Can an electron be in two places at the same time?

[AlphaNumeric]

I'm not mistaking the vector field associated to the electromagnetic field the electron interacts with with the electron field itself. I'm offering assistance. If you don't like it, you offer some assistance.

Correcting a mistake is assistance.

You mentioned the E field of the electron. That's the electric part of the electromagnetic field, which is carried by photons. You then proceeded to talk about the electron diffracting, which is due to the electron's wave function. You explicitly mention the electron's wave function and this hurricane analogy in the same sentence,

"QM says a subatomic object is described by a wave function, so think of the electron wavefunction as being something like a spherical version of a hurricane."

You have conflated the electromagnetic field about an electron with the electron's wave function. There's no two ways about it. Removing the electron's charge and thus all of your hurricane analogy still results in a diffraction pattern, just as it does for the photon's diffraction pattern or the neutron or Sodium or Bucky balls or anything else. The electric field is irrelevant here.

Furthermore you also made a conceptual error in saying to consider the spherical version of the hurricane. The hurricane has an axial symmetry, it rotates about the central axis and this rotation is orthogonal to radial lines coming out from the axis. The electric field example doesn't generalise. In 2d you can draw the radial lines and then consider circles of constant E modulus. These form the concentric rings you refer to. In 2d there's a unique (up to scaling) notion of an orthogonal vector to the radial lines, which form the tangent lines to the circles in question. There isn't any actual rotation here but you can still define radial lines and orthogonal circles to give you this vortex picture.

It doesn't quite work like that in 3d. You define radial lines using the electric field but then there's no unique (up to scaling) orthogonal vector, instead there's an orthogonal plane! Instead of concentric 1d circles you now have concentric 2d spheres. You can't have a rotation without a preferred direction, which is what provides a rotating system with the necessary broken symmetry to induce a magnetic field.

The long and the short of it is that simple assumptions which seem valid in 2d sometimes don't carry over into 3d. Particularly when involving rotations. For example rotations in 2d commute, in 3d they generally don't.

If you want to make sure you're not falling foal of such misunderstandings then you'd be wise to do a basic course in vector calculus. Nothing heavy weight, something you'd cover towards the end of A Level mechanics and the first term of an undergrad course. Enough to be comfortable doing vectors, using matrices, changing coordinates, that sort of thing. I'm not being patronising or anything, I honestly think anyone interested in physics beyond pop science would do themselves a massive favour if they did a basic course in vector calculus. Even the most trivial and basic of published papers assume such things as second nature to the reader, to say nothing of how it would improve grasping multi-dimensional dynamical systems.

And this brings me back to something else I said in my post. I asked you if you could formalise anything you said. You clearly believed that what you'd just outlined was a valid description, it would lead to the correct conclusions. Beyond your utterly unjustified self confidence do you have anything to actually back that up? Remember how you keep complaining how string theory doesn't produce any results? I can't believe you're unaware of the hypocrisy of such comments given your repeated and complete ignoring of every request I've ever made for you to provide a justified working model of anything you wax lyrical about (and you wax a lot).

You challenged me to 'offer assistance'. Unlike you I'm in a position to provide assistance and so I'll offer to do so. If you would like me to suggest a simple, relatively short and general introduction to vector calculus textbook (not a big thing, one of those A5 sized ones) I will do so. Then we could make say a fortnightly thread where you go over your understanding of each chapter in turn, I and others here discuss any issues or misunderstandings you might have, provide elaborations of proofs and yes, even check your answers to the problems in the book. You'd benefit by actually learning something, those of us who've covered it would improve our explanation experience (as well as perhaps blow out some mental cobwebs here and there) and everyone else would see a few good discussions and perhaps want to join in. We actually do this sort of thing at my work. Each week or fortnight someone is given an area of maths to read up on, then do a 30~45 minute overview on it back to everyone and we discuss any issues or interesting things which were encountered.

So how's that for some assistance? You clearly have the time to spare and you clearly have significant holes in your knowledge/understanding (even on conceptual levels). You have nothing to lose but your ignorance.

 

[Aqueous Id]

@Alphanumeric:

Do you agree that a random process is acting on each "particle" shown as a "spot" as the picture develops? What is the nature of this random process, what is is cause, how does it select the "band" and the "phase" within the band, each time a "particle" (or its wave or wavelet equivalent) passes though?

 

[Farsight]

I think my statement is more directed at how the target works. Does it really intercept a particle? How does that work? Or is just measuring a voltage change by the arriving wavefront, not due to the quantum wave, but due to the impinging E-field. I'm not disputing particle-wave duality. I'm questioning how the machine works and what the results really mean.

I don't know. I imagine it's essentially a CCD, but don't take my word for it. Maybe przyk will know the answer to this one.

 

[Farsight]

Correcting a mistake is assistance.

It wasn't a mistake. Give Aqueous some assistance, don't just sit there saying nothing then jumping on people who try to help a guy out.

You mentioned the E field of the electron. That's the electric part of the electromagnetic field, which is carried by photons.

I said what you think of as its E-field because Aqueous said E-field. I was keeping it simple. Many people don't appreciate that an electron has an electromagnetic field, and they don't always know about the fundamentals of electromagnetism as evidenced by the Aharonov-Bohm effect, and this excerpt from wiki:

"In fact Richard Feynman complained [citation needed] that he had been taught electromagnetism from the perspective of E and B, and he wished later in life he had been taught to think in terms of the A field instead, as this would be more fundamental".

