Action

action
action
Just what do you think you're doing, Dave? ~HAL

	Ramond, Weinberg, Planck, Weyl, Levi-Civita, Fermat, Noether, Hilbert, Keyser, Smolin

	This uncertainty relation cannot play a fundamental role in a theory in which itself is not a fundamental quantity. I think one can make a safe guess that uncertainty relations in their present form will not survive in the physics of the future. ~Dirac
Ramond Wilczek Weinberg Planck Weyl Levi-Civita Fermat Hilbert Noether Ne'emann Keyser	It is a most beautiful and awe-inspiring fact that all the fundamental laws of Classical Physics can be understood in terms of one mathematical construct called the Action. It yields the classical equations of motion, and analysis of its invariances leads to quantities conserved in the course of the classical motion. In addition, as Dirac and Feynman have shown, the Action acquires its full importance in Quantum Physics. Ramond Furthermore, and now this is the point, this is the punch line, the symmetries determine the action. This action, this form of the dynamics, is the only one consistent with these symmetries [...] This, I think, is the first time that this has happened in a dynamical theory: that the symmetries of the theory have completely determined the structure of the dynamics, i.e., have completely determined the quantity that produces the rate of change of the state vector with time. Weinberg Thus, the task is, not so much to see what no one has yet seen; but to think what nobody has yet thought, about that which everybody sees. Schrödinger	Roughly speaking, force is the space derivative of energy and the time derivative of momentum. You can take one more step up the ladder: energy and momentum are both derivatives of action: energy is its time derivative, momentum its space derivative. Wilczek Increasingly, many of us have come to think that the missing element that has to be added to quantum mechanics is a principle, or several principles, of symmetry. A symmetry is a statement that there are various ways that you can change the way you look at nature, which actually change the direction the state vector is pointing, but which do not change the rules that govern how the state vector rotates with time. The set of all these changes in point of view is called the symmetry group of nature. It is increasingly clear that the symmetry group of nature is the deepest thing that we understand about nature today. Weinberg The magical formula E = hv from which the whole of quantum theory is developed, establishes a universal relationship between the frequency v of an oscillatory process and the energy E associated with such a process. The quantum of action h is one of the universal constants of nature. It was first discovered by Planck at the turn of the century in the laws of black body radiation; that is, radiation which is enclosed in a cavity and is in thermodynamic equilibrium with matter of a definite temperature, which by emission and absorption causes an exchange of energy between the various frequencies contained in the radiation. Since this equilibrium is independent of the particular nature of the matter involved, Planck considered, as a kind of schematic matter, a system of linear oscillators of all possible frequencies. A charge oscillating with frequency v interacts with the electromagnetic field by emitting and absorbing radiation of the same frequency. Planck assumed that the exchange of energy took place in integral multiples of an energy quantum [...] Weyl How far does the laser move in color space? If the initial point P₀and the final point P₁of the path of a ray of light are fixed, the time taken by the ray to go from P₀to P₁along a line s will obviously be expressed by the integral since m, as we have just said, is the reciprocal of the velocity. Now the line actually followed by the light is the one which makes this integral a minimum, and therefore satisfies the condition This variational equation, which sums up the whole of geometrical optics, is known as Fermat's principle. Levi-Civita	action variation invariant symmetry Erlangen Lagrangian Hamiltonian scattering path
	If is a derived quantity instead of a fundamental one, our whole set of ideas about uncertainty will be altered: is the fundamental quantity that occurs in the Heisenberg uncertainty relation connecting the amount of uncertainty in a position and in a momentum. This uncertainty relation cannot play a fundamental role in a theory in which itself is not a fundamental quantity. I think one can make a safe guess that uncertainty relations in their present form will not survive in the physics of the future. Of course there will not be a return to the determinism of classical physical theory. Evolution does not go backward. It will have to go forward. There will have to be some new development that is quite unexpected, that we cannot make a guess about, which will take us still further from Classical ideas but which will alter completely the discussion of uncertainty relations. And when this new development occurs, people will find it all rather futile to have had so much of a discussion on the role of observation in the theory, because they will have then a much better point of view from which to look at things. So I shall say that if we can find a way to describe the uncertainty relations and the indeterminacy of present quantum mechanics that is satisfying to our philosophical ideas, we can count ourselves lucky. But if we cannot find such a way, it is nothing to be really disturbed about. We simply have to take into account that we are at a transitional stage and that perhaps it is quite impossible to get a satisfactory picture for this stage. Dirac
	She did some good work in invariant theory at Erlangen and was invited to Gottingen by Klein ... and David Hilbert (1862-1943). It was as a result of working with the latter, especially after his involvement with general relativity, that she set on the investigation of the role of symmetry groups in physics in the most general terms. She read her two theorems in 1918, and Klein stressed their standing as extending the Erlanger program to physics. In her first theorem, she showed how the invariance of the action (or of the Lagrangian, Hamiltonian, or, in more modern terms, of the scattering matrix, path integral, etc.) under the action of a finite Lie group implied the conservation of a set of "charges" corresponding to the group's infinitesimal generator algebra. Ne'emann Consider the field of the data of sense—a field of universal interest—and fundamental. We are here in the domain of sights and sounds and motions among other things [...] Do the colors constitute a group?[ ...] Let us pass from colors to figures or shapes—to figures or shapes, I mean, of physical or material objects—rocks, chairs, trees, animals and the like—as known to sense perception [...] And what of sounds—sensations of sound? Are sounds combinable? Is the result always a sound or is it sometimes silence? If we agree to regard silence as a species of sound—as the zero of sound—has the system of sounds the property of a group? Keyser Calabi-Yau manifolds are compact, complex Kähler manifolds that have trivial first Chern classes (over $\mathbb{R}$ ). In most cases, we assume that they have finite fundamental groups. Yau Thus the colors with their various qualities and intensities fulfill the axioms of vector geometry if addition is inter- preted as mixing; consequently, projective geometry applies to the color qualities. Weyl	The connection between symmetries and conservation laws is one of the great discoveries of twentieth century physics . But I think very few non-experts will have heard either of it or its maker — Emily Noether, a great German mathematician. But it is as essential to twentieth century physics as famous ideas like the impossibility of exceeding the speed of light. Smolin Emmy Noether In the judgement of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. Einstein It is just like the mathematics of the addition of vectors, where (a, b, c ) are the components of one vector, and (a', b', c' ) are those of another vector, and the new light Z is then the "sum" of the vectors. This subject has always appealed to physicists and mathematicians. In fact, Schrödinger wrote a wonderful paper on color vision in which he developed this theory of vector analysis as applied to the mixing of colors. Feynman