at any speed.
Deriving Maxwell’s equations is a mathematical nightmare! 😱
For the non-mathematicians out there, here's a new video which includes graphics to explain how the equations relate to electricity and magnetism and ultimately to the speed of light itself.
Why is the speed of light what it is? Maxwell equations visualized - YouTube
Best to start off at 1:48 to get straight into the nitty-gritty!
Discopete,
again, anything that moves in any medium is losing velocity.
If relativity is general, it cannot be distinctive, leave it out.
A fairly stupid definition.
again, anything that moves in any medium is losing velocity.
If relativity is general, it cannot be distinctive, leave it out.
A fairly stupid definition.
This stuff is all over my simplistic head. I am however interested but I don't spend the kind of time on it that you guys do. So the demonstration I saw with the magnetic circuit was still very strong 3 months later when it took a hammer to break away the shorting bar. I found that amazing.
btw, my banana plugs did not arrive. It was reset for tomorrow. So much for the spooky
btw, my banana plugs did not arrive. It was reset for tomorrow. So much for the spooky
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The electric field moves at relativistic speeds in a conductor - not the actual electrons. They move IIRC at about 1mm/sec.
I'd be happy to comment on the demonstration, but first I would have to see it.
I didn't understand your earlier description, with its reference to virtual photons, so could you supply a link?
I am much fascinated by fractional charges in Nature.
Having actually done Millikan's experiment in which we derived the nature of the Electron charge, where in Heck do fractional Quark charges come from? You know, 1/3 and 2/3 charges.
A deep business. 😕
Up around 180 GeV, above the Higgs and the W and Z boson lies the the the third layer the Top Quark:
Top quark - Wikipedia
Terrific particle, IMO. Most people think you can never see a naked 2/3 charge. But this one is so short-lived it spends most of its life as a 2/3 charge before decaying into a a twin quark Meson. What does it mean? No idea. 😀
Dug out my third year efforts at College:
PH 323 Nuclear Physics.
PH 324 Solid State Physics
PH 329 Quantum Physics
Having actually done Millikan's experiment in which we derived the nature of the Electron charge, where in Heck do fractional Quark charges come from? You know, 1/3 and 2/3 charges.
A deep business. 😕
Up around 180 GeV, above the Higgs and the W and Z boson lies the the the third layer the Top Quark:
Top quark - Wikipedia
Terrific particle, IMO. Most people think you can never see a naked 2/3 charge. But this one is so short-lived it spends most of its life as a 2/3 charge before decaying into a a twin quark Meson. What does it mean? No idea. 😀
Dug out my third year efforts at College:
PH 323 Nuclear Physics.
PH 324 Solid State Physics
PH 329 Quantum Physics
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The most up to date and detailed explaining on quantum particles.
How Small Is It - 01 - Preface (1080p) - YouTube
Than watch How big is it for the universe.
How Small Is It - 01 - Preface (1080p) - YouTube
Than watch How big is it for the universe.
cbdb, David Butler reeks of Shaimanism and Witch-doctoring to me. 😀
Actually, if you want to understand fractional charges, you could do worse than than spend time on Borromean Rings:
Borromean rings - Wikipedia
Combined with certain theories of Space-time geometry, we are there.
I might draw up a visual diagram of how it works.
Actually, if you want to understand fractional charges, you could do worse than than spend time on Borromean Rings:
Borromean rings - Wikipedia
Combined with certain theories of Space-time geometry, we are there.
I might draw up a visual diagram of how it works.
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All very interesting. But Magnetism IS a relativistic effect:
Length contraction - Wikipedia
I could be wrong on this back of a beermat calculation, but I think I am right.
If you differentiate Lorentz-Fitzgerald contraction LF = SQRT (1 - v^2/c^2)
You get fractional LF contraction dLF/v = v/c for small v.
Now even a sluggish current at 1mm/second is 3 x 10^ -12 of the speed of light.
And the contraction is proportional to that.
A meter of copper wire will have about 6 X 10^ 21 free electrons using avogadro.
So mysteriously about 1.8X 10^ 10 electrons will appear. That's a LOT! 🙂
Length contraction - Wikipedia
I could be wrong on this back of a beermat calculation, but I think I am right.
If you differentiate Lorentz-Fitzgerald contraction LF = SQRT (1 - v^2/c^2)
You get fractional LF contraction dLF/v = v/c for small v.
Now even a sluggish current at 1mm/second is 3 x 10^ -12 of the speed of light.
And the contraction is proportional to that.
A meter of copper wire will have about 6 X 10^ 21 free electrons using avogadro.
So mysteriously about 1.8X 10^ 10 electrons will appear. That's a LOT! 🙂
Whoops. Got me negative indices muddled there at the end! Why I quit maths at College. I often got me algebra sums wrong. Prefer geometry. 😱
I now get 1.8 x 10^ 8 surplus electrons. Still a lot. The bare Electric force is a powerful monster.
I have discovered something far more mysterious about Lorentz-Fitzgerald contraction.