You then proceeded to talk about the electron diffracting, which is due to the electron's wave function. You explicitly mention the electron's wave function and this hurricane analogy in the same sentence.

You're reading too much into it. Since I mentioned the Aharonov-Bohm effect, note that electron diffraction features in the illustration to this section. The diffraction pattern shifts when the solenoid is turned on, even though there's no electromagnetic field outside the solenoid. And by the way, what we know of as the Aharonov-Bohm effect was predicted by Ehrenberg and Siday in The Refractive Index in Electron Optics and the Principles of Dynamics in 1949. It's a classical paper.

You have conflated the electromagnetic field about an electron with the electron's wave function. There's no two ways about it. Removing the electron's charge and thus all of your hurricane analogy still results in a diffraction pattern, just as it does for the photon's diffraction pattern or the neutron or Sodium or Bucky balls or anything else.

No I haven't. See above. And do note that a photon is associated with an electromagnetic wave, and that a neutron has magnetic moment which is "of particular interest, as magnetic moments are created by the movement of electric charges". A photon has no charge, and a neutron has no net charge, but electromagnetism is still involved. Ditto for sodium atoms and buckyballs.

The electric field is irrelevant here.

An electron doesn't have an electric field. An electron has an electromagnetic field. And whilst a neutron doesn't, a free neutron decays in circa 15 minutes to a proton, electron, and antineutrino. The net charge is still zero, but now the electromagnetism betrayed by that magnetic moment is laid bare.

Furthermore you also made a conceptual error in saying to consider the spherical version of the hurricane. The hurricane has an axial symmetry, it rotates about the central axis and this rotation is orthogonal to radial lines coming out from the axis. The electric field example doesn't generalise. In 2d you can draw the radial lines and then consider circles of constant E modulus. These form the concentric rings you refer to. In 2d there's a unique (up to scaling) notion of an orthogonal vector to the radial lines, which form the tangent lines to the circles in question. There isn't any actual rotation here but you can still define radial lines and orthogonal circles to give you this vortex picture.

Again, I was keeping it simple. The spherical hurricane doesn't quite work because there's no chirality. It has to be quasi-spherical, with a compound rotation.

It doesn't quite work like that in 3d. You define radial lines using the electric field but then there's no unique (up to scaling) orthogonal vector, instead there's an orthogonal plane! Instead of concentric 1d circles you now have concentric 2d spheres. You can't have a rotation without a preferred direction, which is what provides a rotating system with the necessary broken symmetry to induce a magnetic field.

Induce a magnetic field? I really think we ought to go back to Minkowski here:

"Then in the description of the field produced by the electron we see that the separation of the field into electric and magnetic force is a relative one with regard to the underlying time axis; the most perspicious way of describing the two forces together is on a certain analogy with the wrench in mechanics, though the analogy is not complete".

An electron has an electromagnetic field. Place it in region of empty space, and have a test-electron ready in your hand. If you place it down near the first electron such that it has no initial motion relative to it, it is subject to linear force only. We then say "It's in an electric field". If you bowly your test electron such that it does have initial motion, it is subject to rotational force too. If we mask the off the linear force like we do with the current-in-the-wire consisting of negatively charged electrons and positively charged metal ions, we say our test particle is "in a magnetic field". But in both cases the change in motion we see is the result of the interaction between electromagnetic fields.

The long and the short of it is that simple assumptions which seem valid in 2d sometimes don't carry over into 3d. Particularly when involving rotations. For example rotations in 2d commute, in 3d they generally don't.

The current-in-the-wire is a good half-way house to understanding this. You step from a spherical electromagnetic field to a cylindrical scenario with concentric "magnetic field lines" which your test-electron circles round. Bend the wire into a ring and add more rings and you've got a solenoid. Throw your test electron through the middle and it goes around the "magnetic field lines". But you don't actually have a magnetic field per se, merely a combination of electromagnetic fields and relative motion.

If you want to make sure you're not falling foal of such misunderstandings then you'd be wise to do a basic course in vector calculus. Nothing heavy weight, something you'd cover towards the end of A Level mechanics and the first term of an undergrad course. Enough to be comfortable doing vectors, using matrices, changing coordinates, that sort of thing. I'm not being patronising or anything, I honestly think anyone interested in physics beyond pop science would do themselves a massive favour if they did a basic course in vector calculus. Even the most trivial and basic of published papers assume such things as second nature to the reader, to say nothing of how it would improve grasping multi-dimensional dynamical systems.

You're making heavy weather of all this. It is unwarranted.

And this brings me back to something else I said in my post. I asked you if you could formalise anything you said. You clearly believed that what you'd just outlined was a valid description, it would lead to the correct conclusions. Beyond your utterly unjustified self confidence do you have anything to actually back that up?

Electron wavelength is λ = 4πn / c^1½, the n being a dimensionality conversion factor with the value of 1 and the c being a straight number with the value 299,792,458. There's two orthogonal rotations in this "hurricane". Get your calculator out.

Remember how you keep complaining how string theory doesn't produce any results? I can't believe you're unaware of the hypocrisy of such comments given your repeated and complete ignoring of every request I've ever made for you to provide a justified working model of anything you wax lyrical about (and you wax a lot).

I ignore you because you're full of hubris and outraged anger. It's impossible to have a sincere conversation with you. Pack it in.

