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" "Velocity, acceleration, and force are vectors... they have direction as well as magnitude. It is often convenient to describe... [vectors] in terms of their components along specified directions. ...Components of vectors can be negative as well as positive ...Newton's Second Law applies separately to each component... it says... the component of force in any direction is equal to the mass times the corresponding component of acceleration.
Steven Weinberg (born 3 May 1933 – 23 July 2021) was an American physicist. He was awarded the 1979 Nobel Prize in Physics (with colleagues Abdus Salam and Sheldon Glashow) for combining electromagnetism and the weak force into the electroweak force.
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Maybe at the very bottom of it... I really don't like God. You know, it's silly to say I don't like God because I don't believe in God, but in the same sense that I don't like Iago, or the Reverend Slope or any of the other villains of literature, the god of traditional Judaism and Christianity and Islam seems to me a terrible character. He's a god who will... who obsessed the degree to which people worship him and anxious to punish with the most awful torments those who don't worship him in the right way. Now I realise that many people don't believe in that any more who call themselves Muslims or Jews or Christians, but that is the traditional God and he's a terrible character. I don't like him.
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A superconductor of any kind is nothing more or less than a material in which a particular symmetry of the laws of nature, electromagnetic gauge invariance, is spontaneously broken. ... These rotations act on a two-dimensional vector, whose two components are the real and imaginary parts of the electron field, the quantum mechanical operator that in quantum field theories of matter destroys electrons. The rotation angle of the broken symmetry group can vary with location in the superconductor, and then the symmetry transformations also affect the electromagnetic potentials ... The symmetry breaking in a superconductor leaves unbroken a rotation by 180°, which simply changes the sign of the electron field. In consequence of this spontaneous symmetry breaking, products of any even number of electron fields have non-vanishing expectation values in a superconductor, though a single electron field does not. All of the dramatic exact properties of superconductors – zero electrical resistance, the expelling of magnetic fields from superconductors known as the Meissner effect, the quantization of magnetic flux through a thick superconducting ring, and the Josephson formula for the frequency of the AC current at a junction between two superconductors with different voltages – follow from the assumption that electromagnetic gauge invariance is broken in this way, with no need to inquire into the mechanism by which the symmetry is broken.