On the Electron

[Reiku]

I want to explore one of the most controversial theories on the particle _ The Electron. The first part will be to investigate some unusual properties. The second will be to investigate whether the electron really does have a mass.

1)

The Electron

No other particle has been so successful in quantum mechanics. Quantum Electrodynamics, riddled with equations that describe the functions of the electromagnetic field. They describe electrons moving through a wire, giving electricity to every home. But as successful as it has been, it’s been difficult to work with.

Suppose we take the spin of the electron, manipulate it, so that it will rotate 360 degrees and brought finally back to orientation. Now, you would think that the 360 degree spin forward, would be the same as the common unrotated electron, because 360 degrees means a full circle. But it turned out that only atoms with a multiple integer of h/2pi (h is for Plancks Constant 6.626 x 10^-33 Joule sec) will be able to arrive at the same location. This is quantized angular momentum. However, the results for all 1/2-spin particles ''fermions,'' would need to move another 3602 degrees just to arrive at the same location. This obviously goes for all fermions... protons... neutrons ect.

The electron moves to and fro the hearts of atoms, orbiting the nucleus in a cloud of probability. In fact, Dirac showed that the electron actually moved at lightspeed, but was always observed to move slower, because of a mysterious electromagnetic sea, we call in physics, the Zero-Point Energy Field. This Dirac Sea was filled with negatively spinning particles, which would buffet the real electron about on its path in an oscillated zig-zag motion. Because of this, the electron seemed to be moving so much slower. From time to time, when enough energy is added into the vacuum, this field can become excited, and spontaneous quantum foam will appear. This is releasing the energy from the vacuum, to create a particle, and its particles hole (antiparticle).

In fact, the electron could be moving at lightspeed, but not actually going anywhere at all! The electron would be caught in a ‘’knot.’’ It is just another strange thing in quantum mechanics. Another paradox of the calculations, but we can get around it. But doing this, called the Dirac Equation, shows that matter quite literally comes out of the nothingness. Of course, because of this, you might think that then the universe will have a lot of antimatter, but that is not true. There maybe some very small antigalaxies, but that is all.
His equation changed the world of physics, especially for the role of electromagnetism.

The electron, with a position, momentum and energy is totally described by the state vector, given as |Ø>. Although, the rule of complimentarity ruled itself by the uncertainty principle forbids us ever knowing everything about the mathematics behind |Ø>. Though, potentially, anything you want to know is behind that variable. The state/wave vector spreads out over spacetime. It can potentially and theoretically calculate the wave vector of entire galaxies and even the universe itself!

Some really bizarre formulations and speculations have been revised since the electrons discovery. It carries a charge of 1.6 x 10^-19 precisely, and has a mass of 9 x 10^-31, or 1 two thousandth of the mass of a proton (or even one millionth millionth of the mass of a general speck of dust). A bit like compairing the mass of earth compaired to the galaxy.

All attempts to measure the radius of the electron has failed. All we can calculate is that IT MIGHT HAVE something like a radii of 10^-18m; that is, it's supposed radius is about one hundred million times smaller than an atom shell. All consistent theories and assumptions leads us to believe the electron has no real structure at all!!!! Wierd eh?

Why it is puzzling, is how a particle can have no size or structure, but have some type of mass and behave as though it is spinning????

 

[AlphaNumeric]

whether the electron really does have a mass

Experiments say it does.

In fact, Dirac showed that the electron actually moved at lightspeed, but was always observed to move slower

Can you cite a reference please?

because of a mysterious electromagnetic sea, we call in physics, the Zero-Point Energy Field.

Actually it's known as vacuum polarisation. The 'bare charge' of the electron causes the quantum field around the electron to develop virtual dipoles which shield the charge and renormalise it to the quantity we measure. The Zero Point Energy is the result of normal ordering the hamiltonian for the field and picking up an infinite contributions from zero modes.

The corrections to the mass, ie comparing bare mass to measured mass, come from the field's self energy, ie the propogator having to take into account production of loops.

It's explained in detail on p330 of Peskin.

From time to time, when enough energy is added into the vacuum, this field can become excited, and spontaneous quantum foam will appear. This is releasing the energy from the vacuum, to create a particle, and its particles hole (antiparticle).

The Dirac hole model was found to be insufficent more than 70 years ago. It was the first interpretation that Dirac has after he moved from scalar QFT to fermionic QFT. He tried to carry over some of the scalar notions of how the fields worked into the electron field but it didnt' work. Instead, it was reformated into the move viable system of the positive quanta being particles in their own right. This is why the electron field contains two different kinds of operators, the a's and the b's. The a's are the electrons and the b's are the positrons. Scalar QFT doesn't have this, they have just one kind of operator and Dirac initially tried that with electrons but it didn't work.