You challenged me to 'offer assistance'. Unlike you I'm in a position to provide assistance and so I'll offer to do so.

Then do it. Don't leave it all to me and act like some thought-police flunky who comes out of the woodwork to trample on discussions. I'm the one helping here. Pull your finger out and give some help to guys like Aqueous. Find ways to explain things in simple terms, and motivate and interest and enthuse people about physics instead of sneering at them and putting them off. Be civil, be professional.

If you would like me to suggest a simple, relatively short and general introduction to vector calculus textbook (not a big thing, one of those A5 sized ones) I will do so. Then we could make say a fortnightly thread where you go over your understanding of each chapter in turn, I and others here discuss any issues or misunderstandings you might have, provide elaborations of proofs and yes, even check your answers to the problems in the book. You'd benefit by actually learning something, those of us who've covered it would improve our explanation experience (as well as perhaps blow out some mental cobwebs here and there) and everyone else would see a few good discussions and perhaps want to join in. We actually do this sort of thing at my work. Each week or fortnight someone is given an area of maths to read up on, then do a 30~45 minute overview on it back to everyone and we discuss any issues or interesting things which were encountered. So how's that for some assistance? You clearly have the time to spare and you clearly have significant holes in your knowledge/understanding (even on conceptual levels). You have nothing to lose but your ignorance.

And so do you. Go on, let's do it. But not vector calculus in general. There's an issue wherein a vector field relates to what it does rather than what it is. It has to be vector calculus for electromagnetism. And an alpha thread. Any abuse from you and we are done.

 

[Magneto_1]

Electron wavelength is λ = 4πn / c^1½, the n being a dimensionality conversion factor with the value of 1 and the c being a straight number with the value 299,792,458. There's two orthogonal rotations in this "hurricane". Get your calculator out.

Farsight,

You are the funniest "arm-chair" physicist on the planet. You are trying to back your way into a "vortex" theory using the term "hurricane" instead of vortex. This is extremely funny.

Also, neither Prometheus, or AlphaNumeric have questioned you on the above mathematics, and they are PhDs in mathematics & physics? :shrug:

That equation that you keep tossing around, and saying get out your calculator is completely Bogus!! And the equation has absoutely no meaning. Although you claim that the results predict the same result of the Arthur Compton wavelength ($$ \lambda_{Compton} $$).

There is no equation that I am aware of that allows you to predict a wavelength ($$ \lambda $$) with a square root of the speed of light ($$ \sqrt{c_{Light}} $$) in the equation.

If you are going to use a math equation in an attempt at a "vortex" theory, oops, I mean "hurricane" theory, you need to be able prove that it works; now you get your calculator out!

 

[Farsight]

It isn't bogus, Magneto. The half comes out of spin half. And it isn't my expression either. It's Andrew Worsley's. It's to do with spherical harmonics. See where it says this? Spherical harmonics are important in many theoretical and practical applications, particularly in the computation of atomic orbital electron configurations. Turns out they're a bit more important than you think. And look down the page a bit and note this: In 1867, William Thomson (Lord Kelvin) and Peter Guthrie Tait introduced the solid spherical harmonics in their Treatise on Natural Philosophy, and also first introduced the name of "spherical harmonics" for these functions.. But hey, that's all tangential. If you don't like the assistance I'm offering to Aqueous to try to get this across, you give him some assistance.

 

[AlphaNumeric]

I said what you think of as its E-field because Aqueous said E-field. I was keeping it simple. Many people don't appreciate that an electron has an electromagnetic field, and they don't always know about the fundamentals of electromagnetism as evidenced by the Aharonov-Bohm effect, and this excerpt from wiki:

"In fact Richard Feynman complained [citation needed] that he had been taught electromagnetism from the perspective of E and B, and he wished later in life he had been taught to think in terms of the A field instead, as this would be more fundamental".

You say this as if you're well versed in electromagnetism and passing down bits of wisdom to people who might still see electric and magnetic fields as entirely unrelated. You also say it as if you're familiar with the concept and workings of a vector gauge potential. For example, you recently said 'line bundle curvature' in a thread but when Guest pressed you on it you didn't reply.

You're reading too much into it.

You jumped between the electron's wave function and the electromagnetic field around the electron. They are not the same thing. The QM description of the diffraction in the DSE is done by considering the wavefunction. If you turn off the electric charge of the electron and run the QM model again you still get the same DSE behaviours.

Since I mentioned the Aharonov-Bohm effect, note that electron diffraction features in the illustration to this section. The diffraction pattern shifts when the solenoid is turned on, even though there's no electromagnetic field outside the solenoid. And by the way, what we know of as the Aharonov-Bohm effect was predicted by Ehrenberg and Siday in The Refractive Index in Electron Optics and the Principles of Dynamics in 1949. It's a classical paper.

This illustrates what I've been saying about your general behaviour.

There are a great many diffraction experiments, including the AB effect and the DSE. The DSE diffraction is not due to the same thing as the AB effect. The AB effect is explicitly about a field the electron couples to, while the DSE works on particles themselves. Turn off the electron's electric charge and you don't change the general result of the DSE, but you completely change the AB experiment for the electron.

From a field theory point of view there's the electron field and the photon field. The DSE works on the fields themselves. The AB experiment is due to how one field interacts with another.

