You forgot that according to Einstein there is not a unique inertial reference frame. The fact is that the electron when circling the proton maps out the same areal size that the proton maps out while circling the electron. The areas are different not their magnitudes. This makes the rest of your derivation illogical QED. See also my comments directly above.kcdodd wrote:magnetic moment: m = I*A
The angular frequency of both bodies have to be the same: w = v_i/r_i = v_e/r_e.
I = (+/-)e*v/(2*pi*r) = (+/-)e*w/(2*pi)
(the currents are indeed equal and opposite)
A = pi*r^2
but the areas are not.
QED meets GR
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Wow!!! so you can generate a magnetic field around a current without Ampere's law applying? Is this new physics? Icarus' law. Better publish your law soon or you might miss winning the Nobel Prize!icarus wrote:kcdodd:
Ampere's law doesn't come into it, as Prins is saying.
This statement is REALLY naive! If you are correct positronium must have a zero magnetic moment: Guess what is the experimental fact? I leave it to you as an exercise to find out.Sum of the moments NOT a naive moment of the sum of currents. Even more interesting.
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due to the difference in mass, the electron's radius of rotation is about 1,800 times that of a proton and thus so is its speed, and thus, by the biot-savart law for a moving charged particles, so is the strength of the magnetic field it produces. so it's not that the dipole moment is cancelled out, just that it's reduced by a small fraction of a percent. (~1799/1800) of the electron's magnetic moment. (and at the very center there's actually a very small and very weak dipole of opposite polarity. or perhaps at the very center (the protons radius of rotation) they exactly cancel out?)
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"particle" is easy to define:
a "particle" is a conceptual tool for reasoning about physical consequences.
it has never been anything otherwise since the first philosophers first discussed it, and arguably well before that.
more precisely, it must satisfies the following mathematical criteria:
1. it is a spatial region of finite volume that contains energy,
2. has forces eminating from it that act on other "particles",
3. and are likewise effected by such forces from other "particles".
protons and electron, indeed, all baryons and leptons, meet these criteria.
a "particle" is a conceptual tool for reasoning about physical consequences.
it has never been anything otherwise since the first philosophers first discussed it, and arguably well before that.
more precisely, it must satisfies the following mathematical criteria:
1. it is a spatial region of finite volume that contains energy,
2. has forces eminating from it that act on other "particles",
3. and are likewise effected by such forces from other "particles".
protons and electron, indeed, all baryons and leptons, meet these criteria.
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It is already done in high school text books. If you have a straight wire with a constant current I flowing through it, you have circular magnetic rings forming around the wire as mandated by Ampere's law; whether you assume that the positive charges are moving or the negative charges are moving. It is this RELATIVE movement which generates the the magnetic field.kcdodd wrote:johanfprins, why don't you provide the equation you are using and derive zero magnetic moment.
When the wire is a circular ring you still have a magnetic field forming as mandated by Ampere's law. These are bangles around the wire. You can solve for them BY using the law of Biot and Savart. Quite a messy calculation for a round ring; but simpler for a square ring. You really do not expect me to do this calculation here, which any high school, student should be able to do.
The mistake which had been made already by Hendrik Antoon Lorentz in his seminal book on electrodynamics (1909) is to assume that a solitary moving electron constitutes a current. To form a current it has to move relative to a positive charge. On its own it cannot generate a magnetic field, just like a solitary electron has no electric-field energy in the space surrounding it. The electric-field energy of a solitary electron is its mass: There is no other extra electric energy around it within three-dimensional space.
Now let us go to the Bohr atom: There is obviously an electric-field energy between the electron and the proton; but these charges do not move relative to each other since the distance between them, is fixed (or so Bohr claims against all physical reality). Therefore there can be no relative current as required by Ampere's law to form a magnetic field.
I hope this helps.
Last edited by johanfprins on Sun Nov 14, 2010 3:22 pm, edited 1 time in total.
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The Biot-Savart law is only valid for a constant current generated by the RELATIVE movement of charged entities.happyjack27 wrote:due to the difference in mass, the electron's radius of rotation is about 1,800 times that of a proton and thus so is its speed, and thus, by the biot-savart law for a moving charged particles,
I do not want to insult you but I find this reasoning gobbeldygook! The distance between the electron and the proton stays constant: So they are not moving RELATIVE to each other. They can thus NOT generate a magnetic field without violating Einstein's Special Theory of Relativity. No solitary charge following a circular path can do so. For the same reason the magnetic moment of a solitary electron cannot be caused by the electron "spinning".So is the strength of the magnetic field it produces. so it's not that the dipole moment is cancelled out, just that it's reduced by a small fraction of a percent. (~1799/1800) of the electron's magnetic moment. (and at the very center there's actually a very small and very weak dipole of opposite polarity. or perhaps at the very center (the protons radius of rotation) they exactly cancel out?)
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So you agree it is a mathematical construct and NOT a real physical entity? It can thus not exist.happyjack27 wrote:"particle" is easy to define:
a "particle" is a conceptual tool for reasoning about physical consequences.
it has never been anything otherwise since the first philosophers first discussed it, and arguably well before that.
You just now defined a field not a "particle"more precisely, it must satisfies the following mathematical criteria:
1. it is a spatial region of finite volume that contains energy,
The fact that we can mathematically model forces to act at a single point (like the center-of-mass) does not define a "particle". Your own definition defines a "particle" as a field with a point at which forces act. This means that there is no reason whatsoever to say that an electron is an entity which has "complementarity" behavior. It is a field in both cases and its behavior is determined by the boundary conditions under which it finds itself.2. has forces eminating from it that act on other "particles",
3. and are likewise effected by such forces from other "particles".