In fact, the electron could be moving at lightspeed, but not actually going anywhere at all!

Err... what?

Another paradox of the calculations, but we can get around it. But doing this, called the Dirac Equation, shows that matter quite literally comes out of the nothingness.

The Dirac equation is a way of formating quantum mechanics so that the relativistic wave properties of the system are preserved but only using first order derivatives. Matrices were used because it allows for the use of the matrix equation $$\{ \gamma^{a},\gamma^{b}\} = 2\eta^{ab}$$, which means a solution to the Dirac equation also satisfies the Klein Gordon equation, ie the relativistic mass equation. It's got nothing to do with 'avoiding the paradox of knots'. It's explained in detail in the first chapter of Weinberg.

shows that matter quite literally comes out of the nothingness.

No, it requires energy.

The electron, with a position, momentum and energy is totally described by the state vector, given as |Ø>

An enormous simplification. You can write any system in terms of a state vector, but they'll have different Fourier decompositions. As I mentioned, the scalar system only have one kind of operator in it's expansion, the fermion field has two.

Although, the rule of complimentarity ruled itself by the uncertainty principle forbids us ever knowing everything about the mathematics behind |Ø>

We know all we need to know about the mathematics of the state vector. The uncertainty principle comes from the fact that the state vector is nothing but a measure of probability. It's not that we cannot extract information from the state, but that any information we extract is always an amplitude.

It would help if you'd ever done any calculations involve bra-ket notation or even wave functions, rather than reading the Wikipedia page and regurgitating it, having warped it as it went through your head.

Though, potentially, anything you want to know is behind that variable. The state/wave vector spreads out over spacetime. It can potentially and theoretically calculate the wave vector of entire galaxies and even the universe itself!

No, in the case of the Dirac equation it describes just a lepton field, perhaps coupled to a photon field. It doesn't inclde the electroweak sector or the strong sector or the Higgs sector.

Things like the de Witt equation, which use similar notation (ie a ket |a> notation) are formulated in an entirely different manner and just because they use similar notation doesn't mean you can apply one to the area of the other.

Even within the same QFT book or lecture notes, notation will be abused and things like spin states, polarisations and colour indices will be dropped and things which look superficially similar can be very different.

It carries a charge of 1.6 x 10^-19 precisely

No, it doesn't.

Do you even check your facts before posting?

This is an attempt at a discussion about QED but you show you've never studied it in any way other than pop science books and Wikipedia. You show, as usual, no working knowledge.

 

[BenTheMan]

The second will be to investigate whether the electron really does have a mass.

Yeah this is clearly wrong. The electrons mass is very well measured experimentally.

All attempts to measure the radius of the electron has failed. All we can calculate is that IT MIGHT HAVE something like a radii of 10^-18m;

Reiku, I have poited out to you before that this is wrong. Trying to treat the electron as a spinning sphere leads to wrong results. I can show you the calculation again, if you'd like.

 

[Reiku]

God so many questions.

''Can you cite a reference please?''

p100, ''The Spiritual Universe,''

And i've read other documents which say that for an electron to move through space at the speed of light, it would need to be massless. But this was a consequence of linking QM with relativity.

''Actually it's known as vacuum polarisation. The 'bare charge' of the electron causes the quantum field around the electron to develop virtual dipoles which shield the charge and renormalise it to the quantity we measure. The Zero Point Energy is the result of normal ordering the hamiltonian for the field and picking up an infinite contributions from zero modes.

The corrections to the mass, ie comparing bare mass to measured mass, come from the field's self energy, ie the propogator having to take into account production of loops.

It's explained in detail on p330 of Peskin.''

What's wrong with my terminology to yours?

''Err... what?''

Dirac's electron knot. An electron moving at light speed in a confined knot.

''The Dirac equation is a way of formating quantum mechanics so that the relativistic wave properties of the system are preserved but only using first order derivatives. Matrices were used because it allows for the use of the matrix equation , which means a solution to the Dirac equation also satisfies the Klein Gordon equation, ie the relativistic mass equation. It's got nothing to do with 'avoiding the paradox of knots'. It's explained in detail in the first chapter of Weinberg.''

I don't know what i am to argue with again? I know what the Dirac Equation is, and i know it's solutions cover many area's of physics.

''No, it requires energy.''

Yeh, well... i thought that would be plainly obvious by now.

''No, in the case of the Dirac equation it describes just a lepton field, perhaps coupled to a photon field. It doesn't inclde the electroweak sector or the strong sector or the Higgs sector.