You point specifically at the picture on the Wiki page and talk about a 'classical paper'. It doesn't have anything to do with the DSE diffraction phenomenon. It's a different type of diffraction. In the AB experiment you can constantly look at the electrons and you still get the AB effect. I can't help but feel the last few sentences in the above quote of yours are attempts to say "Look, I'm well read, I've read classical papers from decades ago!". Perhaps I wouldn't feel uneasy about such paragraphs in your posts if I knew you were familiar with the basics. Vector potentials, gauge invariances, line bundles. These are things some people don't even cover during their physics degree, some universities push them into masters courses! Certainly bundles, gauge bundles and their curvatures are beyond degree level and that's for people who can do vector calculus in their sleep. You have repeatedly stated you're not a mathematics person so it's a little odd when you start throwing around advanced mathematical concepts which pertain to physics as if you work with them all the time. I know you might read things which mention them all the time but that's a long way from having an understanding, working or otherwise, of them. Hence my offer.

No I haven't. See above. And do note that a photon is associated with an electromagnetic wave, and that a neutron has magnetic moment which is "of particular interest, as magnetic moments are created by the movement of electric charges". A photon has no charge, and a neutron has no net charge, but electromagnetism is still involved. Ditto for sodium atoms and buckyballs.

Yes, you have. As I said, the DSE result is modelled in QM by considering the particle's wave function. Whether or not that particle is charged under any other force is immaterial. Yes, the neutron has small electromagnetic effects, as do plenty of other things formed from the bound states of charged particles. But that doesn't mean their DSE behaviour is due to their electromagnetic properties. As I said, photons don't interact with photons and they diffract. If a particle's behaviour in the DSE was due to its coupling to the EM field then the EM field itself wouldn't work in the DSE!

Let's nail some colours to the mast here. Do you think QM says an electron does what it does in the DSE because it's electromagnetically charged? Do you think QM explains the DSE for all the particles you list because of their residual EM charges? I'll tell you now, the answer is no. Do you agree with this or not? If not, why not and what evidence do you have? If so why are you bringing up the AB effect, which involves the coupling with the EM field?

If you want to see the explaination in a 'classical work' then look up the DSE in Feynman's lectures.

An electron doesn't have an electric field. An electron has an electromagnetic field.

It's an electric charge, it only produces a magnetic field when it's moving (in some frame). Do you think I'm unfamiliar with that? I distinctly remember asking you on PhysOrg to prove Maxwell's equations are Lorentz invariant, after you claimed to be a world expert in it, and I had to tell you the answer in the end.

And besides, I did actually say "You mentioned the E field of the electron. That's the electric part of the electromagnetic field, which is carried by photons". Pay attention.

And whilst a neutron doesn't, a free neutron decays in circa 15 minutes to a proton, electron, and antineutrino.

Again, you throw in irrelevant little factoids which I feel are attempts to look well read. Unfortunately when all your little factoids can be gotten from Wikipedia it just back fires on you.

The net charge is still zero, but now the electromagnetism betrayed by that magnetic moment is laid bare.

The magnetic moment of the neutron has nothing to do with how it decays into a proton et al. Again, you seem to be trying to throw in lots of little things in the hopes it sounds well read. Instead it just seems odd.

Again, I was keeping it simple. The spherical hurricane doesn't quite work because there's no chirality. It has to be quasi-spherical, with a compound rotation.

What's that? I think it's the sound of back peddling!

Please define, precisely, quasi-spherical. I want formal definitions.

Induce a magnetic field?

Moving charges produce magnetic fields. For spherical symmetry you cannot have a preferred direction and if the electron is moving in a particularly direction you have that as a preferred direction and thus you can break the symmetry. An electric field can have spherical symmetry as the field lines are radial. A magnetic field from an electric charge is not, which dovetails with the whole electric-magnetic field transforms under changes of frame.

I really think we ought to go back to Minkowski here:

Again, I find statements like this from you very odd. You have an obsession with physicists/mathematicians from the first half of the 20th century and then only their words, not their actual results. You want to talk about Minkowski but you can't do anything formal with his metric. You want to talk about Feynman but you can't do any of his path integrals. You want to talk about the AB effect but you can't do gauge theory. When are you going to realise you aren't going to grasp their work in any meaningful way until you have a working understanding of it. You rely on people like myself, people who've taken the time to gain such a working understanding, to convert it into terms you understand. You then unfortunately labour under the misconception that you have a good grasp of the specifics.

If you think I've been slap dash with how I've phrased things in my replies to you then perhaps you should look a little closer to home. I'd love to have a quantitative discussion on this with you, I explicitly asked you to formalise your views on the whole hurricane thing but you didn't (couldn't). Look at the excellent thread Cpt made, where the formal details show how amazingly elegant some mathematics can lead to deep physical insight. The problem is that when I ask you to do something formal you can't and if I were to do it you'd not understand.

I'm aware the electron has an electromagnetic field, I know precisely how they couple together in both Maxwell and Dirac's work (which is more than can be said for you). This discussion would be much easier if we could all just flick into differential forms but you wouldn't be able to keep up. Instead you waste your time and mine by repeating back wordy summarises of mathematical physics you've made no attempt to learn or understand. Do yourself a favour and give it a rest, spend your time a little more wisely.

