Sorry for the late reply. I got a bit entangled in this field last days. I traveled from the big bang (the ones in front of us and the ones starting behind us), mass gaps, pseudo-Euclidean metrics, closed, presymplectic differential- and two-forms, Poincaré transformations, the Wightman axioms, tangent-, cotangent, fibre, spin bundles, distributions, superspace, gauge fields (resulting from differential 2-form bundles), correlations (Green's functions), Lie groups and Grassman variables, operator valued distributions, point particles and their limits, to the nature of spin and spacetime, spacetime symmetries, lattice calculations as a non-perturbative approach, the non-applicability of QFT to bound systems, a mirror universe, composite quarks and leptons (no more breaking of an artificial symmetric Higgs potential!), viruses falling in air, and of course symmetries. I just want to know! — AgentTangarine
The B-vector is a pseudo-vector. It has weird relection properties. If the vector is reflected in a mirror parallel to it, it changes direction. When reflected in a mirror perpendicular to it, it stays the same. Contrary to the E-field. — AgentTangarine
Moving on to QFT. The A-field is a field that is not a part of the electron field. It is introduced to compensate for changes in the electron field (a Dirac spinor field, like that of quarks and leptons, and probably two massless sub-particles). If you gauge the electron field [this field assigns to all spacetime points an operator valued distribution (which creates the difference with classical mechanics which uses a real valued function), the operator creating particle states in a Fock space], you mentally rotate the particle state vectors in the complex plane. All the states can be seen as vectors in a complex plane (the plane of complex numbers). You have to rotate space twice to rotate such a vector once, hence these are spin 1/2 spinor fields. The local gauge rotates them differently at different spacetime points. This has an effect on the Lagrangian describing the motion, i.e.the integral over time being stationary, the difference with the classical case being that all varied paths are in facts taken, with a variety of weights. — AgentTangarine
Now, for the Lagrangian (which is the difference between kinetic and potential energy, like the Hamiltonian is the sum) to stay the same, a compensation has to be introduced. That's the A-field, which is a potential energy inserted in the Lagrangian since we started from a free field. Why should the Lagrangian stay the same? That's an axiom. But a reasonable one. — AgentTangarine
It occurs to me, that only a bot could do that in just a few days. — Metaphysician Undercover
What does this mean, to produce a reflection of a vector? You refer to a "mirror", but surely no one holds a mirror to a vector field. What kind of material might be used to create such a reflection? I ask because it's possible that the weird reflection properties you refer to, are a product of the method employed to create the reflection. — Metaphysician Undercover
I must admit, I do not understand "complex numbers". Wikipedia tells me that complex numbers are a combination of real numbers with imaginary numbers. But I apprehend imaginary numbers as logically incompatible with real numbers, each having a different meaning for zero, so any such proposed union would result in some degree of unintelligibility. — Metaphysician Undercover
This is the part which really throws me. How does a physicist dealing with fields distinguish between potential and kinetic energy? — Metaphysician Undercover
The right side and the left side of a figure are differentiated by the location of the figure within a larger environment. — Metaphysician Undercover
You actually mirror the vector in a mirror, like a straight arrow. In curved spacetime the vector becomes an object with variable length..You inverse one of the components, in a suitable base. Sometimes front to back, when the mirror is perpendicular to the arrow, sometimes, the length direction, when the mirror is parallel. The velocity vector stays the same, so vXB doesn't change if you turn B around (which is a reflection). — AgentTangarine
Your right side and left side of your body is identifiable independently of your location. The notion is unconnected to your current environment. — hypericin
So right and left only have meaning in a larger context. If you removed that defining feature, the larger context, how would you know which side of your body is right and which is left? — Metaphysician Undercover
If you removed that defining feature, the larger context, how would you know which side of your body is right and which is left? — Metaphysician Undercover
If you removed that defining feature, the larger context, how would you know which side of your body is right and which is left? — Metaphysician Undercover
How can you define left and right without to referring to spatial arrangements in the first place? — Raymond
We have the context built in to our bodies.
We have a built in forward: this is where our eyes look. We have a built in up: this points out of the top of our heads. These two directions together create a plane. Our bodies are symmetric about this plane. We call one side of the plane right, the other left. No reference to a larger context here. — hypericin
I suggest you research local coordinate systems. — hypericin
Indeed! The argument went like this: tell the alien (who speaks English and physics) to rotate an ἤλεκτρον (a Greek electron, supposing they are not made of anti matter...). Or better, a bunch of them. Tell them to take a circular electrical wire put a voltage on it, and the electrons start to rotate. The electron rotation and the direction of the ensuing magnetic force have a fixed relation. Coordinate the rotation direction and the direction of the magnetic field (like you can coordinate your up direction and front direction with positive numbers).Then place a bunch of Cobalt atoms at the origin of this coordinate frame. Cobalt sends positrons in one direction only. Coordinate this direction with plus. But then... It depends on the way you place this new axis orthogonal to the other two in two ways. To put it differently, you can connect you plane with the two plus directions in two ways with the direction in which the positrons come flying off the Cobalt. So surely he was joking, mr. Feynman. — Raymond
The point was that I think symmetry might make a good principle to compare with our observations of the universe, to see how the universe is not symmetrical, but that means that symmetry does not make a good model — Metaphysician Undercover
Your body is not symmetrical, and negative/positive numbers are not symmetrical, as the need for imaginary numbers shows — Metaphysician Undercover
It's a principle of perfect balance, an ideal, which nothing in reality actually achieves — Metaphysician Undercover
Multiplication (the operation you used) is a scale transformation and, in my humble opinion, has nothing to do with reflection symmetry unless you want to use a do/undo transformation combo. — Agent Smith
A black hole has a perfect cylindrical symmetry. It exists in the real world. — Raymond
I think that is a good example of a mistaken conclusion derived from this misunderstanding of symmetry which I am talking about. — Metaphysician Undercover
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