APPARENTLY the length change is an illusion. It's actually a ROTATION in space, the LENGTH is unchanged. Quaternions and 4D Unitary Matrices!
The invisibility of length contraction – Physics World
Now THAT is very interesting. Almost a fourth spatial dimension. Exactly what we have been looking for the last few pages and wasting time on M and String Theory. I see the Standard Model and a deeper Special Relativity understanding coming back here. Happy Days.
I now get 1.8 x 10^ 8 surplus electrons. Still a lot. The bare Electric force is a powerful monster.
I have discovered something far more mysterious about Lorentz-Fitzgerald contraction.
APPARENTLY the length change is an illusion. It's actually a ROTATION in space, the LENGTH is unchanged. Quaternions and 4D Unitary Matrices!
The invisibility of length contraction – Physics World
Now THAT is very interesting. Almost a fourth spatial dimension. Exactly what we have been looking for the last few pages and wasting time on M and String Theory. I see the Standard Model and a deeper Special Relativity understanding coming back here. Happy Days.
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Some pathological anomalies are bothering me right now.
The definitions say: a field is an algebraic object. A field has characteristic either zero or a prime number. All finite fields must have prime power order. An element of a field is prime if it is an integral domain. An element of a set is an algebraic number if it is a root of a non-zero polynomial with rational coefficients. Every field is an integral domain and must contain a unity. An algebra is unital if it has an identity element. A number field is unique if it has an unit element. An element of a number field is a unit if it is invertible. An element of a number field is irreducible if it is not a unit.
We are in a pesky muddle. The Fundamental Theorem of Calculus says that boundedness is a necessary condition for continuity and continuity is a necessary condition for differentiability, but in Function Theory a differentiable function need not have a continuous derivative. In the definition of limit, the target point is required to be a limit point of the domain, but does not have to be an element of the domain - the set need not to be bounded and continous. In Set Theory, the set is not required to be enumerated to be finite, or even being the member of itself. In the definition of continuity, the target point is required to be in the domain of the function, but does not have to be a limit point. The muddle gets worse. The Axiom of the Power Set states that for any set there is a power set. This conflicts with standard logic saying that the cardinality of the set of all subsets must necessarily be larger than the set. The muddle gets even worse. Algebraic Field Theory says that every nonzero element of a finite dimension must be a unit to be a field, which means that no element of a field can be a prime number.
If you think, that zero to the zeroth power should not be 1, then you may get disappointed or even angry. No real number multiplied by 0 produces 1, and 0 does not have a multiplicative inverse. Solving the problem of integers being an integral domain but not a field, the zeroth power of the base is defined to be unity despite it is not invertible. Any number, including zero, raised to the power of zero is equal to 1 while its zeroth root is indeterminate...
The definitions say: a field is an algebraic object. A field has characteristic either zero or a prime number. All finite fields must have prime power order. An element of a field is prime if it is an integral domain. An element of a set is an algebraic number if it is a root of a non-zero polynomial with rational coefficients. Every field is an integral domain and must contain a unity. An algebra is unital if it has an identity element. A number field is unique if it has an unit element. An element of a number field is a unit if it is invertible. An element of a number field is irreducible if it is not a unit.
We are in a pesky muddle. The Fundamental Theorem of Calculus says that boundedness is a necessary condition for continuity and continuity is a necessary condition for differentiability, but in Function Theory a differentiable function need not have a continuous derivative. In the definition of limit, the target point is required to be a limit point of the domain, but does not have to be an element of the domain - the set need not to be bounded and continous. In Set Theory, the set is not required to be enumerated to be finite, or even being the member of itself. In the definition of continuity, the target point is required to be in the domain of the function, but does not have to be a limit point. The muddle gets worse. The Axiom of the Power Set states that for any set there is a power set. This conflicts with standard logic saying that the cardinality of the set of all subsets must necessarily be larger than the set. The muddle gets even worse. Algebraic Field Theory says that every nonzero element of a finite dimension must be a unit to be a field, which means that no element of a field can be a prime number.
If you think, that zero to the zeroth power should not be 1, then you may get disappointed or even angry. No real number multiplied by 0 produces 1, and 0 does not have a multiplicative inverse. Solving the problem of integers being an integral domain but not a field, the zeroth power of the base is defined to be unity despite it is not invertible. Any number, including zero, raised to the power of zero is equal to 1 while its zeroth root is indeterminate...
NO.
This is a classic recurrent statement.
Good to start tons of arguments.
Some admit and many say it is equal 1...But.
The answer is: 0^0 is undefined.
Much as I respect Euler, Cauchy, Gauss, Klein, Germain, Riemann and even Einstein.
We are lost.
We need an extra dimension. I can see the problems of boundary conditions in 2D complex variable.
I struggle with SPIN. Cue the Bonsai 4D Tesseract:
A thing of great loveliness. 🙂
We are lost.
We need an extra dimension. I can see the problems of boundary conditions in 2D complex variable.
I struggle with SPIN. Cue the Bonsai 4D Tesseract:
A thing of great loveliness. 🙂
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