Exactly! Because they are ALWAYS fields (waves) which morph in shape and/or size when the boundary conditions change: Just as waves have always done in memoriam.protons and electron, indeed, all baryons and leptons, meet these criteria.
Prins:
So clearly this quote is the crux of your argument that was in question (as an aside note how you chose to bait and switch with some BS about high-school physics) .... now where are your equations that you use to show what you are claiming in the above quote .... humour us?To form a current it has to move relative to a positive charge. On its own it cannot generate a magnetic field, just like a solitary electron has no electric-field energy in the space surrounding it. The electric-field energy of a solitary electron is its mass: There is no other extra electric energy around it within three-dimensional space.
Now let us go to the Bohr atom: There is obviously an electric-field energy between the electron and the proton; but these charges do not move relative to each other since the distance between them, is fixed (or so Bohr claims against all physical reality). Therefore there can be no relative current as required by Ampere's law to form a magnetic field.
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I bait??? As far as I know Ampere's law is now taught in high school physics (even here in our third world country) and it should be clear to anybody (even one with a limited intelligence like you) that this law has ONLY been experimentally proved for current through a wire WHERE OPPOSITE CHARGES MOVE RELATIVE TO EACH OTHER!!icarus wrote: So clearly this quote is the crux of your argument that was in question (as an aside note how you chose to bait and switch with some BS about high-school physics)
Thus it is not valid for a solitary charge moving around a circle.
You ask me to prove an experimental fact by deriving equations? Are you really so stupid? How must I derive equations for something that is experimentally not possible? If you say it is, then prove to me that it is..... now where are your equations that you use to show what you are claiming in the above quote .... humour us?
It is obvious that you have never understood first year physics and will probably never have the brainpower to do so. But maybe just maybe (although I despair) you might be able to understand what I am talking about by going to the physics text book by Serway page 1179. Humour me and try it, we never know!!! Miracles are possible, even in your hopeless case!
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john, from your responses, as you say i don't mean to insult you, but it seems like it would be utterly hopeless to persue this topic further. i've stated everything that needs to be stated clearly and concisely but you're hell bent on confusing yourself to come to some pre-ordained conclusions that are fiercly contrary to well-established physics and easily demonstrable logic (which i have clearly demonstrated, only to have it turned inside out and backwards (eg waves DO NOT have forces eminating from them and DO NOT have clear spatial boundaries, which is UTTERLY OBVIOUS). so i shall simply rest my case and move on.
Every electron and every proton acts as an independent source due to the principle of superposition. If you are claiming different then what you are talking about does not appear in any book on classical EM I have read. A solitary electron can most certainly constitute a current.johanfprins wrote: The mistake which had been made already by Hendrik Antoon Lorentz in his seminal book on electrodynamics (1909) is to assume that a solitary moving electron constitutes a current. To form a current it has to move relative to a positive charge. On its own it cannot generate a magnetic field, just like a solitary electron has no electric-field energy in the space surrounding it. The electric-field energy of a solitary electron is its mass: There is no other extra electric energy around it within three-dimensional space.
You cannot simultaneously claim that EM is correct and supports your claims, and is even explained in intro books, while also claiming that EM theory got it all wrong. So, which is it? Either way, if you want others to believe you, then you need to show your work.
Carter
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OK so you did not want to try to understand elementary physics by going to Serway. Can you see why I get exasperated with people like you, and then become ascerbic. I apologize: I should just really not expect so much from you. I should just accept that people have different abilities. So let's be friends, and let me try and explain what I am saying VERY SLOWLY.icarus wrote:So no equations then to describe what you are blathering about?
The first principle of Einstein's special relativity is that there is not a preferred stationary reference frame. Thus for the Bohr atom you cannot say that it is actually the electron which is circling the proton or that it is the proton circling the electron. Now let us assume that the moving electron does generate a magnetic moment, as you "main stream" acolytes are hellbent on believing, then the proton must also generate a magnetic moment while moving around the electron. Both entities (so called "particles": God help physics) plot out the same areas (A ) but their magnetic moments point in opposite directions. Thus the sum of these magnetic moments is ZERO!!! Since you wanted a formula even though it is not valid, since, to repeat, a solitary charge moving through space cannot constitute a magnetic field around it: Here it is:
M(proton)+M(electron)=IA-IA=0. Happy now?
If in this equation IA could be valid for a solitary charge, as the mainstream physicists are hellbent on believing, and you say their sum does not come to zero, you are choosing one of the two reference frames as a unique one and thus throwing Einstein's theory of relativity out of the window.
As I have pointed out time and again kcdodd's derivation assumes that a solitary moving charge generates a magnetic field around it. There is no experimental proof whatsoever that this is actually the case. And as shown by my formula above, even if it were possible, there would be no magnetic moment unless Einstein's theory of Special Relativity is wrong.I didn't think so. kcdodd was kind enough to give quick derivation from first principles and all you can come up with in response is an abusive tirade.... you are a physicist huh?
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You could not define a particle witout cliaming that it must be a region in space with energy: This is the definition of a field NOT a particle. You are really confused my friend. If this is well-established physics: God help physics.happyjack27 wrote: i've stated everything that needs to be stated clearly and concisely but you're hell bent on confusing yourself to come to some pre-ordained conclusions that are fiercly contrary to well-established physics.and easily demonstrable logic (which i have clearly demonstrated, only to have it turned inside out and backwards
Wow!!! Every calculation used to determine chemical bonding assumes that there are forces between waves caused by charge-distributions which can even overlap!(eg waves DO NOT have forces eminating from them
So standing waves on a string do not have clear spatial boundaries? Ag Mein Gott: You are in need of serious help.and DO NOT have clear spatial boundaries, which is UTTERLY OBVIOUS). so i shall simply rest my case and move on.