The current-in-the-wire is a good half-way house to understanding this. You step from a spherical electromagnetic field to a cylindrical scenario with concentric "magnetic field lines" which your test-electron circles round. Bend the wire into a ring and add more rings and you've got a solenoid. Throw your test electron through the middle and it goes around the "magnetic field lines". But you don't actually have a magnetic field per se, merely a combination of electromagnetic fields and relative motion.

This is a perfect example. Rather than waving your arms and giving descriptions open to incorrect interpretation, imprecise description and incorrect intuition we could communicate much more accurately and much faster if you could just do this all mathematically. If you spent more time reading proper papers and textbooks and less time reading pop science you'd know how to describe a set up properly, such as

A solenoid with N turns of length L and radius R has current I passed through it, centre at the origin of 3 dimensional Euclidean space. A test particle of mass m and charge q is placed at $$\mathbf{x}$$ and a uniform external magnetic field $$\mathbf{B}$$ is applied. The equations of motion are therefore.....

Instead you have "Bend it into a ring and it goes around the field lines" . You can't complain I'm being slack with details and yet refuse at every single turn to quantify or formalise anything you say.

You're making heavy weather of all this. It is unwarranted.

I'm calling it like I see it. You've been stuck in whatever intellectual rut you're in for the better part of a decade, clearly you need to be prodded out of it.

Electron wavelength is λ = 4πn / c^1½, the n being a dimensionality conversion factor with the value of 1 and the c being a straight number with the value 299,792,458. There's two orthogonal rotations in this "hurricane". Get your calculator out.

You actually think that's coherent? Please elaborate on what on Earth you're on about.

I ignore you because you're full of hubris and outraged anger. It's impossible to have a sincere conversation with you. Pack it in.

'Outraged anger? I did like your misplaced condescension and belief you're saying something valid or have insight. I did like your hypocrisy too. I don't have anger towards your work, I don't think it's worth anything so why should I be angry about it? Cranks always think I'm angry because I perceive their work as a threat to either my own or the mainstream or something like that. Magneto and Sylwester for instance, they think I'm jealous of them, as if they have anything I could possibly be jealous of. I find the general lack of honesty in you lot distasteful but there isn't the level of anger you seem to think there is. You lot simply aren't that high on my radar.

Besides, the simplest way to shut me up is to prove me wrong. Can you provide a working, quantitative model from you work for anything? String theory can. If your work is supposedly worth 4 Nobel Prizes what does that make string theory then?

If you addressed this contradictory behaviour of yours rather than tried to ignore it and carried on spouting "String theory is dead, it produces nothing!" and the like then perhaps I'd think you deserving of a little more respect. I'm not using a complicated metric here, I'm just pointing out repeated hypocrisy.

Then do it. Don't leave it all to me and act like some thought-police flunky who comes out of the woodwork to trample on discussions. I'm the one helping here.

Giving irrelevant and sometimes nonsensical replies isn't 'helping'. If you can't say something useful then opening your mouth is the opposite of helping.

As I just pointed out, none of your takes on any bit of physics has lead to an experimentally viable working model (or working model of any kind, viable or otherwise). If I were coming into every thread saying "String theory says...." and assuming the matter than closed wouldn't you be complaining? Wouldn't you be pointing out your various talking points about string theory? I imagine so. Hence I think you're showing somewhat of a double standard. If string theory is 'not even wrong' then your take on things is 'not even string theory'.

Pull your finger out and give some help to guys like Aqueous. Find ways to explain things in simple terms, and motivate and interest and enthuse people about physics instead of sneering at them and putting them off. Be civil, be professional.

Just because you're dealt with in a short manner, based on years of experience engaging with you, doesn't mean everyone gets that treatment. I've provided plenty of help to people in other threads. And I don't always jump on you, just when you start coming off as if you understand advanced material, quoting results or areas of physics as if you've got a working understanding (line bundle curvature for instance) when I (and you) know you don't. Tone it down a bit and you slip under the radar like more rational honest people.

And so do you. Go on, let's do it. But not vector calculus in general. There's an issue wherein a vector field relates to what it does rather than what it is. It has to be vector calculus for electromagnetism. And an alpha thread. Any abuse from you and we are done.

Pretty much everything in vector calculus can be given a physical interpretation so there is no 'vector calculus for electromagnetism'. Besides, stuff like special relativity, electrodynamics, quantum mechanics and gauge theory all use similar stuff (and more besides). You can't draw a dividing line through areas like that, that isn't how mathematics works. This is part of what you need to address, a fundamental misconception in how mathematics and physics relate to one another.

However, if you want things to be tailored a little more to what you're interested in I can pull out sections from various lecture notes I have available to me and each iteration we can do another section of them. I can also find a bunch of problems from books and lecture notes which have a more EM tint to them if that's what you're after. The set up could be I provide a bunch of pages on some part of vector calc along with questions based on the material, a week or so goes by and then you provide your attempts to the answers and we (ie you, me and anyone else interested) discuss it. Bear in mind if you want to play by the alpha thread rules you'd be required to answer direct questions about your thinking, understanding and any methodology you might employ to answer the questions. I'll be blunt, I wouldn't put it past you to try to find the answers using Google and then try to proclaim you can do this stuff. Of course you'd only be cheating yourself, wasting an opportunity to have people help you learn (and plenty of students have or do pay for the teaching time of people like myself, Prom, Guest, Cpt etc and you'd get it free).

At some point I can rustle up something on the implementation of div, grad and curl in electromagnetism if you want. Or should I not assume a working familiarity with differentiation, integration and vectors?

