyl spinors and they form a Clifford algebra. The 4 dimensional case is the Dirac matrices which form a Clifford algebra and which act on 4 dimensional Dirac spinors. 4 dimensional Dirac spinors can be written as pairs of two dimensional Weyl spinors, as anyone whose done anything to do with the Dirac equation will have seen first hand. In a particular representation the Dirac matrices are written in terms of the Pauli matrices.

If you claim you've only covered the Pauli matrices in the sense you know they are matrices then you can't then claim you've been investigating the Dirac equation because the Dirac equation is most readily understood in terms of the Pauli matrices and 2d spinors!

Your lack of understanding on topics you want people to think you understand once again leads to you contradicting yourself. Of course you don't realise you contradict yourself but you're daft enough to lie about topics which some of us have worked on. I seriously don't understand why you would lie about physics on a physics forum and then act surprised when someone points out your contradictions and mistakes. It's like not knowing how to speak French, going to France for holiday and then being surprised when people point out you're just making up words when you try to talk to them. If you want to deceive people about your level of knowledge in physics go to an arts forum or move to Alabama.

 

Well, actually, they are requisite to understanding the energy level of the vacuum, but I disagree you must have a qualitative understanding of the matrices to understand the equation.

I could talk a lot of the equation now, without running into the complexities of pauli matrices.