Things like the de Witt equation, which use similar notation (ie a ket |a> notation) are formulated in an entirely different manner and just because they use similar notation doesn't mean you can apply one to the area of the other.

Even within the same QFT book or lecture notes, notation will be abused and things like spin states, polarisations and colour indices will be dropped and things which look superficially similar can be very different.''

I'll have to find that out. I remember reading up on an essay by Cramer saying that the state vector can calculate almost anything we want from a system like an electron.

''No, it doesn't.

Do you even check your facts before posting?

This is an attempt at a discussion about QED but you show you've never studied it in any way other than pop science books and Wikipedia. You show, as usual, no working knowledge.''

Sorry if it was wrong.

What workings do you want from me?

''Reiku, I have poited out to you before that this is wrong. Trying to treat the electron as a spinning sphere leads to wrong results. I can show you the calculation again, if you'd like.''

I know you highlighted that problem a while back. But it still behaves as though it is spinning, so might we come to realize the math isn't all that is might seem in this case?

 

[Reiku]

Oh and Ben...

I know how bra-ket notation works. Why did you say i don't?

Plus, keep your tone modified. I've been more than neutral with you. Thirdly, what makes you think i push my way through wiki...? I don't even trust it.

 

[BenTheMan]

I know you highlighted that problem a while back. But it still behaves as though it is spinning, so might we come to realize the math isn't all that is might seem in this case?

What makes you think that ``spin'' has anything to do with the electron ``spinning''???

Take a classical (solid) sphere and put a uniform charge distribution on it. Now spin it. It creates a magnetic field that points ``up'' along the axis of spinning, just like an electron. Now rotate the sphere by 2pi in a direction perpendicular to the axis of spinning. What happens? The magnetic field comes exactly back to where it was.

Now do the same thing with an electron. The magnetic field goes now in a different direction...``down'' as you have pointed out.

So what the hell makes you think that an electron has ANYthing to do with a classical spinning sphere? I've just showed you that they're different. I showed you that if the electron WERE a classical spinning sphere it would have to spin faster than the speed of light several months ago, something which Dr. Wolf confirmed for you (I know because I emailed him at that time). So I've told you that you were wrong, Dr. Wolf has told you that you were wrong. What else do you want?

 

[Reiku]

I know about all this. I am simply saying, how can spin be fundmental and intrinsic, if it cannot be applied to an electron? Does this mean that the electron is free from certain fundamental qualities>? An electron has a spin afterall does it not>?

*And i told you what Dr. Wolf said as well. What? Didn't you believe me?

 

[Reiku]

Look, i'm not saying your wrong. You are saying i am wrong by saying the electron doesn't have a spin. The electron has a spin, as i believe Samuel A. Goudsmit and George E. Uhlenbeck postulated that the electron had an intrinsic angular momentum that was independent of its orbital characteristics.

A classical object yes can have a magnetic moment if it were spinning so that at the edges there is produced an effective current loop. It was because of this the "electron spin" was used to describe the intrinsic angular momentum; but what does this really say about the spin. This is an honest question? Doesn't it spin, or does it?

 

[BenTheMan]

A classical object yes can have a magnetic moment if it were spinning so that at the edges there is produced an effective current loop. It was because of this the "electron spin" was used to describe the intrinsic angular momentum; but what does this really say about the spin. This is an honest question? Doesn't it spin, or does it?

The electron is a point particle according to what we know. Point-like particles cannot ``spin''.

 

[AlphaNumeric]

Look, i'm not saying your wrong. You are saying i am wrong by saying the electron doesn't have a spin. The electron has a spin, as i believe Samuel A. Goudsmit and George E. Uhlenbeck postulated that the electron had an intrinsic angular momentum that was independent of its orbital characteristics.

Rather than have the ability to recall pointless facts (or just to Google), why not open a real physics book and find out?

Total 'spin' is a sum of angular momentum L and intrinsic spin J, so S=J+L, but that doesn't mean that J is literally a physical spin. It means that if $$\mathbf{J} = (J_{1},J_{2},J_{3})$$ then $$[J_{i},J_{j}] = \epsilon_{ijk}J_{k}$$, which is true for usual angular momentum too. Hence 'spin'. But it's not physical spin, it's a quantity which has an underlying mathematical structure analogous to physical spin but since fermions have such half integer 'spin', it cannot be physical spin.

Open a proper book.

 

[Reiku]

It has nothing to do with me opening a ''proper'' book. Before Ben told me about this a few months back, i was more set back to why i had never learned the above. I accept now that the spin is not the same, but i am misunderstanding how we can call something a spin when it doesn't even.