We can

 

[AlphaNumeric]

You are the funniest "arm-chair" physicist on the planet. You are trying to back your way into a "vortex" theory using the term "hurricane" instead of vortex. This is extremely funny.

At least Farsight has the good sense not to try to do mathematics when he knows he can't. The same cannot be said for you.

Also, neither Prometheus, or AlphaNumeric have questioned you on the above mathematics, and they are PhDs in mathematics & physics? :shrug:

I hadn't even replied! I don't wait online for Farsight or you to post so I can immediately respond. I have other things to do with my life, some of us have jobs. Besides, I really think you should get rid of the chip on your shoulder about not having a PhD. You're a Mr, not a Dr, deal with it.

If you are going to use a math equation in an attempt at a "vortex" theory, oops, I mean "hurricane" theory, you need to be able prove that it works; now you get your calculator out!

You're the guy who can't do coordinate transformations, doesn't understand the difference between a vector and a matrix, doesn't understand metric notation and many other things and yet has written multiple 'textbooks' on relativity! You're hardly in a position to be calling other people out about their laughable work.

 

[Magneto_1]

I hadn't even replied! I don't wait online for Farsight or you to post so I can immediately respond. I have other things to do with my life, some of us have jobs.

Yes, I do think that you wait for Farsight or I to post so I can immediately respond.

Besides, I really think you should get rid of the chip on your shoulder about not having a PhD. You're a Mr, not a Dr, deal with it.

I don't have a chip on my shoulder at all. It does not matter to me whether I have a PhD or not. Me not having a PhD is my choice, and not something that nature prevented me from doing. I am sure that I will get a PhD someday. I am in no rush. If I got a PhD it would not change my life at all, it would be just another feather in my cap full of feathers.

So when, I am making fun of PhDs, it is an inside joke to all scientists, about all egg heads in common, that like math and physics.

You're the guy who can't do coordinate transformations, doesn't understand the difference between a vector and a matrix, doesn't understand metric notation and many other things and yet has written multiple 'textbooks' on relativity! You're hardly in a position to be calling other people out about their laughable work.

Please stop with your laughable keystrokes!!

Here, just for you, I will provide a write up from a book that I will be releasing soon!

Short Explanation about Vectors and Tensors: By Robert Louis Kemp

Best

 

[AlphaNumeric]

Yes, I do think that you wait for Farsight or I to post so I can immediately respond.

Demonstrably false. You only need to look through Farsight's recent post history to see how I either don't reply every time or there's a significant delay.

Here's a tip, if you're going to make up false claims make up ones which can't be disproved in under 30 seconds.

I don't have a chip on my shoulder at all.

You do. You've tried in insult me by calling me Professor, as if to use an academic title as an insult. You also have an obsession with asking people if they have published a book, because you think self publishing counts in terms of academic publications (it does not) while simultaneously claiming that papers published in journals are not the work of the author as the author has to sign over copyright to said journals (which is not true).

You clearly have an issue with academic qualifications and publications, else you'd not say some of the things you say.

It does not matter to me whether I have a PhD or not.

You recently applied to a job at CalTech, as a head of department. You didn't get the job because you're massively under qualified, including not having any peer reviewed published research and thus no PhD. Not having a PhD removed any chance of you getting that job (it being one of many reasons you wouldn't get it) so it clearly does matter even if you don't realise it.

Me not having a PhD is my choice, and not something that nature prevented me from doing.

You might think that but evidence says otherwise.

I am sure that I will get a PhD someday. I am in no rush.

If you're serious about getting a research position then you're not going to get one until at least after your PhD.

If I got a PhD it would not change my life at all, it would be just another feather in my cap full of feathers.

What feathers? You have no peer reviewed published work and your non-reviewed self published work is riddled with high school level mistakes! Your 'academic experience' was teaching at a degree mill which doesn't do any research. You cry conspiracy against people who you think stole your work, despite you having no evidence (and the evidence being against that claim).

Spending years to write multiple books filled with mistakes and then paying someone to print it and advertise it online, where it gets ridiculed, is not a 'feather in ones cap'.

So when, I am making fun of PhDs, it is an inside joke to all scientists

You can't be involved in such an inside joke, you aren't a scientist.

Please stop with your laughable keystrokes!!

Anyone wishing to see your laughable mistakes needs only to check my post history for 'threads created by...' (it's a short list) and then read the one with your name in the title. Your mistakes were too many to list here.

Here, just for you, I will provide a write up from a book that I will be releasing soon!

Short Explanation about Vectors and Tensors: By Robert Louis Kemp

So you've been writing another massive book, which you're again going to pay someone to print and probably advertise, yet at the same time you were showing you don't know the difference between a vector and a matrix or what $$ds^{2}$$ means in a metric or how to change coordinates? Simply compiling your misunderstandings and errors into a single volume doesn't make them go away.

This seems to be a problem you have, you think if you can put everything into a pdf then somehow it becomes more valid. More than once you've said "So where's your published book!" as if the fact you paid someone to print your errors onto paper means they aren't errors. The reason published work in the academic community is given weight is because it's peer reviewed and then [/i]published[/i] by someone. I didn't have to pay to have any of my work published, they did it free. Instead I had to meet a certain standard of work. That's why it's given weight. Simply paying someone to print your work doesn't make it as good or valid as peer reviewed published work. Any nut (and there's plenty of such nuts) can pay a few thousand to a publishing company and get copies of their book. You've done it. Farsight's done it. A few people on various forums I've been on have done it.

What matters is not that it's published but that it's been peer reviewed. 'It's been published' in academic circles is short for 'It's been peer reviewed and passed'. You would know this if you'd ever been in research groups but instead you've been at University of Phoenix.

You said months ago you were going to send your work to a journal. Have you? If not, why not? If you have, what did they say? Whether you did or not I bet you're still not 'published' in the academic sense.

 

[Magneto_1]

What feathers? You have no peer reviewed published work and your non-reviewed self published work is riddled with high school level mistakes!

I see that you have reviewed, some of the work.

I will agree that there are some basic mistakes mainly in symbolism in (GR), but there are not any fundamental mistakes. I have identified all of the mistakes and I will correct them in the next edition.

I thought that you knew physics history. The Principia Mathematica, written by Isaac Newton, that we discuss today is the third (3rd) edition of his Principia. The first (1st) edition of Newton's Principia was also riddled with high school level mistakes.

What made Newton's Principia popular and gave it momentum, was everyone pointing out to Newton where he made mistakes in his Principia. At that time people were getting a big "kick" out of finding errors in Newton's work; and publishing over town the fact. Some even claimed that fixing his errors, meant that they actually claimed credit for solving the problem.

Don't you know, that is what makes physics fun!

This is similar to playing in a basketball game, and you try and block someone's slam dunk. You might get lucky and actually block a dunk in a game, and the crowd will go wild. But the risk is that you may miss, and get slam dunked on; and the crowd goes wild. As you are thought of as the "laughing stock", as the media plays on every station, you getting slam dunked on!

Best.

 

[Farsight]

...However, if you want things to be tailored a little more to what you're interested in I can pull out sections from various lecture notes I have available to me...

No, forget it. Your post above is yet another tirade. I warned you. I said any abuse from you and we are done. It just isn't possible to have a sincere conversation with you. You cannot resist the urge to start arguments and hurl ad-hominem abuse and trash the thread. We are done.

 

[AlphaNumeric]

Do you read my posts imagining my voice to be an angry one? I can assure you I don't type them as such, I just don't suffer fools gladly and I think you two are examples of such people. My offer was honest. If you're unable to accept correction and learn from people then so be it. Part of learning, hell it's part of being a well rounded human being, is being able to say "I was wrong", "I don't know" and "Can you help me". It's plain for anyone to see that there is a significant difference in the attitude hacks have to such sentences compared to competent scientists on these forums. Perhaps you two should think about that.

Your problem Farsight, among other things, is you immediately shut down listening as soon as someone says something you don't want to hear. As a result you seem to struggle to learn things and improve yourself, at least in the realms of science. It's clearly severely handicapped your learning. No doubt you've already decided "I don't have to listen to this, it's another tirade!" but it's an attempt at helpful constructive advice. I'm perfectly calm, I'm not agitated. I'm simply saying my thoughts.

For example, I explained how your posts would benefit a great deal if you could define what you're talking about much more precisely. No more vague wordy arm waving open to misinterpretation, if you had a bit more formal understanding you could get into the habit of properly and precisely defining what you talk about. Was that comment not a viable piece of advice?

I asked you to define quasi-spherical and to explain what you meant in your sentence starting "Electron wavelength is λ = 4πn / c^1½...." because you were simply too vague. If you want to break into the mainstream community (and you obviously do else you'd not be paying for adverts in physics magazines) you need to get into the habit of defining any non-standard terms you use or to be more familiar with proper definitions. If you have poor communication skills when it comes for formal ideas you're not going to get anywhere. Again, is this not a viable relevant piece of advice? Was asking you for clarification too much to ask?

As I mentioned, it's important to be able to say "I was wrong" or "Can you give me a hand?". You were mistaken about the whole electron wave function vs the EM vector potential in the AB experiment. I've explained it several times. I can go into further detail if you wish but there'll be the problems I've already mentioned, you'll struggle to understand what I explain because of a lack of familiarity with the formal stuff. Thus you'll have to either take what I say unquestionably or reject it. Without a working familiarity with stuff like the vector potential in gauge theory you're unable to evaluate concepts for yourself, you're stuck just taking other people's word for it (and let's be honest, that's pretty much your situation for every advanced concept in physics). Again, this only hinders yourself, both in terms of understanding physics, discussing physics and perhaps one day helping to develop physics. If all you can do is parrot complicated summaries you don't understand how can you discuss the specifics, as you cannot put anything accurately into your own words.

This lack of formal capabilities then leads into your works biggest problem, you have absolutely no method to construct a working model of anything. Even if I were to accept your interpretation of things, to say "Your intuitive understanding is bang on, this is how the system works" you're unable to capitalise on that and say "Great, here's my working model, let's compare it with the mainstream!". All you can do is provide unconvincing interpretations. If you had a working model you could convince people you're onto something via "You might think my take on it is unusual but you can't deny it produces the right values". Quantum mechanics worked like that for a long time, crazy but it works! And of course without a working model and numbers to compare you're never going to get pass a journal reviewer, a problem you've experienced many times already.

I say this calming and honestly. You'd be much better off spending your money on textbooks than magazine adverts. You'd be much better off spending your time working through those books than advertising on forums. It might take you 2~5 years to get anywhere close to even degree standard but you clearly have the time, if only you'd redirect your efforts from avoiding the details to meeting them head on.

Until you do I fear you'll be perpetually stuck precisely where you are now. Do you really want to still be here in 2 years time? 5 years? 10 years? It seems to be going that way and I'm sure I'm not the only one who thinks you could use your time and money more wisely.

If you brush this off as a 'tirade' rather than see it for the honest advice it is then you will only be showing an attitude which will prevent you getting anywhere in physics.

As for Magneto....

I see that you have reviewed, some of the work.

Firstly I didn't do it in a professional capacity. Secondly you haven't submitted it anywhere. Thirdly you utterly failed so if you think I count as a reviewer (and I have been a journal reviewer) I can categorically state your work would be rejected without possibility of resubmission.

I will agree that there are some basic mistakes mainly in symbolism in (GR), but there are not any fundamental mistakes. I have identified all of the mistakes and I will correct them in the next edition.

You were wrong on at least a dozen basic and fundamental things which then proceeded to completely invalidate your claims. For instance, you thought ds^{2} = d(s^{2})[/tex], it formed the basis for your 'derivation' of the SC metric. You were wrong. Not only that but your metric coefficients were incorrect too. You couldn't do coordinate transforms properly, you mixed coordinates. You couldn't do linear algebra properly. You couldn't do tensors properly. You couldn't do calculus properly. These aren't just "Opps, I did a typo" but "Opps I can't do basic mathematics".

I thought that you knew physics history. The Principia Mathematica, written by Isaac Newton, that we discuss today is the third (3rd) edition of his Principia. The first (1st) edition of Newton's Principia was also riddled with high school level mistakes.

High school level mistakes? Can you provide evidence for this? Besides, Newton already had a massive amount of published work, he was a researching academic, involved in daily discussions with other academics, high up (eventually head of) in the Royal Society and he did a great deal of experiments. Whatever errors he made were superficial, not fundamental. Your work is fundamentally wrong.

What made Newton's Principia popular and gave it momentum, was everyone pointing out to Newton where he made mistakes in his Principia. At that time people were getting a big "kick" out of finding errors in Newton's work; and publishing over town the fact. Some even claimed that fixing his errors, meant that they actually claimed credit for solving the problem.

Evidence? What made Principia Mathematica popular was the novelty, insightfulness and shear volume of mathematical physics the book contained. I suspect you're inventing a rose tinted view of history to convince yourself you haven't completely screwed up your non-existent physics career.

Don't you know, that is what makes physics fun!

Finding mistakes in other people's work and taking their ideas as your own? No, what makes physics (and research in general) is the thrill of discovering/developing/inventing something no one else on the planet ever has done, to have all of your months of time, effort, frustration and work suddenly converge into something concrete, something elegant and novel, something others will find worthwhile and of use, which you can point to and proudly say "I did that". So no, I don't find picking holes in someone's work the fun part of science. It's a necessary part but it isn't what gets me out of bed in the morning.

Oh and I can't help but notice how you skipped over my demonstration you were wrong in my last post. Do you admit that you were simply wrong (if not lying) when you accused me of lurking so I could reply the instant you or Farsight posted. Not only did you have no evidence, it was actually against you. You need to stop living in your little fantasy work where everyone is sneaking around trying to hinder you. The only person getting in your way is you.

 

[Mind Over Matter]

lol... Just Google "electron mass". This link, http://physics.nist.gov/cgi-bin/cuu/Value?me, will give you the values. I am sure if you want the actual experiments refining the search should produce some further resources.

Since a proton is made up of three point particles, doesn't the proton system have a real volume? If not, then what does have volume?

 

[OnlyMe]

Since a proton is made up of three point particles, doesn't the proton system have a real volume? If not, then what does have volume?

Everything with a mass does have volume. It can even be argued that energy, expressed as quanta, may have some volume.

And yes there are some theoretical models that assume point masses and energy where volume is not a factor. Even black holes are treated at times as if they are point singularities and sometimes as if they have a volume.

 

[prometheus]

Everything with a mass does have volume.

Not true. The only "volume" for fundamental particles comes from the uncertainty principle so if you'd have said "everything with momentum has a volume I would have agreed with you eventually. That is a pretty sloppy way of putting it though.

 

[OnlyMe]

Not true. The only "volume" for fundamental particles comes from the uncertainty principle so if you'd have said "everything with momentum has a volume I would have agreed with you eventually. That is a pretty sloppy way of putting it though.

Doesn't everything with mass have some momentum?

I understand that theoretically we can deal with mass in idealized ways that could suggest a point like nature, but in practice I don't see any mass that has no momentum. If there were any we would likely not be able to observe it.

 

[prometheus]

Doesn't everything with mass have some momentum?

I understand that theoretically we can deal with mass in idealized ways that could suggest a point like nature, but in practice I don't see any mass that has no momentum. If there were any we would likely not be able to observe it.

Yes, but the fact a particle has mass does not imply it has volume, which is what you said.

 

[OnlyMe]

Yes, but the fact a particle has mass does not imply it has volume, which is what you said.

I see your point.

I am so used to viewing things from a practical perspective that I sometimes assume some things are implied by others. They are at least in how I think about them.

 

[prometheus]

Fair enough. I should also have noted in my previous post that there is an important distinction between mass and momentum, as massless particles have momentum but (obv.) no mass.